%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN472-1 : 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 05:39:15 AM UTC 2025
% Result : Unsatisfiable 1.37s 1.53s
% Output : Proof 1.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN472-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:37:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 1.37/1.53 % SZS status Unsatisfiable
% 1.37/1.53 % SZS output start Proof
% 1.37/1.53 tff(c2_1_type, type, (
% 1.37/1.53 c2_1: $i > $o)).
% 1.37/1.53 tff(a730_type, type, (
% 1.37/1.53 a730: $i)).
% 1.37/1.53 tff(c3_1_type, type, (
% 1.37/1.53 c3_1: $i > $o)).
% 1.37/1.53 tff(c0_1_type, type, (
% 1.37/1.53 c0_1: $i > $o)).
% 1.37/1.53 tff(c1_1_type, type, (
% 1.37/1.53 c1_1: $i > $o)).
% 1.37/1.53 tff(ndr1_0_type, type, (
% 1.37/1.53 ndr1_0: $o)).
% 1.37/1.53 tff(a710_type, type, (
% 1.37/1.53 a710: $i)).
% 1.37/1.53 tff(hskp8_type, type, (
% 1.37/1.53 hskp8: $o)).
% 1.37/1.53 tff(a695_type, type, (
% 1.37/1.53 a695: $i)).
% 1.37/1.53 tff(a760_type, type, (
% 1.37/1.53 a760: $i)).
% 1.37/1.53 tff(a738_type, type, (
% 1.37/1.53 a738: $i)).
% 1.37/1.53 tff(hskp16_type, type, (
% 1.37/1.53 hskp16: $o)).
% 1.37/1.53 tff(hskp5_type, type, (
% 1.37/1.53 hskp5: $o)).
% 1.37/1.53 tff(a701_type, type, (
% 1.37/1.53 a701: $i)).
% 1.37/1.53 tff(hskp28_type, type, (
% 1.37/1.53 hskp28: $o)).
% 1.37/1.53 tff(a726_type, type, (
% 1.37/1.53 a726: $i)).
% 1.37/1.53 tff(a763_type, type, (
% 1.37/1.53 a763: $i)).
% 1.37/1.53 tff(hskp23_type, type, (
% 1.37/1.53 hskp23: $o)).
% 1.37/1.53 tff(hskp24_type, type, (
% 1.37/1.53 hskp24: $o)).
% 1.37/1.53 tff(hskp6_type, type, (
% 1.37/1.53 hskp6: $o)).
% 1.37/1.53 tff(a702_type, type, (
% 1.37/1.53 a702: $i)).
% 1.37/1.53 tff(a733_type, type, (
% 1.37/1.53 a733: $i)).
% 1.37/1.53 tff(hskp30_type, type, (
% 1.37/1.53 hskp30: $o)).
% 1.37/1.53 tff(a698_type, type, (
% 1.37/1.53 a698: $i)).
% 1.37/1.53 tff(hskp4_type, type, (
% 1.37/1.53 hskp4: $o)).
% 1.37/1.53 tff(hskp3_type, type, (
% 1.37/1.53 hskp3: $o)).
% 1.37/1.53 tff(a697_type, type, (
% 1.37/1.53 a697: $i)).
% 1.37/1.53 tff(hskp14_type, type, (
% 1.37/1.53 hskp14: $o)).
% 1.37/1.53 tff(a691_type, type, (
% 1.37/1.53 a691: $i)).
% 1.37/1.53 tff(a754_type, type, (
% 1.37/1.53 a754: $i)).
% 1.37/1.53 tff(hskp20_type, type, (
% 1.37/1.53 hskp20: $o)).
% 1.37/1.53 tff(hskp1_type, type, (
% 1.37/1.53 hskp1: $o)).
% 1.37/1.53 tff(a693_type, type, (
% 1.37/1.53 a693: $i)).
% 1.37/1.53 tff(a725_type, type, (
% 1.37/1.53 a725: $i)).
% 1.37/1.53 tff(hskp12_type, type, (
% 1.37/1.53 hskp12: $o)).
% 1.37/1.53 tff(a761_type, type, (
% 1.37/1.53 a761: $i)).
% 1.37/1.53 tff(hskp22_type, type, (
% 1.37/1.53 hskp22: $o)).
% 1.37/1.53 tff(hskp25_type, type, (
% 1.37/1.53 hskp25: $o)).
% 1.37/1.53 tff(hskp27_type, type, (
% 1.37/1.53 hskp27: $o)).
% 1.37/1.53 tff(a764_type, type, (
% 1.37/1.53 a764: $i)).
% 1.37/1.53 tff(a773_type, type, (
% 1.37/1.53 a773: $i)).
% 1.37/1.53 tff(a692_type, type, (
% 1.37/1.53 a692: $i)).
% 1.37/1.53 tff(hskp0_type, type, (
% 1.37/1.53 hskp0: $o)).
% 1.37/1.53 tff(hskp9_type, type, (
% 1.37/1.53 hskp9: $o)).
% 1.37/1.53 tff(a712_type, type, (
% 1.37/1.53 a712: $i)).
% 1.37/1.53 tff(hskp10_type, type, (
% 1.37/1.53 hskp10: $o)).
% 1.37/1.53 tff(a717_type, type, (
% 1.37/1.53 a717: $i)).
% 1.37/1.53 tff(a696_type, type, (
% 1.37/1.53 a696: $i)).
% 1.37/1.53 tff(hskp2_type, type, (
% 1.37/1.53 hskp2: $o)).
% 1.37/1.53 tff(hskp13_type, type, (
% 1.37/1.53 hskp13: $o)).
% 1.37/1.53 tff(a722_type, type, (
% 1.37/1.53 a722: $i)).
% 1.37/1.53 tff(hskp11_type, type, (
% 1.37/1.53 hskp11: $o)).
% 1.37/1.53 tff(a751_type, type, (
% 1.37/1.53 a751: $i)).
% 1.37/1.53 tff(hskp18_type, type, (
% 1.37/1.53 hskp18: $o)).
% 1.37/1.53 tff(hskp21_type, type, (
% 1.37/1.53 hskp21: $o)).
% 1.37/1.53 tff(hskp7_type, type, (
% 1.37/1.53 hskp7: $o)).
% 1.37/1.53 tff(a708_type, type, (
% 1.37/1.53 a708: $i)).
% 1.37/1.53 tff(a744_type, type, (
% 1.37/1.53 a744: $i)).
% 1.37/1.53 tff(hskp17_type, type, (
% 1.37/1.53 hskp17: $o)).
% 1.37/1.53 tff(a713_type, type, (
% 1.37/1.53 a713: $i)).
% 1.37/1.53 tff(hskp29_type, type, (
% 1.37/1.53 hskp29: $o)).
% 1.37/1.53 tff(a734_type, type, (
% 1.37/1.53 a734: $i)).
% 1.37/1.53 tff(hskp15_type, type, (
% 1.37/1.53 hskp15: $o)).
% 1.37/1.53 tff(1,plain,
% 1.37/1.53 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.37/1.53 inference(bind,[status(th)],[])).
% 1.37/1.53 tff(2,plain,
% 1.37/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.37/1.53 inference(quant_intro,[status(thm)],[1])).
% 1.37/1.53 tff(3,plain,
% 1.37/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(4,plain,
% 1.37/1.53 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.37/1.53 inference(bind,[status(th)],[])).
% 1.37/1.53 tff(5,plain,
% 1.37/1.53 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.37/1.53 inference(quant_intro,[status(thm)],[4])).
% 1.37/1.53 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 1.37/1.53 tff(7,plain,
% 1.37/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.37/1.53 tff(8,plain,
% 1.37/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.37/1.53 tff(9,plain,(
% 1.37/1.53 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.37/1.53 inference(skolemize,[status(sab)],[8])).
% 1.37/1.53 tff(10,plain,
% 1.37/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.37/1.53 tff(11,assumption,(~c3_1(a695)), introduced(assumption)).
% 1.37/1.53 tff(12,assumption,(~hskp16), introduced(assumption)).
% 1.37/1.53 tff(13,plain,
% 1.37/1.53 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.37/1.53 inference(bind,[status(th)],[])).
% 1.37/1.53 tff(14,plain,
% 1.37/1.53 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.37/1.53 inference(quant_intro,[status(thm)],[13])).
% 1.37/1.53 tff(15,plain,
% 1.37/1.53 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(16,plain,
% 1.37/1.53 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.37/1.53 inference(bind,[status(th)],[])).
% 1.37/1.53 tff(17,plain,
% 1.37/1.53 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.37/1.53 inference(quant_intro,[status(thm)],[16])).
% 1.37/1.53 tff(18,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.37/1.53 tff(19,plain,
% 1.37/1.53 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.37/1.53 tff(20,plain,
% 1.37/1.53 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.37/1.53 tff(21,plain,(
% 1.37/1.53 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.37/1.53 inference(skolemize,[status(sab)],[20])).
% 1.37/1.53 tff(22,plain,
% 1.37/1.53 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.37/1.53 tff(23,assumption,(hskp5), introduced(assumption)).
% 1.37/1.53 tff(24,plain,
% 1.37/1.53 (((~hskp5) | (~c1_1(a701))) <=> ((~hskp5) | (~c1_1(a701)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(25,plain,
% 1.37/1.53 (((~c1_1(a701)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a701)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(26,axiom,((~c1_1(a701)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.37/1.53 tff(27,plain,
% 1.37/1.53 ((~hskp5) | (~c1_1(a701))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.37/1.53 tff(28,plain,
% 1.37/1.53 ((~hskp5) | (~c1_1(a701))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[27, 24])).
% 1.37/1.53 tff(29,plain,
% 1.37/1.53 (~c1_1(a701)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[28, 23])).
% 1.37/1.53 tff(30,plain,
% 1.37/1.53 (((~hskp5) | c2_1(a701)) <=> ((~hskp5) | c2_1(a701))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(31,axiom,((~hskp5) | c2_1(a701)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.37/1.53 tff(32,plain,
% 1.37/1.53 ((~hskp5) | c2_1(a701)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.37/1.53 tff(33,plain,
% 1.37/1.53 ((~hskp5) | c2_1(a701)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[32, 30])).
% 1.37/1.53 tff(34,plain,
% 1.37/1.53 ((~hskp5) | c2_1(a701)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[33, 30])).
% 1.37/1.53 tff(35,plain,
% 1.37/1.53 ((~hskp5) | c2_1(a701)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[34, 30])).
% 1.37/1.53 tff(36,plain,
% 1.37/1.53 ((~hskp5) | c2_1(a701)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[35, 30])).
% 1.37/1.53 tff(37,plain,
% 1.37/1.53 (c2_1(a701)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[36, 23])).
% 1.37/1.53 tff(38,plain,
% 1.37/1.53 (((~hskp5) | c0_1(a701)) <=> ((~hskp5) | c0_1(a701))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(39,axiom,((~hskp5) | c0_1(a701)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.37/1.53 tff(40,plain,
% 1.37/1.53 ((~hskp5) | c0_1(a701)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.37/1.53 tff(41,plain,
% 1.37/1.53 ((~hskp5) | c0_1(a701)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[40, 38])).
% 1.37/1.53 tff(42,plain,
% 1.37/1.53 ((~hskp5) | c0_1(a701)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[41, 38])).
% 1.37/1.53 tff(43,plain,
% 1.37/1.53 ((~hskp5) | c0_1(a701)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[42, 38])).
% 1.37/1.53 tff(44,plain,
% 1.37/1.53 ((~hskp5) | c0_1(a701)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[43, 38])).
% 1.37/1.53 tff(45,plain,
% 1.37/1.53 (c0_1(a701)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[44, 23])).
% 1.37/1.53 tff(46,plain,
% 1.37/1.53 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.37/1.53 inference(bind,[status(th)],[])).
% 1.37/1.53 tff(47,plain,
% 1.37/1.53 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.53 inference(quant_intro,[status(thm)],[46])).
% 1.37/1.53 tff(48,plain,
% 1.37/1.53 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(49,plain,
% 1.37/1.53 (^[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)) | (~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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.37/1.53 inference(bind,[status(th)],[])).
% 1.37/1.53 tff(50,plain,
% 1.37/1.53 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[49])).
% 1.37/1.54 tff(51,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.37/1.54 tff(52,plain,
% 1.37/1.54 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.37/1.54 tff(53,plain,
% 1.37/1.54 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.37/1.54 tff(54,plain,(
% 1.37/1.54 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.54 inference(skolemize,[status(sab)],[53])).
% 1.37/1.54 tff(55,plain,
% 1.37/1.54 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[54, 47])).
% 1.37/1.54 tff(56,assumption,(~hskp28), introduced(assumption)).
% 1.37/1.54 tff(57,assumption,(hskp6), introduced(assumption)).
% 1.37/1.54 tff(58,plain,
% 1.37/1.54 (((~hskp6) | (~c2_1(a702))) <=> ((~hskp6) | (~c2_1(a702)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(59,plain,
% 1.37/1.54 (((~c2_1(a702)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a702)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(60,axiom,((~c2_1(a702)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.37/1.54 tff(61,plain,
% 1.37/1.54 ((~hskp6) | (~c2_1(a702))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.37/1.54 tff(62,plain,
% 1.37/1.54 ((~hskp6) | (~c2_1(a702))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[61, 58])).
% 1.37/1.54 tff(63,plain,
% 1.37/1.54 (~c2_1(a702)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[62, 57])).
% 1.37/1.54 tff(64,plain,
% 1.37/1.54 (((~hskp6) | c3_1(a702)) <=> ((~hskp6) | c3_1(a702))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(65,axiom,((~hskp6) | c3_1(a702)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.37/1.54 tff(66,plain,
% 1.37/1.54 ((~hskp6) | c3_1(a702)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.37/1.54 tff(67,plain,
% 1.37/1.54 ((~hskp6) | c3_1(a702)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[66, 64])).
% 1.37/1.54 tff(68,plain,
% 1.37/1.54 ((~hskp6) | c3_1(a702)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[67, 64])).
% 1.37/1.54 tff(69,plain,
% 1.37/1.54 ((~hskp6) | c3_1(a702)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[68, 64])).
% 1.37/1.54 tff(70,plain,
% 1.37/1.54 ((~hskp6) | c3_1(a702)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[69, 64])).
% 1.37/1.54 tff(71,plain,
% 1.37/1.54 (c3_1(a702)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[70, 57])).
% 1.37/1.54 tff(72,plain,
% 1.37/1.54 (((~hskp6) | c0_1(a702)) <=> ((~hskp6) | c0_1(a702))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(73,axiom,((~hskp6) | c0_1(a702)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.37/1.54 tff(74,plain,
% 1.37/1.54 ((~hskp6) | c0_1(a702)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.37/1.54 tff(75,plain,
% 1.37/1.54 ((~hskp6) | c0_1(a702)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[74, 72])).
% 1.37/1.54 tff(76,plain,
% 1.37/1.54 ((~hskp6) | c0_1(a702)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[75, 72])).
% 1.37/1.54 tff(77,plain,
% 1.37/1.54 ((~hskp6) | c0_1(a702)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[76, 72])).
% 1.37/1.54 tff(78,plain,
% 1.37/1.54 ((~hskp6) | c0_1(a702)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[77, 72])).
% 1.37/1.54 tff(79,plain,
% 1.37/1.54 (c0_1(a702)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[78, 57])).
% 1.37/1.54 tff(80,plain,
% 1.37/1.54 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(81,plain,
% 1.37/1.54 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[80])).
% 1.37/1.54 tff(82,plain,
% 1.37/1.54 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(83,plain,
% 1.37/1.54 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(84,plain,
% 1.37/1.54 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[83])).
% 1.37/1.54 tff(85,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 1.37/1.54 tff(86,plain,
% 1.37/1.54 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.37/1.54 tff(87,plain,
% 1.37/1.54 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[86, 82])).
% 1.37/1.54 tff(88,plain,(
% 1.37/1.54 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.54 inference(skolemize,[status(sab)],[87])).
% 1.37/1.54 tff(89,plain,
% 1.37/1.54 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[88, 81])).
% 1.37/1.54 tff(90,assumption,(~hskp30), introduced(assumption)).
% 1.37/1.54 tff(91,plain,
% 1.37/1.54 (^[U: $i] : refl((hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(92,plain,
% 1.37/1.54 (![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[91])).
% 1.37/1.54 tff(93,plain,
% 1.37/1.54 (![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(94,plain,
% 1.37/1.54 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp30) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp30))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp30) <=> (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp30) <=> (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(95,plain,
% 1.37/1.54 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp30) <=> ![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[94])).
% 1.37/1.54 tff(96,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.37/1.54 tff(97,plain,
% 1.37/1.54 (![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.37/1.54 tff(98,plain,
% 1.37/1.54 (![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[97, 93])).
% 1.37/1.54 tff(99,plain,(
% 1.37/1.54 ![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.37/1.54 inference(skolemize,[status(sab)],[98])).
% 1.37/1.54 tff(100,plain,
% 1.37/1.54 (![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[99, 92])).
% 1.37/1.54 tff(101,plain,
% 1.37/1.54 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(102,plain,
% 1.37/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[101])).
% 1.37/1.54 tff(103,plain,
% 1.37/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(104,plain,
% 1.37/1.54 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W))), ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)))), (((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(105,plain,
% 1.37/1.54 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[104])).
% 1.37/1.54 tff(106,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 1.37/1.54 tff(107,plain,
% 1.37/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[106, 105])).
% 1.37/1.54 tff(108,plain,
% 1.37/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[107, 103])).
% 1.37/1.54 tff(109,plain,(
% 1.37/1.54 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.37/1.54 inference(skolemize,[status(sab)],[108])).
% 1.37/1.54 tff(110,plain,
% 1.37/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[109, 102])).
% 1.37/1.54 tff(111,plain,
% 1.37/1.54 ((hskp30 | hskp28 | hskp12) <=> (hskp30 | hskp28 | hskp12)),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(112,plain,
% 1.37/1.54 (((hskp28 | hskp30) | hskp12) <=> (hskp30 | hskp28 | hskp12)),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(113,axiom,((hskp28 | hskp30) | hskp12), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 1.37/1.54 tff(114,plain,
% 1.37/1.54 (hskp30 | hskp28 | hskp12),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.37/1.54 tff(115,plain,
% 1.37/1.54 (hskp30 | hskp28 | hskp12),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[114, 111])).
% 1.37/1.54 tff(116,plain,
% 1.37/1.54 (hskp30 | hskp28 | hskp12),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[115, 111])).
% 1.37/1.54 tff(117,plain,
% 1.37/1.54 (hskp30 | hskp28 | hskp12),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[116, 111])).
% 1.37/1.54 tff(118,plain,
% 1.37/1.54 (hskp30 | hskp28 | hskp12),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[117, 111])).
% 1.37/1.54 tff(119,plain,
% 1.37/1.54 (hskp12),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[118, 90, 56])).
% 1.37/1.54 tff(120,plain,
% 1.37/1.54 (((~hskp12) | (~c3_1(a725))) <=> ((~hskp12) | (~c3_1(a725)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(121,plain,
% 1.37/1.54 (((~c3_1(a725)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a725)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(122,axiom,((~c3_1(a725)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.37/1.54 tff(123,plain,
% 1.37/1.54 ((~hskp12) | (~c3_1(a725))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.37/1.54 tff(124,plain,
% 1.37/1.54 ((~hskp12) | (~c3_1(a725))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[123, 120])).
% 1.37/1.54 tff(125,plain,
% 1.37/1.54 (~c3_1(a725)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[124, 119])).
% 1.37/1.54 tff(126,plain,
% 1.37/1.54 (((~hskp12) | (~c1_1(a725))) <=> ((~hskp12) | (~c1_1(a725)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(127,plain,
% 1.37/1.54 (((~c1_1(a725)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a725)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(128,axiom,((~c1_1(a725)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 1.37/1.54 tff(129,plain,
% 1.37/1.54 ((~hskp12) | (~c1_1(a725))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.37/1.54 tff(130,plain,
% 1.37/1.54 ((~hskp12) | (~c1_1(a725))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[129, 126])).
% 1.37/1.54 tff(131,plain,
% 1.37/1.54 (~c1_1(a725)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[130, 119])).
% 1.37/1.54 tff(132,plain,
% 1.37/1.54 (((~hskp12) | (~c0_1(a725))) <=> ((~hskp12) | (~c0_1(a725)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(133,plain,
% 1.37/1.54 (((~c0_1(a725)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a725)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(134,axiom,((~c0_1(a725)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.37/1.54 tff(135,plain,
% 1.37/1.54 ((~hskp12) | (~c0_1(a725))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.37/1.54 tff(136,plain,
% 1.37/1.54 ((~hskp12) | (~c0_1(a725))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[135, 132])).
% 1.37/1.54 tff(137,plain,
% 1.37/1.54 (~c0_1(a725)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[136, 119])).
% 1.37/1.54 tff(138,assumption,(~c3_1(a693)), introduced(assumption)).
% 1.37/1.54 tff(139,plain,
% 1.37/1.54 (^[U: $i] : refl((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(140,plain,
% 1.37/1.54 (![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[139])).
% 1.37/1.54 tff(141,plain,
% 1.37/1.54 (![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(142,plain,
% 1.37/1.54 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp23))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp24) <=> ((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp24))), rewrite(((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp24) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp24) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(143,plain,
% 1.37/1.54 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp24) <=> ![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[142])).
% 1.37/1.54 tff(144,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.37/1.54 tff(145,plain,
% 1.37/1.54 (![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.37/1.54 tff(146,plain,
% 1.37/1.54 (![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[145, 141])).
% 1.37/1.54 tff(147,plain,(
% 1.37/1.54 ![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.54 inference(skolemize,[status(sab)],[146])).
% 1.37/1.54 tff(148,plain,
% 1.37/1.54 (![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[147, 140])).
% 1.37/1.54 tff(149,assumption,(~c1_1(a693)), introduced(assumption)).
% 1.37/1.54 tff(150,plain,
% 1.37/1.54 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(151,plain,
% 1.37/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[150])).
% 1.37/1.54 tff(152,plain,
% 1.37/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(153,plain,
% 1.37/1.54 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(154,plain,
% 1.37/1.54 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[153])).
% 1.37/1.54 tff(155,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 1.37/1.54 tff(156,plain,
% 1.37/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.37/1.54 tff(157,plain,
% 1.37/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[156, 152])).
% 1.37/1.54 tff(158,plain,(
% 1.37/1.54 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.54 inference(skolemize,[status(sab)],[157])).
% 1.37/1.54 tff(159,plain,
% 1.37/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[158, 151])).
% 1.37/1.54 tff(160,assumption,(~c3_1(a697)), introduced(assumption)).
% 1.37/1.54 tff(161,assumption,(~hskp4), introduced(assumption)).
% 1.37/1.54 tff(162,assumption,(~hskp6), introduced(assumption)).
% 1.37/1.54 tff(163,assumption,(~c3_1(a754)), introduced(assumption)).
% 1.37/1.54 tff(164,assumption,(~c0_1(a754)), introduced(assumption)).
% 1.37/1.54 tff(165,assumption,(~c2_1(a754)), introduced(assumption)).
% 1.37/1.54 tff(166,plain,
% 1.37/1.54 (((~hskp20) | c2_1(a754)) <=> ((~hskp20) | c2_1(a754))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(167,axiom,((~hskp20) | c2_1(a754)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.37/1.54 tff(168,plain,
% 1.37/1.54 ((~hskp20) | c2_1(a754)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.37/1.54 tff(169,plain,
% 1.37/1.54 ((~hskp20) | c2_1(a754)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[168, 166])).
% 1.37/1.54 tff(170,plain,
% 1.37/1.54 ((~hskp20) | c2_1(a754)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[169, 166])).
% 1.37/1.54 tff(171,plain,
% 1.37/1.54 ((~hskp20) | c2_1(a754)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[170, 166])).
% 1.37/1.54 tff(172,plain,
% 1.37/1.54 ((~hskp20) | c2_1(a754)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[171, 166])).
% 1.37/1.54 tff(173,plain,
% 1.37/1.54 (~hskp20),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[172, 165])).
% 1.37/1.54 tff(174,plain,
% 1.37/1.54 (^[U: $i] : refl((hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(175,plain,
% 1.37/1.54 (![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[174])).
% 1.37/1.54 tff(176,plain,
% 1.37/1.54 (![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(177,plain,
% 1.37/1.54 (^[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) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_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))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp6) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp6))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp6) <=> (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp6) <=> (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(178,plain,
% 1.37/1.54 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp6) <=> ![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[177])).
% 1.37/1.54 tff(179,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 1.37/1.54 tff(180,plain,
% 1.37/1.54 (![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.37/1.54 tff(181,plain,
% 1.37/1.54 (![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[180, 176])).
% 1.37/1.54 tff(182,plain,(
% 1.37/1.54 ![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(skolemize,[status(sab)],[181])).
% 1.37/1.54 tff(183,plain,
% 1.37/1.54 (![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[182, 175])).
% 1.37/1.54 tff(184,assumption,(~ndr1_0), introduced(assumption)).
% 1.37/1.54 tff(185,plain,
% 1.37/1.54 ((ndr1_0 | (~hskp12)) <=> (ndr1_0 | (~hskp12))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(186,plain,
% 1.37/1.54 (((~hskp12) | ndr1_0) <=> (ndr1_0 | (~hskp12))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(187,axiom,((~hskp12) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause19')).
% 1.37/1.54 tff(188,plain,
% 1.37/1.54 (ndr1_0 | (~hskp12)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[187, 186])).
% 1.37/1.54 tff(189,plain,
% 1.37/1.54 (ndr1_0 | (~hskp12)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[188, 185])).
% 1.37/1.54 tff(190,plain,
% 1.37/1.54 (~hskp12),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[189, 184])).
% 1.37/1.54 tff(191,plain,
% 1.37/1.54 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(192,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.37/1.54 tff(193,plain,
% 1.37/1.54 ((~hskp30) | ndr1_0),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[192, 191])).
% 1.37/1.54 tff(194,plain,
% 1.37/1.54 ((~hskp30) | ndr1_0),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[193, 191])).
% 1.37/1.54 tff(195,plain,
% 1.37/1.54 ((~hskp30) | ndr1_0),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[194, 191])).
% 1.37/1.54 tff(196,plain,
% 1.37/1.54 ((~hskp30) | ndr1_0),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[195, 191])).
% 1.37/1.54 tff(197,plain,
% 1.37/1.54 ((~hskp30) | ndr1_0),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[196, 191])).
% 1.37/1.54 tff(198,plain,
% 1.37/1.54 (~hskp30),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[197, 184])).
% 1.37/1.54 tff(199,plain,
% 1.37/1.54 ((ndr1_0 | (~hskp28)) <=> (ndr1_0 | (~hskp28))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(200,plain,
% 1.37/1.54 (((~hskp28) | ndr1_0) <=> (ndr1_0 | (~hskp28))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(201,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 1.37/1.54 tff(202,plain,
% 1.37/1.54 (ndr1_0 | (~hskp28)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[201, 200])).
% 1.37/1.54 tff(203,plain,
% 1.37/1.55 (ndr1_0 | (~hskp28)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[202, 199])).
% 1.37/1.55 tff(204,plain,
% 1.37/1.55 (~hskp28),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[203, 184])).
% 1.37/1.55 tff(205,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[118, 204, 198, 190])).
% 1.37/1.55 tff(206,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(207,plain,
% 1.37/1.55 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(208,plain,
% 1.37/1.55 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754)) <=> (hskp27 | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(209,plain,
% 1.37/1.55 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0)))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[208])).
% 1.37/1.55 tff(210,plain,
% 1.37/1.55 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))),
% 1.37/1.55 inference(transitivity,[status(thm)],[209, 207])).
% 1.37/1.55 tff(211,plain,
% 1.37/1.55 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(212,plain,
% 1.37/1.55 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[211, 210])).
% 1.37/1.55 tff(213,plain,
% 1.37/1.55 (hskp27 | c2_1(a754) | c3_1(a754)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[212, 206, 162, 164, 183])).
% 1.37/1.55 tff(214,plain,
% 1.37/1.55 (hskp27),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[213, 165, 163])).
% 1.37/1.55 tff(215,plain,
% 1.37/1.55 (^[U: $i] : refl((hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 1.37/1.55 inference(bind,[status(th)],[])).
% 1.37/1.55 tff(216,plain,
% 1.37/1.55 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.55 inference(quant_intro,[status(thm)],[215])).
% 1.37/1.55 tff(217,plain,
% 1.37/1.55 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(218,plain,
% 1.37/1.55 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp30))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) <=> (hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20) <=> ((hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp20))), rewrite(((hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp20) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.37/1.55 inference(bind,[status(th)],[])).
% 1.37/1.55 tff(219,plain,
% 1.37/1.55 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.55 inference(quant_intro,[status(thm)],[218])).
% 1.37/1.55 tff(220,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.37/1.55 tff(221,plain,
% 1.37/1.55 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[220, 219])).
% 1.37/1.55 tff(222,plain,
% 1.37/1.55 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[221, 217])).
% 1.37/1.55 tff(223,plain,(
% 1.37/1.55 ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.55 inference(skolemize,[status(sab)],[222])).
% 1.37/1.55 tff(224,plain,
% 1.37/1.55 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[223, 216])).
% 1.37/1.55 tff(225,assumption,(hskp27), introduced(assumption)).
% 1.37/1.55 tff(226,plain,
% 1.37/1.55 (((~hskp27) | c3_1(a691)) <=> ((~hskp27) | c3_1(a691))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(227,axiom,((~hskp27) | c3_1(a691)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.37/1.55 tff(228,plain,
% 1.37/1.55 ((~hskp27) | c3_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.37/1.55 tff(229,plain,
% 1.37/1.55 ((~hskp27) | c3_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[228, 226])).
% 1.37/1.55 tff(230,plain,
% 1.37/1.55 ((~hskp27) | c3_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[229, 226])).
% 1.37/1.55 tff(231,plain,
% 1.37/1.55 ((~hskp27) | c3_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[230, 226])).
% 1.37/1.55 tff(232,plain,
% 1.37/1.55 ((~hskp27) | c3_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[231, 226])).
% 1.37/1.55 tff(233,plain,
% 1.37/1.55 (c3_1(a691)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[232, 225])).
% 1.37/1.55 tff(234,plain,
% 1.37/1.55 (((~hskp27) | c1_1(a691)) <=> ((~hskp27) | c1_1(a691))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(235,axiom,((~hskp27) | c1_1(a691)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 1.37/1.55 tff(236,plain,
% 1.37/1.55 ((~hskp27) | c1_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[235, 234])).
% 1.37/1.55 tff(237,plain,
% 1.37/1.55 ((~hskp27) | c1_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[236, 234])).
% 1.37/1.55 tff(238,plain,
% 1.37/1.55 ((~hskp27) | c1_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[237, 234])).
% 1.37/1.55 tff(239,plain,
% 1.37/1.55 ((~hskp27) | c1_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[238, 234])).
% 1.37/1.55 tff(240,plain,
% 1.37/1.55 ((~hskp27) | c1_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[239, 234])).
% 1.37/1.55 tff(241,plain,
% 1.37/1.55 (c1_1(a691)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[240, 225])).
% 1.37/1.55 tff(242,plain,
% 1.37/1.55 (((~hskp27) | c0_1(a691)) <=> ((~hskp27) | c0_1(a691))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(243,axiom,((~hskp27) | c0_1(a691)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 1.37/1.55 tff(244,plain,
% 1.37/1.55 ((~hskp27) | c0_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[243, 242])).
% 1.37/1.55 tff(245,plain,
% 1.37/1.55 ((~hskp27) | c0_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[244, 242])).
% 1.37/1.55 tff(246,plain,
% 1.37/1.55 ((~hskp27) | c0_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[245, 242])).
% 1.37/1.55 tff(247,plain,
% 1.37/1.55 ((~hskp27) | c0_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[246, 242])).
% 1.37/1.55 tff(248,plain,
% 1.37/1.55 ((~hskp27) | c0_1(a691)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[247, 242])).
% 1.37/1.55 tff(249,plain,
% 1.37/1.55 (c0_1(a691)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[248, 225])).
% 1.37/1.55 tff(250,assumption,(~hskp20), introduced(assumption)).
% 1.37/1.55 tff(251,plain,
% 1.37/1.55 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(252,plain,
% 1.37/1.55 ((hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691))) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(253,plain,
% 1.37/1.55 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[252])).
% 1.37/1.55 tff(254,plain,
% 1.37/1.55 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[253, 251])).
% 1.37/1.55 tff(255,plain,
% 1.37/1.55 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(256,plain,
% 1.37/1.55 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[255, 254])).
% 1.37/1.55 tff(257,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[256, 90, 206, 250, 249, 241, 233, 224])).
% 1.37/1.55 tff(258,plain,((~hskp27) | hskp30 | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(259,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[258, 214, 173, 90])).
% 1.37/1.55 tff(260,plain,(c2_1(a754) | hskp30 | c3_1(a754) | hskp6 | c0_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(261,plain,
% 1.37/1.55 (c2_1(a754)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[260, 164, 90, 162, 163])).
% 1.37/1.55 tff(262,plain,
% 1.37/1.55 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 1.37/1.55 inference(bind,[status(th)],[])).
% 1.37/1.55 tff(263,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.37/1.55 inference(quant_intro,[status(thm)],[262])).
% 1.37/1.55 tff(264,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(265,plain,
% 1.37/1.55 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 1.37/1.55 inference(bind,[status(th)],[])).
% 1.37/1.55 tff(266,plain,
% 1.37/1.55 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.37/1.55 inference(quant_intro,[status(thm)],[265])).
% 1.37/1.55 tff(267,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.37/1.55 tff(268,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[267, 266])).
% 1.37/1.55 tff(269,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[268, 264])).
% 1.37/1.55 tff(270,plain,(
% 1.37/1.55 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.37/1.55 inference(skolemize,[status(sab)],[269])).
% 1.37/1.55 tff(271,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[270, 263])).
% 1.37/1.55 tff(272,assumption,(hskp24), introduced(assumption)).
% 1.37/1.55 tff(273,plain,
% 1.37/1.55 (((~hskp24) | (~c3_1(a764))) <=> ((~hskp24) | (~c3_1(a764)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(274,plain,
% 1.37/1.55 (((~c3_1(a764)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a764)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(275,axiom,((~c3_1(a764)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.37/1.55 tff(276,plain,
% 1.37/1.55 ((~hskp24) | (~c3_1(a764))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[275, 274])).
% 1.37/1.55 tff(277,plain,
% 1.37/1.55 ((~hskp24) | (~c3_1(a764))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[276, 273])).
% 1.37/1.55 tff(278,plain,
% 1.37/1.55 (~c3_1(a764)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[277, 272])).
% 1.37/1.55 tff(279,plain,
% 1.37/1.55 (((~hskp24) | (~c2_1(a764))) <=> ((~hskp24) | (~c2_1(a764)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(280,plain,
% 1.37/1.55 (((~c2_1(a764)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a764)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(281,axiom,((~c2_1(a764)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 1.37/1.55 tff(282,plain,
% 1.37/1.55 ((~hskp24) | (~c2_1(a764))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[281, 280])).
% 1.37/1.55 tff(283,plain,
% 1.37/1.55 ((~hskp24) | (~c2_1(a764))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[282, 279])).
% 1.37/1.55 tff(284,plain,
% 1.37/1.55 (~c2_1(a764)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[283, 272])).
% 1.37/1.55 tff(285,plain,
% 1.37/1.55 (((~hskp24) | c1_1(a764)) <=> ((~hskp24) | c1_1(a764))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(286,axiom,((~hskp24) | c1_1(a764)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 1.37/1.55 tff(287,plain,
% 1.37/1.55 ((~hskp24) | c1_1(a764)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[286, 285])).
% 1.37/1.55 tff(288,plain,
% 1.37/1.55 ((~hskp24) | c1_1(a764)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[287, 285])).
% 1.37/1.55 tff(289,plain,
% 1.37/1.55 ((~hskp24) | c1_1(a764)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[288, 285])).
% 1.37/1.55 tff(290,plain,
% 1.37/1.55 ((~hskp24) | c1_1(a764)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[289, 285])).
% 1.37/1.55 tff(291,plain,
% 1.37/1.55 ((~hskp24) | c1_1(a764)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[290, 285])).
% 1.37/1.55 tff(292,plain,
% 1.37/1.55 (c1_1(a764)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[291, 272])).
% 1.37/1.55 tff(293,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764) | (~c1_1(a764)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(294,plain,
% 1.37/1.55 ((hskp6 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)) | c3_1(a764) | c0_1(a764) | c2_1(a764)) <=> (hskp6 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764) | (~c1_1(a764)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(295,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)) | c3_1(a764) | c0_1(a764) | c2_1(a764))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764) | (~c1_1(a764))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[294])).
% 1.37/1.55 tff(296,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)) | c3_1(a764) | c0_1(a764) | c2_1(a764))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764) | (~c1_1(a764)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[295, 293])).
% 1.37/1.55 tff(297,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)) | c3_1(a764) | c0_1(a764) | c2_1(a764))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(298,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764) | (~c1_1(a764))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[297, 296])).
% 1.37/1.55 tff(299,plain,
% 1.37/1.55 (c0_1(a764)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[298, 206, 162, 292, 284, 278, 271])).
% 1.37/1.55 tff(300,plain,
% 1.37/1.55 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.37/1.55 inference(bind,[status(th)],[])).
% 1.37/1.55 tff(301,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.55 inference(quant_intro,[status(thm)],[300])).
% 1.37/1.55 tff(302,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(303,plain,
% 1.37/1.55 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.37/1.55 inference(bind,[status(th)],[])).
% 1.37/1.55 tff(304,plain,
% 1.37/1.55 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.55 inference(quant_intro,[status(thm)],[303])).
% 1.37/1.55 tff(305,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 1.37/1.55 tff(306,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[305, 304])).
% 1.37/1.55 tff(307,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[306, 302])).
% 1.37/1.55 tff(308,plain,(
% 1.37/1.55 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.55 inference(skolemize,[status(sab)],[307])).
% 1.37/1.55 tff(309,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[308, 301])).
% 1.37/1.55 tff(310,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a764)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(311,plain,
% 1.37/1.55 ((hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a764)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(312,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a764))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[311])).
% 1.37/1.55 tff(313,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a764)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[312, 310])).
% 1.37/1.55 tff(314,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(315,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a764))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[314, 313])).
% 1.37/1.55 tff(316,plain,
% 1.37/1.55 ((~c2_1(a693)) | (~c0_1(a764))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[315, 206, 56, 284, 278, 149, 138, 309])).
% 1.37/1.55 tff(317,plain,
% 1.37/1.55 (~c2_1(a693)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[316, 299])).
% 1.37/1.55 tff(318,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c1_1(a764)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(319,plain,
% 1.37/1.55 ((hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c1_1(a764)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(320,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c1_1(a764))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[319])).
% 1.37/1.55 tff(321,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c1_1(a764)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[320, 318])).
% 1.37/1.55 tff(322,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(323,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c1_1(a764))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[322, 321])).
% 1.37/1.55 tff(324,plain,
% 1.37/1.55 (~c2_1(a754)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[323, 206, 162, 292, 284, 278, 164, 163, 89])).
% 1.37/1.55 tff(325,plain,
% 1.37/1.55 (~hskp20),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[172, 324])).
% 1.37/1.55 tff(326,plain,
% 1.37/1.55 ((hskp30 | hskp20 | hskp1) <=> (hskp30 | hskp20 | hskp1)),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(327,plain,
% 1.37/1.55 (((hskp30 | hskp20) | hskp1) <=> (hskp30 | hskp20 | hskp1)),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(328,plain,
% 1.37/1.55 ((hskp30 | hskp20) <=> (hskp30 | hskp20)),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(329,plain,
% 1.37/1.55 (((hskp30 | hskp20) | hskp1) <=> ((hskp30 | hskp20) | hskp1)),
% 1.37/1.55 inference(monotonicity,[status(thm)],[328])).
% 1.37/1.55 tff(330,plain,
% 1.37/1.55 (((hskp30 | hskp20) | hskp1) <=> (hskp30 | hskp20 | hskp1)),
% 1.37/1.55 inference(transitivity,[status(thm)],[329, 327])).
% 1.37/1.55 tff(331,axiom,((hskp30 | hskp20) | hskp1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 1.37/1.55 tff(332,plain,
% 1.37/1.55 (hskp30 | hskp20 | hskp1),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[331, 330])).
% 1.37/1.55 tff(333,plain,
% 1.37/1.55 (hskp30 | hskp20 | hskp1),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[332, 326])).
% 1.37/1.55 tff(334,plain,
% 1.37/1.55 (hskp30 | hskp20 | hskp1),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[333, 326])).
% 1.37/1.55 tff(335,plain,
% 1.37/1.55 (hskp30 | hskp20 | hskp1),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[334, 326])).
% 1.37/1.55 tff(336,plain,
% 1.37/1.55 (hskp30 | hskp20 | hskp1),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[335, 326])).
% 1.37/1.55 tff(337,plain,
% 1.37/1.55 (hskp1),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[336, 325, 90])).
% 1.37/1.55 tff(338,plain,
% 1.37/1.55 (((~hskp1) | c2_1(a693)) <=> ((~hskp1) | c2_1(a693))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(339,axiom,((~hskp1) | c2_1(a693)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.37/1.55 tff(340,plain,
% 1.37/1.55 ((~hskp1) | c2_1(a693)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[339, 338])).
% 1.37/1.55 tff(341,plain,
% 1.37/1.55 ((~hskp1) | c2_1(a693)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[340, 338])).
% 1.37/1.55 tff(342,plain,
% 1.37/1.55 ((~hskp1) | c2_1(a693)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[341, 338])).
% 1.37/1.55 tff(343,plain,
% 1.37/1.55 ((~hskp1) | c2_1(a693)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[342, 338])).
% 1.37/1.55 tff(344,plain,
% 1.37/1.55 ((~hskp1) | c2_1(a693)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[343, 338])).
% 1.37/1.55 tff(345,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[344, 337, 317])).
% 1.37/1.55 tff(346,plain,((~hskp24) | hskp30 | hskp28 | c1_1(a693) | c3_1(a693) | hskp6 | c0_1(a754) | c3_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(347,plain,
% 1.37/1.55 (~hskp24),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[346, 164, 56, 149, 138, 90, 162, 163])).
% 1.37/1.55 tff(348,assumption,(c2_1(a754)), introduced(assumption)).
% 1.37/1.55 tff(349,assumption,(~c1_1(a754)), introduced(assumption)).
% 1.37/1.55 tff(350,plain,
% 1.37/1.55 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.37/1.55 inference(bind,[status(th)],[])).
% 1.37/1.55 tff(351,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.55 inference(quant_intro,[status(thm)],[350])).
% 1.37/1.55 tff(352,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(353,plain,
% 1.37/1.55 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.37/1.55 inference(bind,[status(th)],[])).
% 1.37/1.55 tff(354,plain,
% 1.37/1.55 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.55 inference(quant_intro,[status(thm)],[353])).
% 1.37/1.55 tff(355,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 1.37/1.55 tff(356,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[355, 354])).
% 1.37/1.55 tff(357,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[356, 352])).
% 1.37/1.55 tff(358,plain,(
% 1.37/1.55 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.55 inference(skolemize,[status(sab)],[357])).
% 1.37/1.55 tff(359,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[358, 351])).
% 1.37/1.56 tff(360,assumption,(hskp23), introduced(assumption)).
% 1.37/1.56 tff(361,plain,
% 1.37/1.56 (((~hskp23) | (~c2_1(a763))) <=> ((~hskp23) | (~c2_1(a763)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(362,plain,
% 1.37/1.56 (((~c2_1(a763)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a763)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(363,axiom,((~c2_1(a763)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 1.37/1.56 tff(364,plain,
% 1.37/1.56 ((~hskp23) | (~c2_1(a763))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[363, 362])).
% 1.37/1.56 tff(365,plain,
% 1.37/1.56 ((~hskp23) | (~c2_1(a763))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[364, 361])).
% 1.37/1.56 tff(366,plain,
% 1.37/1.56 (~c2_1(a763)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[365, 360])).
% 1.37/1.56 tff(367,plain,
% 1.37/1.56 (((~hskp23) | (~c1_1(a763))) <=> ((~hskp23) | (~c1_1(a763)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(368,plain,
% 1.37/1.56 (((~c1_1(a763)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a763)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(369,axiom,((~c1_1(a763)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.37/1.56 tff(370,plain,
% 1.37/1.56 ((~hskp23) | (~c1_1(a763))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[369, 368])).
% 1.37/1.56 tff(371,plain,
% 1.37/1.56 ((~hskp23) | (~c1_1(a763))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[370, 367])).
% 1.37/1.56 tff(372,plain,
% 1.37/1.56 (~c1_1(a763)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[371, 360])).
% 1.37/1.56 tff(373,plain,
% 1.37/1.56 (((~hskp23) | c0_1(a763)) <=> ((~hskp23) | c0_1(a763))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(374,axiom,((~hskp23) | c0_1(a763)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.37/1.56 tff(375,plain,
% 1.37/1.56 ((~hskp23) | c0_1(a763)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[374, 373])).
% 1.37/1.56 tff(376,plain,
% 1.37/1.56 ((~hskp23) | c0_1(a763)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[375, 373])).
% 1.37/1.56 tff(377,plain,
% 1.37/1.56 ((~hskp23) | c0_1(a763)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[376, 373])).
% 1.37/1.56 tff(378,plain,
% 1.37/1.56 ((~hskp23) | c0_1(a763)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[377, 373])).
% 1.37/1.56 tff(379,plain,
% 1.37/1.56 ((~hskp23) | c0_1(a763)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[378, 373])).
% 1.37/1.56 tff(380,plain,
% 1.37/1.56 (c0_1(a763)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[379, 360])).
% 1.37/1.56 tff(381,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a763)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(382,plain,
% 1.37/1.56 ((hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a763)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(383,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a763))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[382])).
% 1.37/1.56 tff(384,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a763)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[383, 381])).
% 1.37/1.56 tff(385,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(386,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a763))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[385, 384])).
% 1.37/1.56 tff(387,plain,
% 1.37/1.56 ($false),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[386, 206, 56, 380, 348, 372, 366, 164, 359, 349])).
% 1.37/1.56 tff(388,plain,((~hskp23) | hskp28 | (~c2_1(a754)) | c0_1(a754) | c1_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.56 tff(389,plain,
% 1.37/1.56 (~hskp23),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[388, 349, 348, 164, 56])).
% 1.37/1.56 tff(390,assumption,(~hskp24), introduced(assumption)).
% 1.37/1.56 tff(391,plain,
% 1.37/1.56 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.37/1.56 inference(bind,[status(th)],[])).
% 1.37/1.56 tff(392,plain,
% 1.37/1.56 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.37/1.56 inference(quant_intro,[status(thm)],[391])).
% 1.37/1.56 tff(393,plain,
% 1.37/1.56 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(394,plain,
% 1.37/1.56 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.37/1.56 inference(bind,[status(th)],[])).
% 1.37/1.56 tff(395,plain,
% 1.37/1.56 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.37/1.56 inference(quant_intro,[status(thm)],[394])).
% 1.37/1.56 tff(396,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.37/1.56 tff(397,plain,
% 1.37/1.56 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.37/1.56 tff(398,plain,
% 1.37/1.56 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[397, 393])).
% 1.37/1.56 tff(399,plain,(
% 1.37/1.56 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.37/1.56 inference(skolemize,[status(sab)],[398])).
% 1.37/1.56 tff(400,plain,
% 1.37/1.56 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[399, 392])).
% 1.37/1.56 tff(401,plain,
% 1.37/1.56 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(402,plain,
% 1.37/1.56 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp4 | hskp3 | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(403,plain,
% 1.37/1.56 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[402])).
% 1.37/1.56 tff(404,plain,
% 1.37/1.56 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[403, 401])).
% 1.37/1.56 tff(405,plain,
% 1.37/1.56 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(406,plain,
% 1.37/1.56 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[405, 404])).
% 1.37/1.56 tff(407,plain,
% 1.37/1.56 (hskp3 | c1_1(a754)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[406, 206, 161, 348, 164, 400])).
% 1.37/1.56 tff(408,plain,
% 1.37/1.56 (hskp3),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[407, 349])).
% 1.37/1.56 tff(409,assumption,(hskp14), introduced(assumption)).
% 1.37/1.56 tff(410,plain,
% 1.37/1.56 (((~hskp14) | c1_1(a730)) <=> ((~hskp14) | c1_1(a730))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(411,axiom,((~hskp14) | c1_1(a730)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.37/1.56 tff(412,plain,
% 1.37/1.56 ((~hskp14) | c1_1(a730)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[411, 410])).
% 1.37/1.56 tff(413,plain,
% 1.37/1.56 ((~hskp14) | c1_1(a730)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[412, 410])).
% 1.37/1.56 tff(414,plain,
% 1.37/1.56 ((~hskp14) | c1_1(a730)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[413, 410])).
% 1.37/1.56 tff(415,plain,
% 1.37/1.56 ((~hskp14) | c1_1(a730)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[414, 410])).
% 1.37/1.56 tff(416,plain,
% 1.37/1.56 ((~hskp14) | c1_1(a730)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[415, 410])).
% 1.37/1.56 tff(417,plain,
% 1.37/1.56 (c1_1(a730)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[416, 409])).
% 1.37/1.56 tff(418,plain,
% 1.37/1.56 (((~hskp14) | c0_1(a730)) <=> ((~hskp14) | c0_1(a730))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(419,axiom,((~hskp14) | c0_1(a730)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.37/1.56 tff(420,plain,
% 1.37/1.56 ((~hskp14) | c0_1(a730)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[419, 418])).
% 1.37/1.56 tff(421,plain,
% 1.37/1.56 ((~hskp14) | c0_1(a730)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[420, 418])).
% 1.37/1.56 tff(422,plain,
% 1.37/1.56 ((~hskp14) | c0_1(a730)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[421, 418])).
% 1.37/1.56 tff(423,plain,
% 1.37/1.56 ((~hskp14) | c0_1(a730)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[422, 418])).
% 1.37/1.56 tff(424,plain,
% 1.37/1.56 ((~hskp14) | c0_1(a730)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[423, 418])).
% 1.37/1.56 tff(425,plain,
% 1.37/1.56 (c0_1(a730)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[424, 409])).
% 1.37/1.56 tff(426,assumption,(~hskp23), introduced(assumption)).
% 1.37/1.56 tff(427,plain,
% 1.37/1.56 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a730)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(428,plain,
% 1.37/1.56 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c1_1(a730))) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(429,plain,
% 1.37/1.56 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c1_1(a730)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a730))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[428])).
% 1.37/1.56 tff(430,plain,
% 1.37/1.56 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c1_1(a730)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[429, 427])).
% 1.37/1.56 tff(431,plain,
% 1.37/1.56 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c1_1(a730)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(432,plain,
% 1.37/1.56 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a730))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[431, 430])).
% 1.37/1.56 tff(433,plain,
% 1.37/1.56 (~c2_1(a730)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[432, 206, 390, 426, 425, 417, 148])).
% 1.37/1.56 tff(434,plain,
% 1.37/1.56 (((~hskp14) | (~c3_1(a730))) <=> ((~hskp14) | (~c3_1(a730)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(435,plain,
% 1.37/1.56 (((~c3_1(a730)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a730)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(436,axiom,((~c3_1(a730)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.37/1.56 tff(437,plain,
% 1.37/1.56 ((~hskp14) | (~c3_1(a730))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[436, 435])).
% 1.37/1.56 tff(438,plain,
% 1.37/1.56 ((~hskp14) | (~c3_1(a730))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[437, 434])).
% 1.37/1.56 tff(439,plain,
% 1.37/1.56 (~c3_1(a730)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[438, 409])).
% 1.37/1.56 tff(440,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c3_1(a754) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | c2_1(a730) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c3_1(a754) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | c2_1(a730) | c1_1(a754) | (~c2_1(a754)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(441,plain,
% 1.37/1.56 ((hskp28 | (~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754))) <=> (hskp28 | c3_1(a754) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | c2_1(a730) | c1_1(a754) | (~c2_1(a754)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(442,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c3_1(a754) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | c2_1(a730) | c1_1(a754) | (~c2_1(a754))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[441])).
% 1.37/1.56 tff(443,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c3_1(a754) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | c2_1(a730) | c1_1(a754) | (~c2_1(a754)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[442, 440])).
% 1.37/1.56 tff(444,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(445,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c3_1(a754) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | c2_1(a730) | c1_1(a754) | (~c2_1(a754))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[444, 443])).
% 1.37/1.56 tff(446,plain,
% 1.37/1.56 ($false),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[445, 206, 56, 348, 425, 163, 439, 309, 349, 433])).
% 1.37/1.56 tff(447,plain,((~hskp14) | hskp28 | (~c2_1(a754)) | c3_1(a754) | c1_1(a754) | hskp24 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.37/1.56 tff(448,plain,
% 1.37/1.56 (~hskp14),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[447, 389, 348, 163, 349, 390, 56])).
% 1.37/1.56 tff(449,assumption,(~hskp14), introduced(assumption)).
% 1.37/1.56 tff(450,assumption,(hskp3), introduced(assumption)).
% 1.37/1.56 tff(451,plain,
% 1.37/1.56 (((~hskp3) | c0_1(a697)) <=> ((~hskp3) | c0_1(a697))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(452,axiom,((~hskp3) | c0_1(a697)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.37/1.56 tff(453,plain,
% 1.37/1.56 ((~hskp3) | c0_1(a697)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[452, 451])).
% 1.37/1.56 tff(454,plain,
% 1.37/1.56 ((~hskp3) | c0_1(a697)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[453, 451])).
% 1.37/1.56 tff(455,plain,
% 1.37/1.56 ((~hskp3) | c0_1(a697)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[454, 451])).
% 1.37/1.56 tff(456,plain,
% 1.37/1.56 ((~hskp3) | c0_1(a697)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[455, 451])).
% 1.37/1.56 tff(457,plain,
% 1.37/1.56 ((~hskp3) | c0_1(a697)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[456, 451])).
% 1.37/1.56 tff(458,plain,
% 1.37/1.56 (c0_1(a697)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[457, 450])).
% 1.37/1.56 tff(459,plain,
% 1.37/1.56 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(460,plain,
% 1.37/1.56 ((hskp30 | hskp14 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697))) <=> (hskp30 | hskp14 | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(461,plain,
% 1.37/1.56 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697)))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[460])).
% 1.37/1.56 tff(462,plain,
% 1.37/1.56 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))),
% 1.37/1.56 inference(transitivity,[status(thm)],[461, 459])).
% 1.37/1.56 tff(463,plain,
% 1.37/1.56 ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(464,plain,
% 1.37/1.56 ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[463, 462])).
% 1.37/1.56 tff(465,plain,
% 1.37/1.56 (hskp14 | (~c0_1(a697)) | c1_1(a697)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[464, 90, 206, 160, 100])).
% 1.37/1.56 tff(466,plain,
% 1.37/1.56 (c1_1(a697)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[465, 458, 449])).
% 1.37/1.56 tff(467,plain,
% 1.37/1.56 (((~hskp3) | c2_1(a697)) <=> ((~hskp3) | c2_1(a697))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(468,axiom,((~hskp3) | c2_1(a697)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.37/1.56 tff(469,plain,
% 1.37/1.56 ((~hskp3) | c2_1(a697)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[468, 467])).
% 1.37/1.56 tff(470,plain,
% 1.37/1.56 ((~hskp3) | c2_1(a697)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[469, 467])).
% 1.37/1.56 tff(471,plain,
% 1.37/1.56 ((~hskp3) | c2_1(a697)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[470, 467])).
% 1.37/1.56 tff(472,plain,
% 1.37/1.56 ((~hskp3) | c2_1(a697)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[471, 467])).
% 1.37/1.56 tff(473,plain,
% 1.37/1.56 ((~hskp3) | c2_1(a697)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[472, 467])).
% 1.37/1.56 tff(474,plain,
% 1.37/1.56 (c2_1(a697)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[473, 450])).
% 1.37/1.56 tff(475,plain,
% 1.37/1.56 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(476,plain,
% 1.37/1.56 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a697)) | (~c0_1(a697)) | (~c1_1(a697))) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(477,plain,
% 1.37/1.56 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a697)) | (~c0_1(a697)) | (~c1_1(a697)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[476])).
% 1.37/1.56 tff(478,plain,
% 1.37/1.56 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a697)) | (~c0_1(a697)) | (~c1_1(a697)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[477, 475])).
% 1.37/1.56 tff(479,plain,
% 1.37/1.56 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a697)) | (~c0_1(a697)) | (~c1_1(a697)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(480,plain,
% 1.37/1.56 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[479, 478])).
% 1.37/1.56 tff(481,plain,
% 1.37/1.56 ($false),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[480, 206, 390, 426, 458, 474, 148, 466])).
% 1.37/1.56 tff(482,plain,((~hskp3) | hskp24 | hskp23 | hskp14 | hskp30 | c3_1(a697)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.56 tff(483,plain,
% 1.37/1.56 ($false),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[482, 448, 408, 390, 389, 90, 160])).
% 1.37/1.56 tff(484,plain,(c1_1(a754) | hskp24 | hskp30 | c3_1(a697) | (~c2_1(a754)) | c3_1(a754) | hskp28 | hskp4 | c0_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.56 tff(485,plain,
% 1.37/1.56 (c1_1(a754)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[484, 347, 90, 160, 261, 163, 56, 161, 164])).
% 1.37/1.56 tff(486,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(487,plain,
% 1.37/1.56 ((hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a725) | c0_1(a725) | c2_1(a725)) <=> (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(488,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a725) | c0_1(a725) | c2_1(a725))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[487])).
% 1.37/1.56 tff(489,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a725) | c0_1(a725) | c2_1(a725))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[488, 486])).
% 1.37/1.56 tff(490,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a725) | c0_1(a725) | c2_1(a725))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(491,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[490, 489])).
% 1.37/1.56 tff(492,plain,
% 1.37/1.56 (c0_1(a754) | c2_1(a725) | (~c1_1(a754))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[491, 206, 162, 163, 137, 125, 271])).
% 1.37/1.56 tff(493,plain,
% 1.37/1.56 (c2_1(a725)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[492, 485, 164])).
% 1.37/1.56 tff(494,plain,
% 1.37/1.56 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(495,plain,
% 1.37/1.56 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp4 | hskp3 | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(496,plain,
% 1.37/1.56 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[495])).
% 1.37/1.56 tff(497,plain,
% 1.37/1.56 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[496, 494])).
% 1.37/1.56 tff(498,plain,
% 1.37/1.56 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(499,plain,
% 1.37/1.56 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[498, 497])).
% 1.37/1.56 tff(500,plain,
% 1.37/1.56 (hskp4 | hskp3 | (~c2_1(a725))),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[499, 206, 137, 131, 400])).
% 1.37/1.56 tff(501,plain,
% 1.37/1.56 (hskp3),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[500, 493, 161])).
% 1.37/1.56 tff(502,plain,
% 1.37/1.56 (c0_1(a697)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[457, 501])).
% 1.37/1.56 tff(503,plain,
% 1.37/1.56 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W)))),
% 1.37/1.56 inference(bind,[status(th)],[])).
% 1.37/1.56 tff(504,plain,
% 1.37/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.37/1.57 inference(quant_intro,[status(thm)],[503])).
% 1.37/1.57 tff(505,plain,
% 1.37/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(506,plain,
% 1.37/1.57 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | 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(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_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))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_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))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))))),
% 1.37/1.57 inference(bind,[status(th)],[])).
% 1.37/1.57 tff(507,plain,
% 1.37/1.57 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_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)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.37/1.57 inference(quant_intro,[status(thm)],[506])).
% 1.37/1.57 tff(508,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 1.37/1.57 tff(509,plain,
% 1.37/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[508, 507])).
% 1.37/1.57 tff(510,plain,
% 1.37/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[509, 505])).
% 1.37/1.57 tff(511,plain,(
% 1.37/1.57 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.37/1.57 inference(skolemize,[status(sab)],[510])).
% 1.37/1.57 tff(512,plain,
% 1.37/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[511, 504])).
% 1.37/1.57 tff(513,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(514,plain,
% 1.37/1.57 (((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725)) <=> (c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(515,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[514])).
% 1.37/1.57 tff(516,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[515, 513])).
% 1.37/1.57 tff(517,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(518,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[517, 516])).
% 1.37/1.57 tff(519,plain,
% 1.37/1.57 ((~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[518, 206, 163, 137, 131, 160, 512])).
% 1.37/1.57 tff(520,plain,
% 1.37/1.57 (c1_1(a697)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[519, 502, 261, 493, 485])).
% 1.37/1.57 tff(521,plain,
% 1.37/1.57 (c2_1(a697)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[473, 501])).
% 1.37/1.57 tff(522,assumption,(c2_1(a725)), introduced(assumption)).
% 1.37/1.57 tff(523,assumption,(~c1_1(a725)), introduced(assumption)).
% 1.37/1.57 tff(524,assumption,(~c0_1(a725)), introduced(assumption)).
% 1.37/1.57 tff(525,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a763)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(526,plain,
% 1.37/1.57 ((hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a763)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(527,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a763))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[526])).
% 1.37/1.57 tff(528,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a763)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[527, 525])).
% 1.37/1.57 tff(529,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(530,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a763))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[529, 528])).
% 1.37/1.57 tff(531,plain,
% 1.37/1.57 ($false),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[530, 206, 56, 380, 372, 366, 524, 523, 359, 522])).
% 1.37/1.57 tff(532,plain,((~hskp23) | hskp28 | c0_1(a725) | c1_1(a725) | (~c2_1(a725))), inference(lemma,lemma(discharge,[]))).
% 1.37/1.57 tff(533,plain,
% 1.37/1.57 (~hskp23),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[532, 493, 137, 131, 56])).
% 1.37/1.57 tff(534,plain,
% 1.37/1.57 ($false),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[480, 206, 347, 533, 502, 521, 148, 520])).
% 1.37/1.57 tff(535,plain,(c0_1(a754) | c3_1(a754) | c3_1(a697) | hskp4 | hskp28 | hskp6 | hskp30 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.57 tff(536,plain,
% 1.37/1.57 (c0_1(a754)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[535, 163, 160, 161, 56, 162, 90, 149, 138])).
% 1.37/1.57 tff(537,plain,
% 1.37/1.57 (((~hskp20) | (~c0_1(a754))) <=> ((~hskp20) | (~c0_1(a754)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(538,plain,
% 1.37/1.57 (((~c0_1(a754)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a754)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(539,axiom,((~c0_1(a754)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.37/1.57 tff(540,plain,
% 1.37/1.57 ((~hskp20) | (~c0_1(a754))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[539, 538])).
% 1.37/1.57 tff(541,plain,
% 1.37/1.57 ((~hskp20) | (~c0_1(a754))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[540, 537])).
% 1.37/1.57 tff(542,plain,
% 1.37/1.57 (~hskp20),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[541, 536])).
% 1.37/1.57 tff(543,plain,
% 1.37/1.57 (~hskp27),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[258, 542, 90])).
% 1.37/1.57 tff(544,plain,
% 1.37/1.57 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.37/1.57 inference(bind,[status(th)],[])).
% 1.37/1.57 tff(545,plain,
% 1.37/1.57 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.57 inference(quant_intro,[status(thm)],[544])).
% 1.37/1.57 tff(546,plain,
% 1.37/1.57 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(547,plain,
% 1.37/1.57 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.37/1.57 inference(bind,[status(th)],[])).
% 1.37/1.57 tff(548,plain,
% 1.37/1.57 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.57 inference(quant_intro,[status(thm)],[547])).
% 1.37/1.57 tff(549,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.37/1.57 tff(550,plain,
% 1.37/1.57 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[549, 548])).
% 1.37/1.57 tff(551,plain,
% 1.37/1.57 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[550, 546])).
% 1.37/1.57 tff(552,plain,(
% 1.37/1.57 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.57 inference(skolemize,[status(sab)],[551])).
% 1.37/1.57 tff(553,plain,
% 1.37/1.57 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[552, 545])).
% 1.37/1.57 tff(554,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c1_1(a754))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c1_1(a754))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(555,plain,
% 1.37/1.57 ((hskp27 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c0_1(a754)) | c3_1(a725) | c1_1(a725) | c0_1(a725)) <=> (hskp27 | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c1_1(a754))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(556,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c0_1(a754)) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c1_1(a754)))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[555])).
% 1.37/1.57 tff(557,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c0_1(a754)) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c1_1(a754))),
% 1.37/1.57 inference(transitivity,[status(thm)],[556, 554])).
% 1.37/1.57 tff(558,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c0_1(a754)) | c3_1(a725) | c1_1(a725) | c0_1(a725))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(559,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c1_1(a754)),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[558, 557])).
% 1.37/1.57 tff(560,plain,
% 1.37/1.57 (hskp27 | (~c0_1(a754)) | c1_1(a754)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[559, 206, 163, 137, 131, 125, 553])).
% 1.37/1.57 tff(561,plain,
% 1.37/1.57 (c1_1(a754)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[560, 543, 536])).
% 1.37/1.57 tff(562,plain,
% 1.37/1.57 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.37/1.57 inference(bind,[status(th)],[])).
% 1.37/1.57 tff(563,plain,
% 1.37/1.57 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.37/1.57 inference(quant_intro,[status(thm)],[562])).
% 1.37/1.57 tff(564,plain,
% 1.37/1.57 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(565,plain,
% 1.37/1.57 (^[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)) | (~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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | 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)) | (~c1_1(V))) | c3_1(U)) | 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)) | (~c1_1(V))) | c3_1(U)) | 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)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.37/1.57 inference(bind,[status(th)],[])).
% 1.37/1.57 tff(566,plain,
% 1.37/1.57 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.37/1.57 inference(quant_intro,[status(thm)],[565])).
% 1.37/1.57 tff(567,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 1.37/1.57 tff(568,plain,
% 1.37/1.57 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[567, 566])).
% 1.37/1.57 tff(569,plain,
% 1.37/1.57 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[568, 564])).
% 1.37/1.57 tff(570,plain,(
% 1.37/1.57 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.37/1.57 inference(skolemize,[status(sab)],[569])).
% 1.37/1.57 tff(571,plain,
% 1.37/1.57 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[570, 563])).
% 1.37/1.57 tff(572,plain,
% 1.37/1.57 (hskp1),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[336, 542, 90])).
% 1.37/1.57 tff(573,plain,
% 1.37/1.57 (c2_1(a693)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[344, 572])).
% 1.37/1.57 tff(574,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(575,plain,
% 1.37/1.57 ((hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693))) <=> (hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(576,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[575])).
% 1.37/1.57 tff(577,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[576, 574])).
% 1.37/1.57 tff(578,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(579,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[578, 577])).
% 1.37/1.57 tff(580,plain,
% 1.37/1.57 (c2_1(a754) | (~c0_1(a754)) | (~c2_1(a693))),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[579, 206, 56, 163, 149, 138, 309])).
% 1.37/1.57 tff(581,plain,
% 1.37/1.57 (c2_1(a754)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[580, 573, 536])).
% 1.37/1.57 tff(582,plain,
% 1.37/1.57 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(583,plain,
% 1.37/1.57 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725)) <=> (hskp27 | hskp6 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(584,plain,
% 1.37/1.57 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725)))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[583])).
% 1.37/1.57 tff(585,plain,
% 1.37/1.57 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))),
% 1.37/1.57 inference(transitivity,[status(thm)],[584, 582])).
% 1.37/1.57 tff(586,plain,
% 1.37/1.57 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(587,plain,
% 1.37/1.57 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725)),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[586, 585])).
% 1.37/1.57 tff(588,plain,
% 1.37/1.57 (hskp27 | hskp6 | c2_1(a725)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[587, 206, 137, 125, 183])).
% 1.37/1.57 tff(589,plain,
% 1.37/1.57 (c2_1(a725)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[588, 543, 162])).
% 1.37/1.57 tff(590,plain,
% 1.37/1.57 (~hskp23),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[532, 589, 137, 131, 56])).
% 1.37/1.57 tff(591,plain,
% 1.37/1.57 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(592,plain,
% 1.37/1.57 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a754)) | (~c0_1(a754)) | (~c1_1(a754))) <=> (hskp24 | hskp23 | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(593,plain,
% 1.37/1.57 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a754)) | (~c0_1(a754)) | (~c1_1(a754)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[592])).
% 1.37/1.57 tff(594,plain,
% 1.37/1.57 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a754)) | (~c0_1(a754)) | (~c1_1(a754)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[593, 591])).
% 1.37/1.57 tff(595,plain,
% 1.37/1.57 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a754)) | (~c0_1(a754)) | (~c1_1(a754)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(596,plain,
% 1.37/1.57 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[595, 594])).
% 1.37/1.57 tff(597,plain,
% 1.37/1.57 (hskp24),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[596, 206, 590, 581, 536, 148, 561])).
% 1.37/1.57 tff(598,plain,
% 1.37/1.57 (~c3_1(a764)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[277, 597])).
% 1.37/1.57 tff(599,plain,
% 1.37/1.57 (~c2_1(a764)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[283, 597])).
% 1.37/1.57 tff(600,plain,
% 1.37/1.57 (c1_1(a764)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[291, 597])).
% 1.37/1.58 tff(601,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c1_1(a764)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(602,plain,
% 1.37/1.58 ((hskp28 | (~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c1_1(a764)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(603,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c1_1(a764))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[602])).
% 1.37/1.58 tff(604,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c1_1(a764)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[603, 601])).
% 1.37/1.58 tff(605,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(606,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c1_1(a764))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[605, 604])).
% 1.37/1.58 tff(607,plain,
% 1.37/1.58 ($false),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[606, 206, 56, 600, 581, 599, 598, 163, 571, 561])).
% 1.37/1.58 tff(608,plain,(c3_1(a754) | hskp28 | c1_1(a693) | c3_1(a693) | hskp6 | hskp30 | c3_1(a697) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.37/1.58 tff(609,plain,
% 1.37/1.58 (c3_1(a754)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[608, 162, 149, 138, 56, 90, 160, 161])).
% 1.37/1.58 tff(610,plain,
% 1.37/1.58 (((~hskp20) | (~c3_1(a754))) <=> ((~hskp20) | (~c3_1(a754)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(611,plain,
% 1.37/1.58 (((~c3_1(a754)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a754)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(612,axiom,((~c3_1(a754)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.37/1.58 tff(613,plain,
% 1.37/1.58 ((~hskp20) | (~c3_1(a754))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[612, 611])).
% 1.37/1.58 tff(614,plain,
% 1.37/1.58 ((~hskp20) | (~c3_1(a754))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[613, 610])).
% 1.37/1.58 tff(615,plain,
% 1.37/1.58 (~hskp20),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[614, 609])).
% 1.37/1.58 tff(616,plain,
% 1.37/1.58 (~hskp27),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[258, 615, 90])).
% 1.37/1.58 tff(617,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(618,plain,
% 1.37/1.58 ((hskp27 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | c0_1(a725)) <=> (hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(619,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[618])).
% 1.37/1.58 tff(620,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[619, 617])).
% 1.37/1.58 tff(621,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | c0_1(a725))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(622,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[621, 620])).
% 1.37/1.58 tff(623,plain,
% 1.37/1.58 (hskp27 | c1_1(a693) | (~c0_1(a693))),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[622, 206, 137, 131, 125, 138, 553])).
% 1.37/1.58 tff(624,plain,
% 1.37/1.58 (~c0_1(a693)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[623, 616, 149])).
% 1.37/1.58 tff(625,plain,
% 1.37/1.58 (hskp1),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[336, 615, 90])).
% 1.37/1.58 tff(626,plain,
% 1.37/1.58 (c2_1(a693)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[344, 625])).
% 1.37/1.58 tff(627,plain,
% 1.37/1.58 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c1_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(628,plain,
% 1.37/1.58 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a693) | c0_1(a693) | (~c2_1(a693))) <=> (hskp4 | hskp3 | c1_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(629,plain,
% 1.37/1.58 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a693) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c1_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[628])).
% 1.37/1.58 tff(630,plain,
% 1.37/1.58 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a693) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[629, 627])).
% 1.37/1.58 tff(631,plain,
% 1.37/1.58 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a693) | c0_1(a693) | (~c2_1(a693)))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(632,plain,
% 1.37/1.58 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[631, 630])).
% 1.37/1.58 tff(633,plain,
% 1.37/1.58 (hskp4 | hskp3 | c0_1(a693) | (~c2_1(a693))),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[632, 206, 149, 400])).
% 1.37/1.58 tff(634,plain,
% 1.37/1.58 (hskp3),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[633, 626, 161, 624])).
% 1.37/1.58 tff(635,plain,
% 1.37/1.58 (c0_1(a697)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[457, 634])).
% 1.37/1.58 tff(636,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(637,plain,
% 1.37/1.58 ((hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a725) | c1_1(a725) | c0_1(a725)) <=> (hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(638,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697)))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[637])).
% 1.37/1.58 tff(639,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))),
% 1.37/1.58 inference(transitivity,[status(thm)],[638, 636])).
% 1.37/1.58 tff(640,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a725) | c1_1(a725) | c0_1(a725))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(641,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[640, 639])).
% 1.37/1.58 tff(642,plain,
% 1.37/1.58 (hskp27 | (~c0_1(a697)) | c1_1(a697)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[641, 206, 137, 131, 125, 160, 553])).
% 1.37/1.58 tff(643,plain,
% 1.37/1.58 (c1_1(a697)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[642, 635, 616])).
% 1.37/1.58 tff(644,plain,
% 1.37/1.58 (c2_1(a697)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[473, 634])).
% 1.37/1.58 tff(645,plain,
% 1.37/1.58 (c2_1(a725)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[588, 616, 162])).
% 1.37/1.58 tff(646,plain,
% 1.37/1.58 (~hskp23),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[532, 645, 137, 131, 56])).
% 1.37/1.58 tff(647,plain,
% 1.37/1.58 (hskp24),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[480, 206, 646, 635, 644, 148, 643])).
% 1.37/1.58 tff(648,plain,
% 1.37/1.58 (~c3_1(a764)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[277, 647])).
% 1.37/1.58 tff(649,plain,
% 1.37/1.58 (~c2_1(a764)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[283, 647])).
% 1.37/1.58 tff(650,plain,
% 1.37/1.58 (c1_1(a764)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[291, 647])).
% 1.37/1.58 tff(651,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a764)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(652,plain,
% 1.37/1.58 ((hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a764)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(653,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a764))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[652])).
% 1.37/1.58 tff(654,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a764)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[653, 651])).
% 1.37/1.58 tff(655,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(656,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a764))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[655, 654])).
% 1.37/1.58 tff(657,plain,
% 1.37/1.58 ($false),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[656, 206, 56, 650, 644, 649, 648, 160, 571, 643])).
% 1.37/1.58 tff(658,plain,(hskp6 | hskp28 | c3_1(a697) | hskp4 | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.37/1.58 tff(659,plain,
% 1.37/1.58 (hskp6),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[658, 161, 160, 56, 149, 138, 90])).
% 1.37/1.58 tff(660,plain,
% 1.37/1.58 (~c2_1(a702)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[62, 659])).
% 1.37/1.58 tff(661,plain,
% 1.37/1.58 (c0_1(a702)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[78, 659])).
% 1.37/1.58 tff(662,plain,
% 1.37/1.58 (c3_1(a702)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[70, 659])).
% 1.37/1.58 tff(663,assumption,(~c2_1(a702)), introduced(assumption)).
% 1.37/1.58 tff(664,assumption,(c3_1(a702)), introduced(assumption)).
% 1.37/1.58 tff(665,assumption,(c0_1(a702)), introduced(assumption)).
% 1.37/1.58 tff(666,assumption,(hskp25), introduced(assumption)).
% 1.37/1.58 tff(667,plain,
% 1.37/1.58 (((~hskp25) | c2_1(a773)) <=> ((~hskp25) | c2_1(a773))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(668,axiom,((~hskp25) | c2_1(a773)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 1.37/1.58 tff(669,plain,
% 1.37/1.58 ((~hskp25) | c2_1(a773)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[668, 667])).
% 1.37/1.58 tff(670,plain,
% 1.37/1.58 ((~hskp25) | c2_1(a773)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[669, 667])).
% 1.37/1.58 tff(671,plain,
% 1.37/1.58 ((~hskp25) | c2_1(a773)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[670, 667])).
% 1.37/1.58 tff(672,plain,
% 1.37/1.58 ((~hskp25) | c2_1(a773)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[671, 667])).
% 1.37/1.58 tff(673,plain,
% 1.37/1.58 ((~hskp25) | c2_1(a773)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[672, 667])).
% 1.37/1.58 tff(674,plain,
% 1.37/1.58 (c2_1(a773)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[673, 666])).
% 1.37/1.58 tff(675,plain,
% 1.37/1.58 (((~hskp25) | c1_1(a773)) <=> ((~hskp25) | c1_1(a773))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(676,axiom,((~hskp25) | c1_1(a773)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 1.37/1.58 tff(677,plain,
% 1.37/1.58 ((~hskp25) | c1_1(a773)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[676, 675])).
% 1.37/1.58 tff(678,plain,
% 1.37/1.58 ((~hskp25) | c1_1(a773)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[677, 675])).
% 1.37/1.58 tff(679,plain,
% 1.37/1.58 ((~hskp25) | c1_1(a773)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[678, 675])).
% 1.37/1.58 tff(680,plain,
% 1.37/1.58 ((~hskp25) | c1_1(a773)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[679, 675])).
% 1.37/1.58 tff(681,plain,
% 1.37/1.58 ((~hskp25) | c1_1(a773)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[680, 675])).
% 1.37/1.58 tff(682,plain,
% 1.37/1.58 (c1_1(a773)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[681, 666])).
% 1.37/1.58 tff(683,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(684,plain,
% 1.37/1.58 ((hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702))) <=> (hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(685,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[684])).
% 1.37/1.58 tff(686,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[685, 683])).
% 1.37/1.58 tff(687,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(688,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[687, 686])).
% 1.37/1.58 tff(689,plain,
% 1.37/1.58 (~c3_1(a773)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[688, 206, 56, 682, 674, 665, 664, 663, 55])).
% 1.37/1.58 tff(690,plain,
% 1.37/1.58 (((~hskp25) | (~c0_1(a773))) <=> ((~hskp25) | (~c0_1(a773)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(691,plain,
% 1.37/1.58 (((~c0_1(a773)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a773)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(692,axiom,((~c0_1(a773)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.37/1.58 tff(693,plain,
% 1.37/1.58 ((~hskp25) | (~c0_1(a773))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[692, 691])).
% 1.37/1.58 tff(694,plain,
% 1.37/1.58 ((~hskp25) | (~c0_1(a773))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[693, 690])).
% 1.37/1.58 tff(695,plain,
% 1.37/1.58 (~c0_1(a773)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[694, 666])).
% 1.37/1.58 tff(696,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a773) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | (~c2_1(a773)) | (~c1_1(a773)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a773) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | (~c2_1(a773)) | (~c1_1(a773)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(697,plain,
% 1.37/1.58 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | c0_1(a773) | (~c2_1(a773)) | c3_1(a773) | c0_1(a773) | (~c1_1(a773))) <=> (c0_1(a773) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | (~c2_1(a773)) | (~c1_1(a773)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(698,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | c0_1(a773) | (~c2_1(a773)) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a773) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | (~c2_1(a773)) | (~c1_1(a773))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[697])).
% 1.37/1.58 tff(699,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | c0_1(a773) | (~c2_1(a773)) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a773) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | (~c2_1(a773)) | (~c1_1(a773)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[698, 696])).
% 1.37/1.58 tff(700,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | c0_1(a773) | (~c2_1(a773)) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(701,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a773) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | (~c2_1(a773)) | (~c1_1(a773))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[700, 699])).
% 1.37/1.58 tff(702,plain,
% 1.37/1.58 ($false),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[701, 206, 682, 674, 665, 664, 695, 663, 159, 689])).
% 1.37/1.58 tff(703,plain,((~hskp25) | (~c0_1(a702)) | (~c3_1(a702)) | c2_1(a702) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.37/1.58 tff(704,plain,
% 1.37/1.58 (~hskp25),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[703, 662, 661, 660, 56])).
% 1.37/1.58 tff(705,plain,
% 1.37/1.58 ((hskp28 | hskp25 | hskp22) <=> (hskp28 | hskp25 | hskp22)),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(706,plain,
% 1.37/1.58 (((hskp28 | hskp25) | hskp22) <=> (hskp28 | hskp25 | hskp22)),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(707,plain,
% 1.37/1.58 ((hskp28 | hskp25) <=> (hskp28 | hskp25)),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(708,plain,
% 1.37/1.58 (((hskp28 | hskp25) | hskp22) <=> ((hskp28 | hskp25) | hskp22)),
% 1.37/1.58 inference(monotonicity,[status(thm)],[707])).
% 1.37/1.58 tff(709,plain,
% 1.37/1.58 (((hskp28 | hskp25) | hskp22) <=> (hskp28 | hskp25 | hskp22)),
% 1.37/1.58 inference(transitivity,[status(thm)],[708, 706])).
% 1.37/1.58 tff(710,axiom,((hskp28 | hskp25) | hskp22), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 1.37/1.58 tff(711,plain,
% 1.37/1.58 (hskp28 | hskp25 | hskp22),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[710, 709])).
% 1.37/1.58 tff(712,plain,
% 1.37/1.58 (hskp28 | hskp25 | hskp22),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[711, 705])).
% 1.37/1.58 tff(713,plain,
% 1.37/1.58 (hskp28 | hskp25 | hskp22),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[712, 705])).
% 1.37/1.58 tff(714,plain,
% 1.37/1.58 (hskp28 | hskp25 | hskp22),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[713, 705])).
% 1.37/1.58 tff(715,plain,
% 1.37/1.58 (hskp28 | hskp25 | hskp22),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[714, 705])).
% 1.37/1.58 tff(716,plain,
% 1.37/1.58 (hskp22),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[715, 704, 56])).
% 1.37/1.58 tff(717,plain,
% 1.37/1.58 (((~hskp22) | (~c2_1(a761))) <=> ((~hskp22) | (~c2_1(a761)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(718,plain,
% 1.37/1.58 (((~c2_1(a761)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a761)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(719,axiom,((~c2_1(a761)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.37/1.58 tff(720,plain,
% 1.37/1.58 ((~hskp22) | (~c2_1(a761))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[719, 718])).
% 1.37/1.58 tff(721,plain,
% 1.37/1.58 ((~hskp22) | (~c2_1(a761))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[720, 717])).
% 1.37/1.58 tff(722,plain,
% 1.37/1.58 (~c2_1(a761)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[721, 716])).
% 1.37/1.58 tff(723,plain,
% 1.37/1.58 (((~hskp22) | (~c0_1(a761))) <=> ((~hskp22) | (~c0_1(a761)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(724,plain,
% 1.37/1.58 (((~c0_1(a761)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a761)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(725,axiom,((~c0_1(a761)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 1.37/1.58 tff(726,plain,
% 1.37/1.58 ((~hskp22) | (~c0_1(a761))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[725, 724])).
% 1.37/1.58 tff(727,plain,
% 1.37/1.58 ((~hskp22) | (~c0_1(a761))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[726, 723])).
% 1.37/1.58 tff(728,plain,
% 1.37/1.58 (~c0_1(a761)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[727, 716])).
% 1.37/1.58 tff(729,plain,
% 1.37/1.58 (((~hskp22) | c1_1(a761)) <=> ((~hskp22) | c1_1(a761))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(730,axiom,((~hskp22) | c1_1(a761)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.37/1.58 tff(731,plain,
% 1.37/1.58 ((~hskp22) | c1_1(a761)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[730, 729])).
% 1.37/1.58 tff(732,plain,
% 1.37/1.58 ((~hskp22) | c1_1(a761)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[731, 729])).
% 1.37/1.58 tff(733,plain,
% 1.37/1.58 ((~hskp22) | c1_1(a761)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[732, 729])).
% 1.37/1.58 tff(734,plain,
% 1.37/1.58 ((~hskp22) | c1_1(a761)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[733, 729])).
% 1.37/1.58 tff(735,plain,
% 1.37/1.58 ((~hskp22) | c1_1(a761)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[734, 729])).
% 1.37/1.58 tff(736,plain,
% 1.37/1.58 (c1_1(a761)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[735, 716])).
% 1.37/1.58 tff(737,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a761)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(738,plain,
% 1.37/1.58 (((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a725) | c1_1(a725) | c2_1(a725) | c3_1(a725) | c2_1(a725) | c0_1(a725)) <=> (c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a761)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(739,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a725) | c1_1(a725) | c2_1(a725) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a761))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[738])).
% 1.37/1.58 tff(740,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a725) | c1_1(a725) | c2_1(a725) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a761)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[739, 737])).
% 1.37/1.58 tff(741,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a725) | c1_1(a725) | c2_1(a725) | c3_1(a725) | c2_1(a725) | c0_1(a725))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(742,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a761))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[741, 740])).
% 1.37/1.58 tff(743,plain,
% 1.37/1.58 (c2_1(a725)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[742, 206, 736, 728, 722, 137, 131, 125, 110])).
% 1.37/1.58 tff(744,plain,
% 1.37/1.58 (hskp3),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[500, 743, 161])).
% 1.37/1.58 tff(745,plain,
% 1.37/1.58 (c0_1(a697)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[457, 744])).
% 1.37/1.58 tff(746,plain,
% 1.37/1.58 (c2_1(a697)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[473, 744])).
% 1.37/1.58 tff(747,plain,
% 1.37/1.58 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(748,plain,
% 1.37/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[747])).
% 1.37/1.58 tff(749,plain,
% 1.37/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(750,plain,
% 1.37/1.58 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.37/1.59 inference(bind,[status(th)],[])).
% 1.37/1.59 tff(751,plain,
% 1.37/1.59 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.59 inference(quant_intro,[status(thm)],[750])).
% 1.37/1.59 tff(752,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.37/1.59 tff(753,plain,
% 1.37/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[752, 751])).
% 1.37/1.59 tff(754,plain,
% 1.37/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[753, 749])).
% 1.37/1.59 tff(755,plain,(
% 1.37/1.59 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.59 inference(skolemize,[status(sab)],[754])).
% 1.37/1.59 tff(756,plain,
% 1.37/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[755, 748])).
% 1.37/1.59 tff(757,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a761) | c2_1(a761) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a761)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(758,plain,
% 1.37/1.59 (((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761))) <=> (c0_1(a761) | c2_1(a761) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a761)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(759,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a761) | c2_1(a761) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a761))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[758])).
% 1.37/1.59 tff(760,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a761)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[759, 757])).
% 1.37/1.59 tff(761,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(762,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a761))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[761, 760])).
% 1.37/1.59 tff(763,plain,
% 1.37/1.59 ((~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697))),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[762, 206, 736, 728, 722, 160, 756])).
% 1.37/1.59 tff(764,plain,
% 1.37/1.59 (~c1_1(a697)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[763, 746, 745])).
% 1.37/1.59 tff(765,plain,
% 1.37/1.59 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.37/1.59 inference(bind,[status(th)],[])).
% 1.37/1.59 tff(766,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.37/1.59 inference(quant_intro,[status(thm)],[765])).
% 1.37/1.59 tff(767,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(768,plain,
% 1.37/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.37/1.59 inference(bind,[status(th)],[])).
% 1.37/1.59 tff(769,plain,
% 1.37/1.59 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.37/1.59 inference(quant_intro,[status(thm)],[768])).
% 1.37/1.59 tff(770,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 1.37/1.59 tff(771,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[770, 769])).
% 1.37/1.59 tff(772,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[771, 767])).
% 1.37/1.59 tff(773,plain,(
% 1.37/1.59 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.37/1.59 inference(skolemize,[status(sab)],[772])).
% 1.37/1.59 tff(774,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[773, 766])).
% 1.37/1.59 tff(775,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a702) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a702) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(776,plain,
% 1.37/1.59 ((hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697))) <=> (hskp0 | c2_1(a702) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(777,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a702) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c3_1(a702)) | (~c0_1(a702))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[776])).
% 1.37/1.59 tff(778,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a702) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[777, 775])).
% 1.37/1.59 tff(779,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(780,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a702) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c3_1(a702)) | (~c0_1(a702))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[779, 778])).
% 1.37/1.59 tff(781,plain,
% 1.37/1.59 (hskp0 | (~c0_1(a697)) | c1_1(a697)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[780, 206, 661, 662, 660, 160, 774])).
% 1.37/1.59 tff(782,plain,
% 1.37/1.59 (hskp0),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[781, 764, 745])).
% 1.37/1.59 tff(783,plain,
% 1.37/1.59 (((~hskp0) | (~c1_1(a692))) <=> ((~hskp0) | (~c1_1(a692)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(784,plain,
% 1.37/1.59 (((~c1_1(a692)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a692)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(785,axiom,((~c1_1(a692)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.37/1.59 tff(786,plain,
% 1.37/1.59 ((~hskp0) | (~c1_1(a692))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[785, 784])).
% 1.37/1.59 tff(787,plain,
% 1.37/1.59 ((~hskp0) | (~c1_1(a692))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[786, 783])).
% 1.37/1.59 tff(788,plain,
% 1.37/1.59 (~c1_1(a692)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[787, 782])).
% 1.37/1.59 tff(789,plain,
% 1.37/1.59 (((~hskp0) | (~c0_1(a692))) <=> ((~hskp0) | (~c0_1(a692)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(790,plain,
% 1.37/1.59 (((~c0_1(a692)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a692)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(791,axiom,((~c0_1(a692)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.37/1.59 tff(792,plain,
% 1.37/1.59 ((~hskp0) | (~c0_1(a692))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[791, 790])).
% 1.37/1.59 tff(793,plain,
% 1.37/1.59 ((~hskp0) | (~c0_1(a692))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[792, 789])).
% 1.37/1.59 tff(794,plain,
% 1.37/1.59 (~c0_1(a692)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[793, 782])).
% 1.37/1.59 tff(795,plain,
% 1.37/1.59 (hskp14),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[465, 764, 745])).
% 1.37/1.59 tff(796,plain,
% 1.37/1.59 (~c3_1(a730)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[438, 795])).
% 1.37/1.59 tff(797,plain,
% 1.37/1.59 (((~hskp0) | c2_1(a692)) <=> ((~hskp0) | c2_1(a692))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(798,axiom,((~hskp0) | c2_1(a692)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.37/1.59 tff(799,plain,
% 1.37/1.59 ((~hskp0) | c2_1(a692)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[798, 797])).
% 1.37/1.59 tff(800,plain,
% 1.37/1.59 ((~hskp0) | c2_1(a692)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[799, 797])).
% 1.37/1.59 tff(801,plain,
% 1.37/1.59 ((~hskp0) | c2_1(a692)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[800, 797])).
% 1.37/1.59 tff(802,plain,
% 1.37/1.59 ((~hskp0) | c2_1(a692)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[801, 797])).
% 1.37/1.59 tff(803,plain,
% 1.37/1.59 ((~hskp0) | c2_1(a692)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[802, 797])).
% 1.37/1.59 tff(804,plain,
% 1.37/1.59 (c2_1(a692)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[803, 782])).
% 1.37/1.59 tff(805,plain,
% 1.37/1.59 (c1_1(a730)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[416, 795])).
% 1.37/1.59 tff(806,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a730) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a730) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(807,plain,
% 1.37/1.59 (((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692)) <=> (c3_1(a730) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(808,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a730) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[807])).
% 1.37/1.59 tff(809,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a730) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[808, 806])).
% 1.37/1.59 tff(810,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(811,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a730) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[810, 809])).
% 1.37/1.59 tff(812,plain,
% 1.37/1.59 (~c2_1(a730)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[811, 206, 805, 745, 804, 796, 160, 794, 788, 512, 764])).
% 1.37/1.59 tff(813,plain,
% 1.37/1.59 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.37/1.59 inference(bind,[status(th)],[])).
% 1.37/1.59 tff(814,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.59 inference(quant_intro,[status(thm)],[813])).
% 1.37/1.59 tff(815,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(816,plain,
% 1.37/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.37/1.59 inference(bind,[status(th)],[])).
% 1.37/1.59 tff(817,plain,
% 1.37/1.59 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.59 inference(quant_intro,[status(thm)],[816])).
% 1.37/1.59 tff(818,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.37/1.59 tff(819,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[818, 817])).
% 1.37/1.59 tff(820,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[819, 815])).
% 1.37/1.59 tff(821,plain,(
% 1.37/1.59 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.59 inference(skolemize,[status(sab)],[820])).
% 1.37/1.59 tff(822,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[821, 814])).
% 1.37/1.59 tff(823,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a761)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a761)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(824,plain,
% 1.37/1.59 ((hskp27 | (~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp27 | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a761)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(825,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a761))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[824])).
% 1.37/1.59 tff(826,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a761)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[825, 823])).
% 1.37/1.59 tff(827,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(828,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a761))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[827, 826])).
% 1.37/1.59 tff(829,plain,
% 1.37/1.59 (hskp27),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[828, 206, 736, 728, 722, 137, 131, 822, 743])).
% 1.37/1.59 tff(830,plain,
% 1.37/1.59 (hskp20),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[258, 829, 90])).
% 1.37/1.59 tff(831,plain,
% 1.37/1.59 (~c3_1(a754)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[614, 830])).
% 1.37/1.59 tff(832,plain,
% 1.37/1.59 (c2_1(a754)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[172, 830])).
% 1.37/1.59 tff(833,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a754) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a754)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a754) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(834,plain,
% 1.37/1.59 (((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692)) <=> (c3_1(a754) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(835,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a754) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a754)) | (~c2_1(a754))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[834])).
% 1.37/1.59 tff(836,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a754) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[835, 833])).
% 1.37/1.59 tff(837,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(838,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a754) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[837, 836])).
% 1.37/1.59 tff(839,plain,
% 1.37/1.59 (~c1_1(a754)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[838, 206, 832, 745, 804, 831, 160, 794, 788, 512, 764])).
% 1.37/1.59 tff(840,plain,
% 1.37/1.59 (c0_1(a730)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[424, 795])).
% 1.37/1.59 tff(841,plain,
% 1.37/1.59 ($false),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[445, 206, 56, 832, 840, 831, 796, 309, 839, 812])).
% 1.37/1.59 tff(842,plain,(hskp4 | hskp28 | c3_1(a697) | hskp30 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.59 tff(843,plain,
% 1.37/1.59 (hskp4),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[842, 160, 56, 90, 149, 138])).
% 1.37/1.59 tff(844,plain,
% 1.37/1.59 (((~hskp4) | (~c0_1(a698))) <=> ((~hskp4) | (~c0_1(a698)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(845,plain,
% 1.37/1.59 (((~c0_1(a698)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a698)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(846,axiom,((~c0_1(a698)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.37/1.59 tff(847,plain,
% 1.37/1.59 ((~hskp4) | (~c0_1(a698))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[846, 845])).
% 1.37/1.59 tff(848,plain,
% 1.37/1.59 ((~hskp4) | (~c0_1(a698))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[847, 844])).
% 1.37/1.59 tff(849,plain,
% 1.37/1.59 (~c0_1(a698)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[848, 843])).
% 1.37/1.59 tff(850,plain,
% 1.37/1.59 (((~hskp4) | (~c2_1(a698))) <=> ((~hskp4) | (~c2_1(a698)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(851,plain,
% 1.37/1.59 (((~c2_1(a698)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a698)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(852,axiom,((~c2_1(a698)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.37/1.59 tff(853,plain,
% 1.37/1.59 ((~hskp4) | (~c2_1(a698))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[852, 851])).
% 1.37/1.59 tff(854,plain,
% 1.37/1.59 ((~hskp4) | (~c2_1(a698))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[853, 850])).
% 1.37/1.59 tff(855,plain,
% 1.37/1.59 (~c2_1(a698)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[854, 843])).
% 1.37/1.59 tff(856,assumption,(~c2_1(a698)), introduced(assumption)).
% 1.37/1.59 tff(857,assumption,(~c0_1(a698)), introduced(assumption)).
% 1.37/1.59 tff(858,plain,
% 1.37/1.59 (hskp1),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[336, 250, 90])).
% 1.37/1.59 tff(859,plain,
% 1.37/1.59 (c2_1(a693)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[344, 858])).
% 1.37/1.59 tff(860,plain,
% 1.37/1.59 (~hskp27),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[258, 250, 90])).
% 1.37/1.59 tff(861,plain,
% 1.37/1.59 (~c0_1(a693)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[623, 860, 149])).
% 1.37/1.59 tff(862,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c0_1(a698) | c2_1(a698) | c1_1(a693) | (~ndr1_0) | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a698) | c2_1(a698) | c1_1(a693) | (~ndr1_0) | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(863,plain,
% 1.37/1.60 ((hskp27 | (~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c1_1(a693) | c0_1(a693) | (~c2_1(a693))) <=> (hskp27 | c0_1(a698) | c2_1(a698) | c1_1(a693) | (~ndr1_0) | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(864,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c1_1(a693) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c0_1(a698) | c2_1(a698) | c1_1(a693) | (~ndr1_0) | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[863])).
% 1.37/1.60 tff(865,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c1_1(a693) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a698) | c2_1(a698) | c1_1(a693) | (~ndr1_0) | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[864, 862])).
% 1.37/1.60 tff(866,plain,
% 1.37/1.60 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c1_1(a693) | c0_1(a693) | (~c2_1(a693)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(867,plain,
% 1.37/1.60 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a698) | c2_1(a698) | c1_1(a693) | (~ndr1_0) | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[866, 865])).
% 1.37/1.60 tff(868,plain,
% 1.37/1.60 (hskp27 | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693))),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[867, 206, 857, 856, 149, 822])).
% 1.37/1.60 tff(869,plain,
% 1.37/1.60 (~c1_1(a698)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[868, 860, 861, 859])).
% 1.37/1.60 tff(870,plain,
% 1.37/1.60 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(871,plain,
% 1.37/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[870])).
% 1.37/1.60 tff(872,plain,
% 1.37/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(873,plain,
% 1.37/1.60 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(874,plain,
% 1.37/1.60 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[873])).
% 1.37/1.60 tff(875,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 1.37/1.60 tff(876,plain,
% 1.37/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[875, 874])).
% 1.37/1.60 tff(877,plain,
% 1.37/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[876, 872])).
% 1.37/1.60 tff(878,plain,(
% 1.37/1.60 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(skolemize,[status(sab)],[877])).
% 1.37/1.60 tff(879,plain,
% 1.37/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[878, 871])).
% 1.37/1.60 tff(880,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c1_1(a698) | (~c2_1(a693)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c1_1(a698) | (~c2_1(a693)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(881,plain,
% 1.37/1.60 (((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698))) <=> (c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c1_1(a698) | (~c2_1(a693)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(882,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c1_1(a698) | (~c2_1(a693))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[881])).
% 1.37/1.60 tff(883,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c1_1(a698) | (~c2_1(a693)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[882, 880])).
% 1.37/1.60 tff(884,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(885,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c1_1(a698) | (~c2_1(a693))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[884, 883])).
% 1.37/1.60 tff(886,plain,
% 1.37/1.60 (~c3_1(a698)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[885, 206, 859, 857, 856, 149, 138, 879, 869])).
% 1.37/1.60 tff(887,plain,
% 1.37/1.60 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(888,plain,
% 1.37/1.60 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp27 | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(889,plain,
% 1.37/1.60 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0)))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[888])).
% 1.37/1.60 tff(890,plain,
% 1.37/1.60 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))),
% 1.37/1.60 inference(transitivity,[status(thm)],[889, 887])).
% 1.37/1.60 tff(891,plain,
% 1.37/1.60 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(892,plain,
% 1.37/1.60 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[891, 890])).
% 1.37/1.60 tff(893,plain,
% 1.37/1.60 (hskp27 | hskp6 | c0_1(a698) | c3_1(a698)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[892, 206, 856, 183])).
% 1.37/1.60 tff(894,plain,
% 1.37/1.60 (hskp6),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[893, 886, 857, 860])).
% 1.37/1.60 tff(895,plain,
% 1.37/1.60 (c0_1(a702)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[78, 894])).
% 1.37/1.60 tff(896,plain,
% 1.37/1.60 (c3_1(a702)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[70, 894])).
% 1.37/1.60 tff(897,plain,
% 1.37/1.60 (~hskp25),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[703, 896, 895, 663, 56])).
% 1.37/1.60 tff(898,plain,
% 1.37/1.60 (hskp22),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[715, 897, 56])).
% 1.37/1.60 tff(899,plain,
% 1.37/1.60 (~c2_1(a761)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[721, 898])).
% 1.37/1.60 tff(900,plain,
% 1.37/1.60 (~c0_1(a761)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[727, 898])).
% 1.37/1.60 tff(901,plain,
% 1.37/1.60 (c1_1(a761)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[735, 898])).
% 1.37/1.60 tff(902,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a761) | c2_1(a761) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a761)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(903,plain,
% 1.37/1.60 (((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698)) <=> (c0_1(a761) | c2_1(a761) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a761)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(904,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a761) | c2_1(a761) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a761))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[903])).
% 1.37/1.60 tff(905,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a761)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[904, 902])).
% 1.37/1.60 tff(906,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(907,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a761))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[906, 905])).
% 1.37/1.60 tff(908,plain,
% 1.37/1.60 ($false),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[907, 206, 901, 900, 899, 857, 856, 886, 110, 869])).
% 1.37/1.60 tff(909,plain,(hskp20 | c0_1(a698) | c2_1(a698) | hskp28 | c2_1(a702) | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.37/1.60 tff(910,plain,
% 1.37/1.60 (hskp20),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[909, 663, 856, 56, 857, 149, 138, 90])).
% 1.37/1.60 tff(911,plain,
% 1.37/1.60 (~c0_1(a754)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[541, 910])).
% 1.37/1.60 tff(912,plain,
% 1.37/1.60 (~c3_1(a754)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[614, 910])).
% 1.37/1.60 tff(913,assumption,(~hskp9), introduced(assumption)).
% 1.37/1.60 tff(914,plain,
% 1.37/1.60 (hskp1),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[336, 173, 90])).
% 1.37/1.60 tff(915,plain,
% 1.37/1.60 (c2_1(a693)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[344, 914])).
% 1.37/1.60 tff(916,plain,
% 1.37/1.60 (~c0_1(a754)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[580, 915, 165])).
% 1.37/1.60 tff(917,plain,
% 1.37/1.60 (hskp6),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[260, 916, 90, 163, 165])).
% 1.37/1.60 tff(918,plain,
% 1.37/1.60 (c0_1(a702)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[78, 917])).
% 1.37/1.60 tff(919,plain,
% 1.37/1.60 (~hskp27),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[258, 173, 90])).
% 1.37/1.60 tff(920,plain,
% 1.37/1.60 (~c0_1(a693)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[623, 919, 149])).
% 1.37/1.60 tff(921,plain,
% 1.37/1.60 (c3_1(a702)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[70, 917])).
% 1.37/1.60 tff(922,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(923,plain,
% 1.37/1.60 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754))) <=> (c0_1(a754) | c3_1(a754) | c2_1(a702) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(924,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[923])).
% 1.37/1.60 tff(925,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[924, 922])).
% 1.37/1.60 tff(926,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(927,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[926, 925])).
% 1.37/1.60 tff(928,plain,
% 1.37/1.60 (c0_1(a754) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754))),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[927, 206, 163, 663, 138, 159])).
% 1.37/1.60 tff(929,plain,
% 1.37/1.60 (~c1_1(a754)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[928, 921, 915, 916, 920, 918])).
% 1.37/1.60 tff(930,plain,
% 1.37/1.60 (^[U: $i] : refl((hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(931,plain,
% 1.37/1.60 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[930])).
% 1.37/1.60 tff(932,plain,
% 1.37/1.60 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(933,plain,
% 1.37/1.60 (^[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) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_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))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp9) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp9))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp9) <=> (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp9) <=> (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(934,plain,
% 1.37/1.60 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp9) <=> ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[933])).
% 1.37/1.60 tff(935,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.37/1.60 tff(936,plain,
% 1.37/1.60 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[935, 934])).
% 1.37/1.60 tff(937,plain,
% 1.37/1.60 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[936, 932])).
% 1.37/1.60 tff(938,plain,(
% 1.37/1.60 ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.60 inference(skolemize,[status(sab)],[937])).
% 1.37/1.60 tff(939,plain,
% 1.37/1.60 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[938, 931])).
% 1.37/1.60 tff(940,plain,
% 1.37/1.60 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(941,plain,
% 1.37/1.60 ((hskp9 | hskp3 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754)) <=> (hskp9 | hskp3 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(942,plain,
% 1.37/1.60 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0)))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[941])).
% 1.37/1.60 tff(943,plain,
% 1.37/1.60 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))),
% 1.37/1.60 inference(transitivity,[status(thm)],[942, 940])).
% 1.37/1.60 tff(944,plain,
% 1.37/1.60 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(945,plain,
% 1.37/1.60 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[944, 943])).
% 1.37/1.60 tff(946,plain,
% 1.37/1.60 (hskp3 | c2_1(a754) | c0_1(a754)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[945, 206, 913, 163, 939])).
% 1.37/1.60 tff(947,plain,
% 1.37/1.60 (hskp3),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[946, 916, 165])).
% 1.37/1.60 tff(948,plain,
% 1.37/1.60 (c0_1(a697)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[457, 947])).
% 1.37/1.60 tff(949,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(950,plain,
% 1.37/1.60 ((hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a754) | c1_1(a754) | c0_1(a754)) <=> (hskp27 | c0_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(951,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a754) | c1_1(a754) | c0_1(a754))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754)))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[950])).
% 1.37/1.60 tff(952,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a754) | c1_1(a754) | c0_1(a754))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754))),
% 1.45/1.60 inference(transitivity,[status(thm)],[951, 949])).
% 1.45/1.60 tff(953,plain,
% 1.45/1.60 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a754) | c1_1(a754) | c0_1(a754))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(954,plain,
% 1.45/1.60 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754)),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[953, 952])).
% 1.45/1.60 tff(955,plain,
% 1.45/1.60 (hskp27 | c0_1(a754) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[954, 206, 163, 160, 553])).
% 1.45/1.60 tff(956,plain,
% 1.45/1.60 (c1_1(a697)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[955, 948, 919, 916, 929])).
% 1.45/1.60 tff(957,plain,
% 1.45/1.60 (~hskp25),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[703, 921, 918, 663, 56])).
% 1.45/1.60 tff(958,plain,
% 1.45/1.60 (hskp22),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[715, 957, 56])).
% 1.45/1.60 tff(959,plain,
% 1.45/1.60 (~c2_1(a761)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[721, 958])).
% 1.45/1.60 tff(960,plain,
% 1.45/1.60 (~c0_1(a761)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[727, 958])).
% 1.45/1.60 tff(961,plain,
% 1.45/1.60 (c2_1(a697)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[473, 947])).
% 1.45/1.60 tff(962,plain,
% 1.45/1.60 (c1_1(a761)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[735, 958])).
% 1.45/1.60 tff(963,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[762, 206, 962, 948, 961, 960, 959, 160, 756, 956])).
% 1.45/1.60 tff(964,plain,(c2_1(a754) | c3_1(a697) | hskp28 | c3_1(a754) | c2_1(a702) | c3_1(a693) | hskp9 | hskp30 | c1_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(965,plain,
% 1.45/1.61 (c2_1(a754)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[964, 163, 56, 160, 663, 138, 913, 90, 149])).
% 1.45/1.61 tff(966,plain,
% 1.45/1.61 (~hskp24),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[346, 162, 56, 149, 138, 90, 163, 164])).
% 1.45/1.61 tff(967,assumption,(~hskp27), introduced(assumption)).
% 1.45/1.61 tff(968,assumption,(~c3_1(a725)), introduced(assumption)).
% 1.45/1.61 tff(969,plain,
% 1.45/1.61 (hskp27 | hskp6 | c2_1(a725)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[587, 206, 524, 968, 183])).
% 1.45/1.61 tff(970,plain,
% 1.45/1.61 (c2_1(a725)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[969, 967, 162])).
% 1.45/1.61 tff(971,plain,
% 1.45/1.61 (c3_1(a698)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[893, 967, 857, 162])).
% 1.45/1.61 tff(972,plain,
% 1.45/1.61 (((~hskp4) | (~c3_1(a698))) <=> ((~hskp4) | (~c3_1(a698)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(973,plain,
% 1.45/1.61 (((~c3_1(a698)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a698)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(974,axiom,((~c3_1(a698)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.45/1.61 tff(975,plain,
% 1.45/1.61 ((~hskp4) | (~c3_1(a698))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[974, 973])).
% 1.45/1.61 tff(976,plain,
% 1.45/1.61 ((~hskp4) | (~c3_1(a698))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[975, 972])).
% 1.45/1.61 tff(977,plain,
% 1.45/1.61 (~hskp4),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[976, 971])).
% 1.45/1.61 tff(978,plain,
% 1.45/1.61 (hskp4 | hskp3 | (~c2_1(a725))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[499, 206, 524, 523, 400])).
% 1.45/1.61 tff(979,plain,
% 1.45/1.61 (hskp3),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[978, 977, 970])).
% 1.45/1.61 tff(980,plain,
% 1.45/1.61 (c0_1(a697)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[457, 979])).
% 1.45/1.61 tff(981,plain,
% 1.45/1.61 (hskp27 | (~c0_1(a697)) | c1_1(a697)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[641, 206, 524, 523, 968, 160, 553])).
% 1.45/1.61 tff(982,plain,
% 1.45/1.61 (c1_1(a697)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[981, 980, 967])).
% 1.45/1.61 tff(983,plain,
% 1.45/1.61 (c2_1(a697)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[473, 979])).
% 1.45/1.61 tff(984,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[480, 206, 390, 426, 980, 983, 148, 982])).
% 1.45/1.61 tff(985,plain,(hskp27 | hskp24 | hskp23 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | hskp6 | c0_1(a698) | c2_1(a698)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(986,plain,
% 1.45/1.61 (hskp27),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[985, 426, 966, 137, 131, 125, 160, 162, 857, 856])).
% 1.45/1.61 tff(987,plain,
% 1.45/1.61 (c1_1(a691)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[240, 986])).
% 1.45/1.61 tff(988,plain,
% 1.45/1.61 (c0_1(a691)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[248, 986])).
% 1.45/1.61 tff(989,plain,
% 1.45/1.61 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c1_1(a691)) | (~c0_1(a691)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c1_1(a691)) | (~c0_1(a691)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(990,plain,
% 1.45/1.61 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c0_1(a691)) | (~c1_1(a691))) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c1_1(a691)) | (~c0_1(a691)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(991,plain,
% 1.45/1.61 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c1_1(a691)) | (~c0_1(a691))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[990])).
% 1.45/1.61 tff(992,plain,
% 1.45/1.61 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c1_1(a691)) | (~c0_1(a691)))),
% 1.45/1.61 inference(transitivity,[status(thm)],[991, 989])).
% 1.45/1.61 tff(993,plain,
% 1.45/1.61 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(994,plain,
% 1.45/1.61 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c1_1(a691)) | (~c0_1(a691))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[993, 992])).
% 1.45/1.61 tff(995,plain,
% 1.45/1.61 (~c2_1(a691)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[994, 206, 966, 426, 988, 987, 148])).
% 1.45/1.61 tff(996,plain,
% 1.45/1.61 (c3_1(a691)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[232, 986])).
% 1.45/1.61 tff(997,plain,
% 1.45/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(998,plain,
% 1.45/1.61 (((~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754))) <=> (c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(999,plain,
% 1.45/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691)))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[998])).
% 1.45/1.61 tff(1000,plain,
% 1.45/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.61 inference(transitivity,[status(thm)],[999, 997])).
% 1.45/1.61 tff(1001,plain,
% 1.45/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(1002,plain,
% 1.45/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 1.45/1.61 tff(1003,plain,
% 1.45/1.61 (~c1_1(a754)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1002, 206, 988, 996, 348, 164, 163, 159, 995])).
% 1.45/1.61 tff(1004,plain,
% 1.45/1.61 (~hskp14),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[447, 1003, 348, 163, 426, 966, 56])).
% 1.45/1.61 tff(1005,plain,
% 1.45/1.61 (~hskp3),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[482, 1004, 426, 966, 90, 160])).
% 1.45/1.61 tff(1006,plain,
% 1.45/1.61 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(1007,plain,
% 1.45/1.61 ((hskp9 | hskp3 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp9 | hskp3 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(1008,plain,
% 1.45/1.61 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0)))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[1007])).
% 1.45/1.61 tff(1009,plain,
% 1.45/1.61 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))),
% 1.45/1.61 inference(transitivity,[status(thm)],[1008, 1006])).
% 1.45/1.61 tff(1010,plain,
% 1.45/1.61 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(1011,plain,
% 1.45/1.61 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 1.45/1.61 tff(1012,plain,
% 1.45/1.61 (hskp9 | hskp3 | c0_1(a698) | c3_1(a698)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1011, 206, 856, 939])).
% 1.45/1.61 tff(1013,plain,
% 1.45/1.61 (c3_1(a698)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1012, 1005, 857, 913])).
% 1.45/1.61 tff(1014,plain,
% 1.45/1.61 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(1015,plain,
% 1.45/1.61 ((hskp30 | hskp14 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693))) <=> (hskp30 | hskp14 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(1016,plain,
% 1.45/1.61 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[1015])).
% 1.45/1.61 tff(1017,plain,
% 1.45/1.61 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.45/1.61 inference(transitivity,[status(thm)],[1016, 1014])).
% 1.45/1.61 tff(1018,plain,
% 1.45/1.61 ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(1019,plain,
% 1.45/1.61 ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 1.45/1.61 tff(1020,plain,
% 1.45/1.61 (hskp14 | c1_1(a693) | (~c0_1(a693))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1019, 90, 206, 138, 100])).
% 1.45/1.61 tff(1021,plain,
% 1.45/1.61 (~c0_1(a693)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1020, 1004, 149])).
% 1.45/1.61 tff(1022,plain,
% 1.45/1.61 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(1023,plain,
% 1.45/1.61 ((hskp9 | hskp3 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693)) <=> (hskp9 | hskp3 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(1024,plain,
% 1.45/1.61 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693)))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[1023])).
% 1.45/1.61 tff(1025,plain,
% 1.45/1.61 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.45/1.61 inference(transitivity,[status(thm)],[1024, 1022])).
% 1.45/1.61 tff(1026,plain,
% 1.45/1.61 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(1027,plain,
% 1.45/1.61 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 1.45/1.61 tff(1028,plain,
% 1.45/1.61 (hskp9 | hskp3 | c2_1(a693) | c0_1(a693)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1027, 206, 138, 939])).
% 1.45/1.61 tff(1029,plain,
% 1.45/1.61 (c2_1(a693)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1028, 1005, 913, 1021])).
% 1.45/1.61 tff(1030,plain,
% 1.45/1.61 (hskp4),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[633, 1005, 1029, 1021])).
% 1.45/1.61 tff(1031,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[976, 1030, 1013])).
% 1.45/1.61 tff(1032,plain,(hskp23 | c1_1(a693) | hskp9 | c3_1(a693) | c0_1(a698) | c2_1(a698) | hskp30 | c3_1(a697) | (~c2_1(a754)) | c3_1(a754) | hskp28 | c0_1(a754) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(1033,plain,
% 1.45/1.61 (hskp23),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1032, 162, 913, 138, 857, 856, 90, 160, 348, 163, 56, 164, 149])).
% 1.45/1.61 tff(1034,plain,
% 1.45/1.61 (~c2_1(a725)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[532, 1033, 137, 131, 56])).
% 1.45/1.61 tff(1035,plain,
% 1.45/1.61 (c1_1(a754)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[388, 1033, 348, 164, 56])).
% 1.45/1.61 tff(1036,plain,
% 1.45/1.61 (hskp6 | c0_1(a754) | c2_1(a725) | (~c1_1(a754))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[491, 206, 163, 137, 125, 271])).
% 1.45/1.61 tff(1037,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1036, 1035, 1034, 164, 162])).
% 1.45/1.61 tff(1038,plain,(hskp6 | c0_1(a754) | c3_1(a754) | (~c2_1(a754)) | hskp28 | hskp9 | c3_1(a693) | c0_1(a698) | c2_1(a698) | hskp30 | c3_1(a697) | c1_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(1039,plain,
% 1.45/1.61 (hskp6),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1038, 164, 163, 965, 56, 913, 138, 857, 856, 90, 160, 149])).
% 1.45/1.61 tff(1040,plain,
% 1.45/1.61 (c0_1(a702)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[78, 1039])).
% 1.45/1.61 tff(1041,plain,
% 1.45/1.61 (c3_1(a702)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[70, 1039])).
% 1.45/1.61 tff(1042,plain,
% 1.45/1.61 (~hskp25),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[703, 1041, 1040, 663, 56])).
% 1.45/1.61 tff(1043,plain,
% 1.45/1.61 (hskp22),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[715, 1042, 56])).
% 1.45/1.61 tff(1044,plain,
% 1.45/1.61 (~c2_1(a761)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[721, 1043])).
% 1.45/1.61 tff(1045,plain,
% 1.45/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(1046,plain,
% 1.45/1.61 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754))) <=> (c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(1047,plain,
% 1.45/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[1046])).
% 1.45/1.61 tff(1048,plain,
% 1.45/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.45/1.61 inference(transitivity,[status(thm)],[1047, 1045])).
% 1.45/1.61 tff(1049,plain,
% 1.45/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(1050,plain,
% 1.45/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 1.45/1.61 tff(1051,plain,
% 1.45/1.61 (c0_1(a754) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1050, 206, 163, 663, 159])).
% 1.45/1.61 tff(1052,plain,
% 1.45/1.61 (~c1_1(a754)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1051, 1041, 965, 164, 1040])).
% 1.45/1.61 tff(1053,plain,
% 1.45/1.61 (c1_1(a761)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[735, 1043])).
% 1.45/1.61 tff(1054,plain,
% 1.45/1.61 (~c0_1(a761)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[727, 1043])).
% 1.45/1.61 tff(1055,assumption,(~c2_1(a761)), introduced(assumption)).
% 1.45/1.61 tff(1056,assumption,(~c0_1(a761)), introduced(assumption)).
% 1.45/1.61 tff(1057,assumption,(c1_1(a761)), introduced(assumption)).
% 1.45/1.61 tff(1058,plain,
% 1.45/1.61 (c2_1(a725)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[742, 206, 1057, 1056, 1055, 137, 131, 125, 110])).
% 1.45/1.61 tff(1059,plain,
% 1.45/1.61 (~hskp23),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[532, 1058, 137, 131, 56])).
% 1.45/1.61 tff(1060,plain,
% 1.45/1.61 (hskp27),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[828, 206, 1057, 1056, 1055, 137, 131, 822, 1058])).
% 1.45/1.61 tff(1061,plain,
% 1.45/1.61 (hskp20),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[258, 1060, 90])).
% 1.45/1.61 tff(1062,plain,
% 1.45/1.61 (~c3_1(a754)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[614, 1061])).
% 1.45/1.61 tff(1063,plain,
% 1.45/1.61 (c2_1(a754)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[172, 1061])).
% 1.45/1.61 tff(1064,plain,
% 1.45/1.61 (~hskp14),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[447, 390, 56, 1063, 1062, 349, 1059])).
% 1.45/1.61 tff(1065,plain,
% 1.45/1.61 (~hskp3),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[482, 1064, 1059, 390, 90, 160])).
% 1.45/1.61 tff(1066,plain,
% 1.45/1.61 (c3_1(a698)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1012, 1065, 857, 913])).
% 1.45/1.61 tff(1067,plain,
% 1.45/1.61 (~c0_1(a693)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1020, 1064, 149])).
% 1.45/1.61 tff(1068,plain,
% 1.45/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a693) | c0_1(a761) | c2_1(a761) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a693) | c0_1(a761) | c2_1(a761) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a761)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(1069,plain,
% 1.45/1.61 (((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a693) | c1_1(a693) | c2_1(a693) | c3_1(a693) | c2_1(a693) | c0_1(a693)) <=> (c2_1(a693) | c0_1(a761) | c2_1(a761) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a761)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(1070,plain,
% 1.45/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a693) | c1_1(a693) | c2_1(a693) | c3_1(a693) | c2_1(a693) | c0_1(a693))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a693) | c0_1(a761) | c2_1(a761) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a761))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[1069])).
% 1.45/1.61 tff(1071,plain,
% 1.45/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a693) | c1_1(a693) | c2_1(a693) | c3_1(a693) | c2_1(a693) | c0_1(a693))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a693) | c0_1(a761) | c2_1(a761) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a761)))),
% 1.45/1.61 inference(transitivity,[status(thm)],[1070, 1068])).
% 1.45/1.61 tff(1072,plain,
% 1.45/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a693) | c1_1(a693) | c2_1(a693) | c3_1(a693) | c2_1(a693) | c0_1(a693))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(1073,plain,
% 1.45/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a693) | c0_1(a761) | c2_1(a761) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a761))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 1.45/1.61 tff(1074,plain,
% 1.45/1.61 (c2_1(a693) | c0_1(a693)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1073, 206, 1057, 1056, 1055, 149, 138, 110])).
% 1.45/1.61 tff(1075,plain,
% 1.45/1.61 (c2_1(a693)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1074, 1067])).
% 1.45/1.61 tff(1076,plain,
% 1.45/1.61 (hskp4),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[633, 1065, 1075, 1067])).
% 1.45/1.61 tff(1077,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[976, 1076, 1066])).
% 1.45/1.61 tff(1078,plain,(hskp24 | c1_1(a693) | c0_1(a698) | hskp9 | c2_1(a698) | (~c1_1(a761)) | c0_1(a761) | c2_1(a761) | c3_1(a693) | hskp30 | c3_1(a697) | hskp28 | c1_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(1079,plain,
% 1.45/1.61 (hskp24),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1078, 1054, 857, 913, 856, 1053, 1052, 1044, 138, 90, 160, 56, 149])).
% 1.45/1.61 tff(1080,plain,
% 1.45/1.61 (~c3_1(a764)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[277, 1079])).
% 1.45/1.61 tff(1081,plain,
% 1.45/1.61 (c1_1(a764)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[291, 1079])).
% 1.45/1.61 tff(1082,plain,
% 1.45/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a764) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)) | c0_1(a764) | (~c1_1(a764)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(1083,plain,
% 1.45/1.61 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764))) <=> (c3_1(a764) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)) | c0_1(a764) | (~c1_1(a764)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(1084,plain,
% 1.45/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a764) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)) | c0_1(a764) | (~c1_1(a764))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[1083])).
% 1.45/1.61 tff(1085,plain,
% 1.45/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)) | c0_1(a764) | (~c1_1(a764)))),
% 1.45/1.61 inference(transitivity,[status(thm)],[1084, 1082])).
% 1.45/1.61 tff(1086,plain,
% 1.45/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(1087,plain,
% 1.45/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)) | c0_1(a764) | (~c1_1(a764))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 1.45/1.62 tff(1088,plain,
% 1.45/1.62 (c0_1(a764)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1087, 206, 1081, 965, 1040, 1041, 1080, 164, 163, 663, 159])).
% 1.45/1.62 tff(1089,plain,
% 1.45/1.62 (~c2_1(a764)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[283, 1079])).
% 1.45/1.62 tff(1090,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a764)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1091,plain,
% 1.45/1.62 ((hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a764)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1092,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a764))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1091])).
% 1.45/1.62 tff(1093,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a764)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1092, 1090])).
% 1.45/1.62 tff(1094,plain,
% 1.45/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1095,plain,
% 1.45/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a764))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.45/1.62 tff(1096,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1095, 206, 56, 965, 1089, 1080, 163, 309, 1052, 1088])).
% 1.45/1.62 tff(1097,plain,(c0_1(a754) | hskp28 | c3_1(a754) | c2_1(a702) | c0_1(a698) | hskp9 | c2_1(a698) | c3_1(a693) | hskp30 | c3_1(a697) | c1_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(1098,plain,
% 1.45/1.62 (hskp9),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1097, 912, 56, 663, 857, 911, 856, 138, 90, 160, 149])).
% 1.45/1.62 tff(1099,plain,
% 1.45/1.62 (((~hskp9) | (~c1_1(a712))) <=> ((~hskp9) | (~c1_1(a712)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1100,plain,
% 1.45/1.62 (((~c1_1(a712)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a712)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1101,axiom,((~c1_1(a712)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.45/1.62 tff(1102,plain,
% 1.45/1.62 ((~hskp9) | (~c1_1(a712))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 1.45/1.62 tff(1103,plain,
% 1.45/1.62 ((~hskp9) | (~c1_1(a712))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1102, 1099])).
% 1.45/1.62 tff(1104,plain,
% 1.45/1.62 (~c1_1(a712)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1103, 1098])).
% 1.45/1.62 tff(1105,plain,
% 1.45/1.62 (((~hskp9) | (~c0_1(a712))) <=> ((~hskp9) | (~c0_1(a712)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1106,plain,
% 1.45/1.62 (((~c0_1(a712)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a712)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1107,axiom,((~c0_1(a712)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.45/1.62 tff(1108,plain,
% 1.45/1.62 ((~hskp9) | (~c0_1(a712))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 1.45/1.62 tff(1109,plain,
% 1.45/1.62 ((~hskp9) | (~c0_1(a712))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1108, 1105])).
% 1.45/1.62 tff(1110,plain,
% 1.45/1.62 (~c0_1(a712)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1109, 1098])).
% 1.45/1.62 tff(1111,plain,
% 1.45/1.62 (((~hskp9) | (~c2_1(a712))) <=> ((~hskp9) | (~c2_1(a712)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1112,plain,
% 1.45/1.62 (((~c2_1(a712)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a712)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1113,axiom,((~c2_1(a712)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.45/1.62 tff(1114,plain,
% 1.45/1.62 ((~hskp9) | (~c2_1(a712))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 1.45/1.62 tff(1115,plain,
% 1.45/1.62 ((~hskp9) | (~c2_1(a712))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1114, 1111])).
% 1.45/1.62 tff(1116,plain,
% 1.45/1.62 (~c2_1(a712)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1115, 1098])).
% 1.45/1.62 tff(1117,assumption,(~c2_1(a712)), introduced(assumption)).
% 1.45/1.62 tff(1118,assumption,(~c1_1(a712)), introduced(assumption)).
% 1.45/1.62 tff(1119,assumption,(~c0_1(a712)), introduced(assumption)).
% 1.45/1.62 tff(1120,assumption,(hskp22), introduced(assumption)).
% 1.45/1.62 tff(1121,plain,
% 1.45/1.62 (~c2_1(a761)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[721, 1120])).
% 1.45/1.62 tff(1122,plain,
% 1.45/1.62 (~c0_1(a761)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[727, 1120])).
% 1.45/1.62 tff(1123,plain,
% 1.45/1.62 (c1_1(a761)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[735, 1120])).
% 1.45/1.62 tff(1124,plain,
% 1.45/1.62 (c2_1(a725)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[742, 206, 1123, 1122, 1121, 524, 523, 968, 110])).
% 1.45/1.62 tff(1125,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a725) | c3_1(a725) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a725) | c3_1(a725) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | (~c2_1(a725)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1126,plain,
% 1.45/1.62 (((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712))) <=> (c1_1(a725) | c3_1(a725) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | (~c2_1(a725)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1127,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a725) | c3_1(a725) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | (~c2_1(a725))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1126])).
% 1.45/1.62 tff(1128,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a725) | c3_1(a725) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | (~c2_1(a725)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1127, 1125])).
% 1.45/1.62 tff(1129,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1130,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a725) | c3_1(a725) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | (~c2_1(a725))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1129, 1128])).
% 1.45/1.62 tff(1131,plain,
% 1.45/1.62 (c0_1(a712) | (~c3_1(a712)) | (~c2_1(a725))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1130, 206, 523, 968, 1118, 1117, 879])).
% 1.45/1.62 tff(1132,plain,
% 1.45/1.62 (~c3_1(a712)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1131, 1124, 1119])).
% 1.45/1.62 tff(1133,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a761) | c2_1(a761) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a761)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1134,plain,
% 1.45/1.62 (((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712)) <=> (c0_1(a761) | c2_1(a761) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a761)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1135,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a761) | c2_1(a761) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a761))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1134])).
% 1.45/1.62 tff(1136,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a761)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1135, 1133])).
% 1.45/1.62 tff(1137,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1138,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a761))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 1.45/1.62 tff(1139,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1138, 206, 1123, 1122, 1121, 1119, 1118, 1117, 110, 1132])).
% 1.45/1.62 tff(1140,plain,((~hskp22) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a725) | c3_1(a725) | c0_1(a725)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(1141,plain,
% 1.45/1.62 (~hskp22),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1140, 1119, 1118, 1117, 131, 125, 137])).
% 1.45/1.62 tff(1142,plain,
% 1.45/1.62 (hskp25),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[715, 1141, 56])).
% 1.45/1.62 tff(1143,plain,
% 1.45/1.62 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1144,plain,
% 1.45/1.62 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a712) | c0_1(a712) | c2_1(a712)) <=> (hskp27 | hskp6 | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1145,plain,
% 1.45/1.62 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a712) | c0_1(a712) | c2_1(a712))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1144])).
% 1.45/1.62 tff(1146,plain,
% 1.45/1.62 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a712) | c0_1(a712) | c2_1(a712))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1145, 1143])).
% 1.45/1.62 tff(1147,plain,
% 1.45/1.62 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a712) | c0_1(a712) | c2_1(a712))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1148,plain,
% 1.45/1.62 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1147, 1146])).
% 1.45/1.62 tff(1149,plain,
% 1.45/1.62 (hskp27 | hskp6 | c0_1(a712) | c3_1(a712)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1148, 206, 1117, 183])).
% 1.45/1.62 tff(1150,plain,
% 1.45/1.62 (c3_1(a712)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1149, 860, 1119, 162])).
% 1.45/1.62 tff(1151,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a712)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1152,plain,
% 1.45/1.62 (((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712))) <=> (c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a712)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1153,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a712))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1152])).
% 1.45/1.62 tff(1154,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a712)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1153, 1151])).
% 1.45/1.62 tff(1155,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1156,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a712))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 1.45/1.62 tff(1157,plain,
% 1.45/1.62 (c0_1(a712) | (~c2_1(a693)) | (~c3_1(a712))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1156, 206, 1118, 1117, 149, 138, 879])).
% 1.45/1.62 tff(1158,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1157, 1150, 859, 1119])).
% 1.45/1.62 tff(1159,plain,(hskp20 | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | hskp6 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(1160,plain,
% 1.45/1.62 (hskp20),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1159, 162, 1118, 1117, 149, 138, 1119, 90])).
% 1.45/1.62 tff(1161,plain,
% 1.45/1.62 (~c0_1(a754)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[541, 1160])).
% 1.45/1.62 tff(1162,plain,
% 1.45/1.62 (c2_1(a754)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[172, 1160])).
% 1.45/1.62 tff(1163,plain,
% 1.45/1.62 (~c3_1(a754)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[614, 1160])).
% 1.45/1.62 tff(1164,assumption,(c3_1(a712)), introduced(assumption)).
% 1.45/1.62 tff(1165,plain,
% 1.45/1.62 (~c2_1(a725)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1131, 1164, 1119])).
% 1.45/1.62 tff(1166,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a754) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | c1_1(a754) | (~c2_1(a754)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1167,plain,
% 1.45/1.62 (((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712))) <=> (c3_1(a754) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | c1_1(a754) | (~c2_1(a754)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1168,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a754) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | c1_1(a754) | (~c2_1(a754))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1167])).
% 1.45/1.62 tff(1169,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | c1_1(a754) | (~c2_1(a754)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1168, 1166])).
% 1.45/1.62 tff(1170,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1171,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | c1_1(a754) | (~c2_1(a754))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 1.45/1.62 tff(1172,plain,
% 1.45/1.62 ((~c3_1(a712)) | c1_1(a754)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1171, 206, 348, 163, 1119, 1118, 1117, 879])).
% 1.45/1.62 tff(1173,plain,
% 1.45/1.62 (c1_1(a754)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1172, 1164])).
% 1.45/1.62 tff(1174,plain,
% 1.45/1.62 (c2_1(a725) | (~c1_1(a754))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[491, 206, 162, 164, 163, 524, 968, 271])).
% 1.45/1.62 tff(1175,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1174, 1173, 1165])).
% 1.45/1.62 tff(1176,plain,((~c3_1(a712)) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~c2_1(a754)) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a725)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(1177,plain,
% 1.45/1.62 (~c3_1(a712)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1176, 1161, 162, 1163, 137, 125, 1162, 1119, 1118, 1117, 131])).
% 1.45/1.62 tff(1178,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a754)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1179,plain,
% 1.45/1.62 ((hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a712) | c0_1(a712) | c2_1(a712)) <=> (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a754)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1180,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a712) | c0_1(a712) | c2_1(a712))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a754))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1179])).
% 1.45/1.62 tff(1181,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a712) | c0_1(a712) | c2_1(a712))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a754)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1180, 1178])).
% 1.45/1.62 tff(1182,plain,
% 1.45/1.62 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a712) | c0_1(a712) | c2_1(a712))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1183,plain,
% 1.45/1.62 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a754))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 1.45/1.62 tff(1184,plain,
% 1.45/1.62 (~c1_1(a754)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1183, 206, 162, 1161, 1163, 1119, 1117, 271, 1177])).
% 1.45/1.62 tff(1185,plain,
% 1.45/1.62 (~hskp23),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[388, 1184, 1162, 1161, 56])).
% 1.45/1.62 tff(1186,plain,
% 1.45/1.62 (c3_1(a712)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1149, 967, 1119, 162])).
% 1.45/1.62 tff(1187,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1131, 970, 1186, 1119])).
% 1.45/1.62 tff(1188,plain,(hskp27 | c0_1(a712) | c1_1(a725) | c3_1(a725) | c1_1(a712) | c2_1(a712) | hskp6 | c0_1(a725)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(1189,plain,
% 1.45/1.62 (hskp27),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1188, 162, 131, 125, 1118, 1117, 1119, 137])).
% 1.45/1.62 tff(1190,plain,
% 1.45/1.62 (c1_1(a691)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[240, 1189])).
% 1.45/1.62 tff(1191,plain,
% 1.45/1.62 (c0_1(a691)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[248, 1189])).
% 1.45/1.62 tff(1192,plain,
% 1.45/1.62 (~hskp24),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[346, 1163, 56, 149, 138, 90, 162, 1161])).
% 1.45/1.62 tff(1193,plain,
% 1.45/1.62 (hskp23 | (~c2_1(a691))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[994, 206, 1192, 1191, 1190, 148])).
% 1.45/1.62 tff(1194,plain,
% 1.45/1.62 (~c2_1(a691)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1193, 1185])).
% 1.45/1.62 tff(1195,plain,
% 1.45/1.62 (c2_1(a773)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[673, 1142])).
% 1.45/1.62 tff(1196,plain,
% 1.45/1.62 (c1_1(a773)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[681, 1142])).
% 1.45/1.62 tff(1197,plain,
% 1.45/1.62 (c3_1(a691)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[232, 1189])).
% 1.45/1.62 tff(1198,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1199,plain,
% 1.45/1.62 ((hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691))) <=> (hskp28 | (~ndr1_0) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1200,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1199])).
% 1.45/1.62 tff(1201,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.62 inference(transitivity,[status(thm)],[1200, 1198])).
% 1.45/1.62 tff(1202,plain,
% 1.45/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(1203,plain,
% 1.45/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 1.45/1.62 tff(1204,plain,
% 1.45/1.62 (~c3_1(a773)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1203, 206, 56, 1191, 1197, 1196, 1195, 55, 1194])).
% 1.45/1.62 tff(1205,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a712) | c1_1(a712) | c2_1(a712) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c3_1(a712))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c3_1(a712))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(1206,plain,
% 1.45/1.62 (((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712)) <=> (c0_1(a712) | c1_1(a712) | c2_1(a712) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c3_1(a712))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1207,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a712) | c1_1(a712) | c2_1(a712) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c3_1(a712)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1206])).
% 1.45/1.63 tff(1208,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c3_1(a712))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1207, 1205])).
% 1.45/1.63 tff(1209,plain,
% 1.45/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1210,plain,
% 1.45/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c3_1(a712)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 1.45/1.63 tff(1211,plain,
% 1.45/1.63 (~c1_1(a698)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1210, 206, 1119, 1118, 1117, 857, 856, 110, 1177])).
% 1.45/1.63 tff(1212,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a754) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | (~ndr1_0) | c1_1(a698) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | (~ndr1_0) | c1_1(a698) | c1_1(a754) | (~c2_1(a754)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1213,plain,
% 1.45/1.63 (((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698))) <=> (c3_1(a754) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | (~ndr1_0) | c1_1(a698) | c1_1(a754) | (~c2_1(a754)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1214,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a754) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | (~ndr1_0) | c1_1(a698) | c1_1(a754) | (~c2_1(a754))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1213])).
% 1.45/1.63 tff(1215,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | (~ndr1_0) | c1_1(a698) | c1_1(a754) | (~c2_1(a754)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1214, 1212])).
% 1.45/1.63 tff(1216,plain,
% 1.45/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1217,plain,
% 1.45/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | (~ndr1_0) | c1_1(a698) | c1_1(a754) | (~c2_1(a754))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 1.45/1.63 tff(1218,plain,
% 1.45/1.63 (~c3_1(a698)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1217, 206, 1162, 1163, 857, 856, 879, 1211, 1184])).
% 1.45/1.63 tff(1219,plain,
% 1.45/1.63 (~c0_1(a773)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[694, 1142])).
% 1.45/1.63 tff(1220,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a773) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c3_1(a773) | (~c1_1(a773)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a773) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c3_1(a773) | (~c1_1(a773)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1221,plain,
% 1.45/1.63 ((hskp6 | (~ndr1_0) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp6 | c0_1(a773) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c3_1(a773) | (~c1_1(a773)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1222,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a773) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c3_1(a773) | (~c1_1(a773))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1221])).
% 1.45/1.63 tff(1223,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a773) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c3_1(a773) | (~c1_1(a773)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1222, 1220])).
% 1.45/1.63 tff(1224,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1225,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a773) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c3_1(a773) | (~c1_1(a773))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 1.45/1.63 tff(1226,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1225, 206, 162, 1196, 1219, 857, 856, 1218, 271, 1204])).
% 1.45/1.63 tff(1227,plain,(hskp6 | c0_1(a698) | c2_1(a698) | hskp28 | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1228,plain,
% 1.45/1.63 (hskp6),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1227, 1119, 856, 56, 857, 1118, 1117, 149, 138, 90])).
% 1.45/1.63 tff(1229,plain,
% 1.45/1.63 (c0_1(a702)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[78, 1228])).
% 1.45/1.63 tff(1230,plain,
% 1.45/1.63 (c3_1(a702)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[70, 1228])).
% 1.45/1.63 tff(1231,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[703, 1230, 1229, 1142, 663, 56])).
% 1.45/1.63 tff(1232,plain,(c0_1(a712) | c2_1(a702) | hskp28 | c2_1(a698) | c0_1(a698) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1233,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1232, 1116, 1110, 56, 856, 857, 663, 1104, 149, 138, 90])).
% 1.45/1.63 tff(1234,plain,(c2_1(a702) | hskp28 | c2_1(a698) | c0_1(a698) | c1_1(a693) | c3_1(a693) | hskp30 | c3_1(a697)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1235,plain,
% 1.45/1.63 (c2_1(a702)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1234, 857, 856, 56, 149, 138, 90, 160])).
% 1.45/1.63 tff(1236,plain,
% 1.45/1.63 (~hskp6),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[62, 1235])).
% 1.45/1.63 tff(1237,assumption,(hskp9), introduced(assumption)).
% 1.45/1.63 tff(1238,plain,
% 1.45/1.63 (~c0_1(a712)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1109, 1237])).
% 1.45/1.63 tff(1239,plain,
% 1.45/1.63 (~c1_1(a712)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1103, 1237])).
% 1.45/1.63 tff(1240,plain,
% 1.45/1.63 (~c2_1(a712)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1115, 1237])).
% 1.45/1.63 tff(1241,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1227, 1240, 1239, 856, 56, 857, 162, 1238, 149, 138, 90])).
% 1.45/1.63 tff(1242,plain,((~hskp9) | c2_1(a698) | hskp28 | c0_1(a698) | hskp6 | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1243,plain,
% 1.45/1.63 (~hskp9),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1242, 857, 56, 856, 1236, 149, 138, 90])).
% 1.45/1.63 tff(1244,plain,
% 1.45/1.63 (c2_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[260, 164, 90, 1236, 163])).
% 1.45/1.63 tff(1245,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1038, 1244, 164, 1236, 1243, 56, 163, 138, 857, 856, 90, 160, 149])).
% 1.45/1.63 tff(1246,plain,(c0_1(a754) | hskp28 | c3_1(a754) | c3_1(a693) | c0_1(a698) | c2_1(a698) | hskp30 | c3_1(a697) | c1_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1247,plain,
% 1.45/1.63 (c0_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1246, 163, 56, 138, 857, 856, 90, 160, 149])).
% 1.45/1.63 tff(1248,plain,
% 1.45/1.63 (~hskp20),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[541, 1247])).
% 1.45/1.63 tff(1249,plain,
% 1.45/1.63 (~hskp27),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[258, 1248, 90])).
% 1.45/1.63 tff(1250,plain,
% 1.45/1.63 (c1_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[560, 1249, 1247])).
% 1.45/1.63 tff(1251,plain,
% 1.45/1.63 (c2_1(a725)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[588, 1249, 1236])).
% 1.45/1.63 tff(1252,plain,
% 1.45/1.63 (~hskp23),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[532, 1251, 137, 131, 56])).
% 1.45/1.63 tff(1253,plain,
% 1.45/1.63 (hskp24),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[985, 1252, 1249, 137, 131, 125, 160, 1236, 857, 856])).
% 1.45/1.63 tff(1254,plain,
% 1.45/1.63 (~c3_1(a764)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[277, 1253])).
% 1.45/1.63 tff(1255,plain,
% 1.45/1.63 (~c2_1(a764)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[283, 1253])).
% 1.45/1.63 tff(1256,plain,
% 1.45/1.63 (hskp1),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[336, 1248, 90])).
% 1.45/1.63 tff(1257,plain,
% 1.45/1.63 (c2_1(a693)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[344, 1256])).
% 1.45/1.63 tff(1258,plain,
% 1.45/1.63 (c2_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[580, 1257, 1247])).
% 1.45/1.63 tff(1259,plain,
% 1.45/1.63 (c1_1(a764)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[291, 1253])).
% 1.45/1.63 tff(1260,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[606, 206, 56, 1259, 1258, 1255, 1254, 163, 571, 1250])).
% 1.45/1.63 tff(1261,plain,(c3_1(a754) | hskp28 | c3_1(a697) | c0_1(a698) | c2_1(a698) | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1262,plain,
% 1.45/1.63 (c3_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1261, 857, 160, 56, 856, 149, 138, 90])).
% 1.45/1.63 tff(1263,plain,
% 1.45/1.63 (~hskp20),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[614, 1262])).
% 1.45/1.63 tff(1264,plain,
% 1.45/1.63 (~hskp27),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[258, 1263, 90])).
% 1.45/1.63 tff(1265,plain,
% 1.45/1.63 (c2_1(a725)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[588, 1264, 1236])).
% 1.45/1.63 tff(1266,plain,
% 1.45/1.63 (c3_1(a698)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[893, 1264, 857, 1236])).
% 1.45/1.63 tff(1267,plain,
% 1.45/1.63 (~hskp4),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[976, 1266])).
% 1.45/1.63 tff(1268,plain,
% 1.45/1.63 (hskp3),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[500, 1267, 1265])).
% 1.45/1.63 tff(1269,plain,
% 1.45/1.63 (c0_1(a697)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[457, 1268])).
% 1.45/1.63 tff(1270,plain,
% 1.45/1.63 (c1_1(a697)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[642, 1269, 1264])).
% 1.45/1.63 tff(1271,plain,
% 1.45/1.63 (~hskp23),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[532, 1265, 137, 131, 56])).
% 1.45/1.63 tff(1272,plain,
% 1.45/1.63 (hskp24),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[985, 1271, 1264, 137, 131, 125, 160, 1236, 857, 856])).
% 1.45/1.63 tff(1273,plain,
% 1.45/1.63 (~c3_1(a764)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[277, 1272])).
% 1.45/1.63 tff(1274,plain,
% 1.45/1.63 (~c2_1(a764)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[283, 1272])).
% 1.45/1.63 tff(1275,plain,
% 1.45/1.63 (c2_1(a697)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[473, 1268])).
% 1.45/1.63 tff(1276,plain,
% 1.45/1.63 (c1_1(a764)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[291, 1272])).
% 1.45/1.63 tff(1277,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[656, 206, 56, 1276, 1275, 1274, 1273, 160, 571, 1270])).
% 1.45/1.63 tff(1278,plain,(c0_1(a698) | hskp28 | c3_1(a697) | c2_1(a698) | hskp30 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1279,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1278, 855, 849, 160, 56, 90, 149, 138])).
% 1.45/1.63 tff(1280,plain,(c3_1(a697) | hskp28 | hskp30 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1281,plain,
% 1.45/1.63 (c3_1(a697)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1280, 149, 90, 56, 138])).
% 1.45/1.63 tff(1282,plain,
% 1.45/1.63 (((~hskp3) | (~c3_1(a697))) <=> ((~hskp3) | (~c3_1(a697)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1283,plain,
% 1.45/1.63 (((~c3_1(a697)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a697)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1284,axiom,((~c3_1(a697)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.45/1.63 tff(1285,plain,
% 1.45/1.63 ((~hskp3) | (~c3_1(a697))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 1.45/1.63 tff(1286,plain,
% 1.45/1.63 ((~hskp3) | (~c3_1(a697))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1285, 1282])).
% 1.45/1.63 tff(1287,plain,
% 1.45/1.63 (~hskp3),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1286, 1281])).
% 1.45/1.63 tff(1288,assumption,(hskp4), introduced(assumption)).
% 1.45/1.63 tff(1289,plain,
% 1.45/1.63 (~c3_1(a698)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[976, 1288])).
% 1.45/1.63 tff(1290,plain,
% 1.45/1.63 (~c2_1(a698)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[854, 1288])).
% 1.45/1.63 tff(1291,plain,
% 1.45/1.63 (~c0_1(a698)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[848, 1288])).
% 1.45/1.63 tff(1292,plain,
% 1.45/1.63 (~hskp9),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1242, 1290, 56, 162, 1291, 149, 138, 90])).
% 1.45/1.63 tff(1293,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1011, 206, 1292, 1287, 1291, 1290, 1289, 939])).
% 1.45/1.63 tff(1294,plain,((~hskp4) | hskp28 | hskp6 | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1295,plain,
% 1.45/1.63 (~hskp4),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1294, 162, 56, 149, 138, 90])).
% 1.45/1.63 tff(1296,plain,
% 1.45/1.63 (~c2_1(a725)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[500, 1295, 1287])).
% 1.45/1.63 tff(1297,plain,
% 1.45/1.63 (hskp27),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[588, 1296, 162])).
% 1.45/1.63 tff(1298,plain,
% 1.45/1.63 (hskp20),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[258, 1297, 90])).
% 1.45/1.63 tff(1299,plain,
% 1.45/1.63 (~c0_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[541, 1298])).
% 1.45/1.63 tff(1300,plain,
% 1.45/1.63 (c0_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[260, 165, 90, 162, 163])).
% 1.45/1.63 tff(1301,plain,
% 1.45/1.63 (~c2_1(a693)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[580, 165, 1300])).
% 1.45/1.63 tff(1302,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[344, 914, 1301])).
% 1.45/1.63 tff(1303,plain,(c2_1(a754) | hskp30 | hskp28 | c3_1(a754) | c1_1(a693) | c3_1(a693) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1304,plain,
% 1.45/1.63 (c2_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1303, 162, 56, 163, 149, 138, 90])).
% 1.45/1.63 tff(1305,plain,
% 1.45/1.63 (hskp4 | c0_1(a754) | c1_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[406, 206, 1287, 1304, 400])).
% 1.45/1.63 tff(1306,plain,
% 1.45/1.63 (c1_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1305, 1299, 1295])).
% 1.45/1.63 tff(1307,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1036, 1306, 1299, 162, 1296])).
% 1.45/1.63 tff(1308,plain,(hskp6 | c3_1(a754) | hskp30 | hskp28 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1309,plain,
% 1.45/1.63 (hskp6),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1308, 163, 90, 56, 149, 138])).
% 1.45/1.63 tff(1310,plain,
% 1.45/1.63 (~c2_1(a702)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[62, 1309])).
% 1.45/1.63 tff(1311,plain,
% 1.45/1.63 (c0_1(a702)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[78, 1309])).
% 1.45/1.63 tff(1312,plain,
% 1.45/1.63 (c3_1(a702)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[70, 1309])).
% 1.45/1.63 tff(1313,plain,
% 1.45/1.63 (~hskp25),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[703, 1312, 1311, 1310, 56])).
% 1.45/1.63 tff(1314,plain,
% 1.45/1.63 (hskp22),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[715, 1313, 56])).
% 1.45/1.63 tff(1315,plain,
% 1.45/1.63 (~c2_1(a761)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[721, 1314])).
% 1.45/1.63 tff(1316,plain,
% 1.45/1.63 (~c0_1(a761)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[727, 1314])).
% 1.45/1.63 tff(1317,plain,
% 1.45/1.63 (c1_1(a761)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[735, 1314])).
% 1.45/1.63 tff(1318,plain,
% 1.45/1.63 (c2_1(a725)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[742, 206, 1317, 1316, 1315, 137, 131, 125, 110])).
% 1.45/1.63 tff(1319,plain,
% 1.45/1.63 (hskp4),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[500, 1318, 1287])).
% 1.45/1.63 tff(1320,plain,
% 1.45/1.63 (~c3_1(a698)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[976, 1319])).
% 1.45/1.63 tff(1321,plain,
% 1.45/1.63 (~c0_1(a698)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[848, 1319])).
% 1.45/1.63 tff(1322,plain,
% 1.45/1.63 (hskp27),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[828, 206, 1317, 1316, 1315, 137, 131, 822, 1318])).
% 1.45/1.63 tff(1323,plain,
% 1.45/1.63 (hskp20),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[258, 1322, 90])).
% 1.45/1.63 tff(1324,plain,
% 1.45/1.63 (~c0_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[541, 1323])).
% 1.45/1.63 tff(1325,plain,
% 1.45/1.63 (c2_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[172, 1323])).
% 1.45/1.63 tff(1326,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | c0_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | c0_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1327,plain,
% 1.45/1.63 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a698) | c0_1(a698) | (~c1_1(a698))) <=> (c0_1(a754) | c3_1(a754) | c2_1(a702) | c0_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1328,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a698) | c0_1(a698) | (~c1_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | c0_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1327])).
% 1.45/1.63 tff(1329,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a698) | c0_1(a698) | (~c1_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | c0_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1328, 1326])).
% 1.45/1.63 tff(1330,plain,
% 1.45/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a698) | c0_1(a698) | (~c1_1(a698)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1331,plain,
% 1.45/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | c0_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 1.45/1.63 tff(1332,plain,
% 1.45/1.63 (~c1_1(a698)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1331, 206, 1325, 1311, 1312, 1324, 163, 1310, 1321, 1320, 159])).
% 1.45/1.63 tff(1333,plain,
% 1.45/1.63 (~c2_1(a698)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[854, 1319])).
% 1.45/1.63 tff(1334,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[907, 206, 1317, 1316, 1315, 1321, 1333, 1320, 110, 1332])).
% 1.45/1.63 tff(1335,plain,(c3_1(a754) | hskp30 | hskp28 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1336,plain,
% 1.45/1.63 (c3_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1335, 149, 56, 90, 138])).
% 1.45/1.63 tff(1337,plain,
% 1.45/1.63 (~hskp20),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[614, 1336])).
% 1.45/1.63 tff(1338,plain,
% 1.45/1.63 (hskp1),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[336, 1337, 90])).
% 1.45/1.63 tff(1339,plain,
% 1.45/1.63 (c2_1(a693)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[344, 1338])).
% 1.45/1.63 tff(1340,plain,
% 1.45/1.63 (~hskp27),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[258, 1337, 90])).
% 1.45/1.63 tff(1341,plain,
% 1.45/1.63 (~c0_1(a693)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[623, 1340, 149])).
% 1.45/1.63 tff(1342,plain,
% 1.45/1.63 (hskp4),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[633, 1341, 1287, 1339])).
% 1.45/1.63 tff(1343,plain,
% 1.45/1.63 (hskp6),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1294, 1342, 56, 149, 138, 90])).
% 1.45/1.63 tff(1344,plain,
% 1.45/1.63 (~c0_1(a698)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[848, 1342])).
% 1.45/1.63 tff(1345,plain,
% 1.45/1.63 (~c2_1(a698)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[854, 1342])).
% 1.45/1.63 tff(1346,plain,
% 1.45/1.63 (c2_1(a702)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[909, 1345, 1337, 56, 1344, 149, 138, 90])).
% 1.45/1.63 tff(1347,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[62, 1346, 1343])).
% 1.45/1.63 tff(1348,plain,(c1_1(a693) | hskp28 | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1349,plain,
% 1.45/1.63 (c1_1(a693)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1348, 138, 56, 90])).
% 1.45/1.63 tff(1350,plain,
% 1.45/1.63 (((~hskp1) | (~c1_1(a693))) <=> ((~hskp1) | (~c1_1(a693)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1351,plain,
% 1.45/1.63 (((~c1_1(a693)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a693)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1352,axiom,((~c1_1(a693)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.45/1.63 tff(1353,plain,
% 1.45/1.63 ((~hskp1) | (~c1_1(a693))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 1.45/1.63 tff(1354,plain,
% 1.45/1.63 ((~hskp1) | (~c1_1(a693))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1353, 1350])).
% 1.45/1.63 tff(1355,plain,
% 1.45/1.63 (~hskp1),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1354, 1349])).
% 1.45/1.63 tff(1356,plain,
% 1.45/1.63 (hskp20),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[336, 1355, 90])).
% 1.45/1.63 tff(1357,plain,
% 1.45/1.63 (~c3_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[614, 1356])).
% 1.45/1.63 tff(1358,plain,
% 1.45/1.63 (~c0_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[541, 1356])).
% 1.45/1.63 tff(1359,plain,
% 1.45/1.63 (c2_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[172, 1356])).
% 1.45/1.63 tff(1360,assumption,(c1_1(a693)), introduced(assumption)).
% 1.45/1.63 tff(1361,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a693) | c0_1(a754) | c3_1(a754) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a693) | c0_1(a754) | c3_1(a754) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a754)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1362,plain,
% 1.45/1.63 ((hskp6 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp6 | c2_1(a693) | c0_1(a754) | c3_1(a754) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a754)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1363,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a693) | c0_1(a754) | c3_1(a754) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a754))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1362])).
% 1.45/1.63 tff(1364,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a693) | c0_1(a754) | c3_1(a754) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a754)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1363, 1361])).
% 1.45/1.63 tff(1365,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1366,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a693) | c0_1(a754) | c3_1(a754) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a754))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 1.45/1.63 tff(1367,plain,
% 1.45/1.63 (hskp6 | c2_1(a693)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1366, 206, 348, 164, 163, 1360, 138, 89])).
% 1.45/1.63 tff(1368,plain,
% 1.45/1.63 (c2_1(a693)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1367, 162])).
% 1.45/1.63 tff(1369,assumption,(c2_1(a693)), introduced(assumption)).
% 1.45/1.63 tff(1370,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c1_1(a764)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1371,plain,
% 1.45/1.63 ((hskp28 | (~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c1_1(a764)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1372,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c1_1(a764))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1371])).
% 1.45/1.63 tff(1373,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c1_1(a764)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1372, 1370])).
% 1.45/1.63 tff(1374,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1375,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c1_1(a764))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 1.45/1.63 tff(1376,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1375, 206, 56, 292, 1369, 284, 278, 1360, 138, 571])).
% 1.45/1.63 tff(1377,plain,((~hskp24) | hskp28 | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(1378,plain,
% 1.45/1.63 (~hskp24),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1377, 1368, 56, 1360, 138])).
% 1.45/1.63 tff(1379,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1380,plain,
% 1.45/1.63 ((hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1381,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1380])).
% 1.45/1.63 tff(1382,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1381, 1379])).
% 1.45/1.63 tff(1383,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1384,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 1.45/1.63 tff(1385,plain,
% 1.45/1.63 (c0_1(a693)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1384, 206, 162, 1291, 1290, 1289, 1360, 138, 271])).
% 1.45/1.63 tff(1386,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a754)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1387,plain,
% 1.45/1.63 ((hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a754)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1388,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a754))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1387])).
% 1.45/1.63 tff(1389,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a754)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1388, 1386])).
% 1.45/1.63 tff(1390,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1391,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a754))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 1.45/1.63 tff(1392,plain,
% 1.45/1.63 (~c1_1(a754)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1391, 206, 162, 164, 163, 1291, 1290, 1289, 271])).
% 1.45/1.63 tff(1393,plain,
% 1.45/1.63 (~hskp23),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[388, 1392, 348, 164, 56])).
% 1.45/1.63 tff(1394,plain,
% 1.45/1.63 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~c1_1(a693)) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~c1_1(a693)) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1395,plain,
% 1.45/1.63 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a693)) | (~c1_1(a693))) <=> (hskp24 | hskp23 | (~c1_1(a693)) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(1396,plain,
% 1.45/1.63 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a693)) | (~c1_1(a693)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~c1_1(a693)) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[1395])).
% 1.45/1.63 tff(1397,plain,
% 1.45/1.63 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a693)) | (~c1_1(a693)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~c1_1(a693)) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[1396, 1394])).
% 1.45/1.63 tff(1398,plain,
% 1.45/1.63 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a693)) | (~c1_1(a693)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(1399,plain,
% 1.45/1.63 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~c1_1(a693)) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 1.45/1.63 tff(1400,plain,
% 1.45/1.63 (hskp24 | hskp23 | (~c0_1(a693)) | (~c2_1(a693))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1399, 206, 1360, 148])).
% 1.45/1.63 tff(1401,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1400, 1393, 1385, 1368, 1378])).
% 1.45/1.64 tff(1402,plain,((~hskp4) | (~c1_1(a693)) | (~c2_1(a754)) | c0_1(a754) | hskp28 | hskp6 | c3_1(a693) | c3_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(1403,plain,
% 1.45/1.64 (~hskp4),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1402, 162, 1359, 1358, 56, 1349, 138, 1357])).
% 1.45/1.64 tff(1404,plain,
% 1.45/1.64 (^[U: $i] : refl((hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.45/1.64 inference(bind,[status(th)],[])).
% 1.45/1.64 tff(1405,plain,
% 1.45/1.64 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.64 inference(quant_intro,[status(thm)],[1404])).
% 1.45/1.64 tff(1406,plain,
% 1.45/1.64 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1407,plain,
% 1.45/1.64 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1) <=> ((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.45/1.64 inference(bind,[status(th)],[])).
% 1.45/1.64 tff(1408,plain,
% 1.45/1.64 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.64 inference(quant_intro,[status(thm)],[1407])).
% 1.45/1.64 tff(1409,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.45/1.64 tff(1410,plain,
% 1.45/1.64 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1409, 1408])).
% 1.45/1.64 tff(1411,plain,
% 1.45/1.64 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1410, 1406])).
% 1.45/1.64 tff(1412,plain,(
% 1.45/1.64 ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.64 inference(skolemize,[status(sab)],[1411])).
% 1.45/1.64 tff(1413,plain,
% 1.45/1.64 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1412, 1405])).
% 1.45/1.64 tff(1414,plain,
% 1.45/1.64 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1415,plain,
% 1.45/1.64 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a725) | c1_1(a725) | c0_1(a725)) <=> (hskp1 | hskp0 | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1416,plain,
% 1.45/1.64 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1415])).
% 1.45/1.64 tff(1417,plain,
% 1.45/1.64 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1416, 1414])).
% 1.45/1.64 tff(1418,plain,
% 1.45/1.64 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a725) | c1_1(a725) | c0_1(a725))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1419,plain,
% 1.45/1.64 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 1.45/1.64 tff(1420,plain,
% 1.45/1.64 (hskp1 | hskp0),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1419, 206, 137, 131, 125, 1413])).
% 1.45/1.64 tff(1421,plain,
% 1.45/1.64 (hskp0),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1420, 1355])).
% 1.45/1.64 tff(1422,plain,
% 1.45/1.64 (~c1_1(a692)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[787, 1421])).
% 1.45/1.64 tff(1423,plain,
% 1.45/1.64 (~c0_1(a692)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[793, 1421])).
% 1.45/1.64 tff(1424,plain,
% 1.45/1.64 (c2_1(a692)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[803, 1421])).
% 1.45/1.64 tff(1425,plain,
% 1.45/1.64 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1426,plain,
% 1.45/1.64 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a692) | c0_1(a692) | (~c2_1(a692))) <=> (hskp4 | hskp3 | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1427,plain,
% 1.45/1.64 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1426])).
% 1.45/1.64 tff(1428,plain,
% 1.45/1.64 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1427, 1425])).
% 1.45/1.64 tff(1429,plain,
% 1.45/1.64 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1430,plain,
% 1.45/1.64 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1429, 1428])).
% 1.45/1.64 tff(1431,plain,
% 1.45/1.64 (hskp4 | hskp3),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1430, 206, 1424, 1423, 1422, 400])).
% 1.45/1.64 tff(1432,plain,
% 1.45/1.64 (hskp3),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1431, 1403])).
% 1.45/1.64 tff(1433,plain,
% 1.45/1.64 (c2_1(a697)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[473, 1432])).
% 1.45/1.64 tff(1434,plain,
% 1.45/1.64 (c0_1(a697)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[457, 1432])).
% 1.45/1.64 tff(1435,plain,
% 1.45/1.64 (hskp6 | c2_1(a693)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1366, 206, 1359, 1358, 1357, 1349, 138, 89])).
% 1.45/1.64 tff(1436,plain,
% 1.45/1.64 (c2_1(a693)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1435, 162])).
% 1.45/1.64 tff(1437,plain,
% 1.45/1.64 (~hskp24),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1377, 1436, 56, 1349, 138])).
% 1.45/1.64 tff(1438,plain,
% 1.45/1.64 (~c3_1(a697)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1286, 1432])).
% 1.45/1.64 tff(1439,plain,
% 1.45/1.64 (c1_1(a754)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[484, 1438, 90, 1358, 1359, 1357, 56, 1403, 1437])).
% 1.45/1.64 tff(1440,plain,
% 1.45/1.64 (hskp6 | c2_1(a725) | (~c1_1(a754))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[491, 206, 1358, 1357, 137, 125, 271])).
% 1.45/1.64 tff(1441,plain,
% 1.45/1.64 (c2_1(a725)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1440, 1439, 162])).
% 1.45/1.64 tff(1442,plain,
% 1.45/1.64 (~hskp23),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[532, 1441, 137, 131, 56])).
% 1.45/1.64 tff(1443,plain,
% 1.45/1.64 (~c1_1(a697)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[480, 206, 1437, 1442, 1434, 1433, 148])).
% 1.45/1.64 tff(1444,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[518, 206, 1359, 1434, 1357, 137, 131, 1438, 512, 1441, 1439, 1443])).
% 1.45/1.64 tff(1445,plain,(hskp6 | hskp28 | hskp30 | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(1446,plain,
% 1.45/1.64 (hskp6),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1445, 138, 90, 56])).
% 1.45/1.64 tff(1447,plain,
% 1.45/1.64 (~c2_1(a702)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[62, 1446])).
% 1.45/1.64 tff(1448,plain,
% 1.45/1.64 (c0_1(a702)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[78, 1446])).
% 1.45/1.64 tff(1449,plain,
% 1.45/1.64 (c3_1(a702)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[70, 1446])).
% 1.45/1.64 tff(1450,plain,
% 1.45/1.64 (~hskp25),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[703, 1449, 1448, 1447, 56])).
% 1.45/1.64 tff(1451,plain,
% 1.45/1.64 (hskp22),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[715, 1450, 56])).
% 1.45/1.64 tff(1452,plain,
% 1.45/1.64 (~c2_1(a761)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[721, 1451])).
% 1.45/1.64 tff(1453,plain,
% 1.45/1.64 (~c0_1(a761)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[727, 1451])).
% 1.45/1.64 tff(1454,plain,
% 1.45/1.64 (c1_1(a761)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[735, 1451])).
% 1.45/1.64 tff(1455,plain,
% 1.45/1.64 (c2_1(a725)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[742, 206, 1454, 1453, 1452, 137, 131, 125, 110])).
% 1.45/1.64 tff(1456,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1457,plain,
% 1.45/1.64 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a693) | c0_1(a693) | (~c1_1(a693))) <=> (c0_1(a754) | c3_1(a754) | c2_1(a702) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1458,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1457])).
% 1.45/1.64 tff(1459,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1458, 1456])).
% 1.45/1.64 tff(1460,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1461,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1460, 1459])).
% 1.45/1.64 tff(1462,plain,
% 1.45/1.64 (c0_1(a693)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1461, 206, 1359, 1448, 1449, 1358, 1357, 1447, 1349, 138, 159])).
% 1.45/1.64 tff(1463,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a761) | c2_1(a761) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)) | (~c1_1(a761)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1464,plain,
% 1.45/1.64 (((~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a693) | (~c1_1(a693)) | (~c0_1(a693)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761))) <=> (c0_1(a761) | c2_1(a761) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)) | (~c1_1(a761)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1465,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a693) | (~c1_1(a693)) | (~c0_1(a693)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a761) | c2_1(a761) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)) | (~c1_1(a761))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1464])).
% 1.45/1.64 tff(1466,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a693) | (~c1_1(a693)) | (~c0_1(a693)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)) | (~c1_1(a761)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1465, 1463])).
% 1.45/1.64 tff(1467,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a693) | (~c1_1(a693)) | (~c0_1(a693)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1468,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)) | (~c1_1(a761))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 1.45/1.64 tff(1469,plain,
% 1.45/1.64 (~c2_1(a693)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1468, 206, 1454, 1453, 1452, 1349, 138, 756, 1462])).
% 1.45/1.64 tff(1470,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a693) | c1_1(a725) | c3_1(a725) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a693) | c1_1(a725) | c3_1(a725) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a725)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1471,plain,
% 1.45/1.64 ((hskp28 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725))) <=> (hskp28 | c2_1(a693) | c1_1(a725) | c3_1(a725) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a725)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1472,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a693) | c1_1(a725) | c3_1(a725) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a725))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1471])).
% 1.45/1.64 tff(1473,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a693) | c1_1(a725) | c3_1(a725) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a725)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1472, 1470])).
% 1.45/1.64 tff(1474,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1475,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a693) | c1_1(a725) | c3_1(a725) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a725))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1474, 1473])).
% 1.45/1.64 tff(1476,plain,
% 1.45/1.64 (c2_1(a693) | (~c0_1(a693)) | (~c2_1(a725))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1475, 206, 56, 131, 125, 138, 309])).
% 1.45/1.64 tff(1477,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1476, 1469, 1462, 1455])).
% 1.45/1.64 tff(1478,plain,(c3_1(a693) | hskp28 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(1479,plain,
% 1.45/1.64 (c3_1(a693)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1478, 90, 56])).
% 1.45/1.64 tff(1480,plain,
% 1.45/1.64 (((~hskp1) | (~c3_1(a693))) <=> ((~hskp1) | (~c3_1(a693)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1481,plain,
% 1.45/1.64 (((~c3_1(a693)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a693)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1482,axiom,((~c3_1(a693)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.45/1.64 tff(1483,plain,
% 1.45/1.64 ((~hskp1) | (~c3_1(a693))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 1.45/1.64 tff(1484,plain,
% 1.45/1.64 ((~hskp1) | (~c3_1(a693))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1483, 1480])).
% 1.45/1.64 tff(1485,plain,
% 1.45/1.64 (~hskp1),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1484, 1479])).
% 1.45/1.64 tff(1486,plain,
% 1.45/1.64 (hskp20),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[336, 1485, 90])).
% 1.45/1.64 tff(1487,plain,
% 1.45/1.64 (~c0_1(a754)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[541, 1486])).
% 1.45/1.64 tff(1488,plain,
% 1.45/1.64 (~c3_1(a754)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[614, 1486])).
% 1.45/1.64 tff(1489,plain,
% 1.45/1.64 (c2_1(a754)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[172, 1486])).
% 1.45/1.64 tff(1490,plain,
% 1.45/1.64 (c0_1(a764)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1087, 206, 292, 348, 665, 664, 278, 164, 163, 663, 159])).
% 1.45/1.64 tff(1491,plain,
% 1.45/1.64 (~c1_1(a754)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1050, 206, 348, 665, 664, 164, 163, 663, 159])).
% 1.45/1.64 tff(1492,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1095, 206, 56, 348, 284, 278, 163, 309, 1491, 1490])).
% 1.45/1.64 tff(1493,plain,((~hskp24) | hskp28 | (~c2_1(a754)) | c3_1(a754) | (~c0_1(a702)) | (~c3_1(a702)) | c0_1(a754) | c2_1(a702)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(1494,plain,
% 1.45/1.64 (~hskp24),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1493, 79, 1489, 1488, 56, 71, 1487, 63])).
% 1.45/1.64 tff(1495,plain,
% 1.45/1.64 (~hskp25),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[703, 71, 79, 63, 56])).
% 1.45/1.64 tff(1496,plain,
% 1.45/1.64 (hskp22),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[715, 1495, 56])).
% 1.45/1.64 tff(1497,plain,
% 1.45/1.64 (~c2_1(a761)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[721, 1496])).
% 1.45/1.64 tff(1498,plain,
% 1.45/1.64 (~c0_1(a761)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[727, 1496])).
% 1.45/1.64 tff(1499,plain,
% 1.45/1.64 (c1_1(a761)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[735, 1496])).
% 1.45/1.64 tff(1500,plain,
% 1.45/1.64 (c2_1(a725)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[742, 206, 1499, 1498, 1497, 137, 131, 125, 110])).
% 1.45/1.64 tff(1501,plain,
% 1.45/1.64 (hskp27),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[828, 206, 1499, 1498, 1497, 137, 131, 822, 1500])).
% 1.45/1.64 tff(1502,plain,
% 1.45/1.64 (c1_1(a691)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[240, 1501])).
% 1.45/1.64 tff(1503,plain,
% 1.45/1.64 (c0_1(a691)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[248, 1501])).
% 1.45/1.64 tff(1504,plain,
% 1.45/1.64 (~hskp23),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[532, 1500, 137, 131, 56])).
% 1.45/1.64 tff(1505,plain,
% 1.45/1.64 (hskp24 | (~c2_1(a691))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[994, 206, 1504, 1503, 1502, 148])).
% 1.45/1.64 tff(1506,plain,
% 1.45/1.64 (~c2_1(a691)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1505, 1494])).
% 1.45/1.64 tff(1507,plain,
% 1.45/1.64 (^[U: $i] : refl((hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 1.45/1.64 inference(bind,[status(th)],[])).
% 1.45/1.64 tff(1508,plain,
% 1.45/1.64 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.45/1.64 inference(quant_intro,[status(thm)],[1507])).
% 1.45/1.64 tff(1509,plain,
% 1.45/1.64 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1510,plain,
% 1.45/1.64 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp1))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp1) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.45/1.64 inference(bind,[status(th)],[])).
% 1.45/1.64 tff(1511,plain,
% 1.45/1.64 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.45/1.64 inference(quant_intro,[status(thm)],[1510])).
% 1.45/1.64 tff(1512,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.45/1.64 tff(1513,plain,
% 1.45/1.64 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 1.45/1.64 tff(1514,plain,
% 1.45/1.64 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1513, 1509])).
% 1.45/1.64 tff(1515,plain,(
% 1.45/1.64 ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.45/1.64 inference(skolemize,[status(sab)],[1514])).
% 1.45/1.64 tff(1516,plain,
% 1.45/1.64 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1515, 1508])).
% 1.45/1.64 tff(1517,plain,
% 1.45/1.64 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp5 | hskp1 | (~ndr1_0) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1518,plain,
% 1.45/1.64 ((hskp5 | hskp1 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691))) <=> (hskp5 | hskp1 | (~ndr1_0) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1519,plain,
% 1.45/1.64 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1518])).
% 1.45/1.64 tff(1520,plain,
% 1.45/1.64 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp5 | hskp1 | (~ndr1_0) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1519, 1517])).
% 1.45/1.64 tff(1521,plain,
% 1.45/1.64 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1522,plain,
% 1.45/1.64 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp5 | hskp1 | (~ndr1_0) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 1.45/1.64 tff(1523,plain,
% 1.45/1.64 (hskp5 | c2_1(a691)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1522, 206, 1485, 1503, 1502, 1516])).
% 1.45/1.64 tff(1524,plain,
% 1.45/1.64 (hskp5),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1523, 1506])).
% 1.45/1.64 tff(1525,plain,
% 1.45/1.64 (~c1_1(a701)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[28, 1524])).
% 1.45/1.64 tff(1526,plain,
% 1.45/1.64 (c0_1(a701)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[44, 1524])).
% 1.45/1.64 tff(1527,plain,
% 1.45/1.64 (~c1_1(a754)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1050, 206, 1489, 79, 71, 1487, 1488, 63, 159])).
% 1.45/1.64 tff(1528,plain,
% 1.45/1.64 (~hskp14),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[447, 1494, 1489, 1488, 1527, 1504, 56])).
% 1.45/1.64 tff(1529,plain,
% 1.45/1.64 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | c1_1(a701) | (~ndr1_0) | c3_1(a701) | (~c0_1(a701)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c1_1(a701) | (~ndr1_0) | c3_1(a701) | (~c0_1(a701)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1530,plain,
% 1.45/1.64 ((hskp30 | hskp14 | (~ndr1_0) | c3_1(a701) | c1_1(a701) | (~c0_1(a701))) <=> (hskp30 | hskp14 | c1_1(a701) | (~ndr1_0) | c3_1(a701) | (~c0_1(a701)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1531,plain,
% 1.45/1.64 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | c1_1(a701) | (~ndr1_0) | c3_1(a701) | (~c0_1(a701))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1530])).
% 1.45/1.64 tff(1532,plain,
% 1.45/1.64 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c1_1(a701) | (~ndr1_0) | c3_1(a701) | (~c0_1(a701)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1531, 1529])).
% 1.45/1.64 tff(1533,plain,
% 1.45/1.64 ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(1534,plain,
% 1.45/1.64 ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c1_1(a701) | (~ndr1_0) | c3_1(a701) | (~c0_1(a701))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 1.45/1.64 tff(1535,plain,
% 1.45/1.64 (c3_1(a701)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1534, 90, 206, 1528, 1526, 1525, 100])).
% 1.45/1.64 tff(1536,plain,
% 1.45/1.64 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.45/1.64 inference(bind,[status(th)],[])).
% 1.45/1.64 tff(1537,plain,
% 1.45/1.64 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.45/1.64 inference(quant_intro,[status(thm)],[1536])).
% 1.45/1.64 tff(1538,plain,
% 1.45/1.64 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(1539,plain,
% 1.45/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(1540,plain,
% 1.45/1.65 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[1539])).
% 1.45/1.65 tff(1541,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.45/1.65 tff(1542,plain,
% 1.45/1.65 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 1.45/1.65 tff(1543,plain,
% 1.45/1.65 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1542, 1538])).
% 1.45/1.65 tff(1544,plain,(
% 1.45/1.65 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.45/1.65 inference(skolemize,[status(sab)],[1543])).
% 1.45/1.65 tff(1545,plain,
% 1.45/1.65 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1544, 1537])).
% 1.45/1.65 tff(1546,plain,
% 1.45/1.65 (c2_1(a701)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[36, 1524])).
% 1.45/1.65 tff(1547,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a754) | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a754) | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1548,plain,
% 1.45/1.65 ((hskp14 | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754))) <=> (hskp14 | c3_1(a754) | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1549,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a754) | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1548])).
% 1.45/1.65 tff(1550,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a754) | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[1549, 1547])).
% 1.45/1.65 tff(1551,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(1552,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a754) | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 1.45/1.65 tff(1553,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1552, 206, 1528, 1489, 1526, 1546, 1488, 1545, 1527, 1535])).
% 1.45/1.65 tff(1554,plain,((~hskp6) | hskp30 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(1555,plain,
% 1.45/1.65 (~hskp6),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1554, 90, 56])).
% 1.45/1.65 tff(1556,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[323, 206, 162, 292, 348, 284, 278, 164, 163, 89])).
% 1.45/1.65 tff(1557,plain,((~hskp24) | hskp6 | (~c2_1(a754)) | c0_1(a754) | c3_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(1558,plain,
% 1.45/1.65 (~hskp24),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1557, 162, 1489, 1487, 1488])).
% 1.45/1.65 tff(1559,plain,
% 1.45/1.65 (c1_1(a754)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[484, 161, 90, 1487, 1489, 1488, 56, 1558, 160])).
% 1.45/1.65 tff(1560,plain,
% 1.45/1.65 (hskp0),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1420, 1485])).
% 1.45/1.65 tff(1561,plain,
% 1.45/1.65 (~c1_1(a692)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[787, 1560])).
% 1.45/1.65 tff(1562,plain,
% 1.45/1.65 (~c0_1(a692)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[793, 1560])).
% 1.45/1.65 tff(1563,plain,
% 1.45/1.65 (c2_1(a692)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[803, 1560])).
% 1.45/1.65 tff(1564,plain,
% 1.45/1.65 (hskp4 | hskp3),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1430, 206, 1563, 1562, 1561, 400])).
% 1.45/1.65 tff(1565,plain,
% 1.45/1.65 (hskp3),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1564, 161])).
% 1.45/1.65 tff(1566,plain,
% 1.45/1.65 (c0_1(a697)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[457, 1565])).
% 1.45/1.65 tff(1567,plain,
% 1.45/1.65 ((~c0_1(a697)) | c1_1(a697) | (~c1_1(a754))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[838, 206, 1489, 1563, 1488, 160, 1562, 1561, 512])).
% 1.45/1.65 tff(1568,plain,
% 1.45/1.65 (c1_1(a697)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1567, 1566, 1559])).
% 1.45/1.65 tff(1569,plain,
% 1.45/1.65 (c2_1(a697)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[473, 1565])).
% 1.45/1.65 tff(1570,plain,
% 1.45/1.65 (hskp6 | c2_1(a725) | (~c1_1(a754))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[491, 206, 1487, 1488, 137, 125, 271])).
% 1.45/1.65 tff(1571,plain,
% 1.45/1.65 (c2_1(a725)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1570, 1559, 162])).
% 1.45/1.65 tff(1572,plain,
% 1.45/1.65 (~hskp23),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[532, 1571, 137, 131, 56])).
% 1.45/1.65 tff(1573,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[480, 206, 1558, 1572, 1566, 1569, 148, 1568])).
% 1.45/1.65 tff(1574,plain,(hskp4 | hskp28 | c3_1(a697) | hskp6 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(1575,plain,
% 1.45/1.65 (hskp4),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1574, 160, 56, 1555, 90])).
% 1.45/1.65 tff(1576,plain,
% 1.45/1.65 (~c3_1(a698)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[976, 1575])).
% 1.45/1.65 tff(1577,plain,
% 1.45/1.65 (~c2_1(a698)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[854, 1575])).
% 1.45/1.65 tff(1578,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a754) | c3_1(a754) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a754) | c3_1(a754) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c2_1(a754)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1579,plain,
% 1.45/1.65 ((hskp6 | (~ndr1_0) | c3_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp6 | c0_1(a754) | c3_1(a754) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c2_1(a754)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1580,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a754) | c3_1(a754) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c2_1(a754))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1579])).
% 1.45/1.65 tff(1581,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a754) | c3_1(a754) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c2_1(a754)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[1580, 1578])).
% 1.45/1.65 tff(1582,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(1583,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a754) | c3_1(a754) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c2_1(a754))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1582, 1581])).
% 1.45/1.65 tff(1584,plain,
% 1.45/1.65 (~c1_1(a698)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1583, 206, 1555, 1489, 1487, 1488, 1577, 1576, 89])).
% 1.45/1.65 tff(1585,plain,
% 1.45/1.65 (~c0_1(a698)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[848, 1575])).
% 1.45/1.65 tff(1586,plain,
% 1.45/1.65 (hskp27),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[892, 206, 1555, 1585, 1577, 1576, 183])).
% 1.45/1.65 tff(1587,plain,
% 1.45/1.65 (c1_1(a691)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[240, 1586])).
% 1.45/1.65 tff(1588,plain,
% 1.45/1.65 (c0_1(a691)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[248, 1586])).
% 1.45/1.65 tff(1589,plain,
% 1.45/1.65 (~c1_1(a754)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1391, 206, 1555, 1487, 1488, 1585, 1577, 1576, 271])).
% 1.45/1.65 tff(1590,plain,
% 1.45/1.65 (~hskp23),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[388, 1589, 1489, 1487, 56])).
% 1.45/1.65 tff(1591,plain,
% 1.45/1.65 (~hskp24),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1557, 1555, 1489, 1487, 1488])).
% 1.45/1.65 tff(1592,plain,
% 1.45/1.65 (~c2_1(a691)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[994, 206, 1591, 1590, 1588, 1587, 148])).
% 1.45/1.65 tff(1593,plain,
% 1.45/1.65 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(1594,plain,
% 1.45/1.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[1593])).
% 1.45/1.65 tff(1595,plain,
% 1.45/1.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1596,plain,
% 1.45/1.65 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(1597,plain,
% 1.45/1.65 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[1596])).
% 1.45/1.65 tff(1598,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.45/1.65 tff(1599,plain,
% 1.45/1.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 1.45/1.65 tff(1600,plain,
% 1.45/1.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1599, 1595])).
% 1.45/1.65 tff(1601,plain,(
% 1.45/1.65 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.45/1.65 inference(skolemize,[status(sab)],[1600])).
% 1.45/1.65 tff(1602,plain,
% 1.45/1.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1601, 1594])).
% 1.45/1.65 tff(1603,plain,
% 1.45/1.65 (~hskp14),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[447, 1589, 1489, 1488, 1591, 1590, 56])).
% 1.45/1.65 tff(1604,plain,
% 1.45/1.65 (~hskp3),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[482, 1590, 1591, 160, 90, 1603])).
% 1.45/1.65 tff(1605,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1606,plain,
% 1.45/1.65 ((hskp3 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)) | c3_1(a698) | c1_1(a698) | c2_1(a698)) <=> (hskp3 | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1607,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)) | c3_1(a698) | c1_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691)))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1606])).
% 1.45/1.65 tff(1608,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)) | c3_1(a698) | c1_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.65 inference(transitivity,[status(thm)],[1607, 1605])).
% 1.45/1.65 tff(1609,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)) | c3_1(a698) | c1_1(a698) | c2_1(a698))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(1610,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 1.45/1.65 tff(1611,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1610, 206, 1604, 1588, 1587, 1577, 1576, 1602, 1592, 1584])).
% 1.45/1.65 tff(1612,plain,(c3_1(a697) | hskp30 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(1613,plain,
% 1.45/1.65 (c3_1(a697)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1612, 90, 56])).
% 1.45/1.65 tff(1614,plain,
% 1.45/1.65 (~hskp3),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1286, 1613])).
% 1.45/1.65 tff(1615,plain,
% 1.45/1.65 (hskp4),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1564, 1614])).
% 1.45/1.65 tff(1616,plain,
% 1.45/1.65 (~c3_1(a698)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[976, 1615])).
% 1.45/1.65 tff(1617,plain,
% 1.45/1.65 (~c2_1(a698)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[854, 1615])).
% 1.45/1.65 tff(1618,plain,
% 1.45/1.65 (~c1_1(a698)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1583, 206, 1555, 1489, 1487, 1488, 1617, 1616, 89])).
% 1.45/1.65 tff(1619,plain,
% 1.45/1.65 (~c0_1(a698)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[848, 1615])).
% 1.45/1.65 tff(1620,plain,
% 1.45/1.65 (hskp27),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[892, 206, 1555, 1619, 1617, 1616, 183])).
% 1.45/1.65 tff(1621,plain,
% 1.45/1.65 (c1_1(a691)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[240, 1620])).
% 1.45/1.65 tff(1622,plain,
% 1.45/1.65 (c0_1(a691)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[248, 1620])).
% 1.45/1.65 tff(1623,plain,
% 1.45/1.65 (~c1_1(a754)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1391, 206, 1555, 1487, 1488, 1619, 1617, 1616, 271])).
% 1.45/1.65 tff(1624,plain,
% 1.45/1.65 (~hskp23),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[388, 1623, 1489, 1487, 56])).
% 1.45/1.65 tff(1625,plain,
% 1.45/1.65 (~c2_1(a691)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[994, 206, 1591, 1624, 1622, 1621, 148])).
% 1.45/1.65 tff(1626,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1610, 206, 1614, 1622, 1621, 1617, 1616, 1602, 1625, 1618])).
% 1.45/1.65 tff(1627,plain,(hskp30 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(1628,plain,
% 1.45/1.65 (hskp30),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1627, 56])).
% 1.45/1.65 tff(1629,plain,
% 1.45/1.65 (((~hskp30) | c3_1(a733)) <=> ((~hskp30) | c3_1(a733))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1630,axiom,((~hskp30) | c3_1(a733)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.45/1.65 tff(1631,plain,
% 1.45/1.65 ((~hskp30) | c3_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 1.45/1.65 tff(1632,plain,
% 1.45/1.65 ((~hskp30) | c3_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1631, 1629])).
% 1.45/1.65 tff(1633,plain,
% 1.45/1.65 ((~hskp30) | c3_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1632, 1629])).
% 1.45/1.65 tff(1634,plain,
% 1.45/1.65 ((~hskp30) | c3_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1633, 1629])).
% 1.45/1.65 tff(1635,plain,
% 1.45/1.65 ((~hskp30) | c3_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1634, 1629])).
% 1.45/1.65 tff(1636,plain,
% 1.45/1.65 (c3_1(a733)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1635, 1628])).
% 1.45/1.65 tff(1637,plain,
% 1.45/1.65 (((~hskp30) | c2_1(a733)) <=> ((~hskp30) | c2_1(a733))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1638,axiom,((~hskp30) | c2_1(a733)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 1.45/1.65 tff(1639,plain,
% 1.45/1.65 ((~hskp30) | c2_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 1.45/1.65 tff(1640,plain,
% 1.45/1.65 ((~hskp30) | c2_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1639, 1637])).
% 1.45/1.65 tff(1641,plain,
% 1.45/1.65 ((~hskp30) | c2_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1640, 1637])).
% 1.45/1.65 tff(1642,plain,
% 1.45/1.65 ((~hskp30) | c2_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1641, 1637])).
% 1.45/1.65 tff(1643,plain,
% 1.45/1.65 ((~hskp30) | c2_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1642, 1637])).
% 1.45/1.65 tff(1644,plain,
% 1.45/1.65 (c2_1(a733)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1643, 1628])).
% 1.45/1.65 tff(1645,plain,
% 1.45/1.65 (((~hskp30) | c1_1(a733)) <=> ((~hskp30) | c1_1(a733))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1646,axiom,((~hskp30) | c1_1(a733)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 1.45/1.65 tff(1647,plain,
% 1.45/1.65 ((~hskp30) | c1_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 1.45/1.65 tff(1648,plain,
% 1.45/1.65 ((~hskp30) | c1_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1647, 1645])).
% 1.45/1.65 tff(1649,plain,
% 1.45/1.65 ((~hskp30) | c1_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1648, 1645])).
% 1.45/1.65 tff(1650,plain,
% 1.45/1.65 ((~hskp30) | c1_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1649, 1645])).
% 1.45/1.65 tff(1651,plain,
% 1.45/1.65 ((~hskp30) | c1_1(a733)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1650, 1645])).
% 1.45/1.65 tff(1652,plain,
% 1.45/1.65 (c1_1(a733)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1651, 1628])).
% 1.45/1.65 tff(1653,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1654,plain,
% 1.45/1.65 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702))) <=> (hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1655,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a702)) | (~c0_1(a702))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1654])).
% 1.45/1.65 tff(1656,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[1655, 1653])).
% 1.45/1.65 tff(1657,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(1658,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a702)) | (~c0_1(a702))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 1.45/1.65 tff(1659,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1658, 206, 56, 1652, 1644, 1636, 79, 71, 63, 55])).
% 1.45/1.65 tff(1660,plain,((~hskp6) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(1661,plain,
% 1.45/1.65 (~hskp6),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1660, 56])).
% 1.45/1.65 tff(1662,plain,
% 1.45/1.65 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(1663,plain,
% 1.45/1.65 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[1662])).
% 1.45/1.65 tff(1664,plain,
% 1.45/1.65 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1665,plain,
% 1.45/1.65 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(1666,plain,
% 1.45/1.65 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[1665])).
% 1.45/1.65 tff(1667,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 1.45/1.65 tff(1668,plain,
% 1.45/1.65 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1667, 1666])).
% 1.45/1.65 tff(1669,plain,
% 1.45/1.65 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1668, 1664])).
% 1.45/1.65 tff(1670,plain,(
% 1.45/1.65 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.65 inference(skolemize,[status(sab)],[1669])).
% 1.45/1.65 tff(1671,plain,
% 1.45/1.65 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1670, 1663])).
% 1.45/1.65 tff(1672,plain,
% 1.45/1.65 (hskp27 | hskp6 | c2_1(a754) | c0_1(a754)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[212, 206, 163, 183])).
% 1.45/1.65 tff(1673,plain,
% 1.45/1.65 (hskp27),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1672, 165, 162, 164])).
% 1.45/1.65 tff(1674,plain,
% 1.45/1.65 (c0_1(a691)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[248, 1673])).
% 1.45/1.65 tff(1675,plain,
% 1.45/1.65 (c3_1(a691)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[232, 1673])).
% 1.45/1.65 tff(1676,assumption,(~c2_1(a691)), introduced(assumption)).
% 1.45/1.65 tff(1677,assumption,(c3_1(a691)), introduced(assumption)).
% 1.45/1.65 tff(1678,assumption,(c0_1(a691)), introduced(assumption)).
% 1.45/1.65 tff(1679,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1680,plain,
% 1.45/1.65 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691))) <=> (hskp28 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1681,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691)))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1680])).
% 1.45/1.65 tff(1682,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.45/1.65 inference(transitivity,[status(thm)],[1681, 1679])).
% 1.45/1.65 tff(1683,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(1684,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 1.45/1.65 tff(1685,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1684, 206, 56, 1652, 1644, 1636, 1678, 1677, 55, 1676])).
% 1.45/1.65 tff(1686,plain,(c2_1(a691) | hskp28 | (~c0_1(a691)) | (~c3_1(a691))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(1687,plain,
% 1.45/1.65 (c2_1(a691)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1686, 1675, 1674, 56])).
% 1.45/1.65 tff(1688,plain,
% 1.45/1.65 (c1_1(a691)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[240, 1673])).
% 1.45/1.65 tff(1689,assumption,(c2_1(a691)), introduced(assumption)).
% 1.45/1.65 tff(1690,plain,
% 1.45/1.65 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(1691,plain,
% 1.45/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[1690])).
% 1.45/1.65 tff(1692,plain,
% 1.45/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(1693,plain,
% 1.45/1.65 (^[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)) | c3_1(V) | (~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)) | c3_1(V) | (~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)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~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)) | c3_1(V) | (~c1_1(V)) | (~c0_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)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 1.45/1.66 inference(bind,[status(th)],[])).
% 1.45/1.66 tff(1694,plain,
% 1.45/1.66 (![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)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.45/1.66 inference(quant_intro,[status(thm)],[1693])).
% 1.45/1.66 tff(1695,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)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.45/1.66 tff(1696,plain,
% 1.45/1.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1695, 1694])).
% 1.45/1.66 tff(1697,plain,
% 1.45/1.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1696, 1692])).
% 1.45/1.66 tff(1698,plain,(
% 1.45/1.66 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.45/1.66 inference(skolemize,[status(sab)],[1697])).
% 1.45/1.66 tff(1699,plain,
% 1.45/1.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1698, 1691])).
% 1.45/1.66 tff(1700,plain,
% 1.45/1.66 (hskp27),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1672, 164, 162, 165])).
% 1.45/1.66 tff(1701,plain,
% 1.45/1.66 (c3_1(a691)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[232, 1700])).
% 1.45/1.66 tff(1702,plain,
% 1.45/1.66 (c0_1(a691)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[248, 1700])).
% 1.45/1.66 tff(1703,plain,
% 1.45/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a754) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1704,plain,
% 1.45/1.66 (((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a754) | c2_1(a754) | c0_1(a754)) <=> (c2_1(a754) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1705,plain,
% 1.45/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a754) | c2_1(a754) | c0_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a754) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[1704])).
% 1.45/1.66 tff(1706,plain,
% 1.45/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a754) | c2_1(a754) | c0_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[1705, 1703])).
% 1.45/1.66 tff(1707,plain,
% 1.45/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a754) | c2_1(a754) | c0_1(a754))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(1708,plain,
% 1.45/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 1.45/1.66 tff(1709,plain,
% 1.45/1.66 (~c0_1(a764)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1708, 206, 1702, 1701, 292, 165, 278, 164, 163, 1699, 1689])).
% 1.45/1.66 tff(1710,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[298, 206, 162, 292, 284, 278, 271, 1709])).
% 1.45/1.66 tff(1711,plain,((~hskp24) | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~c2_1(a691))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(1712,plain,
% 1.45/1.66 (~hskp24),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1711, 1687, 165, 164, 163, 162])).
% 1.45/1.66 tff(1713,plain,
% 1.45/1.66 (hskp23),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[994, 206, 1712, 1674, 1688, 148, 1687])).
% 1.45/1.66 tff(1714,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1715,plain,
% 1.45/1.66 ((hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a754) | c0_1(a754) | c2_1(a754)) <=> (hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1716,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a754) | c0_1(a754) | c2_1(a754))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[1715])).
% 1.45/1.66 tff(1717,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a754) | c0_1(a754) | c2_1(a754))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[1716, 1714])).
% 1.45/1.66 tff(1718,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a754) | c0_1(a754) | c2_1(a754))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(1719,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1718, 1717])).
% 1.45/1.66 tff(1720,plain,
% 1.45/1.66 (hskp6 | c2_1(a754) | c0_1(a754) | (~c1_1(a754))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1719, 206, 163, 271])).
% 1.45/1.66 tff(1721,plain,
% 1.45/1.66 (~c1_1(a754)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1720, 165, 162, 164])).
% 1.45/1.66 tff(1722,plain,
% 1.45/1.66 (~c2_1(a763)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[365, 1713])).
% 1.45/1.66 tff(1723,plain,
% 1.45/1.66 (~c1_1(a763)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[371, 1713])).
% 1.45/1.66 tff(1724,plain,
% 1.45/1.66 (c0_1(a763)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[379, 1713])).
% 1.45/1.66 tff(1725,assumption,(hskp0), introduced(assumption)).
% 1.45/1.66 tff(1726,plain,
% 1.45/1.66 (~c1_1(a692)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[787, 1725])).
% 1.45/1.66 tff(1727,plain,
% 1.45/1.66 (~c0_1(a692)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[793, 1725])).
% 1.45/1.66 tff(1728,assumption,(~c2_1(a763)), introduced(assumption)).
% 1.45/1.66 tff(1729,assumption,(~c1_1(a763)), introduced(assumption)).
% 1.45/1.66 tff(1730,plain,
% 1.45/1.66 (c2_1(a692)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[803, 1725])).
% 1.45/1.66 tff(1731,assumption,(c0_1(a763)), introduced(assumption)).
% 1.45/1.66 tff(1732,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a763)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1733,plain,
% 1.45/1.66 ((hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692))) <=> (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a763)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1734,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a763))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[1733])).
% 1.45/1.66 tff(1735,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a763)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[1734, 1732])).
% 1.45/1.66 tff(1736,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(1737,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a763))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 1.45/1.66 tff(1738,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1737, 206, 56, 1731, 1730, 1729, 1728, 1727, 1726, 359])).
% 1.45/1.66 tff(1739,plain,((~hskp0) | hskp28 | (~c0_1(a763)) | c1_1(a763) | c2_1(a763)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(1740,plain,
% 1.45/1.66 (~hskp0),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1739, 1724, 56, 1723, 1722])).
% 1.45/1.66 tff(1741,plain,
% 1.45/1.66 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | c1_1(a754))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | c1_1(a754))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1742,plain,
% 1.45/1.66 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | c0_1(a754)) <=> (hskp1 | hskp0 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | c1_1(a754))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1743,plain,
% 1.45/1.66 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | c0_1(a754))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | c1_1(a754)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[1742])).
% 1.45/1.66 tff(1744,plain,
% 1.45/1.66 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | c0_1(a754))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | c1_1(a754))),
% 1.45/1.66 inference(transitivity,[status(thm)],[1743, 1741])).
% 1.45/1.66 tff(1745,plain,
% 1.45/1.66 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | c0_1(a754))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(1746,plain,
% 1.45/1.66 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | c1_1(a754)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 1.45/1.66 tff(1747,plain,
% 1.45/1.66 (hskp1 | hskp0 | c0_1(a754) | c1_1(a754)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1746, 206, 163, 1413])).
% 1.45/1.66 tff(1748,plain,
% 1.45/1.66 (hskp1),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1747, 1740, 164, 1721])).
% 1.45/1.66 tff(1749,plain,
% 1.45/1.66 (~c1_1(a693)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1354, 1748])).
% 1.45/1.66 tff(1750,plain,
% 1.45/1.66 (~c3_1(a693)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1484, 1748])).
% 1.45/1.66 tff(1751,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a763) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a763)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a763) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a763)) | (~c0_1(a763)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1752,plain,
% 1.45/1.66 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763))) <=> (hskp28 | c2_1(a763) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a763)) | (~c0_1(a763)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1753,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a763) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a763)) | (~c0_1(a763))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[1752])).
% 1.45/1.66 tff(1754,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a763) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a763)) | (~c0_1(a763)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[1753, 1751])).
% 1.45/1.66 tff(1755,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(1756,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a763) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a763)) | (~c0_1(a763))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1755, 1754])).
% 1.45/1.66 tff(1757,plain,
% 1.45/1.66 (~c3_1(a763)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1756, 206, 56, 1652, 1644, 1636, 380, 366, 55])).
% 1.45/1.66 tff(1758,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | c3_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | c3_1(a763) | (~c0_1(a763)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1759,plain,
% 1.45/1.66 ((hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693))) <=> (hskp28 | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | c3_1(a763) | (~c0_1(a763)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1760,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | c3_1(a763) | (~c0_1(a763))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[1759])).
% 1.45/1.66 tff(1761,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | c3_1(a763) | (~c0_1(a763)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[1760, 1758])).
% 1.45/1.66 tff(1762,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(1763,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | c3_1(a763) | (~c0_1(a763))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 1.45/1.66 tff(1764,plain,
% 1.45/1.66 (~c2_1(a693)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1763, 206, 56, 380, 366, 149, 138, 309, 1757])).
% 1.45/1.66 tff(1765,plain,
% 1.45/1.66 (~hskp1),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[344, 1764])).
% 1.45/1.66 tff(1766,plain,
% 1.45/1.66 (hskp0),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1747, 1765, 164, 349])).
% 1.45/1.66 tff(1767,plain,
% 1.45/1.66 (~c1_1(a692)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[787, 1766])).
% 1.45/1.66 tff(1768,plain,
% 1.45/1.66 (~c0_1(a692)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[793, 1766])).
% 1.45/1.66 tff(1769,plain,
% 1.45/1.66 (c2_1(a692)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[803, 1766])).
% 1.45/1.66 tff(1770,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1737, 206, 56, 380, 1769, 372, 366, 1768, 1767, 359])).
% 1.45/1.66 tff(1771,plain,((~hskp23) | hskp28 | c0_1(a754) | c1_1(a754) | c3_1(a754) | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(1772,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1771, 1750, 1749, 164, 1721, 163, 1713, 56])).
% 1.45/1.66 tff(1773,plain,(c2_1(a754) | c0_1(a754) | c3_1(a754) | hskp28 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(1774,plain,
% 1.45/1.66 (c2_1(a754)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1773, 164, 163, 56, 162])).
% 1.45/1.66 tff(1775,plain,
% 1.45/1.66 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.45/1.66 inference(bind,[status(th)],[])).
% 1.45/1.66 tff(1776,plain,
% 1.45/1.66 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.66 inference(quant_intro,[status(thm)],[1775])).
% 1.45/1.66 tff(1777,plain,
% 1.45/1.66 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1778,plain,
% 1.45/1.66 (^[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)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.45/1.66 inference(bind,[status(th)],[])).
% 1.45/1.66 tff(1779,plain,
% 1.45/1.66 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.66 inference(quant_intro,[status(thm)],[1778])).
% 1.45/1.66 tff(1780,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)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.45/1.66 tff(1781,plain,
% 1.45/1.66 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 1.45/1.66 tff(1782,plain,
% 1.45/1.66 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1781, 1777])).
% 1.45/1.66 tff(1783,plain,(
% 1.45/1.66 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.66 inference(skolemize,[status(sab)],[1782])).
% 1.45/1.66 tff(1784,plain,
% 1.45/1.66 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1783, 1776])).
% 1.45/1.66 tff(1785,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1786,plain,
% 1.45/1.66 ((hskp8 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(1787,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[1786])).
% 1.45/1.66 tff(1788,plain,
% 1.45/1.66 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[1787, 1785])).
% 1.45/1.66 tff(1789,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(1790,plain,
% 1.45/1.66 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 1.45/1.66 tff(1791,plain,
% 1.45/1.66 (hskp8 | c0_1(a754) | (~c2_1(a754))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1790, 206, 1652, 1644, 1636, 163, 1784])).
% 1.45/1.67 tff(1792,plain,
% 1.45/1.67 (hskp8),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1791, 1774, 164])).
% 1.45/1.67 tff(1793,plain,
% 1.45/1.67 (((~hskp8) | (~c0_1(a710))) <=> ((~hskp8) | (~c0_1(a710)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1794,plain,
% 1.45/1.67 (((~c0_1(a710)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a710)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1795,axiom,((~c0_1(a710)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.45/1.67 tff(1796,plain,
% 1.45/1.67 ((~hskp8) | (~c0_1(a710))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1795, 1794])).
% 1.45/1.67 tff(1797,plain,
% 1.45/1.67 ((~hskp8) | (~c0_1(a710))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1796, 1793])).
% 1.45/1.67 tff(1798,plain,
% 1.45/1.67 (~c0_1(a710)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1797, 1792])).
% 1.45/1.67 tff(1799,plain,
% 1.45/1.67 (((~hskp8) | c3_1(a710)) <=> ((~hskp8) | c3_1(a710))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1800,axiom,((~hskp8) | c3_1(a710)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.45/1.67 tff(1801,plain,
% 1.45/1.67 ((~hskp8) | c3_1(a710)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.45/1.67 tff(1802,plain,
% 1.45/1.67 ((~hskp8) | c3_1(a710)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1801, 1799])).
% 1.45/1.67 tff(1803,plain,
% 1.45/1.67 ((~hskp8) | c3_1(a710)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1802, 1799])).
% 1.45/1.67 tff(1804,plain,
% 1.45/1.67 ((~hskp8) | c3_1(a710)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1803, 1799])).
% 1.45/1.67 tff(1805,plain,
% 1.45/1.67 ((~hskp8) | c3_1(a710)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1804, 1799])).
% 1.45/1.67 tff(1806,plain,
% 1.45/1.67 (c3_1(a710)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1805, 1792])).
% 1.45/1.67 tff(1807,assumption,(hskp10), introduced(assumption)).
% 1.45/1.67 tff(1808,plain,
% 1.45/1.67 (((~hskp10) | (~c2_1(a717))) <=> ((~hskp10) | (~c2_1(a717)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1809,plain,
% 1.45/1.67 (((~c2_1(a717)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a717)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1810,axiom,((~c2_1(a717)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.45/1.67 tff(1811,plain,
% 1.45/1.67 ((~hskp10) | (~c2_1(a717))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1810, 1809])).
% 1.45/1.67 tff(1812,plain,
% 1.45/1.67 ((~hskp10) | (~c2_1(a717))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1811, 1808])).
% 1.45/1.67 tff(1813,plain,
% 1.45/1.67 (~c2_1(a717)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1812, 1807])).
% 1.45/1.67 tff(1814,plain,
% 1.45/1.67 (((~hskp10) | c3_1(a717)) <=> ((~hskp10) | c3_1(a717))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1815,axiom,((~hskp10) | c3_1(a717)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.45/1.67 tff(1816,plain,
% 1.45/1.67 ((~hskp10) | c3_1(a717)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1815, 1814])).
% 1.45/1.67 tff(1817,plain,
% 1.45/1.67 ((~hskp10) | c3_1(a717)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1816, 1814])).
% 1.45/1.67 tff(1818,plain,
% 1.45/1.67 ((~hskp10) | c3_1(a717)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1817, 1814])).
% 1.45/1.67 tff(1819,plain,
% 1.45/1.67 ((~hskp10) | c3_1(a717)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1818, 1814])).
% 1.45/1.67 tff(1820,plain,
% 1.45/1.67 ((~hskp10) | c3_1(a717)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1819, 1814])).
% 1.45/1.67 tff(1821,plain,
% 1.45/1.67 (c3_1(a717)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1820, 1807])).
% 1.45/1.67 tff(1822,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | (~c0_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | (~c0_1(a717)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1823,plain,
% 1.45/1.67 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717))) <=> (hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | (~c0_1(a717)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1824,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | (~c0_1(a717))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[1823])).
% 1.45/1.67 tff(1825,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | (~c0_1(a717)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[1824, 1822])).
% 1.45/1.67 tff(1826,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(1827,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | (~c0_1(a717))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 1.45/1.67 tff(1828,plain,
% 1.45/1.67 (~c0_1(a717)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1827, 206, 56, 1652, 1644, 1636, 1821, 1813, 55])).
% 1.45/1.67 tff(1829,plain,
% 1.45/1.67 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.45/1.67 inference(bind,[status(th)],[])).
% 1.45/1.67 tff(1830,plain,
% 1.45/1.67 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.45/1.67 inference(quant_intro,[status(thm)],[1829])).
% 1.45/1.67 tff(1831,plain,
% 1.45/1.67 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1832,plain,
% 1.45/1.67 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.45/1.67 inference(bind,[status(th)],[])).
% 1.45/1.67 tff(1833,plain,
% 1.45/1.67 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.45/1.67 inference(quant_intro,[status(thm)],[1832])).
% 1.45/1.67 tff(1834,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.45/1.67 tff(1835,plain,
% 1.45/1.67 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1834, 1833])).
% 1.45/1.67 tff(1836,plain,
% 1.45/1.67 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1835, 1831])).
% 1.45/1.67 tff(1837,plain,(
% 1.45/1.67 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.45/1.67 inference(skolemize,[status(sab)],[1836])).
% 1.45/1.67 tff(1838,plain,
% 1.45/1.67 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1837, 1830])).
% 1.45/1.67 tff(1839,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | c0_1(a717))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | c0_1(a717))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1840,plain,
% 1.45/1.67 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a717) | c2_1(a717) | (~c3_1(a717))) <=> (hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | c0_1(a717))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1841,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a717) | c2_1(a717) | (~c3_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | c0_1(a717)))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[1840])).
% 1.45/1.67 tff(1842,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a717) | c2_1(a717) | (~c3_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | c0_1(a717))),
% 1.45/1.67 inference(transitivity,[status(thm)],[1841, 1839])).
% 1.45/1.67 tff(1843,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a717) | c2_1(a717) | (~c3_1(a717)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(1844,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | c0_1(a717)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 1.45/1.67 tff(1845,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1844, 206, 56, 1652, 1644, 1636, 1821, 1813, 1838, 1828])).
% 1.45/1.67 tff(1846,plain,((~hskp10) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(1847,plain,
% 1.45/1.67 (~hskp10),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1846, 56])).
% 1.45/1.67 tff(1848,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a754) | c3_1(a754) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a754) | c3_1(a754) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c2_1(a754)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1849,plain,
% 1.45/1.67 ((hskp10 | (~ndr1_0) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp10 | c0_1(a754) | c3_1(a754) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c2_1(a754)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1850,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a754) | c3_1(a754) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c2_1(a754))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[1849])).
% 1.45/1.67 tff(1851,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a754) | c3_1(a754) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c2_1(a754)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[1850, 1848])).
% 1.45/1.67 tff(1852,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(1853,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a754) | c3_1(a754) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c2_1(a754))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1852, 1851])).
% 1.45/1.67 tff(1854,plain,
% 1.45/1.67 (~c1_1(a710)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1853, 206, 1847, 1774, 1806, 164, 163, 1798, 1671])).
% 1.45/1.67 tff(1855,plain,
% 1.45/1.67 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.45/1.67 inference(bind,[status(th)],[])).
% 1.45/1.67 tff(1856,plain,
% 1.45/1.67 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.67 inference(quant_intro,[status(thm)],[1855])).
% 1.45/1.67 tff(1857,plain,
% 1.45/1.67 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1858,plain,
% 1.45/1.67 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_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))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_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))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.45/1.67 inference(bind,[status(th)],[])).
% 1.45/1.67 tff(1859,plain,
% 1.45/1.67 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.67 inference(quant_intro,[status(thm)],[1858])).
% 1.45/1.67 tff(1860,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 1.45/1.67 tff(1861,plain,
% 1.45/1.67 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1860, 1859])).
% 1.45/1.67 tff(1862,plain,
% 1.45/1.67 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1861, 1857])).
% 1.45/1.67 tff(1863,plain,(
% 1.45/1.67 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.67 inference(skolemize,[status(sab)],[1862])).
% 1.45/1.67 tff(1864,plain,
% 1.45/1.67 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1863, 1856])).
% 1.45/1.67 tff(1865,plain,
% 1.45/1.67 (((~hskp8) | c2_1(a710)) <=> ((~hskp8) | c2_1(a710))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1866,axiom,((~hskp8) | c2_1(a710)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.45/1.67 tff(1867,plain,
% 1.45/1.67 ((~hskp8) | c2_1(a710)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 1.45/1.67 tff(1868,plain,
% 1.45/1.67 ((~hskp8) | c2_1(a710)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1867, 1865])).
% 1.45/1.67 tff(1869,plain,
% 1.45/1.67 ((~hskp8) | c2_1(a710)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1868, 1865])).
% 1.45/1.67 tff(1870,plain,
% 1.45/1.67 ((~hskp8) | c2_1(a710)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1869, 1865])).
% 1.45/1.67 tff(1871,plain,
% 1.45/1.67 ((~hskp8) | c2_1(a710)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1870, 1865])).
% 1.45/1.67 tff(1872,plain,
% 1.45/1.67 (c2_1(a710)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1871, 1792])).
% 1.45/1.67 tff(1873,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp2 | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1874,plain,
% 1.45/1.67 ((hskp2 | (~ndr1_0) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c1_1(a710) | c0_1(a710) | (~c2_1(a710))) <=> (hskp2 | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1875,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c1_1(a710) | c0_1(a710) | (~c2_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp2 | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710)))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[1874])).
% 1.45/1.67 tff(1876,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c1_1(a710) | c0_1(a710) | (~c2_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))),
% 1.45/1.67 inference(transitivity,[status(thm)],[1875, 1873])).
% 1.45/1.67 tff(1877,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c1_1(a710) | c0_1(a710) | (~c2_1(a710)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(1878,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1877, 1876])).
% 1.45/1.67 tff(1879,plain,
% 1.45/1.67 (hskp2),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1878, 206, 1872, 1806, 1798, 1864, 1854])).
% 1.45/1.67 tff(1880,plain,
% 1.45/1.67 (((~hskp2) | (~c2_1(a696))) <=> ((~hskp2) | (~c2_1(a696)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1881,plain,
% 1.45/1.67 (((~c2_1(a696)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a696)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1882,axiom,((~c2_1(a696)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.45/1.67 tff(1883,plain,
% 1.45/1.67 ((~hskp2) | (~c2_1(a696))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1882, 1881])).
% 1.45/1.67 tff(1884,plain,
% 1.45/1.67 ((~hskp2) | (~c2_1(a696))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1883, 1880])).
% 1.45/1.67 tff(1885,plain,
% 1.45/1.67 (~c2_1(a696)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1884, 1879])).
% 1.45/1.67 tff(1886,plain,
% 1.45/1.67 (((~hskp2) | c0_1(a696)) <=> ((~hskp2) | c0_1(a696))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1887,axiom,((~hskp2) | c0_1(a696)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.45/1.67 tff(1888,plain,
% 1.45/1.67 ((~hskp2) | c0_1(a696)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1887, 1886])).
% 1.45/1.67 tff(1889,plain,
% 1.45/1.67 ((~hskp2) | c0_1(a696)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1888, 1886])).
% 1.45/1.67 tff(1890,plain,
% 1.45/1.67 ((~hskp2) | c0_1(a696)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1889, 1886])).
% 1.45/1.67 tff(1891,plain,
% 1.45/1.67 ((~hskp2) | c0_1(a696)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1890, 1886])).
% 1.45/1.67 tff(1892,plain,
% 1.45/1.67 ((~hskp2) | c0_1(a696)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1891, 1886])).
% 1.45/1.67 tff(1893,plain,
% 1.45/1.67 (c0_1(a696)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1892, 1879])).
% 1.45/1.67 tff(1894,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a696) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a696)) | (~c0_1(a696)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a696) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a696)) | (~c0_1(a696)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1895,plain,
% 1.45/1.67 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a696) | (~c3_1(a696)) | (~c0_1(a696))) <=> (hskp28 | c2_1(a696) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a696)) | (~c0_1(a696)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1896,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a696) | (~c3_1(a696)) | (~c0_1(a696)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a696) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a696)) | (~c0_1(a696))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[1895])).
% 1.45/1.67 tff(1897,plain,
% 1.45/1.67 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a696) | (~c3_1(a696)) | (~c0_1(a696)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a696) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a696)) | (~c0_1(a696)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[1896, 1894])).
% 1.45/1.67 tff(1898,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a696) | (~c3_1(a696)) | (~c0_1(a696)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(1899,plain,
% 1.45/1.67 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a696) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a696)) | (~c0_1(a696))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1898, 1897])).
% 1.45/1.67 tff(1900,plain,
% 1.45/1.67 (~c3_1(a696)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1899, 206, 56, 1652, 1644, 1636, 1893, 1885, 55])).
% 1.45/1.67 tff(1901,plain,
% 1.45/1.67 (((~hskp2) | c1_1(a696)) <=> ((~hskp2) | c1_1(a696))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1902,axiom,((~hskp2) | c1_1(a696)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.45/1.67 tff(1903,plain,
% 1.45/1.67 ((~hskp2) | c1_1(a696)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1902, 1901])).
% 1.45/1.67 tff(1904,plain,
% 1.45/1.67 ((~hskp2) | c1_1(a696)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1903, 1901])).
% 1.45/1.67 tff(1905,plain,
% 1.45/1.67 ((~hskp2) | c1_1(a696)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1904, 1901])).
% 1.45/1.67 tff(1906,plain,
% 1.45/1.67 ((~hskp2) | c1_1(a696)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1905, 1901])).
% 1.45/1.67 tff(1907,plain,
% 1.45/1.67 ((~hskp2) | c1_1(a696)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1906, 1901])).
% 1.45/1.67 tff(1908,plain,
% 1.45/1.67 (c1_1(a696)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1907, 1879])).
% 1.45/1.67 tff(1909,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a710) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a710) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1910,plain,
% 1.45/1.67 (((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c1_1(a696)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710))) <=> (c0_1(a710) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(1911,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c1_1(a696)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a710) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710)))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[1910])).
% 1.45/1.67 tff(1912,plain,
% 1.45/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c1_1(a696)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a710) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))),
% 1.45/1.67 inference(transitivity,[status(thm)],[1911, 1909])).
% 1.45/1.67 tff(1913,plain,
% 1.45/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c1_1(a696)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(1914,plain,
% 1.45/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a710) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 1.45/1.67 tff(1915,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1914, 206, 1872, 1806, 1908, 1798, 1885, 10, 1900, 1854])).
% 1.45/1.67 tff(1916,plain,(c0_1(a754) | hskp28 | c3_1(a754) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(1917,plain,
% 1.45/1.67 (c0_1(a754)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1916, 162, 163, 56])).
% 1.45/1.67 tff(1918,plain,
% 1.45/1.67 (~hskp20),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[541, 1917])).
% 1.45/1.67 tff(1919,assumption,(~c3_1(a764)), introduced(assumption)).
% 1.45/1.67 tff(1920,assumption,(~c2_1(a764)), introduced(assumption)).
% 1.45/1.67 tff(1921,assumption,(c1_1(a764)), introduced(assumption)).
% 1.45/1.67 tff(1922,plain,
% 1.45/1.67 (c0_1(a764)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[298, 206, 162, 1921, 1920, 1919, 271])).
% 1.45/1.67 tff(1923,assumption,(hskp13), introduced(assumption)).
% 1.45/1.67 tff(1924,plain,
% 1.45/1.67 (((~hskp13) | (~c3_1(a726))) <=> ((~hskp13) | (~c3_1(a726)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1925,plain,
% 1.45/1.68 (((~c3_1(a726)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a726)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1926,axiom,((~c3_1(a726)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.45/1.68 tff(1927,plain,
% 1.45/1.68 ((~hskp13) | (~c3_1(a726))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1926, 1925])).
% 1.45/1.68 tff(1928,plain,
% 1.45/1.68 ((~hskp13) | (~c3_1(a726))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1927, 1924])).
% 1.45/1.68 tff(1929,plain,
% 1.45/1.68 (~c3_1(a726)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1928, 1923])).
% 1.45/1.68 tff(1930,plain,
% 1.45/1.68 (((~hskp13) | (~c0_1(a726))) <=> ((~hskp13) | (~c0_1(a726)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1931,plain,
% 1.45/1.68 (((~c0_1(a726)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a726)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1932,axiom,((~c0_1(a726)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.45/1.68 tff(1933,plain,
% 1.45/1.68 ((~hskp13) | (~c0_1(a726))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 1.45/1.68 tff(1934,plain,
% 1.45/1.68 ((~hskp13) | (~c0_1(a726))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1933, 1930])).
% 1.45/1.68 tff(1935,plain,
% 1.45/1.68 (~c0_1(a726)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1934, 1923])).
% 1.45/1.68 tff(1936,plain,
% 1.45/1.68 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1937,plain,
% 1.45/1.68 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726)) <=> (hskp27 | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1938,plain,
% 1.45/1.68 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726)))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[1937])).
% 1.45/1.68 tff(1939,plain,
% 1.45/1.68 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))),
% 1.45/1.68 inference(transitivity,[status(thm)],[1938, 1936])).
% 1.45/1.68 tff(1940,plain,
% 1.45/1.68 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(1941,plain,
% 1.45/1.68 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 1.45/1.68 tff(1942,plain,
% 1.45/1.68 (c2_1(a726)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1941, 206, 967, 162, 1935, 1929, 183])).
% 1.45/1.68 tff(1943,plain,
% 1.45/1.68 (((~hskp13) | c1_1(a726)) <=> ((~hskp13) | c1_1(a726))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1944,axiom,((~hskp13) | c1_1(a726)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.45/1.68 tff(1945,plain,
% 1.45/1.68 ((~hskp13) | c1_1(a726)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1944, 1943])).
% 1.45/1.68 tff(1946,plain,
% 1.45/1.68 ((~hskp13) | c1_1(a726)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1945, 1943])).
% 1.45/1.68 tff(1947,plain,
% 1.45/1.68 ((~hskp13) | c1_1(a726)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1946, 1943])).
% 1.45/1.68 tff(1948,plain,
% 1.45/1.68 ((~hskp13) | c1_1(a726)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1947, 1943])).
% 1.45/1.68 tff(1949,plain,
% 1.45/1.68 ((~hskp13) | c1_1(a726)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1948, 1943])).
% 1.45/1.68 tff(1950,plain,
% 1.45/1.68 (c1_1(a726)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1949, 1923])).
% 1.45/1.68 tff(1951,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c1_1(a764)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1952,plain,
% 1.45/1.68 ((hskp28 | (~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c1_1(a764)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1953,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c1_1(a764))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[1952])).
% 1.45/1.68 tff(1954,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c1_1(a764)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[1953, 1951])).
% 1.45/1.68 tff(1955,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(1956,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c1_1(a764))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1955, 1954])).
% 1.45/1.68 tff(1957,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1956, 206, 56, 1921, 1950, 1920, 1919, 1929, 571, 1942])).
% 1.45/1.68 tff(1958,plain,((~hskp13) | hskp28 | (~c1_1(a764)) | c2_1(a764) | c3_1(a764) | hskp27 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(1959,plain,
% 1.45/1.68 (~hskp13),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1958, 967, 1921, 1920, 1919, 56, 162])).
% 1.45/1.68 tff(1960,plain,
% 1.45/1.68 ((hskp20 | hskp13 | hskp12) <=> (hskp20 | hskp13 | hskp12)),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1961,plain,
% 1.45/1.68 (((hskp13 | hskp20) | hskp12) <=> (hskp20 | hskp13 | hskp12)),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1962,axiom,((hskp13 | hskp20) | hskp12), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 1.45/1.68 tff(1963,plain,
% 1.45/1.68 (hskp20 | hskp13 | hskp12),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1962, 1961])).
% 1.45/1.68 tff(1964,plain,
% 1.45/1.68 (hskp20 | hskp13 | hskp12),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1963, 1960])).
% 1.45/1.68 tff(1965,plain,
% 1.45/1.68 (hskp20 | hskp13 | hskp12),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1964, 1960])).
% 1.45/1.68 tff(1966,plain,
% 1.45/1.68 (hskp20 | hskp13 | hskp12),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1965, 1960])).
% 1.45/1.68 tff(1967,plain,
% 1.45/1.68 (hskp20 | hskp13 | hskp12),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1966, 1960])).
% 1.45/1.68 tff(1968,plain,
% 1.45/1.68 (hskp12),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1967, 1959, 250])).
% 1.45/1.68 tff(1969,plain,
% 1.45/1.68 (~c3_1(a725)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[124, 1968])).
% 1.45/1.68 tff(1970,plain,
% 1.45/1.68 (~c0_1(a725)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[136, 1968])).
% 1.45/1.68 tff(1971,plain,
% 1.45/1.68 (c2_1(a725)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[587, 206, 967, 162, 1970, 1969, 183])).
% 1.45/1.68 tff(1972,plain,
% 1.45/1.68 (~c1_1(a725)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[130, 1968])).
% 1.45/1.68 tff(1973,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a764)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1974,plain,
% 1.45/1.68 ((hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a764)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1975,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a764))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[1974])).
% 1.45/1.68 tff(1976,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a764)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[1975, 1973])).
% 1.45/1.68 tff(1977,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(1978,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a764))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1977, 1976])).
% 1.45/1.68 tff(1979,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1978, 206, 56, 1920, 1919, 1972, 1969, 309, 1971, 1922])).
% 1.45/1.68 tff(1980,plain,(hskp27 | hskp28 | c2_1(a764) | c3_1(a764) | hskp6 | hskp20 | (~c1_1(a764))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(1981,plain,
% 1.45/1.68 (hskp27),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1980, 284, 56, 278, 162, 250, 292])).
% 1.45/1.68 tff(1982,plain,
% 1.45/1.68 (c3_1(a691)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[232, 1981])).
% 1.45/1.68 tff(1983,plain,
% 1.45/1.68 (c0_1(a691)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[248, 1981])).
% 1.45/1.68 tff(1984,plain,
% 1.45/1.68 (c2_1(a691)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1686, 1982, 1983, 56])).
% 1.45/1.68 tff(1985,assumption,(c0_1(a764)), introduced(assumption)).
% 1.45/1.68 tff(1986,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1987,plain,
% 1.45/1.68 (((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726)) <=> (c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1988,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[1987])).
% 1.45/1.68 tff(1989,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[1988, 1986])).
% 1.45/1.68 tff(1990,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(1991,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1990, 1989])).
% 1.45/1.68 tff(1992,plain,
% 1.45/1.68 (c2_1(a726)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1991, 206, 1678, 1677, 1921, 1919, 1935, 1929, 1699, 1689, 1985])).
% 1.45/1.68 tff(1993,plain,
% 1.45/1.68 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 1.45/1.68 inference(bind,[status(th)],[])).
% 1.45/1.68 tff(1994,plain,
% 1.45/1.68 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.45/1.68 inference(quant_intro,[status(thm)],[1993])).
% 1.45/1.68 tff(1995,plain,
% 1.45/1.68 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(1996,plain,
% 1.45/1.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 1.45/1.68 inference(bind,[status(th)],[])).
% 1.45/1.68 tff(1997,plain,
% 1.45/1.68 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.45/1.68 inference(quant_intro,[status(thm)],[1996])).
% 1.45/1.68 tff(1998,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 1.45/1.68 tff(1999,plain,
% 1.45/1.68 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 1.45/1.68 tff(2000,plain,
% 1.45/1.68 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1999, 1995])).
% 1.45/1.68 tff(2001,plain,(
% 1.45/1.68 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.45/1.68 inference(skolemize,[status(sab)],[2000])).
% 1.45/1.68 tff(2002,plain,
% 1.45/1.68 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2001, 1994])).
% 1.45/1.68 tff(2003,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2004,plain,
% 1.45/1.68 ((hskp20 | (~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726))) <=> (hskp20 | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2005,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[2004])).
% 1.45/1.68 tff(2006,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[2005, 2003])).
% 1.45/1.68 tff(2007,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(2008,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2007, 2006])).
% 1.45/1.68 tff(2009,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2008, 206, 250, 1678, 1677, 1950, 1929, 2002, 1689, 1992])).
% 1.45/1.68 tff(2010,plain,((~hskp13) | hskp20 | (~c0_1(a691)) | (~c3_1(a691)) | (~c2_1(a691)) | (~c1_1(a764)) | c3_1(a764) | (~c0_1(a764))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(2011,plain,
% 1.45/1.68 (~hskp13),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2010, 1983, 250, 1982, 1984, 292, 278, 299])).
% 1.45/1.68 tff(2012,plain,
% 1.45/1.68 (hskp12),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1967, 2011, 250])).
% 1.45/1.68 tff(2013,plain,
% 1.45/1.68 (~c0_1(a725)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[136, 2012])).
% 1.45/1.68 tff(2014,plain,
% 1.45/1.68 (~c1_1(a725)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[130, 2012])).
% 1.45/1.68 tff(2015,plain,
% 1.45/1.68 (c2_1(a691)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1686, 1677, 1678, 56])).
% 1.45/1.68 tff(2016,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2017,plain,
% 1.45/1.68 (((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a725) | c2_1(a725) | c0_1(a725)) <=> (c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2018,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[2017])).
% 1.45/1.68 tff(2019,plain,
% 1.45/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[2018, 2016])).
% 1.45/1.68 tff(2020,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a725) | c2_1(a725) | c0_1(a725))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(2021,plain,
% 1.45/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[2020, 2019])).
% 1.45/1.68 tff(2022,plain,
% 1.45/1.68 (c2_1(a725)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2021, 206, 1678, 1677, 1921, 1919, 524, 968, 1699, 2015, 1985])).
% 1.45/1.68 tff(2023,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1978, 206, 56, 1920, 1919, 523, 968, 309, 2022, 1985])).
% 1.45/1.68 tff(2024,plain,(c3_1(a725) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | (~c0_1(a764)) | (~c0_1(a691)) | (~c3_1(a691)) | (~c1_1(a764)) | c0_1(a725)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(2025,plain,
% 1.45/1.68 (c3_1(a725)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2024, 523, 1920, 1919, 56, 1985, 1678, 1677, 1921, 524])).
% 1.45/1.68 tff(2026,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | c2_1(a725))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | c2_1(a725))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2027,plain,
% 1.45/1.68 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a725) | c2_1(a725) | (~c3_1(a725))) <=> (hskp28 | c0_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | c2_1(a725))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(2028,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a725) | c2_1(a725) | (~c3_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | c2_1(a725)))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[2027])).
% 1.45/1.68 tff(2029,plain,
% 1.45/1.68 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a725) | c2_1(a725) | (~c3_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | c2_1(a725))),
% 1.45/1.68 inference(transitivity,[status(thm)],[2028, 2026])).
% 1.45/1.68 tff(2030,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a725) | c2_1(a725) | (~c3_1(a725)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(2031,plain,
% 1.45/1.68 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | c2_1(a725)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2030, 2029])).
% 1.45/1.69 tff(2032,plain,
% 1.45/1.69 ((~c3_1(a725)) | c2_1(a725)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2031, 206, 56, 1652, 1644, 1636, 524, 1838])).
% 1.45/1.69 tff(2033,plain,
% 1.45/1.69 (c2_1(a725)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2032, 2025])).
% 1.45/1.69 tff(2034,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a725) | c1_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a725) | c1_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2035,plain,
% 1.45/1.69 (((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a725) | (~c2_1(a725)) | (~c3_1(a725)) | c0_1(a725) | (~c3_1(a725)) | (~c2_1(a725))) <=> (c2_1(a764) | c3_1(a764) | c0_1(a725) | c1_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2036,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a725) | (~c2_1(a725)) | (~c3_1(a725)) | c0_1(a725) | (~c3_1(a725)) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a725) | c1_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[2035])).
% 1.45/1.69 tff(2037,plain,
% 1.45/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a725) | (~c2_1(a725)) | (~c3_1(a725)) | c0_1(a725) | (~c3_1(a725)) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a725) | c1_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[2036, 2034])).
% 1.45/1.69 tff(2038,plain,
% 1.45/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a725) | (~c2_1(a725)) | (~c3_1(a725)) | c0_1(a725) | (~c3_1(a725)) | (~c2_1(a725)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(2039,plain,
% 1.45/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a725) | c1_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2038, 2037])).
% 1.45/1.69 tff(2040,plain,
% 1.45/1.69 ((~c3_1(a725)) | (~c2_1(a725))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2039, 206, 1921, 1920, 1919, 524, 523, 10])).
% 1.45/1.69 tff(2041,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2040, 2033, 2025])).
% 1.45/1.69 tff(2042,plain,(c1_1(a725) | (~c1_1(a764)) | c2_1(a764) | c3_1(a764) | c0_1(a725) | hskp28 | (~c0_1(a764)) | (~c0_1(a691)) | (~c3_1(a691))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(2043,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2042, 2014, 2013, 284, 278, 292, 56, 299, 1983, 1982])).
% 1.45/1.69 tff(2044,plain,((~hskp24) | hskp28 | hskp20 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(2045,plain,
% 1.45/1.69 (~hskp24),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2044, 1918, 56, 162])).
% 1.45/1.69 tff(2046,plain,
% 1.45/1.69 (c2_1(a691)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1686, 233, 249, 56])).
% 1.45/1.69 tff(2047,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[994, 206, 390, 426, 249, 241, 148, 2046])).
% 1.45/1.69 tff(2048,plain,((~hskp27) | hskp24 | hskp23 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(2049,plain,
% 1.45/1.69 (~hskp27),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2048, 426, 390, 56])).
% 1.45/1.69 tff(2050,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[892, 206, 967, 162, 1291, 1290, 1289, 183])).
% 1.45/1.69 tff(2051,plain,((~hskp4) | hskp27 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(2052,plain,
% 1.45/1.69 (~hskp4),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2051, 2049, 162])).
% 1.45/1.69 tff(2053,plain,
% 1.45/1.69 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2054,plain,
% 1.45/1.69 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a733)) | (~c0_1(a733)) | (~c1_1(a733))) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2055,plain,
% 1.45/1.69 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a733)) | (~c0_1(a733)) | (~c1_1(a733)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a733)) | (~c1_1(a733)) | (~c2_1(a733))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[2054])).
% 1.45/1.69 tff(2056,plain,
% 1.45/1.69 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a733)) | (~c0_1(a733)) | (~c1_1(a733)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[2055, 2053])).
% 1.45/1.69 tff(2057,plain,
% 1.45/1.69 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a733)) | (~c0_1(a733)) | (~c1_1(a733)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(2058,plain,
% 1.45/1.69 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a733)) | (~c1_1(a733)) | (~c2_1(a733))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 1.45/1.69 tff(2059,plain,
% 1.45/1.69 (hskp24 | hskp23 | (~c0_1(a733))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2058, 206, 1652, 1644, 148])).
% 1.45/1.69 tff(2060,plain,
% 1.45/1.69 (~c0_1(a733)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2059, 426, 390])).
% 1.45/1.69 tff(2061,plain,
% 1.45/1.69 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.45/1.69 inference(bind,[status(th)],[])).
% 1.45/1.69 tff(2062,plain,
% 1.45/1.69 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.45/1.69 inference(quant_intro,[status(thm)],[2061])).
% 1.45/1.69 tff(2063,plain,
% 1.45/1.69 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2064,plain,
% 1.45/1.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.45/1.69 inference(bind,[status(th)],[])).
% 1.45/1.69 tff(2065,plain,
% 1.45/1.69 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.45/1.69 inference(quant_intro,[status(thm)],[2064])).
% 1.45/1.69 tff(2066,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.45/1.69 tff(2067,plain,
% 1.45/1.69 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2066, 2065])).
% 1.45/1.69 tff(2068,plain,
% 1.45/1.69 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2067, 2063])).
% 1.45/1.69 tff(2069,plain,(
% 1.45/1.69 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.45/1.69 inference(skolemize,[status(sab)],[2068])).
% 1.45/1.69 tff(2070,plain,
% 1.45/1.69 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[2069, 2062])).
% 1.45/1.69 tff(2071,plain,
% 1.45/1.69 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.45/1.69 inference(bind,[status(th)],[])).
% 1.45/1.69 tff(2072,plain,
% 1.45/1.69 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.45/1.69 inference(quant_intro,[status(thm)],[2071])).
% 1.45/1.69 tff(2073,plain,
% 1.45/1.69 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(2074,plain,
% 1.45/1.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(2075,plain,
% 1.53/1.69 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[2074])).
% 1.53/1.69 tff(2076,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 1.53/1.69 tff(2077,plain,
% 1.53/1.69 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2076, 2075])).
% 1.53/1.69 tff(2078,plain,
% 1.53/1.69 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2077, 2073])).
% 1.53/1.69 tff(2079,plain,(
% 1.53/1.69 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.53/1.69 inference(skolemize,[status(sab)],[2078])).
% 1.53/1.69 tff(2080,plain,
% 1.53/1.69 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2079, 2072])).
% 1.53/1.69 tff(2081,plain,
% 1.53/1.69 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(2082,plain,
% 1.53/1.69 ((hskp11 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733))) <=> (hskp11 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(2083,plain,
% 1.53/1.69 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733))))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[2082])).
% 1.53/1.69 tff(2084,plain,
% 1.53/1.69 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)))),
% 1.53/1.69 inference(transitivity,[status(thm)],[2083, 2081])).
% 1.53/1.69 tff(2085,plain,
% 1.53/1.69 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733)))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(2086,plain,
% 1.53/1.69 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2085, 2084])).
% 1.53/1.69 tff(2087,plain,
% 1.53/1.69 (hskp11),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2086, 206, 1644, 1636, 165, 1917, 163, 2080, 2060])).
% 1.53/1.69 tff(2088,plain,
% 1.53/1.69 (((~hskp11) | (~c1_1(a722))) <=> ((~hskp11) | (~c1_1(a722)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(2089,plain,
% 1.53/1.69 (((~c1_1(a722)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a722)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(2090,axiom,((~c1_1(a722)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.53/1.69 tff(2091,plain,
% 1.53/1.69 ((~hskp11) | (~c1_1(a722))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2090, 2089])).
% 1.53/1.69 tff(2092,plain,
% 1.53/1.69 ((~hskp11) | (~c1_1(a722))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2091, 2088])).
% 1.53/1.69 tff(2093,plain,
% 1.53/1.69 (~c1_1(a722)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2092, 2087])).
% 1.53/1.69 tff(2094,plain,
% 1.53/1.69 (((~hskp11) | c0_1(a722)) <=> ((~hskp11) | c0_1(a722))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(2095,axiom,((~hskp11) | c0_1(a722)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.53/1.69 tff(2096,plain,
% 1.53/1.69 ((~hskp11) | c0_1(a722)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2095, 2094])).
% 1.53/1.69 tff(2097,plain,
% 1.53/1.69 ((~hskp11) | c0_1(a722)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2096, 2094])).
% 1.53/1.69 tff(2098,plain,
% 1.53/1.69 ((~hskp11) | c0_1(a722)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2097, 2094])).
% 1.53/1.69 tff(2099,plain,
% 1.53/1.69 ((~hskp11) | c0_1(a722)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2098, 2094])).
% 1.53/1.69 tff(2100,plain,
% 1.53/1.69 ((~hskp11) | c0_1(a722)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2099, 2094])).
% 1.53/1.69 tff(2101,plain,
% 1.53/1.69 (c0_1(a722)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2100, 2087])).
% 1.53/1.69 tff(2102,plain,
% 1.53/1.69 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c2_1(a722) | (~c0_1(a722)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c2_1(a722) | (~c0_1(a722)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(2103,plain,
% 1.53/1.69 ((hskp4 | (~ndr1_0) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733))) <=> (hskp4 | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c2_1(a722) | (~c0_1(a722)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(2104,plain,
% 1.53/1.69 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c2_1(a722) | (~c0_1(a722))))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[2103])).
% 1.53/1.69 tff(2105,plain,
% 1.53/1.69 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c2_1(a722) | (~c0_1(a722)))),
% 1.53/1.69 inference(transitivity,[status(thm)],[2104, 2102])).
% 1.53/1.69 tff(2106,plain,
% 1.53/1.69 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(2107,plain,
% 1.53/1.69 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c2_1(a722) | (~c0_1(a722))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 1.53/1.69 tff(2108,plain,
% 1.53/1.69 (hskp4 | c2_1(a722)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2107, 206, 1652, 1636, 2101, 2093, 2070, 2060])).
% 1.53/1.69 tff(2109,plain,
% 1.53/1.69 (c2_1(a722)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2108, 2052])).
% 1.53/1.69 tff(2110,assumption,(c0_1(a754)), introduced(assumption)).
% 1.53/1.69 tff(2111,plain,
% 1.53/1.69 (c1_1(a693) | (~c2_1(a693))),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[579, 206, 56, 165, 2110, 163, 138, 309])).
% 1.53/1.69 tff(2112,plain,
% 1.53/1.69 (~c2_1(a693)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2111, 149])).
% 1.53/1.69 tff(2113,plain,
% 1.53/1.69 (~hskp1),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[344, 2112])).
% 1.53/1.69 tff(2114,assumption,(~hskp0), introduced(assumption)).
% 1.53/1.69 tff(2115,plain,
% 1.53/1.69 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(2116,plain,
% 1.53/1.69 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | c0_1(a693)) <=> (hskp1 | hskp0 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(2117,plain,
% 1.53/1.69 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | c0_1(a693))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693)))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[2116])).
% 1.53/1.69 tff(2118,plain,
% 1.53/1.69 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | c0_1(a693))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.53/1.69 inference(transitivity,[status(thm)],[2117, 2115])).
% 1.53/1.69 tff(2119,plain,
% 1.53/1.69 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | c0_1(a693))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(2120,plain,
% 1.53/1.69 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2119, 2118])).
% 1.53/1.69 tff(2121,plain,
% 1.53/1.69 (hskp1 | hskp0 | c1_1(a693) | c0_1(a693)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2120, 206, 138, 1413])).
% 1.53/1.69 tff(2122,plain,
% 1.53/1.69 (c0_1(a693)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[2121, 2114, 149, 2113])).
% 1.53/1.69 tff(2123,plain,
% 1.53/1.69 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(2124,plain,
% 1.53/1.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[2123])).
% 1.53/1.69 tff(2125,plain,
% 1.53/1.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(2126,plain,
% 1.53/1.69 (^[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)) | (~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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(2127,plain,
% 1.53/1.69 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[2126])).
% 1.53/1.69 tff(2128,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.53/1.69 tff(2129,plain,
% 1.53/1.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 1.53/1.69 tff(2130,plain,
% 1.53/1.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2129, 2125])).
% 1.53/1.69 tff(2131,plain,(
% 1.53/1.69 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.53/1.69 inference(skolemize,[status(sab)],[2130])).
% 1.53/1.69 tff(2132,plain,
% 1.53/1.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[2131, 2124])).
% 1.53/1.69 tff(2133,assumption,(c0_1(a693)), introduced(assumption)).
% 1.53/1.69 tff(2134,assumption,(~hskp3), introduced(assumption)).
% 1.53/1.69 tff(2135,plain,
% 1.53/1.69 (^[U: $i] : refl((hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(2136,plain,
% 1.53/1.69 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[2135])).
% 1.53/1.69 tff(2137,plain,
% 1.53/1.69 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(2138,plain,
% 1.53/1.69 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp3) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp3))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp3) <=> (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp3) <=> (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(2139,plain,
% 1.53/1.70 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp3) <=> ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[2138])).
% 1.53/1.70 tff(2140,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 1.53/1.70 tff(2141,plain,
% 1.53/1.70 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 1.53/1.70 tff(2142,plain,
% 1.53/1.70 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2141, 2137])).
% 1.53/1.70 tff(2143,plain,(
% 1.53/1.70 ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.70 inference(skolemize,[status(sab)],[2142])).
% 1.53/1.70 tff(2144,plain,
% 1.53/1.70 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2143, 2136])).
% 1.53/1.70 tff(2145,plain,
% 1.53/1.70 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp14 | hskp3 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp14 | hskp3 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2146,plain,
% 1.53/1.70 ((hskp14 | hskp3 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693))) <=> (hskp14 | hskp3 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2147,plain,
% 1.53/1.70 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp14 | hskp3 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2146])).
% 1.53/1.70 tff(2148,plain,
% 1.53/1.70 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp14 | hskp3 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2147, 2145])).
% 1.53/1.70 tff(2149,plain,
% 1.53/1.70 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2150,plain,
% 1.53/1.70 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp14 | hskp3 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2149, 2148])).
% 1.53/1.70 tff(2151,plain,
% 1.53/1.70 (hskp14 | hskp3 | c1_1(a693) | (~c0_1(a693))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2150, 206, 138, 2144])).
% 1.53/1.70 tff(2152,plain,
% 1.53/1.70 (hskp14),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2151, 2134, 149, 2133])).
% 1.53/1.70 tff(2153,plain,
% 1.53/1.70 (~c3_1(a730)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[438, 2152])).
% 1.53/1.70 tff(2154,plain,
% 1.53/1.70 (c0_1(a730)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[424, 2152])).
% 1.53/1.70 tff(2155,assumption,(c3_1(a733)), introduced(assumption)).
% 1.53/1.70 tff(2156,assumption,(c2_1(a733)), introduced(assumption)).
% 1.53/1.70 tff(2157,assumption,(c1_1(a733)), introduced(assumption)).
% 1.53/1.70 tff(2158,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a730)) | (~c2_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a730)) | (~c2_1(a730)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2159,plain,
% 1.53/1.70 ((hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c0_1(a730))) <=> (hskp3 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a730)) | (~c2_1(a730)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2160,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c0_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a730)) | (~c2_1(a730))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2159])).
% 1.53/1.70 tff(2161,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c0_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a730)) | (~c2_1(a730)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2160, 2158])).
% 1.53/1.70 tff(2162,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c0_1(a730)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2163,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a730)) | (~c2_1(a730))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 1.53/1.70 tff(2164,plain,
% 1.53/1.70 (~c2_1(a730)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2163, 206, 2134, 2157, 2156, 2155, 2154, 2153, 2132])).
% 1.53/1.70 tff(2165,assumption,(~c2_1(a693)), introduced(assumption)).
% 1.53/1.70 tff(2166,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c2_1(a754) | c2_1(a693) | (~c0_1(a754)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a754) | c2_1(a693) | (~c0_1(a754)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c1_1(a754)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2167,plain,
% 1.53/1.70 ((hskp3 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c3_1(a693) | c1_1(a693) | c2_1(a693)) <=> (hskp3 | c2_1(a754) | c2_1(a693) | (~c0_1(a754)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c1_1(a754)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2168,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c3_1(a693) | c1_1(a693) | c2_1(a693))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c2_1(a754) | c2_1(a693) | (~c0_1(a754)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c1_1(a754))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2167])).
% 1.53/1.70 tff(2169,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c3_1(a693) | c1_1(a693) | c2_1(a693))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a754) | c2_1(a693) | (~c0_1(a754)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c1_1(a754)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2168, 2166])).
% 1.53/1.70 tff(2170,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c3_1(a693) | c1_1(a693) | c2_1(a693))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2171,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a754) | c2_1(a693) | (~c0_1(a754)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c1_1(a754))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2170, 2169])).
% 1.53/1.70 tff(2172,plain,
% 1.53/1.70 (hskp3 | c2_1(a693) | c1_1(a693) | (~c1_1(a754))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2171, 206, 165, 2110, 138, 1602])).
% 1.53/1.70 tff(2173,plain,
% 1.53/1.70 (~c1_1(a754)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2172, 2134, 149, 2165])).
% 1.53/1.70 tff(2174,plain,
% 1.53/1.70 (c1_1(a730)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[416, 2152])).
% 1.53/1.70 tff(2175,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c2_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | c2_1(a730) | c1_1(a754))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | c2_1(a730) | c1_1(a754))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2176,plain,
% 1.53/1.70 ((hskp3 | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c3_1(a754) | c1_1(a754) | c2_1(a754)) <=> (hskp3 | c2_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | c2_1(a730) | c1_1(a754))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2177,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c3_1(a754) | c1_1(a754) | c2_1(a754))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c2_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | c2_1(a730) | c1_1(a754)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2176])).
% 1.53/1.70 tff(2178,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c3_1(a754) | c1_1(a754) | c2_1(a754))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | c2_1(a730) | c1_1(a754))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2177, 2175])).
% 1.53/1.70 tff(2179,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c3_1(a754) | c1_1(a754) | c2_1(a754))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2180,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | c2_1(a730) | c1_1(a754)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2179, 2178])).
% 1.53/1.70 tff(2181,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2180, 206, 2134, 165, 2154, 2174, 163, 1602, 2173, 2164])).
% 1.53/1.70 tff(2182,plain,(hskp3 | c2_1(a754) | c3_1(a754) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a733)) | c1_1(a693) | (~c0_1(a693)) | c3_1(a693) | c2_1(a693) | (~c0_1(a754))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2183,plain,
% 1.53/1.70 (hskp3),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2182, 2122, 163, 1652, 1644, 1636, 149, 165, 138, 2112, 2110])).
% 1.53/1.70 tff(2184,plain,
% 1.53/1.70 (~c3_1(a697)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1286, 2183])).
% 1.53/1.70 tff(2185,plain,
% 1.53/1.70 (c2_1(a697)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[473, 2183])).
% 1.53/1.70 tff(2186,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2187,plain,
% 1.53/1.70 ((hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697))) <=> (hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2188,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | c1_1(a697) | (~c2_1(a697))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2187])).
% 1.53/1.70 tff(2189,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2188, 2186])).
% 1.53/1.70 tff(2190,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2191,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | c1_1(a697) | (~c2_1(a697))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2190, 2189])).
% 1.53/1.70 tff(2192,plain,
% 1.53/1.70 (c1_1(a697)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2191, 206, 56, 165, 2185, 2110, 163, 2184, 309])).
% 1.53/1.70 tff(2193,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a754)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2194,plain,
% 1.53/1.70 ((hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a754) | c2_1(a754) | (~c1_1(a754))) <=> (hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a754)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2195,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a754))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2194])).
% 1.53/1.70 tff(2196,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a754)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2195, 2193])).
% 1.53/1.70 tff(2197,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2198,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a754))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2197, 2196])).
% 1.53/1.70 tff(2199,plain,
% 1.53/1.70 ((~c1_1(a697)) | (~c1_1(a754))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2198, 206, 56, 165, 2185, 163, 2184, 571])).
% 1.53/1.70 tff(2200,plain,
% 1.53/1.70 (~c1_1(a754)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2199, 2192])).
% 1.53/1.70 tff(2201,plain,
% 1.53/1.70 (~hskp20),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[541, 2110])).
% 1.53/1.70 tff(2202,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a697)) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a697)) | (~c2_1(a697)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2203,plain,
% 1.53/1.70 ((hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697))) <=> (hskp20 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a697)) | (~c2_1(a697)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2204,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a697)) | (~c2_1(a697))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2203])).
% 1.53/1.70 tff(2205,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a697)) | (~c2_1(a697)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2204, 2202])).
% 1.53/1.70 tff(2206,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2207,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a697)) | (~c2_1(a697))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2206, 2205])).
% 1.53/1.70 tff(2208,plain,
% 1.53/1.70 ((~c0_1(a733)) | (~c1_1(a697))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2207, 206, 2201, 1644, 1636, 2185, 2184, 2002])).
% 1.53/1.70 tff(2209,plain,
% 1.53/1.70 (~c0_1(a733)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2208, 2192])).
% 1.53/1.70 tff(2210,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c2_1(a754) | (~c0_1(a754)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c1_1(a754))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c2_1(a754) | (~c0_1(a754)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c1_1(a754))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2211,plain,
% 1.53/1.70 ((hskp4 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733))) <=> (hskp4 | c2_1(a754) | (~c0_1(a754)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c1_1(a754))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2212,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c2_1(a754) | (~c0_1(a754)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c1_1(a754)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2211])).
% 1.53/1.70 tff(2213,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c2_1(a754) | (~c0_1(a754)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c1_1(a754))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2212, 2210])).
% 1.53/1.70 tff(2214,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2215,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c2_1(a754) | (~c0_1(a754)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c1_1(a754)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2214, 2213])).
% 1.53/1.70 tff(2216,plain,
% 1.53/1.70 (hskp4),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2215, 206, 1652, 1636, 165, 2110, 2070, 2200, 2209])).
% 1.53/1.70 tff(2217,plain,
% 1.53/1.70 (~c3_1(a698)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[976, 2216])).
% 1.53/1.70 tff(2218,plain,
% 1.53/1.70 (~c2_1(a698)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[854, 2216])).
% 1.53/1.70 tff(2219,plain,
% 1.53/1.70 (~c0_1(a698)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[848, 2216])).
% 1.53/1.70 tff(2220,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c1_1(a754))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2221,plain,
% 1.53/1.70 (((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a698) | c2_1(a698) | c0_1(a698)) <=> (c2_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c1_1(a754))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2222,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c1_1(a754)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2221])).
% 1.53/1.70 tff(2223,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c1_1(a754))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2222, 2220])).
% 1.53/1.70 tff(2224,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a698) | c2_1(a698) | c0_1(a698))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2225,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c1_1(a754)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2224, 2223])).
% 1.53/1.70 tff(2226,plain,
% 1.53/1.70 (~c1_1(a698)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2225, 206, 165, 163, 2219, 2218, 2217, 110, 2200])).
% 1.53/1.70 tff(2227,plain,
% 1.53/1.70 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2228,plain,
% 1.53/1.70 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a698) | c1_1(a698) | c0_1(a698)) <=> (hskp1 | hskp0 | c0_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2229,plain,
% 1.53/1.70 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a698) | c1_1(a698) | c0_1(a698))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2228])).
% 1.53/1.70 tff(2230,plain,
% 1.53/1.70 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a698) | c1_1(a698) | c0_1(a698))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2229, 2227])).
% 1.53/1.70 tff(2231,plain,
% 1.53/1.70 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a698) | c1_1(a698) | c0_1(a698))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2232,plain,
% 1.53/1.70 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 1.53/1.70 tff(2233,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2232, 206, 2113, 2114, 2219, 2217, 1413, 2226])).
% 1.53/1.70 tff(2234,plain,(hskp0 | c2_1(a754) | c3_1(a754) | (~c0_1(a754)) | hskp28 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2235,plain,
% 1.53/1.70 (hskp0),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2234, 149, 163, 1917, 56, 165, 138])).
% 1.53/1.70 tff(2236,plain,
% 1.53/1.70 (~c1_1(a692)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[787, 2235])).
% 1.53/1.70 tff(2237,plain,
% 1.53/1.70 (~c0_1(a692)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[793, 2235])).
% 1.53/1.70 tff(2238,plain,
% 1.53/1.70 (c2_1(a692)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[803, 2235])).
% 1.53/1.70 tff(2239,plain,
% 1.53/1.70 (c1_1(a693) | (~c2_1(a693))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[579, 206, 56, 165, 1917, 163, 138, 309])).
% 1.53/1.71 tff(2240,plain,
% 1.53/1.71 (~c2_1(a693)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2239, 149])).
% 1.53/1.71 tff(2241,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a693) | c1_1(a693) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a693) | c1_1(a693) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a693)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2242,plain,
% 1.53/1.71 ((hskp28 | (~ndr1_0) | c1_1(a693) | c2_1(a693) | (~c0_1(a693)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692))) <=> (hskp28 | c2_1(a693) | c1_1(a693) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a693)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2243,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a693) | c2_1(a693) | (~c0_1(a693)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a693) | c1_1(a693) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a693))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2242])).
% 1.53/1.71 tff(2244,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a693) | c2_1(a693) | (~c0_1(a693)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a693) | c1_1(a693) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a693)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2243, 2241])).
% 1.53/1.71 tff(2245,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a693) | c2_1(a693) | (~c0_1(a693)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2246,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a693) | c1_1(a693) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a693))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2245, 2244])).
% 1.53/1.71 tff(2247,plain,
% 1.53/1.71 (~c0_1(a693)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2246, 206, 56, 2240, 2238, 149, 2237, 2236, 359])).
% 1.53/1.71 tff(2248,plain,
% 1.53/1.71 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2249,plain,
% 1.53/1.71 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693)) <=> (hskp27 | hskp6 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2250,plain,
% 1.53/1.71 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2249])).
% 1.53/1.71 tff(2251,plain,
% 1.53/1.71 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2250, 2248])).
% 1.53/1.71 tff(2252,plain,
% 1.53/1.71 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2253,plain,
% 1.53/1.71 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2252, 2251])).
% 1.53/1.71 tff(2254,plain,
% 1.53/1.71 (hskp27 | c2_1(a693) | c0_1(a693)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2253, 206, 162, 138, 183])).
% 1.53/1.71 tff(2255,plain,
% 1.53/1.71 (hskp27),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2254, 2247, 2240])).
% 1.53/1.71 tff(2256,plain,
% 1.53/1.71 (c0_1(a691)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[248, 2255])).
% 1.53/1.71 tff(2257,plain,
% 1.53/1.71 (c3_1(a691)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[232, 2255])).
% 1.53/1.71 tff(2258,plain,
% 1.53/1.71 (c2_1(a691)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1686, 2257, 2256, 56])).
% 1.53/1.71 tff(2259,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a693) | (~c0_1(a754)) | c3_1(a754) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a693) | (~c0_1(a754)) | c3_1(a754) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2260,plain,
% 1.53/1.71 (((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a693) | c2_1(a693) | c0_1(a693)) <=> (c2_1(a693) | (~c0_1(a754)) | c3_1(a754) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2261,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a693) | c2_1(a693) | c0_1(a693))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a693) | (~c0_1(a754)) | c3_1(a754) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2260])).
% 1.53/1.71 tff(2262,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a693) | c2_1(a693) | c0_1(a693))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a693) | (~c0_1(a754)) | c3_1(a754) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2261, 2259])).
% 1.53/1.71 tff(2263,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a693) | c2_1(a693) | c0_1(a693))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2264,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a693) | (~c0_1(a754)) | c3_1(a754) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2263, 2262])).
% 1.53/1.71 tff(2265,plain,
% 1.53/1.71 (~c1_1(a754)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2264, 206, 2256, 2257, 2240, 1917, 163, 138, 1699, 2258, 2247])).
% 1.53/1.71 tff(2266,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a754) | (~c0_1(a754)) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c1_1(a754))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c1_1(a754))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2267,plain,
% 1.53/1.71 ((hskp28 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692))) <=> (hskp28 | c2_1(a754) | (~c0_1(a754)) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c1_1(a754))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2268,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a754) | (~c0_1(a754)) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c1_1(a754)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2267])).
% 1.53/1.71 tff(2269,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c1_1(a754))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2268, 2266])).
% 1.53/1.71 tff(2270,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2271,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c1_1(a754)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 1.53/1.71 tff(2272,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2271, 206, 56, 165, 2238, 1917, 2237, 2236, 359, 2265])).
% 1.53/1.71 tff(2273,plain,(c1_1(a693) | hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a693) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2274,plain,
% 1.53/1.71 (c1_1(a693)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2273, 138, 165, 163, 56, 162])).
% 1.53/1.71 tff(2275,plain,
% 1.53/1.71 (((~hskp11) | c3_1(a722)) <=> ((~hskp11) | c3_1(a722))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2276,axiom,((~hskp11) | c3_1(a722)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.53/1.71 tff(2277,plain,
% 1.53/1.71 ((~hskp11) | c3_1(a722)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2276, 2275])).
% 1.53/1.71 tff(2278,plain,
% 1.53/1.71 ((~hskp11) | c3_1(a722)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2277, 2275])).
% 1.53/1.71 tff(2279,plain,
% 1.53/1.71 ((~hskp11) | c3_1(a722)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2278, 2275])).
% 1.53/1.71 tff(2280,plain,
% 1.53/1.71 ((~hskp11) | c3_1(a722)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2279, 2275])).
% 1.53/1.71 tff(2281,plain,
% 1.53/1.71 ((~hskp11) | c3_1(a722)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2280, 2275])).
% 1.53/1.71 tff(2282,plain,
% 1.53/1.71 (c3_1(a722)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2281, 2087])).
% 1.53/1.71 tff(2283,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a693) | c1_1(a722) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a693) | c1_1(a722) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2284,plain,
% 1.53/1.71 (((~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733))) <=> (c2_1(a693) | c1_1(a722) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2285,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a693) | c1_1(a722) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2284])).
% 1.53/1.71 tff(2286,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a693) | c1_1(a722) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2285, 2283])).
% 1.53/1.71 tff(2287,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2288,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a693) | c1_1(a722) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2287, 2286])).
% 1.53/1.71 tff(2289,plain,
% 1.53/1.71 (c2_1(a693) | (~c2_1(a722))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2288, 206, 1644, 1636, 2282, 2093, 2274, 138, 10, 2060])).
% 1.53/1.71 tff(2290,plain,
% 1.53/1.71 (c2_1(a693)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2289, 2109])).
% 1.53/1.71 tff(2291,plain,
% 1.53/1.71 (hskp24 | hskp23 | (~c0_1(a693)) | (~c2_1(a693))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1399, 206, 2274, 148])).
% 1.53/1.71 tff(2292,plain,
% 1.53/1.71 (~c0_1(a693)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2291, 2290, 390, 426])).
% 1.53/1.71 tff(2293,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c0_1(a693) | (~c2_1(a693)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2294,plain,
% 1.53/1.71 ((hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693))) <=> (hskp10 | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c0_1(a693) | (~c2_1(a693)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2295,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c0_1(a693) | (~c2_1(a693))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2294])).
% 1.53/1.71 tff(2296,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c0_1(a693) | (~c2_1(a693)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2295, 2293])).
% 1.53/1.71 tff(2297,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2298,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c0_1(a693) | (~c2_1(a693))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2297, 2296])).
% 1.53/1.71 tff(2299,plain,
% 1.53/1.71 (c0_1(a693) | (~c2_1(a693))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2298, 206, 1847, 1652, 1636, 138, 1671, 2060])).
% 1.53/1.71 tff(2300,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2299, 2292, 2290])).
% 1.53/1.71 tff(2301,plain,(hskp23 | c3_1(a693) | hskp24 | hskp6 | c2_1(a754) | c3_1(a754) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2302,plain,
% 1.53/1.71 (hskp23),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2301, 138, 2045, 162, 165, 163, 56])).
% 1.53/1.71 tff(2303,plain,
% 1.53/1.71 (~hskp1),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1354, 2274])).
% 1.53/1.71 tff(2304,assumption,(~hskp1), introduced(assumption)).
% 1.53/1.71 tff(2305,plain,
% 1.53/1.71 (~hskp0),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1739, 372, 56, 380, 366])).
% 1.53/1.71 tff(2306,assumption,(hskp12), introduced(assumption)).
% 1.53/1.71 tff(2307,plain,
% 1.53/1.71 (~c3_1(a725)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[124, 2306])).
% 1.53/1.71 tff(2308,plain,
% 1.53/1.71 (~c1_1(a725)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[130, 2306])).
% 1.53/1.71 tff(2309,plain,
% 1.53/1.71 (~c0_1(a725)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[136, 2306])).
% 1.53/1.71 tff(2310,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1419, 206, 2304, 2114, 2309, 2308, 2307, 1413])).
% 1.53/1.71 tff(2311,plain,((~hskp12) | hskp1 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2312,plain,
% 1.53/1.71 (~hskp12),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2311, 2305, 2304])).
% 1.53/1.71 tff(2313,plain,
% 1.53/1.71 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(2314,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[2313])).
% 1.53/1.71 tff(2315,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2316,plain,
% 1.53/1.71 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(2317,plain,
% 1.53/1.71 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[2316])).
% 1.53/1.71 tff(2318,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.53/1.71 tff(2319,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2318, 2317])).
% 1.53/1.71 tff(2320,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2319, 2315])).
% 1.53/1.71 tff(2321,plain,(
% 1.53/1.71 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.53/1.71 inference(skolemize,[status(sab)],[2320])).
% 1.53/1.71 tff(2322,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2321, 2314])).
% 1.53/1.71 tff(2323,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | c2_1(a754) | c1_1(a763) | c2_1(a763) | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp12 | c2_1(a754) | c1_1(a763) | c2_1(a763) | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c0_1(a763)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2324,plain,
% 1.53/1.71 ((hskp12 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763))) <=> (hskp12 | c2_1(a754) | c1_1(a763) | c2_1(a763) | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c0_1(a763)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2325,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | c2_1(a754) | c1_1(a763) | c2_1(a763) | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c0_1(a763))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2324])).
% 1.53/1.71 tff(2326,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp12 | c2_1(a754) | c1_1(a763) | c2_1(a763) | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c0_1(a763)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2325, 2323])).
% 1.53/1.71 tff(2327,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2328,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp12 | c2_1(a754) | c1_1(a763) | c2_1(a763) | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c0_1(a763))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2327, 2326])).
% 1.53/1.71 tff(2329,plain,
% 1.53/1.71 (hskp12 | (~c1_1(a754))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2328, 206, 380, 165, 372, 366, 2110, 2322])).
% 1.53/1.71 tff(2330,plain,
% 1.53/1.71 (~c1_1(a754)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2329, 2312])).
% 1.53/1.71 tff(2331,plain,
% 1.53/1.71 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(2332,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[2331])).
% 1.53/1.71 tff(2333,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2334,plain,
% 1.53/1.71 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(2335,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[2334])).
% 1.53/1.71 tff(2336,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.53/1.71 tff(2337,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2336, 2335])).
% 1.53/1.71 tff(2338,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2337, 2333])).
% 1.53/1.72 tff(2339,plain,(
% 1.53/1.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.53/1.72 inference(skolemize,[status(sab)],[2338])).
% 1.53/1.72 tff(2340,plain,
% 1.53/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2339, 2332])).
% 1.53/1.72 tff(2341,plain,
% 1.53/1.72 (hskp13),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1967, 2312, 2201])).
% 1.53/1.72 tff(2342,plain,
% 1.53/1.72 (~c3_1(a726)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1928, 2341])).
% 1.53/1.72 tff(2343,plain,
% 1.53/1.72 (~c0_1(a726)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1934, 2341])).
% 1.53/1.72 tff(2344,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c1_1(a754))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2345,plain,
% 1.53/1.72 (((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726))) <=> (c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c1_1(a754))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2346,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c1_1(a754)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2345])).
% 1.53/1.72 tff(2347,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c1_1(a754))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2346, 2344])).
% 1.53/1.72 tff(2348,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2349,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c1_1(a754)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2348, 2347])).
% 1.53/1.72 tff(2350,plain,
% 1.53/1.72 (~c2_1(a726)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2349, 206, 165, 2110, 163, 2343, 2342, 2340, 2330])).
% 1.53/1.72 tff(2351,plain,
% 1.53/1.72 (c1_1(a726)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1949, 2341])).
% 1.53/1.72 tff(2352,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a754) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c1_1(a754))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2353,plain,
% 1.53/1.72 (((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a726) | c2_1(a726) | c0_1(a726)) <=> (c2_1(a754) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c1_1(a754))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2354,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a754) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c1_1(a754)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2353])).
% 1.53/1.72 tff(2355,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c1_1(a754))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2354, 2352])).
% 1.53/1.72 tff(2356,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a726) | c2_1(a726) | c0_1(a726))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2357,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c1_1(a754)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 1.53/1.72 tff(2358,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2357, 206, 165, 2351, 163, 2343, 2342, 110, 2330, 2350])).
% 1.53/1.72 tff(2359,plain,((~hskp23) | c2_1(a754) | c3_1(a754) | (~c0_1(a754)) | hskp1 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2360,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2359, 2303, 2302, 163, 1917, 165, 56])).
% 1.53/1.72 tff(2361,plain,(c3_1(a693) | c3_1(a754) | c2_1(a754) | hskp28 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2362,plain,
% 1.53/1.72 (c3_1(a693)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2361, 165, 163, 56, 162])).
% 1.53/1.72 tff(2363,plain,
% 1.53/1.72 (~hskp1),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1484, 2362])).
% 1.53/1.72 tff(2364,plain,
% 1.53/1.72 (~hskp23),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2359, 2363, 163, 1917, 165, 56])).
% 1.53/1.72 tff(2365,plain,
% 1.53/1.72 (~c0_1(a733)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2059, 2364, 2045])).
% 1.53/1.72 tff(2366,plain,
% 1.53/1.72 (hskp11),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2086, 206, 1644, 1636, 165, 1917, 163, 2080, 2365])).
% 1.53/1.72 tff(2367,plain,
% 1.53/1.72 (~c1_1(a722)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2092, 2366])).
% 1.53/1.72 tff(2368,plain,
% 1.53/1.72 (c0_1(a722)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2100, 2366])).
% 1.53/1.72 tff(2369,plain,
% 1.53/1.72 (~hskp27),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2048, 2364, 2045, 56])).
% 1.53/1.72 tff(2370,plain,
% 1.53/1.72 (~hskp4),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2051, 2369, 162])).
% 1.53/1.72 tff(2371,plain,
% 1.53/1.72 (c2_1(a722)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2107, 206, 2370, 1652, 1636, 2368, 2367, 2070, 2365])).
% 1.53/1.72 tff(2372,plain,
% 1.53/1.72 (c3_1(a722)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2281, 2366])).
% 1.53/1.72 tff(2373,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a754) | c3_1(a754) | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a754) | c3_1(a754) | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a754)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2374,plain,
% 1.53/1.72 (((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733))) <=> (c2_1(a754) | c3_1(a754) | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a754)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2375,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a754) | c3_1(a754) | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a754))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2374])).
% 1.53/1.72 tff(2376,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a754) | c3_1(a754) | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a754)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2375, 2373])).
% 1.53/1.72 tff(2377,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2378,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a754) | c3_1(a754) | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a754))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2377, 2376])).
% 1.53/1.72 tff(2379,plain,
% 1.53/1.72 ((~c2_1(a722)) | (~c1_1(a754))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2378, 206, 1644, 1636, 165, 2372, 163, 2367, 10, 2365])).
% 1.53/1.72 tff(2380,plain,
% 1.53/1.72 (~c1_1(a754)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2379, 2371])).
% 1.53/1.72 tff(2381,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2215, 206, 2370, 1652, 1636, 165, 1917, 2070, 2380, 2365])).
% 1.53/1.72 tff(2382,plain,(c2_1(a754) | c3_1(a754) | hskp6 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2383,plain,
% 1.53/1.72 (c2_1(a754)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2382, 162, 163, 56])).
% 1.53/1.72 tff(2384,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2385,plain,
% 1.53/1.72 ((hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c0_1(a754))) <=> (hskp3 | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2386,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c0_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2385])).
% 1.53/1.72 tff(2387,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c0_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2386, 2384])).
% 1.53/1.72 tff(2388,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c0_1(a754)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2389,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2388, 2387])).
% 1.53/1.72 tff(2390,plain,
% 1.53/1.72 (hskp3 | (~c0_1(a754)) | (~c2_1(a754))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2389, 206, 1652, 1644, 1636, 163, 2132])).
% 1.53/1.72 tff(2391,plain,
% 1.53/1.72 (hskp3),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2390, 2383, 1917])).
% 1.53/1.72 tff(2392,plain,
% 1.53/1.72 (~c3_1(a697)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1286, 2391])).
% 1.53/1.72 tff(2393,plain,
% 1.53/1.72 (c2_1(a697)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[473, 2391])).
% 1.53/1.72 tff(2394,assumption,(c0_1(a733)), introduced(assumption)).
% 1.53/1.72 tff(2395,assumption,(c2_1(a697)), introduced(assumption)).
% 1.53/1.72 tff(2396,plain,
% 1.53/1.72 ((~c0_1(a733)) | (~c1_1(a697))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2207, 206, 250, 1644, 1636, 2395, 160, 2002])).
% 1.53/1.72 tff(2397,plain,
% 1.53/1.72 (~c1_1(a697)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2396, 2394])).
% 1.53/1.72 tff(2398,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c1_1(a697) | (~c2_1(a697)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2399,plain,
% 1.53/1.72 ((hskp14 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697))) <=> (hskp14 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c1_1(a697) | (~c2_1(a697)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2400,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c1_1(a697) | (~c2_1(a697))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2399])).
% 1.53/1.72 tff(2401,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c1_1(a697) | (~c2_1(a697)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2400, 2398])).
% 1.53/1.72 tff(2402,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2403,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c1_1(a697) | (~c2_1(a697))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2402, 2401])).
% 1.53/1.72 tff(2404,plain,
% 1.53/1.72 (hskp14 | (~c0_1(a733)) | c1_1(a697)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2403, 206, 1644, 1636, 2395, 160, 1545])).
% 1.53/1.72 tff(2405,plain,
% 1.53/1.72 (hskp14),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2404, 2394, 2397])).
% 1.53/1.72 tff(2406,plain,
% 1.53/1.72 (~c3_1(a730)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[438, 2405])).
% 1.53/1.72 tff(2407,plain,
% 1.53/1.72 (c1_1(a730)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[416, 2405])).
% 1.53/1.72 tff(2408,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a730)) | (~c2_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2409,plain,
% 1.53/1.72 ((hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730))) <=> (hskp20 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2410,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a730)) | (~c2_1(a730))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2409])).
% 1.53/1.72 tff(2411,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2410, 2408])).
% 1.53/1.72 tff(2412,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2413,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a730)) | (~c2_1(a730))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2412, 2411])).
% 1.53/1.72 tff(2414,plain,
% 1.53/1.72 (~c2_1(a730)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2413, 206, 250, 1644, 1636, 2407, 2406, 2002, 2394])).
% 1.53/1.72 tff(2415,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a754)) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2416,plain,
% 1.53/1.72 ((hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754))) <=> (hskp20 | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2417,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a754)) | (~c2_1(a754))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2416])).
% 1.53/1.72 tff(2418,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2417, 2415])).
% 1.53/1.72 tff(2419,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2420,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2419, 2418])).
% 1.53/1.72 tff(2421,plain,
% 1.53/1.72 (hskp20 | (~c0_1(a733)) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2420, 206, 1644, 1636, 163, 2002])).
% 1.53/1.72 tff(2422,plain,
% 1.53/1.72 (~c1_1(a754)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2421, 2394, 250, 348])).
% 1.53/1.72 tff(2423,plain,
% 1.53/1.72 (c0_1(a730)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[424, 2405])).
% 1.53/1.72 tff(2424,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[445, 206, 56, 348, 2423, 163, 2406, 309, 2422, 2414])).
% 1.53/1.72 tff(2425,plain,((~c0_1(a733)) | hskp28 | (~c2_1(a754)) | c3_1(a754) | hskp20 | (~c2_1(a697)) | c3_1(a697)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2426,plain,
% 1.53/1.72 (~c0_1(a733)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2425, 2383, 56, 163, 1918, 2393, 2392])).
% 1.53/1.72 tff(2427,assumption,(~c0_1(a733)), introduced(assumption)).
% 1.53/1.72 tff(2428,assumption,(~hskp10), introduced(assumption)).
% 1.53/1.72 tff(2429,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a726)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2430,plain,
% 1.53/1.72 ((hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726))) <=> (hskp10 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a726)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2431,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a726))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2430])).
% 1.53/1.72 tff(2432,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a726)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2431, 2429])).
% 1.53/1.72 tff(2433,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2434,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a726))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 1.53/1.72 tff(2435,plain,
% 1.53/1.72 (~c2_1(a726)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2434, 206, 2428, 2157, 2155, 1935, 1929, 1671, 2427])).
% 1.53/1.72 tff(2436,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2437,plain,
% 1.53/1.72 ((hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)) | c3_1(a726) | c0_1(a726) | c2_1(a726)) <=> (hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2438,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2437])).
% 1.53/1.72 tff(2439,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2438, 2436])).
% 1.53/1.72 tff(2440,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)) | c3_1(a726) | c0_1(a726) | c2_1(a726))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2441,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2440, 2439])).
% 1.53/1.73 tff(2442,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2441, 206, 162, 1950, 1935, 1929, 271, 2435])).
% 1.53/1.73 tff(2443,plain,((~hskp13) | hskp6 | hskp10 | (~c1_1(a733)) | (~c3_1(a733)) | c0_1(a733)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2444,plain,
% 1.53/1.73 (~hskp13),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2443, 2426, 1847, 1652, 1636, 162])).
% 1.53/1.73 tff(2445,plain,
% 1.53/1.73 (hskp12),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1967, 2444, 1918])).
% 1.53/1.73 tff(2446,plain,
% 1.53/1.73 (~hskp13),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2443, 2427, 2428, 2157, 2155, 162])).
% 1.53/1.73 tff(2447,plain,
% 1.53/1.73 (hskp12),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1967, 2446, 250])).
% 1.53/1.73 tff(2448,plain,
% 1.53/1.73 (~c0_1(a725)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[136, 2447])).
% 1.53/1.73 tff(2449,plain,
% 1.53/1.73 (~c3_1(a725)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[124, 2447])).
% 1.53/1.73 tff(2450,plain,
% 1.53/1.73 (c3_1(a725) | c2_1(a725)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[587, 206, 967, 162, 524, 183])).
% 1.53/1.73 tff(2451,plain,
% 1.53/1.73 (c2_1(a725)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2450, 968])).
% 1.53/1.73 tff(2452,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a725)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2453,plain,
% 1.53/1.73 ((hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp10 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a725)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2454,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a725))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2453])).
% 1.53/1.73 tff(2455,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a725)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2454, 2452])).
% 1.53/1.73 tff(2456,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2457,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a725))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2456, 2455])).
% 1.53/1.73 tff(2458,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2457, 206, 2428, 2157, 2155, 524, 968, 1671, 2451, 2427])).
% 1.53/1.73 tff(2459,plain,(c3_1(a725) | hskp10 | (~c1_1(a733)) | (~c3_1(a733)) | c0_1(a725) | c0_1(a733) | hskp27 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2460,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2459, 2449, 2448, 2157, 2155, 2428, 2427, 967, 162])).
% 1.53/1.73 tff(2461,plain,(c0_1(a733) | (~c1_1(a733)) | (~c3_1(a733)) | hskp10 | hskp27 | hskp6 | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2462,plain,
% 1.53/1.73 (hskp27),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2461, 2426, 1636, 1847, 1652, 162, 1918])).
% 1.53/1.73 tff(2463,plain,
% 1.53/1.73 (hskp23),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2048, 2462, 2045, 56])).
% 1.53/1.73 tff(2464,plain,
% 1.53/1.73 (~c2_1(a763)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[365, 2463])).
% 1.53/1.73 tff(2465,plain,
% 1.53/1.73 (c0_1(a763)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[379, 2463])).
% 1.53/1.73 tff(2466,plain,
% 1.53/1.73 (~c1_1(a763)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[371, 2463])).
% 1.53/1.73 tff(2467,plain,
% 1.53/1.73 (~hskp0),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1739, 2466, 56, 2465, 2464])).
% 1.53/1.73 tff(2468,plain,
% 1.53/1.73 (hskp1),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2311, 2467, 2445])).
% 1.53/1.73 tff(2469,plain,
% 1.53/1.73 (~c3_1(a693)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1484, 2468])).
% 1.53/1.73 tff(2470,plain,
% 1.53/1.73 (c2_1(a693)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[344, 2468])).
% 1.53/1.73 tff(2471,plain,
% 1.53/1.73 (c0_1(a693)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2298, 206, 1847, 1652, 1636, 2470, 2469, 1671, 2426])).
% 1.53/1.73 tff(2472,plain,
% 1.53/1.73 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(2473,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[2472])).
% 1.53/1.73 tff(2474,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2475,plain,
% 1.53/1.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(2476,plain,
% 1.53/1.73 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[2475])).
% 1.53/1.73 tff(2477,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 1.53/1.73 tff(2478,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2477, 2476])).
% 1.53/1.73 tff(2479,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2478, 2474])).
% 1.53/1.73 tff(2480,plain,(
% 1.53/1.73 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.53/1.73 inference(skolemize,[status(sab)],[2479])).
% 1.53/1.73 tff(2481,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2480, 2473])).
% 1.53/1.73 tff(2482,plain,
% 1.53/1.73 (~c1_1(a693)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1354, 2468])).
% 1.53/1.73 tff(2483,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | c1_1(a763) | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c3_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a763) | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c3_1(a763)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2484,plain,
% 1.53/1.73 ((hskp13 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c1_1(a763) | c2_1(a763) | (~c3_1(a763))) <=> (hskp13 | c1_1(a763) | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c3_1(a763)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2485,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c1_1(a763) | c2_1(a763) | (~c3_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | c1_1(a763) | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c3_1(a763))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2484])).
% 1.53/1.73 tff(2486,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c1_1(a763) | c2_1(a763) | (~c3_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a763) | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c3_1(a763)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2485, 2483])).
% 1.53/1.73 tff(2487,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c1_1(a763) | c2_1(a763) | (~c3_1(a763)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2488,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a763) | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c3_1(a763))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2487, 2486])).
% 1.53/1.73 tff(2489,plain,
% 1.53/1.73 (~c3_1(a763)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2488, 206, 2444, 2466, 2464, 2482, 2469, 2481, 2471])).
% 1.53/1.73 tff(2490,plain,
% 1.53/1.73 (c0_1(a691)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[248, 2462])).
% 1.53/1.73 tff(2491,plain,
% 1.53/1.73 (c3_1(a691)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[232, 2462])).
% 1.53/1.73 tff(2492,plain,
% 1.53/1.73 (c2_1(a691)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1686, 2491, 2490, 56])).
% 1.53/1.73 tff(2493,plain,
% 1.53/1.73 (~c0_1(a725)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[136, 2445])).
% 1.53/1.73 tff(2494,plain,
% 1.53/1.73 (~c1_1(a725)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[130, 2445])).
% 1.53/1.73 tff(2495,plain,
% 1.53/1.73 (~c2_1(a725)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[532, 2494, 2463, 2493, 56])).
% 1.53/1.73 tff(2496,plain,
% 1.53/1.73 (~c3_1(a725)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[124, 2445])).
% 1.53/1.73 tff(2497,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2498,plain,
% 1.53/1.73 (((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a725) | c2_1(a725) | c0_1(a725)) <=> ((~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2499,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2498])).
% 1.53/1.73 tff(2500,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2499, 2497])).
% 1.53/1.73 tff(2501,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a725) | c2_1(a725) | c0_1(a725))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2502,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2501, 2500])).
% 1.53/1.73 tff(2503,plain,
% 1.53/1.73 (~c1_1(a754)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2502, 206, 2490, 2491, 1917, 163, 2493, 2496, 1699, 2495, 2492])).
% 1.53/1.73 tff(2504,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a763) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2505,plain,
% 1.53/1.73 ((hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754))) <=> (hskp28 | c2_1(a763) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2506,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a763) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2505])).
% 1.53/1.73 tff(2507,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2506, 2504])).
% 1.53/1.73 tff(2508,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2509,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2508, 2507])).
% 1.53/1.73 tff(2510,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2509, 206, 56, 2465, 2383, 2464, 163, 309, 2503, 2489])).
% 1.53/1.73 tff(2511,plain,(hskp6 | hskp28 | c3_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2512,plain,
% 1.53/1.73 (c3_1(a754)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2511, 1661, 56])).
% 1.53/1.73 tff(2513,plain,
% 1.53/1.73 (~hskp20),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[614, 2512])).
% 1.53/1.73 tff(2514,plain,
% 1.53/1.73 (~hskp24),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2044, 2513, 56, 1661])).
% 1.53/1.73 tff(2515,plain,
% 1.53/1.73 (c0_1(a733)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2461, 967, 1636, 1847, 1652, 1661, 2513])).
% 1.53/1.73 tff(2516,plain,
% 1.53/1.73 (hskp23),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2059, 2515, 2514])).
% 1.53/1.73 tff(2517,plain,
% 1.53/1.73 (~c2_1(a763)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[365, 2516])).
% 1.53/1.73 tff(2518,plain,
% 1.53/1.73 (c0_1(a763)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[379, 2516])).
% 1.53/1.73 tff(2519,plain,
% 1.53/1.73 (~c3_1(a763)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1756, 206, 56, 1652, 1644, 1636, 2518, 2517, 55])).
% 1.53/1.73 tff(2520,plain,
% 1.53/1.73 (^[U: $i] : refl((hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(2521,plain,
% 1.53/1.73 (![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[2520])).
% 1.53/1.73 tff(2522,plain,
% 1.53/1.73 (![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2523,plain,
% 1.53/1.73 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp18) <=> ((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp18))), rewrite(((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp18) <=> (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(2524,plain,
% 1.53/1.73 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp18) <=> ![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[2523])).
% 1.53/1.73 tff(2525,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.53/1.73 tff(2526,plain,
% 1.53/1.73 (![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2525, 2524])).
% 1.53/1.73 tff(2527,plain,
% 1.53/1.73 (![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2526, 2522])).
% 1.53/1.73 tff(2528,plain,(
% 1.53/1.73 ![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(skolemize,[status(sab)],[2527])).
% 1.53/1.73 tff(2529,plain,
% 1.53/1.73 (![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2528, 2521])).
% 1.53/1.73 tff(2530,plain,
% 1.53/1.73 (((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c1_1(a733)))) <=> ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c1_1(a733)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2531,plain,
% 1.53/1.73 ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c1_1(a733)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2532,plain,
% 1.53/1.73 ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c1_1(a733))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2531, 2530])).
% 1.53/1.73 tff(2533,plain,
% 1.53/1.73 (hskp27 | hskp18 | (~c0_1(a733))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2532, 206, 1652, 1636, 2529])).
% 1.53/1.73 tff(2534,plain,
% 1.53/1.73 (hskp18),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2533, 2515, 967])).
% 1.53/1.73 tff(2535,plain,
% 1.53/1.73 (((~hskp18) | (~c3_1(a751))) <=> ((~hskp18) | (~c3_1(a751)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2536,plain,
% 1.53/1.73 (((~c3_1(a751)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a751)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2537,axiom,((~c3_1(a751)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.53/1.73 tff(2538,plain,
% 1.53/1.73 ((~hskp18) | (~c3_1(a751))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2537, 2536])).
% 1.53/1.73 tff(2539,plain,
% 1.53/1.73 ((~hskp18) | (~c3_1(a751))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2538, 2535])).
% 1.53/1.73 tff(2540,plain,
% 1.53/1.73 (~c3_1(a751)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2539, 2534])).
% 1.53/1.73 tff(2541,plain,
% 1.53/1.73 (((~hskp18) | (~c1_1(a751))) <=> ((~hskp18) | (~c1_1(a751)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2542,plain,
% 1.53/1.73 (((~c1_1(a751)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a751)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2543,axiom,((~c1_1(a751)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.53/1.73 tff(2544,plain,
% 1.53/1.73 ((~hskp18) | (~c1_1(a751))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2543, 2542])).
% 1.53/1.73 tff(2545,plain,
% 1.53/1.73 ((~hskp18) | (~c1_1(a751))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2544, 2541])).
% 1.53/1.73 tff(2546,plain,
% 1.53/1.73 (~c1_1(a751)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2545, 2534])).
% 1.53/1.73 tff(2547,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a763) | c1_1(a751) | c3_1(a751) | (~ndr1_0) | (~c2_1(a751)) | c3_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c1_1(a751) | c3_1(a751) | (~ndr1_0) | (~c2_1(a751)) | c3_1(a763) | (~c0_1(a763)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2548,plain,
% 1.53/1.73 ((hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a751) | c1_1(a751) | (~c2_1(a751))) <=> (hskp28 | c2_1(a763) | c1_1(a751) | c3_1(a751) | (~ndr1_0) | (~c2_1(a751)) | c3_1(a763) | (~c0_1(a763)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2549,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a751) | c1_1(a751) | (~c2_1(a751)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a763) | c1_1(a751) | c3_1(a751) | (~ndr1_0) | (~c2_1(a751)) | c3_1(a763) | (~c0_1(a763))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2548])).
% 1.53/1.73 tff(2550,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a751) | c1_1(a751) | (~c2_1(a751)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c1_1(a751) | c3_1(a751) | (~ndr1_0) | (~c2_1(a751)) | c3_1(a763) | (~c0_1(a763)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2549, 2547])).
% 1.53/1.73 tff(2551,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a751) | c1_1(a751) | (~c2_1(a751)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2552,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c1_1(a751) | c3_1(a751) | (~ndr1_0) | (~c2_1(a751)) | c3_1(a763) | (~c0_1(a763))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2551, 2550])).
% 1.53/1.73 tff(2553,plain,
% 1.53/1.73 (~c2_1(a751)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2552, 206, 56, 2518, 2517, 2546, 2540, 309, 2519])).
% 1.53/1.73 tff(2554,plain,
% 1.53/1.73 (~c1_1(a763)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[371, 2516])).
% 1.53/1.73 tff(2555,plain,
% 1.53/1.73 (((~hskp18) | c0_1(a751)) <=> ((~hskp18) | c0_1(a751))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2556,axiom,((~hskp18) | c0_1(a751)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.53/1.73 tff(2557,plain,
% 1.53/1.73 ((~hskp18) | c0_1(a751)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2556, 2555])).
% 1.53/1.73 tff(2558,plain,
% 1.53/1.73 ((~hskp18) | c0_1(a751)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2557, 2555])).
% 1.53/1.73 tff(2559,plain,
% 1.53/1.73 ((~hskp18) | c0_1(a751)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2558, 2555])).
% 1.53/1.73 tff(2560,plain,
% 1.53/1.73 ((~hskp18) | c0_1(a751)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2559, 2555])).
% 1.53/1.73 tff(2561,plain,
% 1.53/1.73 ((~hskp18) | c0_1(a751)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2560, 2555])).
% 1.53/1.73 tff(2562,plain,
% 1.53/1.73 (c0_1(a751)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2561, 2534])).
% 1.53/1.73 tff(2563,assumption,(~c2_1(a751)), introduced(assumption)).
% 1.53/1.73 tff(2564,assumption,(~c3_1(a751)), introduced(assumption)).
% 1.53/1.73 tff(2565,assumption,(c0_1(a751)), introduced(assumption)).
% 1.53/1.73 tff(2566,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2567,plain,
% 1.53/1.73 (((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2568,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2567])).
% 1.53/1.73 tff(2569,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2568, 2566])).
% 1.53/1.73 tff(2570,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2571,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2570, 2569])).
% 1.53/1.73 tff(2572,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2571, 206, 1731, 2565, 1729, 1728, 2564, 524, 968, 2340, 2451, 2563])).
% 1.53/1.73 tff(2573,plain,(c3_1(a725) | (~c0_1(a763)) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c2_1(a751) | hskp27 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2574,plain,
% 1.53/1.73 (c3_1(a725)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2573, 524, 2562, 2554, 2517, 2540, 2518, 2553, 967, 1661])).
% 1.53/1.74 tff(2575,plain,
% 1.53/1.74 (c2_1(a725)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2032, 2574])).
% 1.53/1.74 tff(2576,plain,
% 1.53/1.74 (~hskp4),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2051, 967, 1661])).
% 1.53/1.74 tff(2577,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a725) | (~c1_1(a725)) | (~c3_1(a725)) | (~ndr1_0) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a725) | (~c1_1(a725)) | (~c3_1(a725)) | (~ndr1_0) | (~c0_1(a763)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2578,plain,
% 1.53/1.74 ((hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a725) | (~c3_1(a725)) | (~c1_1(a725))) <=> (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a725) | (~c1_1(a725)) | (~c3_1(a725)) | (~ndr1_0) | (~c0_1(a763)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2579,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a725) | (~c3_1(a725)) | (~c1_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a725) | (~c1_1(a725)) | (~c3_1(a725)) | (~ndr1_0) | (~c0_1(a763))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2578])).
% 1.53/1.74 tff(2580,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a725) | (~c3_1(a725)) | (~c1_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a725) | (~c1_1(a725)) | (~c3_1(a725)) | (~ndr1_0) | (~c0_1(a763)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2579, 2577])).
% 1.53/1.74 tff(2581,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a725) | (~c3_1(a725)) | (~c1_1(a725)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2582,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a725) | (~c1_1(a725)) | (~c3_1(a725)) | (~ndr1_0) | (~c0_1(a763))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2581, 2580])).
% 1.53/1.74 tff(2583,plain,
% 1.53/1.74 ((~c1_1(a725)) | (~c3_1(a725))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2582, 206, 2576, 2518, 2554, 2517, 524, 2070])).
% 1.53/1.74 tff(2584,plain,
% 1.53/1.74 (~c1_1(a725)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2583, 2574])).
% 1.53/1.74 tff(2585,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[532, 2584, 2575, 2516, 524, 56])).
% 1.53/1.74 tff(2586,plain,(c0_1(a725) | hskp28 | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2587,plain,
% 1.53/1.74 (c0_1(a725)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2586, 967, 56])).
% 1.53/1.74 tff(2588,plain,
% 1.53/1.74 (~hskp12),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[136, 2587])).
% 1.53/1.74 tff(2589,plain,
% 1.53/1.74 (hskp13),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1967, 2588, 2513])).
% 1.53/1.74 tff(2590,plain,
% 1.53/1.74 (~c3_1(a726)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1928, 2589])).
% 1.53/1.74 tff(2591,plain,
% 1.53/1.74 (~c0_1(a726)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1934, 2589])).
% 1.53/1.74 tff(2592,plain,
% 1.53/1.74 (c1_1(a726)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1949, 2589])).
% 1.53/1.74 tff(2593,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a751) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c2_1(a751))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a751) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c2_1(a751))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2594,plain,
% 1.53/1.74 (((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a751) | c1_1(a751) | c2_1(a751) | c3_1(a726) | c2_1(a726) | c0_1(a726)) <=> (c1_1(a751) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c2_1(a751))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2595,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a751) | c1_1(a751) | c2_1(a751) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a751) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c2_1(a751)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2594])).
% 1.53/1.74 tff(2596,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a751) | c1_1(a751) | c2_1(a751) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a751) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c2_1(a751))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2595, 2593])).
% 1.53/1.74 tff(2597,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a751) | c1_1(a751) | c2_1(a751) | c3_1(a726) | c2_1(a726) | c0_1(a726))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2598,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a751) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c2_1(a751)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2597, 2596])).
% 1.53/1.74 tff(2599,plain,
% 1.53/1.74 (c2_1(a726)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2598, 206, 2592, 2546, 2540, 2591, 2590, 110, 2553])).
% 1.53/1.74 tff(2600,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2601,plain,
% 1.53/1.74 (((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726))) <=> (c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2602,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2601])).
% 1.53/1.74 tff(2603,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2602, 2600])).
% 1.53/1.74 tff(2604,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2605,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2604, 2603])).
% 1.53/1.74 tff(2606,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2605, 206, 2518, 2562, 2554, 2517, 2540, 2591, 2590, 2340, 2553, 2599])).
% 1.53/1.74 tff(2607,plain,(hskp27 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2608,plain,
% 1.53/1.74 (hskp27),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2607, 56])).
% 1.53/1.74 tff(2609,plain,
% 1.53/1.74 (hskp23),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2048, 2608, 2514, 56])).
% 1.53/1.74 tff(2610,plain,
% 1.53/1.74 (~c2_1(a763)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[365, 2609])).
% 1.53/1.74 tff(2611,plain,
% 1.53/1.74 (c0_1(a763)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[379, 2609])).
% 1.53/1.74 tff(2612,plain,
% 1.53/1.74 (~c3_1(a763)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1756, 206, 56, 1652, 1644, 1636, 2611, 2610, 55])).
% 1.53/1.74 tff(2613,plain,
% 1.53/1.74 (~c1_1(a763)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[371, 2609])).
% 1.53/1.74 tff(2614,plain,
% 1.53/1.74 (~hskp0),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1739, 2613, 56, 2611, 2610])).
% 1.53/1.74 tff(2615,assumption,(hskp1), introduced(assumption)).
% 1.53/1.74 tff(2616,plain,
% 1.53/1.74 (~c3_1(a693)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1484, 2615])).
% 1.53/1.74 tff(2617,plain,
% 1.53/1.74 (~c1_1(a693)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1354, 2615])).
% 1.53/1.74 tff(2618,plain,
% 1.53/1.74 (c2_1(a693)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[344, 2615])).
% 1.53/1.74 tff(2619,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1763, 206, 56, 2611, 2618, 2610, 2617, 2616, 309, 2612])).
% 1.53/1.74 tff(2620,plain,((~hskp1) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2621,plain,
% 1.53/1.74 (~hskp1),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2620, 56])).
% 1.53/1.74 tff(2622,plain,
% 1.53/1.74 (~hskp12),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2311, 2621, 2614])).
% 1.53/1.74 tff(2623,plain,
% 1.53/1.74 (hskp13),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1967, 2622, 2513])).
% 1.53/1.74 tff(2624,plain,
% 1.53/1.74 (~c3_1(a726)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1928, 2623])).
% 1.53/1.74 tff(2625,plain,
% 1.53/1.74 (~c0_1(a726)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1934, 2623])).
% 1.53/1.74 tff(2626,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c3_1(a763) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c3_1(a763) | (~c0_1(a763)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2627,plain,
% 1.53/1.74 (((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726))) <=> (c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c3_1(a763) | (~c0_1(a763)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2628,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c3_1(a763) | (~c0_1(a763))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2627])).
% 1.53/1.74 tff(2629,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c3_1(a763) | (~c0_1(a763)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2628, 2626])).
% 1.53/1.74 tff(2630,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2631,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c3_1(a763) | (~c0_1(a763))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2630, 2629])).
% 1.53/1.74 tff(2632,plain,
% 1.53/1.74 (~c2_1(a726)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2631, 206, 2611, 2613, 2610, 2625, 2624, 2340, 2612])).
% 1.53/1.74 tff(2633,plain,
% 1.53/1.74 (c1_1(a726)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1949, 2623])).
% 1.53/1.74 tff(2634,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c3_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c3_1(a763))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2635,plain,
% 1.53/1.74 (((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a763) | c1_1(a763) | c2_1(a763) | c3_1(a726) | c2_1(a726) | c0_1(a726)) <=> (c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c3_1(a763))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2636,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a763) | c1_1(a763) | c2_1(a763) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c3_1(a763)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2635])).
% 1.53/1.74 tff(2637,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a763) | c1_1(a763) | c2_1(a763) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c3_1(a763))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2636, 2634])).
% 1.53/1.74 tff(2638,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a763) | c1_1(a763) | c2_1(a763) | c3_1(a726) | c2_1(a726) | c0_1(a726))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2639,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c3_1(a763)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2638, 2637])).
% 1.53/1.74 tff(2640,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2639, 206, 2633, 2613, 2610, 2625, 2624, 110, 2612, 2632])).
% 1.53/1.74 tff(2641,plain,(hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2642,plain,
% 1.53/1.74 (((~hskp28) | c2_1(a695)) <=> ((~hskp28) | c2_1(a695))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2643,axiom,((~hskp28) | c2_1(a695)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.53/1.74 tff(2644,plain,
% 1.53/1.74 ((~hskp28) | c2_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2643, 2642])).
% 1.53/1.74 tff(2645,plain,
% 1.53/1.74 ((~hskp28) | c2_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2644, 2642])).
% 1.53/1.74 tff(2646,plain,
% 1.53/1.74 ((~hskp28) | c2_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2645, 2642])).
% 1.53/1.74 tff(2647,plain,
% 1.53/1.74 ((~hskp28) | c2_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2646, 2642])).
% 1.53/1.74 tff(2648,plain,
% 1.53/1.74 ((~hskp28) | c2_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2647, 2642])).
% 1.53/1.74 tff(2649,plain,
% 1.53/1.74 (c2_1(a695)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2648, 2641])).
% 1.53/1.74 tff(2650,plain,
% 1.53/1.74 (((~hskp28) | c1_1(a695)) <=> ((~hskp28) | c1_1(a695))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2651,axiom,((~hskp28) | c1_1(a695)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.53/1.74 tff(2652,plain,
% 1.53/1.74 ((~hskp28) | c1_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2651, 2650])).
% 1.53/1.74 tff(2653,plain,
% 1.53/1.74 ((~hskp28) | c1_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2652, 2650])).
% 1.53/1.74 tff(2654,plain,
% 1.53/1.74 ((~hskp28) | c1_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2653, 2650])).
% 1.53/1.74 tff(2655,plain,
% 1.53/1.74 ((~hskp28) | c1_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2654, 2650])).
% 1.53/1.74 tff(2656,plain,
% 1.53/1.74 ((~hskp28) | c1_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2655, 2650])).
% 1.53/1.74 tff(2657,plain,
% 1.53/1.74 (c1_1(a695)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2656, 2641])).
% 1.53/1.74 tff(2658,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a701) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a701)) | (~c0_1(a701)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a701) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a701)) | (~c0_1(a701)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2659,plain,
% 1.53/1.74 ((hskp16 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c1_1(a701) | (~c2_1(a701)) | (~c0_1(a701))) <=> (hskp16 | c1_1(a701) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a701)) | (~c0_1(a701)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2660,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c1_1(a701) | (~c2_1(a701)) | (~c0_1(a701)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a701) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a701)) | (~c0_1(a701))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2659])).
% 1.53/1.74 tff(2661,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c1_1(a701) | (~c2_1(a701)) | (~c0_1(a701)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a701) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a701)) | (~c0_1(a701)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2660, 2658])).
% 1.53/1.74 tff(2662,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c1_1(a701) | (~c2_1(a701)) | (~c0_1(a701)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2663,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a701) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a701)) | (~c0_1(a701))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2662, 2661])).
% 1.53/1.74 tff(2664,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2663, 206, 12, 2657, 2649, 45, 37, 29, 22, 11])).
% 1.53/1.74 tff(2665,plain,((~hskp5) | hskp16 | c3_1(a695)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2666,plain,
% 1.53/1.74 (~hskp5),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2665, 12, 11])).
% 1.53/1.74 tff(2667,assumption,(~hskp21), introduced(assumption)).
% 1.53/1.74 tff(2668,plain,
% 1.53/1.74 (^[U: $i] : refl((hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.53/1.74 inference(bind,[status(th)],[])).
% 1.53/1.74 tff(2669,plain,
% 1.53/1.74 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.74 inference(quant_intro,[status(thm)],[2668])).
% 1.53/1.74 tff(2670,plain,
% 1.53/1.74 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2671,plain,
% 1.53/1.74 (^[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)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp22) <=> ((hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp22))), rewrite(((hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp22) <=> (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.53/1.74 inference(bind,[status(th)],[])).
% 1.53/1.74 tff(2672,plain,
% 1.53/1.74 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp22) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.74 inference(quant_intro,[status(thm)],[2671])).
% 1.53/1.74 tff(2673,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 1.53/1.74 tff(2674,plain,
% 1.53/1.74 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 1.53/1.74 tff(2675,plain,
% 1.53/1.74 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2674, 2670])).
% 1.53/1.74 tff(2676,plain,(
% 1.53/1.74 ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.74 inference(skolemize,[status(sab)],[2675])).
% 1.53/1.74 tff(2677,plain,
% 1.53/1.74 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2676, 2669])).
% 1.53/1.74 tff(2678,plain,
% 1.53/1.74 (((~hskp28) | c0_1(a695)) <=> ((~hskp28) | c0_1(a695))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2679,axiom,((~hskp28) | c0_1(a695)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.53/1.74 tff(2680,plain,
% 1.53/1.74 ((~hskp28) | c0_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2679, 2678])).
% 1.53/1.74 tff(2681,plain,
% 1.53/1.74 ((~hskp28) | c0_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2680, 2678])).
% 1.53/1.74 tff(2682,plain,
% 1.53/1.74 ((~hskp28) | c0_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2681, 2678])).
% 1.53/1.74 tff(2683,plain,
% 1.53/1.74 ((~hskp28) | c0_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2682, 2678])).
% 1.53/1.74 tff(2684,plain,
% 1.53/1.74 ((~hskp28) | c0_1(a695)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2683, 2678])).
% 1.53/1.74 tff(2685,plain,
% 1.53/1.74 (c0_1(a695)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2684, 2641])).
% 1.53/1.74 tff(2686,plain,
% 1.53/1.74 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp21 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2687,plain,
% 1.53/1.74 ((hskp22 | hskp21 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695))) <=> (hskp22 | hskp21 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2688,plain,
% 1.53/1.74 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2687])).
% 1.53/1.74 tff(2689,plain,
% 1.53/1.74 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp21 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2688, 2686])).
% 1.53/1.74 tff(2690,plain,
% 1.53/1.74 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2691,plain,
% 1.53/1.74 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp21 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2690, 2689])).
% 1.53/1.74 tff(2692,plain,
% 1.53/1.74 (hskp22 | hskp21 | c3_1(a695)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2691, 206, 2685, 2649, 2677])).
% 1.53/1.74 tff(2693,plain,
% 1.53/1.74 (hskp22),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2692, 11, 2667])).
% 1.53/1.74 tff(2694,plain,
% 1.53/1.74 (~c2_1(a761)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[721, 2693])).
% 1.53/1.74 tff(2695,plain,
% 1.53/1.74 (~c0_1(a761)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[727, 2693])).
% 1.53/1.74 tff(2696,plain,
% 1.53/1.74 (c1_1(a761)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[735, 2693])).
% 1.53/1.74 tff(2697,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a761) | c2_1(a761) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c1_1(a761)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2698,plain,
% 1.53/1.75 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761))) <=> (c0_1(a761) | c2_1(a761) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c1_1(a761)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2699,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a761) | c2_1(a761) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c1_1(a761))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2698])).
% 1.53/1.75 tff(2700,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c1_1(a761)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2699, 2697])).
% 1.53/1.75 tff(2701,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2702,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c1_1(a761))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2701, 2700])).
% 1.53/1.75 tff(2703,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2702, 206, 2685, 2657, 2649, 2696, 2695, 2694, 756, 11])).
% 1.53/1.75 tff(2704,plain,(c3_1(a695) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2705,plain,
% 1.53/1.75 (hskp21),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2704, 11])).
% 1.53/1.75 tff(2706,plain,
% 1.53/1.75 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 1.53/1.75 inference(bind,[status(th)],[])).
% 1.53/1.75 tff(2707,plain,
% 1.53/1.75 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.53/1.75 inference(quant_intro,[status(thm)],[2706])).
% 1.53/1.75 tff(2708,plain,
% 1.53/1.75 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2709,plain,
% 1.53/1.75 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 1.53/1.75 inference(bind,[status(th)],[])).
% 1.53/1.75 tff(2710,plain,
% 1.53/1.75 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.53/1.75 inference(quant_intro,[status(thm)],[2709])).
% 1.53/1.75 tff(2711,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 1.53/1.75 tff(2712,plain,
% 1.53/1.75 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2711, 2710])).
% 1.53/1.75 tff(2713,plain,
% 1.53/1.75 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2712, 2708])).
% 1.53/1.75 tff(2714,plain,(
% 1.53/1.75 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.53/1.75 inference(skolemize,[status(sab)],[2713])).
% 1.53/1.75 tff(2715,plain,
% 1.53/1.75 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2714, 2707])).
% 1.53/1.75 tff(2716,plain,
% 1.53/1.75 (^[U: $i] : refl((hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.53/1.75 inference(bind,[status(th)],[])).
% 1.53/1.75 tff(2717,plain,
% 1.53/1.75 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.75 inference(quant_intro,[status(thm)],[2716])).
% 1.53/1.75 tff(2718,plain,
% 1.53/1.75 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2719,plain,
% 1.53/1.75 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp7))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp13) <=> ((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp13))), rewrite(((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp13) <=> (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp13) <=> (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.53/1.75 inference(bind,[status(th)],[])).
% 1.53/1.75 tff(2720,plain,
% 1.53/1.75 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp13) <=> ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.75 inference(quant_intro,[status(thm)],[2719])).
% 1.53/1.75 tff(2721,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.53/1.75 tff(2722,plain,
% 1.53/1.75 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2721, 2720])).
% 1.53/1.75 tff(2723,plain,
% 1.53/1.75 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2722, 2718])).
% 1.53/1.75 tff(2724,plain,(
% 1.53/1.75 ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.75 inference(skolemize,[status(sab)],[2723])).
% 1.53/1.75 tff(2725,plain,
% 1.53/1.75 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2724, 2717])).
% 1.53/1.75 tff(2726,plain,
% 1.53/1.75 (c2_1(a726)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2441, 206, 162, 1950, 1935, 1929, 271])).
% 1.53/1.75 tff(2727,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a726)) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2728,plain,
% 1.53/1.75 ((hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726))) <=> (hskp20 | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2729,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a726)) | (~c2_1(a726))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2728])).
% 1.53/1.75 tff(2730,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2729, 2727])).
% 1.53/1.75 tff(2731,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2732,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a726)) | (~c2_1(a726))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2731, 2730])).
% 1.53/1.75 tff(2733,plain,
% 1.53/1.75 ((~c3_1(a695)) | (~c2_1(a726))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2732, 206, 250, 2685, 2649, 1950, 1929, 2002])).
% 1.53/1.75 tff(2734,plain,
% 1.53/1.75 (~c3_1(a695)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2733, 2726])).
% 1.53/1.75 tff(2735,plain,
% 1.53/1.75 (~hskp4),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2051, 967, 162])).
% 1.53/1.75 tff(2736,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2737,plain,
% 1.53/1.75 ((hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2738,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2737])).
% 1.53/1.75 tff(2739,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2738, 2736])).
% 1.53/1.75 tff(2740,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2741,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2740, 2739])).
% 1.53/1.75 tff(2742,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2741, 206, 162, 1921, 1920, 1919, 524, 968, 89, 2451])).
% 1.53/1.75 tff(2743,plain,(c3_1(a725) | hskp6 | (~c1_1(a764)) | c2_1(a764) | c3_1(a764) | c0_1(a725) | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2744,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2743, 2307, 2309, 1921, 1920, 1919, 162, 967])).
% 1.53/1.75 tff(2745,plain,((~hskp12) | (~c1_1(a764)) | c2_1(a764) | c3_1(a764) | hskp6 | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2746,plain,
% 1.53/1.75 (~hskp12),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2745, 292, 284, 278, 162, 967])).
% 1.53/1.75 tff(2747,plain,
% 1.53/1.75 (hskp13),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1967, 2746, 250])).
% 1.53/1.75 tff(2748,plain,
% 1.53/1.75 (~c3_1(a726)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1928, 2747])).
% 1.53/1.75 tff(2749,plain,
% 1.53/1.75 (~c0_1(a726)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1934, 2747])).
% 1.53/1.75 tff(2750,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c1_1(a764)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2751,plain,
% 1.53/1.75 ((hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726))) <=> (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c1_1(a764)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2752,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c1_1(a764))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2751])).
% 1.53/1.75 tff(2753,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c1_1(a764)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2752, 2750])).
% 1.53/1.75 tff(2754,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2755,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c1_1(a764))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2754, 2753])).
% 1.53/1.75 tff(2756,plain,
% 1.53/1.75 (~c2_1(a726)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2755, 206, 162, 292, 284, 278, 2749, 2748, 89])).
% 1.53/1.75 tff(2757,plain,
% 1.53/1.75 (c1_1(a726)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1949, 2747])).
% 1.53/1.75 tff(2758,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2441, 206, 162, 2757, 2749, 2748, 271, 2756])).
% 1.53/1.75 tff(2759,plain,((~hskp24) | hskp6 | hskp20 | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2760,plain,
% 1.53/1.75 (~hskp24),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2759, 250, 162, 967])).
% 1.53/1.75 tff(2761,plain,
% 1.53/1.75 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2762,plain,
% 1.53/1.75 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a695)) | (~c0_1(a695)) | (~c1_1(a695))) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2763,plain,
% 1.53/1.75 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a695)) | (~c0_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a695)) | (~c1_1(a695)) | (~c2_1(a695))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2762])).
% 1.53/1.75 tff(2764,plain,
% 1.53/1.75 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a695)) | (~c0_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2763, 2761])).
% 1.53/1.75 tff(2765,plain,
% 1.53/1.75 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a695)) | (~c0_1(a695)) | (~c1_1(a695)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2766,plain,
% 1.53/1.75 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a695)) | (~c1_1(a695)) | (~c2_1(a695))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2765, 2764])).
% 1.53/1.75 tff(2767,plain,
% 1.53/1.75 (hskp24 | hskp23),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2766, 206, 2685, 2657, 2649, 148])).
% 1.53/1.75 tff(2768,plain,
% 1.53/1.75 (hskp23),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2767, 2760])).
% 1.53/1.75 tff(2769,plain,
% 1.53/1.75 (~c2_1(a763)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[365, 2768])).
% 1.53/1.75 tff(2770,plain,
% 1.53/1.75 (~c1_1(a763)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[371, 2768])).
% 1.53/1.75 tff(2771,plain,
% 1.53/1.75 (c0_1(a763)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[379, 2768])).
% 1.53/1.75 tff(2772,plain,
% 1.53/1.75 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a761) | c2_1(a761) | (~ndr1_0) | c3_1(a761))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a761) | c2_1(a761) | (~ndr1_0) | c3_1(a761))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2773,plain,
% 1.53/1.75 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a761) | c0_1(a761) | c2_1(a761)) <=> (hskp27 | hskp6 | c0_1(a761) | c2_1(a761) | (~ndr1_0) | c3_1(a761))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2774,plain,
% 1.53/1.75 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a761) | c0_1(a761) | c2_1(a761))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a761) | c2_1(a761) | (~ndr1_0) | c3_1(a761)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2773])).
% 1.53/1.75 tff(2775,plain,
% 1.53/1.75 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a761) | c0_1(a761) | c2_1(a761))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a761) | c2_1(a761) | (~ndr1_0) | c3_1(a761))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2774, 2772])).
% 1.53/1.75 tff(2776,plain,
% 1.53/1.75 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a761) | c0_1(a761) | c2_1(a761))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2777,plain,
% 1.53/1.75 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a761) | c2_1(a761) | (~ndr1_0) | c3_1(a761)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2776, 2775])).
% 1.53/1.75 tff(2778,plain,
% 1.53/1.75 (c3_1(a761)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2777, 206, 967, 162, 1122, 1121, 183])).
% 1.53/1.75 tff(2779,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a761) | (~ndr1_0) | (~c3_1(a761)) | (~c1_1(a761)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a761) | (~ndr1_0) | (~c3_1(a761)) | (~c1_1(a761)) | (~c0_1(a763)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2780,plain,
% 1.53/1.75 ((hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a761) | (~c3_1(a761)) | (~c1_1(a761))) <=> (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a761) | (~ndr1_0) | (~c3_1(a761)) | (~c1_1(a761)) | (~c0_1(a763)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2781,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a761) | (~c3_1(a761)) | (~c1_1(a761)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a761) | (~ndr1_0) | (~c3_1(a761)) | (~c1_1(a761)) | (~c0_1(a763))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2780])).
% 1.53/1.75 tff(2782,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a761) | (~c3_1(a761)) | (~c1_1(a761)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a761) | (~ndr1_0) | (~c3_1(a761)) | (~c1_1(a761)) | (~c0_1(a763)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2781, 2779])).
% 1.53/1.75 tff(2783,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a761) | (~c3_1(a761)) | (~c1_1(a761)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2784,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a761) | (~ndr1_0) | (~c3_1(a761)) | (~c1_1(a761)) | (~c0_1(a763))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2783, 2782])).
% 1.53/1.75 tff(2785,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2784, 206, 2735, 1731, 1123, 1729, 1728, 1122, 2070, 2778])).
% 1.53/1.75 tff(2786,plain,((~hskp22) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | hskp27 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2787,plain,
% 1.53/1.75 (~hskp22),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2786, 2771, 2770, 2769, 967, 162])).
% 1.53/1.75 tff(2788,assumption,(hskp21), introduced(assumption)).
% 1.53/1.75 tff(2789,plain,
% 1.53/1.75 (((~hskp21) | (~c0_1(a760))) <=> ((~hskp21) | (~c0_1(a760)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2790,plain,
% 1.53/1.75 (((~c0_1(a760)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a760)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2791,axiom,((~c0_1(a760)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.53/1.75 tff(2792,plain,
% 1.53/1.75 ((~hskp21) | (~c0_1(a760))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2791, 2790])).
% 1.53/1.75 tff(2793,plain,
% 1.53/1.75 ((~hskp21) | (~c0_1(a760))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2792, 2789])).
% 1.53/1.75 tff(2794,plain,
% 1.53/1.75 (~c0_1(a760)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2793, 2788])).
% 1.53/1.75 tff(2795,plain,
% 1.53/1.75 (((~hskp21) | c3_1(a760)) <=> ((~hskp21) | c3_1(a760))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2796,axiom,((~hskp21) | c3_1(a760)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.53/1.75 tff(2797,plain,
% 1.53/1.75 ((~hskp21) | c3_1(a760)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2796, 2795])).
% 1.53/1.75 tff(2798,plain,
% 1.53/1.75 ((~hskp21) | c3_1(a760)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2797, 2795])).
% 1.53/1.75 tff(2799,plain,
% 1.53/1.75 ((~hskp21) | c3_1(a760)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2798, 2795])).
% 1.53/1.75 tff(2800,plain,
% 1.53/1.75 ((~hskp21) | c3_1(a760)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2799, 2795])).
% 1.53/1.75 tff(2801,plain,
% 1.53/1.75 ((~hskp21) | c3_1(a760)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2800, 2795])).
% 1.53/1.75 tff(2802,plain,
% 1.53/1.75 (c3_1(a760)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2801, 2788])).
% 1.53/1.75 tff(2803,plain,
% 1.53/1.75 (((~hskp21) | c1_1(a760)) <=> ((~hskp21) | c1_1(a760))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2804,axiom,((~hskp21) | c1_1(a760)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.53/1.75 tff(2805,plain,
% 1.53/1.75 ((~hskp21) | c1_1(a760)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2804, 2803])).
% 1.53/1.75 tff(2806,plain,
% 1.53/1.75 ((~hskp21) | c1_1(a760)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2805, 2803])).
% 1.53/1.75 tff(2807,plain,
% 1.53/1.75 ((~hskp21) | c1_1(a760)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2806, 2803])).
% 1.53/1.75 tff(2808,plain,
% 1.53/1.75 ((~hskp21) | c1_1(a760)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2807, 2803])).
% 1.53/1.75 tff(2809,plain,
% 1.53/1.75 ((~hskp21) | c1_1(a760)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2808, 2803])).
% 1.53/1.75 tff(2810,plain,
% 1.53/1.75 (c1_1(a760)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2809, 2788])).
% 1.53/1.75 tff(2811,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a760) | (~ndr1_0) | (~c3_1(a760)) | (~c1_1(a760)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a760) | (~ndr1_0) | (~c3_1(a760)) | (~c1_1(a760)) | (~c0_1(a763)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2812,plain,
% 1.53/1.75 ((hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760))) <=> (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a760) | (~ndr1_0) | (~c3_1(a760)) | (~c1_1(a760)) | (~c0_1(a763)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2813,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a760) | (~ndr1_0) | (~c3_1(a760)) | (~c1_1(a760)) | (~c0_1(a763))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2812])).
% 1.53/1.75 tff(2814,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a760) | (~ndr1_0) | (~c3_1(a760)) | (~c1_1(a760)) | (~c0_1(a763)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2813, 2811])).
% 1.53/1.75 tff(2815,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2816,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a760) | (~ndr1_0) | (~c3_1(a760)) | (~c1_1(a760)) | (~c0_1(a763))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2815, 2814])).
% 1.53/1.75 tff(2817,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2816, 206, 161, 1731, 2810, 2802, 1729, 1728, 2794, 2070])).
% 1.53/1.75 tff(2818,plain,((~hskp21) | hskp4 | (~c0_1(a763)) | c1_1(a763) | c2_1(a763)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2819,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2818, 372, 380, 161, 2788, 366])).
% 1.53/1.75 tff(2820,plain,((~hskp23) | hskp4 | (~hskp21)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2821,plain,
% 1.53/1.75 (~hskp21),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2820, 2768, 2735])).
% 1.53/1.75 tff(2822,plain,
% 1.53/1.75 (c3_1(a695)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2704, 2821])).
% 1.53/1.75 tff(2823,plain,
% 1.53/1.75 (((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp18 | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2824,plain,
% 1.53/1.75 ((hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a695)) | (~c0_1(a695)) | (~c1_1(a695))) <=> (hskp27 | hskp18 | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2825,plain,
% 1.53/1.75 (((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a695)) | (~c0_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c1_1(a695))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2824])).
% 1.53/1.76 tff(2826,plain,
% 1.53/1.76 (((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a695)) | (~c0_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp18 | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2825, 2823])).
% 1.53/1.76 tff(2827,plain,
% 1.53/1.76 ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a695)) | (~c0_1(a695)) | (~c1_1(a695)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2828,plain,
% 1.53/1.76 ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp18 | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c1_1(a695))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2827, 2826])).
% 1.53/1.76 tff(2829,plain,
% 1.53/1.76 (hskp27 | hskp18 | (~c3_1(a695))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2828, 206, 2685, 2657, 2529])).
% 1.53/1.76 tff(2830,plain,
% 1.53/1.76 (hskp18),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2829, 2822, 967])).
% 1.53/1.76 tff(2831,plain,
% 1.53/1.76 (~c3_1(a751)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2539, 2830])).
% 1.53/1.76 tff(2832,plain,
% 1.53/1.76 (c0_1(a751)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2561, 2830])).
% 1.53/1.76 tff(2833,plain,
% 1.53/1.76 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | (~c2_1(a751)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp21 | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | (~c2_1(a751)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2834,plain,
% 1.53/1.76 ((hskp22 | hskp21 | (~ndr1_0) | c3_1(a751) | (~c2_1(a751)) | (~c0_1(a751))) <=> (hskp22 | hskp21 | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | (~c2_1(a751)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2835,plain,
% 1.53/1.76 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a751) | (~c2_1(a751)) | (~c0_1(a751)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | (~c2_1(a751))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2834])).
% 1.53/1.76 tff(2836,plain,
% 1.53/1.76 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a751) | (~c2_1(a751)) | (~c0_1(a751)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp21 | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | (~c2_1(a751)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2835, 2833])).
% 1.53/1.76 tff(2837,plain,
% 1.53/1.76 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a751) | (~c2_1(a751)) | (~c0_1(a751)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2838,plain,
% 1.53/1.76 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp21 | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | (~c2_1(a751))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2837, 2836])).
% 1.53/1.76 tff(2839,plain,
% 1.53/1.76 (hskp22 | (~c2_1(a751))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2838, 206, 2821, 2832, 2831, 2677])).
% 1.53/1.76 tff(2840,plain,
% 1.53/1.76 (~c2_1(a751)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2839, 2787])).
% 1.53/1.76 tff(2841,plain,
% 1.53/1.76 (~c1_1(a751)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2545, 2830])).
% 1.53/1.76 tff(2842,plain,
% 1.53/1.76 (~c2_1(a726)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2605, 206, 1731, 2565, 1729, 1728, 2564, 1935, 1929, 2340, 2563])).
% 1.53/1.76 tff(2843,assumption,(~c1_1(a751)), introduced(assumption)).
% 1.53/1.76 tff(2844,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2598, 206, 1950, 2843, 2564, 1935, 1929, 110, 2563, 2842])).
% 1.53/1.76 tff(2845,plain,((~hskp13) | c1_1(a751) | c3_1(a751) | c2_1(a751) | (~c0_1(a763)) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2846,plain,
% 1.53/1.76 (~hskp13),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2845, 2841, 2831, 2840, 2771, 2832, 2770, 2769])).
% 1.53/1.76 tff(2847,plain,
% 1.53/1.76 (hskp12),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1967, 2846, 250])).
% 1.53/1.76 tff(2848,plain,
% 1.53/1.76 (~c0_1(a725)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[136, 2847])).
% 1.53/1.76 tff(2849,plain,
% 1.53/1.76 (~c3_1(a725)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[124, 2847])).
% 1.53/1.76 tff(2850,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2573, 2849, 2848, 162, 2771, 2769, 2770, 2832, 2831, 967, 2840])).
% 1.53/1.76 tff(2851,plain,(hskp20 | hskp6 | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2852,plain,
% 1.53/1.76 (hskp20),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2851, 967, 162])).
% 1.53/1.76 tff(2853,plain,
% 1.53/1.76 (~c0_1(a754)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[541, 2852])).
% 1.53/1.76 tff(2854,plain,
% 1.53/1.76 (~c3_1(a754)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[614, 2852])).
% 1.53/1.76 tff(2855,plain,
% 1.53/1.76 (c2_1(a754)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[172, 2852])).
% 1.53/1.76 tff(2856,plain,
% 1.53/1.76 (~hskp24),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1557, 2855, 162, 2854, 2853])).
% 1.53/1.76 tff(2857,plain,
% 1.53/1.76 (hskp23),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2767, 2856])).
% 1.53/1.76 tff(2858,plain,
% 1.53/1.76 (~hskp21),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2820, 2857, 2735])).
% 1.53/1.76 tff(2859,plain,
% 1.53/1.76 (c3_1(a695)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2704, 2858])).
% 1.53/1.76 tff(2860,plain,
% 1.53/1.76 (hskp18),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2829, 2859, 967])).
% 1.53/1.76 tff(2861,plain,
% 1.53/1.76 (~c3_1(a751)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2539, 2860])).
% 1.53/1.76 tff(2862,plain,
% 1.53/1.76 (c0_1(a751)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2561, 2860])).
% 1.53/1.76 tff(2863,plain,
% 1.53/1.76 (~c2_1(a763)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[365, 2857])).
% 1.53/1.76 tff(2864,plain,
% 1.53/1.76 (~c1_1(a763)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[371, 2857])).
% 1.53/1.76 tff(2865,plain,
% 1.53/1.76 (c0_1(a763)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[379, 2857])).
% 1.53/1.76 tff(2866,plain,
% 1.53/1.76 (~hskp22),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2786, 2865, 2864, 2863, 967, 162])).
% 1.53/1.76 tff(2867,plain,
% 1.53/1.76 (~c2_1(a751)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2838, 206, 2866, 2858, 2862, 2861, 2677])).
% 1.53/1.76 tff(2868,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | c2_1(a751) | (~c2_1(a754)) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | c2_1(a751) | (~c2_1(a754)) | (~c0_1(a763)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2869,plain,
% 1.53/1.76 (((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | c2_1(a751) | (~c2_1(a754)) | (~c0_1(a763)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2870,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | c2_1(a751) | (~c2_1(a754)) | (~c0_1(a763))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2869])).
% 1.53/1.76 tff(2871,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | c2_1(a751) | (~c2_1(a754)) | (~c0_1(a763)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2870, 2868])).
% 1.53/1.76 tff(2872,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2873,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | c2_1(a751) | (~c2_1(a754)) | (~c0_1(a763))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2872, 2871])).
% 1.53/1.76 tff(2874,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2873, 206, 2865, 2855, 2862, 2864, 2863, 2853, 2854, 2861, 2340, 2867])).
% 1.53/1.76 tff(2875,plain,(hskp27 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2876,plain,
% 1.53/1.76 (hskp27),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2875, 162])).
% 1.53/1.76 tff(2877,plain,
% 1.53/1.76 (hskp30),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[258, 250, 2876])).
% 1.53/1.76 tff(2878,plain,
% 1.53/1.76 (c3_1(a733)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1635, 2877])).
% 1.53/1.76 tff(2879,plain,
% 1.53/1.76 (c1_1(a733)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1651, 2877])).
% 1.53/1.76 tff(2880,plain,
% 1.53/1.76 (c2_1(a733)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1643, 2877])).
% 1.53/1.76 tff(2881,plain,
% 1.53/1.76 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a726)) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2882,plain,
% 1.53/1.76 ((hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726))) <=> (hskp20 | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2883,plain,
% 1.53/1.76 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a726)) | (~c2_1(a726))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2882])).
% 1.53/1.76 tff(2884,plain,
% 1.53/1.76 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2883, 2881])).
% 1.53/1.76 tff(2885,plain,
% 1.53/1.76 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2886,plain,
% 1.53/1.76 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a726)) | (~c2_1(a726))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2885, 2884])).
% 1.53/1.76 tff(2887,plain,
% 1.53/1.76 ((~c0_1(a733)) | (~c2_1(a726))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2886, 206, 250, 2880, 2878, 1950, 1929, 2002])).
% 1.53/1.76 tff(2888,plain,
% 1.53/1.76 (~c0_1(a733)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2887, 2726])).
% 1.53/1.76 tff(2889,plain,
% 1.53/1.76 (hskp10),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2443, 2888, 1923, 2879, 2878, 162])).
% 1.53/1.76 tff(2890,plain,
% 1.53/1.76 (~c2_1(a717)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1812, 2889])).
% 1.53/1.76 tff(2891,plain,
% 1.53/1.76 (((~hskp10) | c1_1(a717)) <=> ((~hskp10) | c1_1(a717))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2892,axiom,((~hskp10) | c1_1(a717)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.53/1.76 tff(2893,plain,
% 1.53/1.76 ((~hskp10) | c1_1(a717)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2892, 2891])).
% 1.53/1.76 tff(2894,plain,
% 1.53/1.76 ((~hskp10) | c1_1(a717)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2893, 2891])).
% 1.53/1.76 tff(2895,plain,
% 1.53/1.76 ((~hskp10) | c1_1(a717)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2894, 2891])).
% 1.53/1.76 tff(2896,plain,
% 1.53/1.76 ((~hskp10) | c1_1(a717)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2895, 2891])).
% 1.53/1.76 tff(2897,plain,
% 1.53/1.76 ((~hskp10) | c1_1(a717)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2896, 2891])).
% 1.53/1.76 tff(2898,plain,
% 1.53/1.76 (c1_1(a717)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2897, 2889])).
% 1.53/1.76 tff(2899,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c0_1(a717) | (~c1_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c0_1(a717) | (~c1_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2900,plain,
% 1.53/1.76 (((~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717))) <=> (c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c0_1(a717) | (~c1_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2901,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c0_1(a717) | (~c1_1(a717)) | (~c1_1(a726)) | (~c2_1(a726))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2900])).
% 1.53/1.76 tff(2902,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c0_1(a717) | (~c1_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2901, 2899])).
% 1.53/1.76 tff(2903,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2904,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c0_1(a717) | (~c1_1(a717)) | (~c1_1(a726)) | (~c2_1(a726))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2903, 2902])).
% 1.53/1.76 tff(2905,plain,
% 1.53/1.76 (c0_1(a717)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2904, 206, 2685, 2657, 1950, 2898, 1929, 2890, 756, 2734, 2726])).
% 1.53/1.76 tff(2906,plain,
% 1.53/1.76 (c3_1(a717)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1820, 2889])).
% 1.53/1.76 tff(2907,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a726) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2908,plain,
% 1.53/1.76 (((~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726))) <=> (c0_1(a726) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2909,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a726) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)) | (~c1_1(a726)) | (~c2_1(a726))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2908])).
% 1.53/1.76 tff(2910,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2909, 2907])).
% 1.53/1.76 tff(2911,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2912,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)) | (~c1_1(a726)) | (~c2_1(a726))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2911, 2910])).
% 1.53/1.76 tff(2913,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2912, 206, 1950, 2906, 1935, 1929, 2890, 159, 2726, 2905])).
% 1.53/1.76 tff(2914,plain,((~hskp13) | hskp6 | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2915,plain,
% 1.53/1.76 (~hskp13),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2914, 250, 162])).
% 1.53/1.76 tff(2916,plain,
% 1.53/1.76 (c0_1(a691)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[248, 2876])).
% 1.53/1.76 tff(2917,plain,
% 1.53/1.76 (c3_1(a691)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[232, 2876])).
% 1.53/1.76 tff(2918,plain,
% 1.53/1.76 (c1_1(a691)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[240, 2876])).
% 1.53/1.76 tff(2919,assumption,(c1_1(a691)), introduced(assumption)).
% 1.53/1.76 tff(2920,assumption,(~hskp13), introduced(assumption)).
% 1.53/1.76 tff(2921,assumption,(~c2_1(a725)), introduced(assumption)).
% 1.53/1.76 tff(2922,plain,
% 1.53/1.76 (hskp12),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1967, 2920, 250])).
% 1.53/1.76 tff(2923,plain,
% 1.53/1.76 (~c3_1(a725)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[124, 2922])).
% 1.53/1.76 tff(2924,plain,
% 1.53/1.76 (~c0_1(a725)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[136, 2922])).
% 1.53/1.76 tff(2925,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2926,plain,
% 1.53/1.76 (((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725)) <=> (c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2927,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2926])).
% 1.53/1.76 tff(2928,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2927, 2925])).
% 1.53/1.76 tff(2929,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2930,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2929, 2928])).
% 1.53/1.76 tff(2931,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2930, 206, 2685, 2657, 1678, 1677, 524, 968, 1699, 2921, 1689, 11])).
% 1.53/1.76 tff(2932,plain,((~c2_1(a691)) | (~c0_1(a691)) | (~c3_1(a691)) | c0_1(a725) | c3_1(a725) | c2_1(a725) | c3_1(a695)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2933,plain,
% 1.53/1.76 (~c2_1(a691)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2932, 2921, 1677, 2924, 2923, 1678, 11])).
% 1.53/1.76 tff(2934,plain,
% 1.53/1.76 (^[U: $i] : refl((hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.53/1.76 inference(bind,[status(th)],[])).
% 1.53/1.76 tff(2935,plain,
% 1.53/1.76 (![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.76 inference(quant_intro,[status(thm)],[2934])).
% 1.53/1.76 tff(2936,plain,
% 1.53/1.76 (![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2937,plain,
% 1.53/1.76 (^[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)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) | hskp20) <=> ((hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp20))), rewrite(((hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp20) <=> (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) | hskp20) <=> (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.53/1.76 inference(bind,[status(th)],[])).
% 1.53/1.76 tff(2938,plain,
% 1.53/1.76 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) | hskp20) <=> ![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.76 inference(quant_intro,[status(thm)],[2937])).
% 1.53/1.76 tff(2939,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 1.53/1.76 tff(2940,plain,
% 1.53/1.76 (![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2939, 2938])).
% 1.53/1.76 tff(2941,plain,
% 1.53/1.76 (![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2940, 2936])).
% 1.53/1.76 tff(2942,plain,(
% 1.53/1.76 ![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.76 inference(skolemize,[status(sab)],[2941])).
% 1.53/1.76 tff(2943,plain,
% 1.53/1.76 (![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2942, 2935])).
% 1.53/1.76 tff(2944,plain,
% 1.53/1.76 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | c2_1(a691))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | c2_1(a691))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2945,plain,
% 1.53/1.76 ((hskp20 | hskp16 | (~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c1_1(a691))) <=> (hskp20 | hskp16 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | c2_1(a691))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2946,plain,
% 1.53/1.76 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | c2_1(a691)))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2945])).
% 1.53/1.77 tff(2947,plain,
% 1.53/1.77 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | c2_1(a691))),
% 1.53/1.77 inference(transitivity,[status(thm)],[2946, 2944])).
% 1.53/1.77 tff(2948,plain,
% 1.53/1.77 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c1_1(a691)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(2949,plain,
% 1.53/1.77 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | c2_1(a691)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2948, 2947])).
% 1.53/1.77 tff(2950,plain,
% 1.53/1.77 (hskp20 | hskp16 | c2_1(a691)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2949, 206, 2919, 1677, 2943])).
% 1.53/1.77 tff(2951,plain,
% 1.53/1.77 (hskp16),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2950, 2933, 250])).
% 1.53/1.77 tff(2952,plain,
% 1.53/1.77 (((~hskp16) | c3_1(a738)) <=> ((~hskp16) | c3_1(a738))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2953,axiom,((~hskp16) | c3_1(a738)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.53/1.77 tff(2954,plain,
% 1.53/1.77 ((~hskp16) | c3_1(a738)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2953, 2952])).
% 1.53/1.77 tff(2955,plain,
% 1.53/1.77 ((~hskp16) | c3_1(a738)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2954, 2952])).
% 1.53/1.77 tff(2956,plain,
% 1.53/1.77 ((~hskp16) | c3_1(a738)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2955, 2952])).
% 1.53/1.77 tff(2957,plain,
% 1.53/1.77 ((~hskp16) | c3_1(a738)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2956, 2952])).
% 1.53/1.77 tff(2958,plain,
% 1.53/1.77 ((~hskp16) | c3_1(a738)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2957, 2952])).
% 1.53/1.77 tff(2959,plain,
% 1.53/1.77 (c3_1(a738)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2958, 2951])).
% 1.53/1.77 tff(2960,plain,
% 1.53/1.77 (((~hskp16) | c2_1(a738)) <=> ((~hskp16) | c2_1(a738))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2961,axiom,((~hskp16) | c2_1(a738)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.53/1.77 tff(2962,plain,
% 1.53/1.77 ((~hskp16) | c2_1(a738)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2961, 2960])).
% 1.53/1.77 tff(2963,plain,
% 1.53/1.77 ((~hskp16) | c2_1(a738)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2962, 2960])).
% 1.53/1.77 tff(2964,plain,
% 1.53/1.77 ((~hskp16) | c2_1(a738)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2963, 2960])).
% 1.53/1.77 tff(2965,plain,
% 1.53/1.77 ((~hskp16) | c2_1(a738)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2964, 2960])).
% 1.53/1.77 tff(2966,plain,
% 1.53/1.77 ((~hskp16) | c2_1(a738)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2965, 2960])).
% 1.53/1.77 tff(2967,plain,
% 1.53/1.77 (c2_1(a738)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2966, 2951])).
% 1.53/1.77 tff(2968,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2969,plain,
% 1.53/1.77 (((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725)) <=> (c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2970,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2969])).
% 1.53/1.77 tff(2971,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[2970, 2968])).
% 1.53/1.77 tff(2972,plain,
% 1.53/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(2973,plain,
% 1.53/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2972, 2971])).
% 1.53/1.77 tff(2974,plain,
% 1.53/1.77 (~c0_1(a738)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2973, 206, 2685, 2657, 2967, 2959, 2924, 2923, 1699, 2921, 11])).
% 1.53/1.77 tff(2975,plain,
% 1.53/1.77 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)))),
% 1.53/1.77 inference(bind,[status(th)],[])).
% 1.53/1.77 tff(2976,plain,
% 1.53/1.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.53/1.77 inference(quant_intro,[status(thm)],[2975])).
% 1.53/1.77 tff(2977,plain,
% 1.53/1.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2978,plain,
% 1.53/1.77 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | c1_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))))),
% 1.53/1.77 inference(bind,[status(th)],[])).
% 1.53/1.77 tff(2979,plain,
% 1.53/1.77 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.53/1.77 inference(quant_intro,[status(thm)],[2978])).
% 1.53/1.77 tff(2980,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.53/1.77 tff(2981,plain,
% 1.53/1.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2980, 2979])).
% 1.53/1.77 tff(2982,plain,
% 1.53/1.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2981, 2977])).
% 1.53/1.77 tff(2983,plain,(
% 1.53/1.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.53/1.77 inference(skolemize,[status(sab)],[2982])).
% 1.53/1.77 tff(2984,plain,
% 1.53/1.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2983, 2976])).
% 1.53/1.77 tff(2985,plain,
% 1.53/1.77 (((~hskp16) | (~c1_1(a738))) <=> ((~hskp16) | (~c1_1(a738)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2986,plain,
% 1.53/1.77 (((~c1_1(a738)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a738)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2987,axiom,((~c1_1(a738)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.53/1.77 tff(2988,plain,
% 1.53/1.77 ((~hskp16) | (~c1_1(a738))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2987, 2986])).
% 1.53/1.77 tff(2989,plain,
% 1.53/1.77 ((~hskp16) | (~c1_1(a738))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2988, 2985])).
% 1.53/1.77 tff(2990,plain,
% 1.53/1.77 (~c1_1(a738)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2989, 2951])).
% 1.53/1.77 tff(2991,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a763) | c2_1(a763) | c1_1(a738) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2992,plain,
% 1.53/1.77 (((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763)) <=> (c1_1(a763) | c2_1(a763) | c1_1(a738) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2993,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a763) | c2_1(a763) | c1_1(a738) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2992])).
% 1.53/1.77 tff(2994,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[2993, 2991])).
% 1.53/1.77 tff(2995,plain,
% 1.53/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(2996,plain,
% 1.53/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2995, 2994])).
% 1.53/1.77 tff(2997,plain,
% 1.53/1.77 (~c3_1(a763)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2996, 206, 2685, 2657, 2967, 2959, 1729, 1728, 2990, 2984, 11])).
% 1.53/1.77 tff(2998,plain,
% 1.53/1.77 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2999,plain,
% 1.53/1.77 ((hskp13 | hskp7 | (~ndr1_0) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738))) <=> (hskp13 | hskp7 | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3000,plain,
% 1.53/1.77 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2999])).
% 1.53/1.77 tff(3001,plain,
% 1.53/1.77 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[3000, 2998])).
% 1.53/1.77 tff(3002,plain,
% 1.53/1.77 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(3003,plain,
% 1.53/1.77 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3002, 3001])).
% 1.53/1.77 tff(3004,plain,
% 1.53/1.77 (hskp7),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3003, 206, 2920, 2967, 2959, 2990, 2725])).
% 1.53/1.77 tff(3005,plain,
% 1.53/1.77 (((~hskp7) | (~c3_1(a708))) <=> ((~hskp7) | (~c3_1(a708)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3006,plain,
% 1.53/1.77 (((~c3_1(a708)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a708)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3007,axiom,((~c3_1(a708)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.53/1.77 tff(3008,plain,
% 1.53/1.77 ((~hskp7) | (~c3_1(a708))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3007, 3006])).
% 1.53/1.77 tff(3009,plain,
% 1.53/1.77 ((~hskp7) | (~c3_1(a708))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3008, 3005])).
% 1.53/1.77 tff(3010,plain,
% 1.53/1.77 (~c3_1(a708)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3009, 3004])).
% 1.53/1.77 tff(3011,plain,
% 1.53/1.77 (((~hskp7) | c2_1(a708)) <=> ((~hskp7) | c2_1(a708))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3012,axiom,((~hskp7) | c2_1(a708)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.53/1.77 tff(3013,plain,
% 1.53/1.77 ((~hskp7) | c2_1(a708)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3012, 3011])).
% 1.53/1.77 tff(3014,plain,
% 1.53/1.77 ((~hskp7) | c2_1(a708)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3013, 3011])).
% 1.53/1.77 tff(3015,plain,
% 1.53/1.77 ((~hskp7) | c2_1(a708)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3014, 3011])).
% 1.53/1.77 tff(3016,plain,
% 1.53/1.77 ((~hskp7) | c2_1(a708)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3015, 3011])).
% 1.53/1.77 tff(3017,plain,
% 1.53/1.77 ((~hskp7) | c2_1(a708)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3016, 3011])).
% 1.53/1.77 tff(3018,plain,
% 1.53/1.77 (c2_1(a708)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3017, 3004])).
% 1.53/1.77 tff(3019,plain,
% 1.53/1.77 (((~hskp7) | c1_1(a708)) <=> ((~hskp7) | c1_1(a708))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3020,axiom,((~hskp7) | c1_1(a708)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.53/1.77 tff(3021,plain,
% 1.53/1.77 ((~hskp7) | c1_1(a708)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3020, 3019])).
% 1.53/1.77 tff(3022,plain,
% 1.53/1.77 ((~hskp7) | c1_1(a708)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3021, 3019])).
% 1.53/1.77 tff(3023,plain,
% 1.53/1.77 ((~hskp7) | c1_1(a708)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3022, 3019])).
% 1.53/1.77 tff(3024,plain,
% 1.53/1.77 ((~hskp7) | c1_1(a708)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3023, 3019])).
% 1.53/1.77 tff(3025,plain,
% 1.53/1.77 ((~hskp7) | c1_1(a708)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3024, 3019])).
% 1.53/1.77 tff(3026,plain,
% 1.53/1.77 (c1_1(a708)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3025, 3004])).
% 1.53/1.77 tff(3027,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a763) | c1_1(a738) | c3_1(a708) | (~ndr1_0) | (~c1_1(a708)) | (~c2_1(a708)) | (~c2_1(a738)) | c0_1(a738) | c3_1(a763) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a763) | c1_1(a738) | c3_1(a708) | (~ndr1_0) | (~c1_1(a708)) | (~c2_1(a708)) | (~c2_1(a738)) | c0_1(a738) | c3_1(a763) | (~c0_1(a763)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3028,plain,
% 1.53/1.77 (((~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c3_1(a763) | c1_1(a763) | (~c0_1(a763)) | c0_1(a738) | (~c2_1(a738)) | c1_1(a738)) <=> (c1_1(a763) | c1_1(a738) | c3_1(a708) | (~ndr1_0) | (~c1_1(a708)) | (~c2_1(a708)) | (~c2_1(a738)) | c0_1(a738) | c3_1(a763) | (~c0_1(a763)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3029,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c3_1(a763) | c1_1(a763) | (~c0_1(a763)) | c0_1(a738) | (~c2_1(a738)) | c1_1(a738))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a763) | c1_1(a738) | c3_1(a708) | (~ndr1_0) | (~c1_1(a708)) | (~c2_1(a708)) | (~c2_1(a738)) | c0_1(a738) | c3_1(a763) | (~c0_1(a763))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[3028])).
% 1.53/1.77 tff(3030,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c3_1(a763) | c1_1(a763) | (~c0_1(a763)) | c0_1(a738) | (~c2_1(a738)) | c1_1(a738))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a763) | c1_1(a738) | c3_1(a708) | (~ndr1_0) | (~c1_1(a708)) | (~c2_1(a708)) | (~c2_1(a738)) | c0_1(a738) | c3_1(a763) | (~c0_1(a763)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[3029, 3027])).
% 1.53/1.77 tff(3031,plain,
% 1.53/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c3_1(a763) | c1_1(a763) | (~c0_1(a763)) | c0_1(a738) | (~c2_1(a738)) | c1_1(a738))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(3032,plain,
% 1.53/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a763) | c1_1(a738) | c3_1(a708) | (~ndr1_0) | (~c1_1(a708)) | (~c2_1(a708)) | (~c2_1(a738)) | c0_1(a738) | c3_1(a763) | (~c0_1(a763))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3031, 3030])).
% 1.53/1.77 tff(3033,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3032, 206, 1731, 2967, 3026, 3018, 1729, 2990, 3010, 512, 2997, 2974])).
% 1.53/1.77 tff(3034,plain,(c2_1(a725) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | c3_1(a695) | hskp13 | hskp20 | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(3035,plain,
% 1.53/1.77 (c2_1(a725)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3034, 11, 372, 1728, 1731, 2920, 250, 2919, 1677, 1678])).
% 1.53/1.77 tff(3036,plain,
% 1.53/1.77 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3037,plain,
% 1.53/1.77 ((hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695))) <=> (hskp3 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3038,plain,
% 1.53/1.77 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[3037])).
% 1.53/1.77 tff(3039,plain,
% 1.53/1.77 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[3038, 3036])).
% 1.53/1.77 tff(3040,plain,
% 1.53/1.77 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(3041,plain,
% 1.53/1.77 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3040, 3039])).
% 1.53/1.77 tff(3042,plain,
% 1.53/1.77 (hskp3),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3041, 206, 2157, 2156, 2155, 2685, 2649, 2132, 11])).
% 1.53/1.77 tff(3043,plain,
% 1.53/1.77 (~c3_1(a697)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1286, 3042])).
% 1.53/1.77 tff(3044,plain,
% 1.53/1.77 (~c1_1(a725)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[130, 2922])).
% 1.53/1.77 tff(3045,plain,
% 1.53/1.77 (c0_1(a697)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[457, 3042])).
% 1.53/1.77 tff(3046,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3047,plain,
% 1.53/1.77 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725)) <=> (c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3048,plain,
% 1.53/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3047])).
% 1.53/1.78 tff(3049,plain,
% 1.53/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3048, 3046])).
% 1.53/1.78 tff(3050,plain,
% 1.53/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3051,plain,
% 1.53/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3050, 3049])).
% 1.53/1.78 tff(3052,plain,
% 1.53/1.78 (c1_1(a697) | (~c2_1(a725))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3051, 206, 2657, 2649, 3045, 2924, 3044, 3043, 512, 11])).
% 1.53/1.78 tff(3053,plain,
% 1.53/1.78 (c1_1(a697)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3052, 3035])).
% 1.53/1.78 tff(3054,plain,
% 1.53/1.78 (~c0_1(a760)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2793, 2705])).
% 1.53/1.78 tff(3055,plain,
% 1.53/1.78 (c3_1(a760)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2801, 2705])).
% 1.53/1.78 tff(3056,plain,
% 1.53/1.78 (c1_1(a760)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2809, 2705])).
% 1.53/1.78 tff(3057,plain,
% 1.53/1.78 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a760) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a760)) | (~c1_1(a760)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3058,plain,
% 1.53/1.78 ((hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp10 | c0_1(a760) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a760)) | (~c1_1(a760)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3059,plain,
% 1.53/1.78 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a760) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a760)) | (~c1_1(a760))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3058])).
% 1.53/1.78 tff(3060,plain,
% 1.53/1.78 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a760)) | (~c1_1(a760)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3059, 3057])).
% 1.53/1.78 tff(3061,plain,
% 1.53/1.78 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3062,plain,
% 1.53/1.78 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a760)) | (~c1_1(a760))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3061, 3060])).
% 1.53/1.78 tff(3063,plain,
% 1.53/1.78 (hskp10 | (~c2_1(a725))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3062, 206, 3056, 3055, 3054, 2924, 2923, 1671])).
% 1.53/1.78 tff(3064,plain,
% 1.53/1.78 (hskp10),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3063, 3035])).
% 1.53/1.78 tff(3065,plain,
% 1.53/1.78 (~c2_1(a717)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1812, 3064])).
% 1.53/1.78 tff(3066,plain,
% 1.53/1.78 (c2_1(a697)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[473, 3042])).
% 1.53/1.78 tff(3067,plain,
% 1.53/1.78 (c1_1(a717)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2897, 3064])).
% 1.53/1.78 tff(3068,plain,
% 1.53/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | c0_1(a717) | (~c1_1(a717)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3069,plain,
% 1.53/1.78 (((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717))) <=> (c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | c0_1(a717) | (~c1_1(a717)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3070,plain,
% 1.53/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | c0_1(a717) | (~c1_1(a717))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3069])).
% 1.53/1.78 tff(3071,plain,
% 1.53/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | c0_1(a717) | (~c1_1(a717)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3070, 3068])).
% 1.53/1.78 tff(3072,plain,
% 1.53/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3073,plain,
% 1.53/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | c0_1(a717) | (~c1_1(a717))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3072, 3071])).
% 1.53/1.78 tff(3074,plain,
% 1.53/1.78 (c0_1(a717)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3073, 206, 3067, 3045, 3066, 3065, 3043, 756, 3053])).
% 1.53/1.78 tff(3075,plain,
% 1.53/1.78 (hskp4),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2820, 2705, 360])).
% 1.53/1.78 tff(3076,plain,
% 1.53/1.78 (~c3_1(a698)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[976, 3075])).
% 1.53/1.78 tff(3077,plain,
% 1.53/1.78 (~c2_1(a698)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[854, 3075])).
% 1.53/1.78 tff(3078,plain,
% 1.53/1.78 (~c0_1(a698)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[848, 3075])).
% 1.53/1.78 tff(3079,plain,
% 1.53/1.78 (c3_1(a717)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1820, 3064])).
% 1.53/1.78 tff(3080,plain,
% 1.53/1.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c2_1(a717) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a717) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3081,plain,
% 1.53/1.78 ((hskp0 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp0 | c2_1(a717) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3082,plain,
% 1.53/1.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c2_1(a717) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3081])).
% 1.53/1.78 tff(3083,plain,
% 1.53/1.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a717) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3082, 3080])).
% 1.53/1.78 tff(3084,plain,
% 1.53/1.78 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3085,plain,
% 1.53/1.78 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a717) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3084, 3083])).
% 1.53/1.78 tff(3086,plain,
% 1.53/1.78 (hskp0),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3085, 206, 3079, 3065, 3078, 3077, 3076, 2715, 3074])).
% 1.53/1.78 tff(3087,plain,
% 1.53/1.78 (~c1_1(a692)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[787, 3086])).
% 1.53/1.78 tff(3088,plain,
% 1.53/1.78 (~c0_1(a692)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[793, 3086])).
% 1.53/1.78 tff(3089,plain,
% 1.53/1.78 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.53/1.78 inference(bind,[status(th)],[])).
% 1.53/1.78 tff(3090,plain,
% 1.53/1.78 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.78 inference(quant_intro,[status(thm)],[3089])).
% 1.53/1.78 tff(3091,plain,
% 1.53/1.78 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3092,plain,
% 1.53/1.78 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.53/1.78 inference(bind,[status(th)],[])).
% 1.53/1.78 tff(3093,plain,
% 1.53/1.78 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.78 inference(quant_intro,[status(thm)],[3092])).
% 1.53/1.78 tff(3094,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.53/1.78 tff(3095,plain,
% 1.53/1.78 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3094, 3093])).
% 1.53/1.78 tff(3096,plain,
% 1.53/1.78 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3095, 3091])).
% 1.53/1.78 tff(3097,plain,(
% 1.53/1.78 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.78 inference(skolemize,[status(sab)],[3096])).
% 1.53/1.78 tff(3098,plain,
% 1.53/1.78 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3097, 3090])).
% 1.63/1.78 tff(3099,plain,
% 1.63/1.78 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c3_1(a717)) | (~c1_1(a717)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3100,plain,
% 1.63/1.78 ((hskp17 | (~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717))) <=> (hskp17 | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c3_1(a717)) | (~c1_1(a717)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3101,plain,
% 1.63/1.78 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c3_1(a717)) | (~c1_1(a717))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[3100])).
% 1.63/1.78 tff(3102,plain,
% 1.63/1.78 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c3_1(a717)) | (~c1_1(a717)))),
% 1.63/1.78 inference(transitivity,[status(thm)],[3101, 3099])).
% 1.63/1.78 tff(3103,plain,
% 1.63/1.78 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(3104,plain,
% 1.63/1.78 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c3_1(a717)) | (~c1_1(a717))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[3103, 3102])).
% 1.63/1.78 tff(3105,plain,
% 1.63/1.78 (hskp17),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[3104, 206, 3067, 3079, 3045, 3065, 3043, 3098, 3053])).
% 1.63/1.78 tff(3106,plain,
% 1.63/1.78 (((~hskp17) | (~c3_1(a744))) <=> ((~hskp17) | (~c3_1(a744)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3107,plain,
% 1.63/1.78 (((~c3_1(a744)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a744)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3108,axiom,((~c3_1(a744)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.63/1.78 tff(3109,plain,
% 1.63/1.78 ((~hskp17) | (~c3_1(a744))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[3108, 3107])).
% 1.63/1.78 tff(3110,plain,
% 1.63/1.78 ((~hskp17) | (~c3_1(a744))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[3109, 3106])).
% 1.63/1.78 tff(3111,plain,
% 1.63/1.78 (~c3_1(a744)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[3110, 3105])).
% 1.63/1.78 tff(3112,plain,
% 1.63/1.78 (((~hskp17) | (~c1_1(a744))) <=> ((~hskp17) | (~c1_1(a744)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3113,plain,
% 1.63/1.78 (((~c1_1(a744)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a744)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3114,axiom,((~c1_1(a744)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.63/1.78 tff(3115,plain,
% 1.63/1.78 ((~hskp17) | (~c1_1(a744))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[3114, 3113])).
% 1.63/1.78 tff(3116,plain,
% 1.63/1.78 ((~hskp17) | (~c1_1(a744))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[3115, 3112])).
% 1.63/1.78 tff(3117,plain,
% 1.63/1.78 (~c1_1(a744)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[3116, 3105])).
% 1.63/1.78 tff(3118,plain,
% 1.63/1.78 (c2_1(a692)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[803, 3086])).
% 1.63/1.78 tff(3119,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a744) | c3_1(a744) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c0_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a744) | c3_1(a744) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c0_1(a744)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3120,plain,
% 1.63/1.78 (((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692)) <=> (c1_1(a744) | c3_1(a744) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c0_1(a744)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3121,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a744) | c3_1(a744) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c0_1(a744))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[3120])).
% 1.63/1.78 tff(3122,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a744) | c3_1(a744) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c0_1(a744)))),
% 1.63/1.78 inference(transitivity,[status(thm)],[3121, 3119])).
% 1.63/1.78 tff(3123,plain,
% 1.63/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(3124,plain,
% 1.63/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a744) | c3_1(a744) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c0_1(a744))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[3123, 3122])).
% 1.63/1.78 tff(3125,plain,
% 1.63/1.78 (~c0_1(a744)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[3124, 206, 3066, 3118, 3117, 3111, 3043, 3088, 3087, 512, 3053])).
% 1.63/1.78 tff(3126,plain,
% 1.63/1.78 (((~hskp17) | (~c2_1(a744))) <=> ((~hskp17) | (~c2_1(a744)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3127,plain,
% 1.63/1.78 (((~c2_1(a744)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a744)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3128,axiom,((~c2_1(a744)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.63/1.78 tff(3129,plain,
% 1.63/1.78 ((~hskp17) | (~c2_1(a744))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[3128, 3127])).
% 1.63/1.78 tff(3130,plain,
% 1.63/1.78 ((~hskp17) | (~c2_1(a744))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[3129, 3126])).
% 1.63/1.78 tff(3131,plain,
% 1.63/1.78 (~c2_1(a744)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[3130, 3105])).
% 1.63/1.78 tff(3132,plain,
% 1.63/1.78 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c1_1(a717)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3133,plain,
% 1.63/1.78 ((hskp20 | hskp16 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717))) <=> (hskp20 | hskp16 | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c1_1(a717)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3134,plain,
% 1.63/1.78 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c1_1(a717))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[3133])).
% 1.63/1.78 tff(3135,plain,
% 1.63/1.78 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c1_1(a717)))),
% 1.63/1.78 inference(transitivity,[status(thm)],[3134, 3132])).
% 1.63/1.78 tff(3136,plain,
% 1.63/1.78 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(3137,plain,
% 1.63/1.78 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c1_1(a717))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[3136, 3135])).
% 1.63/1.78 tff(3138,plain,
% 1.63/1.78 (hskp16),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[3137, 206, 250, 3067, 3079, 3065, 2943])).
% 1.63/1.78 tff(3139,plain,
% 1.63/1.78 (c3_1(a738)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2958, 3138])).
% 1.63/1.78 tff(3140,plain,
% 1.63/1.78 (c2_1(a738)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2966, 3138])).
% 1.63/1.78 tff(3141,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c0_1(a744))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3142,plain,
% 1.63/1.78 (((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744)) <=> (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c0_1(a744))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3143,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c0_1(a744)))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[3142])).
% 1.63/1.78 tff(3144,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c0_1(a744))),
% 1.63/1.78 inference(transitivity,[status(thm)],[3143, 3141])).
% 1.63/1.78 tff(3145,plain,
% 1.63/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(3146,plain,
% 1.63/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c0_1(a744)),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[3145, 3144])).
% 1.63/1.78 tff(3147,plain,
% 1.63/1.78 (~c0_1(a738)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[3146, 206, 3140, 3139, 3045, 3131, 3111, 3043, 1699, 3125, 3053])).
% 1.63/1.78 tff(3148,plain,
% 1.63/1.78 (~c1_1(a738)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[2989, 3138])).
% 1.63/1.78 tff(3149,plain,
% 1.63/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 1.63/1.78 inference(rewrite,[status(thm)],[])).
% 1.63/1.78 tff(3150,plain,
% 1.63/1.78 (((~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763)) <=> (c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3151,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[3150])).
% 1.63/1.79 tff(3152,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[3151, 3149])).
% 1.63/1.79 tff(3153,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(3154,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3153, 3152])).
% 1.63/1.79 tff(3155,plain,
% 1.63/1.79 (~c3_1(a763)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3154, 206, 3140, 3139, 3045, 372, 1728, 3148, 3043, 2984, 3053])).
% 1.63/1.79 tff(3156,plain,
% 1.63/1.79 (hskp7),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3003, 206, 2920, 3140, 3139, 3148, 2725])).
% 1.63/1.79 tff(3157,plain,
% 1.63/1.79 (~c3_1(a708)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3009, 3156])).
% 1.63/1.79 tff(3158,plain,
% 1.63/1.79 (c2_1(a708)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3017, 3156])).
% 1.63/1.79 tff(3159,plain,
% 1.63/1.79 (c1_1(a708)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3025, 3156])).
% 1.63/1.79 tff(3160,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3032, 206, 1731, 3140, 3159, 3158, 372, 3148, 3157, 512, 3155, 3147])).
% 1.63/1.79 tff(3161,plain,(c3_1(a695) | (~c0_1(a763)) | c2_1(a763) | hskp13 | hskp20 | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a733)) | (~hskp23)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(3162,plain,
% 1.63/1.79 (c3_1(a695)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3161, 2920, 1728, 1731, 250, 2919, 1677, 1678, 2157, 2156, 2155, 360])).
% 1.63/1.79 tff(3163,assumption,(c3_1(a695)), introduced(assumption)).
% 1.63/1.79 tff(3164,assumption,(hskp7), introduced(assumption)).
% 1.63/1.79 tff(3165,plain,
% 1.63/1.79 (~c3_1(a708)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3009, 3164])).
% 1.63/1.79 tff(3166,plain,
% 1.63/1.79 (c2_1(a708)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3017, 3164])).
% 1.63/1.79 tff(3167,plain,
% 1.63/1.79 (c1_1(a708)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3025, 3164])).
% 1.63/1.79 tff(3168,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a708) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a708)) | (~c2_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a708) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a708)) | (~c2_1(a708)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3169,plain,
% 1.63/1.79 ((hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708))) <=> (hskp20 | c3_1(a708) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a708)) | (~c2_1(a708)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3170,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a708) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a708)) | (~c2_1(a708))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[3169])).
% 1.63/1.79 tff(3171,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a708) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a708)) | (~c2_1(a708)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[3170, 3168])).
% 1.63/1.79 tff(3172,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(3173,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a708) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a708)) | (~c2_1(a708))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3172, 3171])).
% 1.63/1.79 tff(3174,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3173, 206, 250, 2685, 2649, 3167, 3166, 3165, 2002, 3163])).
% 1.63/1.79 tff(3175,plain,((~hskp7) | hskp20 | (~c3_1(a695))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(3176,plain,
% 1.63/1.79 (~hskp7),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3175, 3162, 250])).
% 1.63/1.79 tff(3177,assumption,(hskp16), introduced(assumption)).
% 1.63/1.79 tff(3178,plain,
% 1.63/1.79 (~c1_1(a738)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2989, 3177])).
% 1.63/1.79 tff(3179,plain,
% 1.63/1.79 (c3_1(a738)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2958, 3177])).
% 1.63/1.79 tff(3180,plain,
% 1.63/1.79 (c2_1(a738)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[2966, 3177])).
% 1.63/1.79 tff(3181,assumption,(~hskp7), introduced(assumption)).
% 1.63/1.79 tff(3182,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3003, 206, 2920, 3181, 3180, 3179, 3178, 2725])).
% 1.63/1.79 tff(3183,plain,((~hskp16) | hskp13 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(3184,plain,
% 1.63/1.79 (~hskp16),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3183, 2920, 3176])).
% 1.63/1.79 tff(3185,plain,
% 1.63/1.79 (^[U: $i] : refl((hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 1.63/1.79 inference(bind,[status(th)],[])).
% 1.63/1.79 tff(3186,plain,
% 1.63/1.79 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.63/1.79 inference(quant_intro,[status(thm)],[3185])).
% 1.63/1.79 tff(3187,plain,
% 1.63/1.79 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3188,plain,
% 1.63/1.79 (^[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) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_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))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7) <=> ((hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp7))), rewrite(((hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 1.63/1.79 inference(bind,[status(th)],[])).
% 1.63/1.79 tff(3189,plain,
% 1.63/1.79 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.63/1.79 inference(quant_intro,[status(thm)],[3188])).
% 1.63/1.79 tff(3190,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.63/1.79 tff(3191,plain,
% 1.63/1.79 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3190, 3189])).
% 1.63/1.79 tff(3192,plain,
% 1.63/1.79 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3191, 3187])).
% 1.63/1.79 tff(3193,plain,(
% 1.63/1.79 ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.63/1.79 inference(skolemize,[status(sab)],[3192])).
% 1.63/1.79 tff(3194,plain,
% 1.63/1.79 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3193, 3186])).
% 1.63/1.79 tff(3195,plain,
% 1.63/1.79 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3196,plain,
% 1.63/1.79 ((hskp7 | hskp2 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725)) <=> (hskp7 | hskp2 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3197,plain,
% 1.63/1.79 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725)))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[3196])).
% 1.63/1.79 tff(3198,plain,
% 1.63/1.79 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))),
% 1.63/1.79 inference(transitivity,[status(thm)],[3197, 3195])).
% 1.63/1.79 tff(3199,plain,
% 1.63/1.79 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(3200,plain,
% 1.63/1.79 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3199, 3198])).
% 1.63/1.79 tff(3201,plain,
% 1.63/1.79 (hskp7 | hskp2 | c2_1(a725)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3200, 206, 524, 968, 3194])).
% 1.63/1.79 tff(3202,plain,
% 1.63/1.79 (hskp2),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3201, 2921, 3181])).
% 1.63/1.79 tff(3203,plain,
% 1.63/1.79 (~c3_1(a697)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1286, 450])).
% 1.63/1.79 tff(3204,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a725))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3205,plain,
% 1.63/1.79 (((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a725) | c2_1(a725) | c0_1(a725)) <=> (c0_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a725))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3206,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a725)))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[3205])).
% 1.63/1.79 tff(3207,plain,
% 1.63/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a725))),
% 1.63/1.79 inference(transitivity,[status(thm)],[3206, 3204])).
% 1.63/1.79 tff(3208,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a725) | c2_1(a725) | c0_1(a725))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(3209,plain,
% 1.63/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a725)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3208, 3207])).
% 1.63/1.79 tff(3210,plain,
% 1.63/1.79 (~c1_1(a697)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3209, 206, 2685, 2649, 458, 524, 968, 3203, 1699, 2921, 3163])).
% 1.63/1.79 tff(3211,plain,
% 1.63/1.79 (^[U: $i] : refl((hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.63/1.79 inference(bind,[status(th)],[])).
% 1.63/1.79 tff(3212,plain,
% 1.63/1.79 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.79 inference(quant_intro,[status(thm)],[3211])).
% 1.63/1.79 tff(3213,plain,
% 1.63/1.79 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3214,plain,
% 1.63/1.79 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp16) <=> ((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16))), rewrite(((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp16) <=> (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.63/1.79 inference(bind,[status(th)],[])).
% 1.63/1.79 tff(3215,plain,
% 1.63/1.79 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp16) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.79 inference(quant_intro,[status(thm)],[3214])).
% 1.63/1.79 tff(3216,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 1.63/1.79 tff(3217,plain,
% 1.63/1.79 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3216, 3215])).
% 1.63/1.79 tff(3218,plain,
% 1.63/1.79 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3217, 3213])).
% 1.63/1.79 tff(3219,plain,(
% 1.63/1.79 ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.79 inference(skolemize,[status(sab)],[3218])).
% 1.63/1.79 tff(3220,plain,
% 1.63/1.79 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3219, 3212])).
% 1.63/1.79 tff(3221,plain,
% 1.63/1.79 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3222,plain,
% 1.63/1.79 ((hskp16 | hskp7 | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697))) <=> (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3223,plain,
% 1.63/1.79 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[3222])).
% 1.63/1.79 tff(3224,plain,
% 1.63/1.79 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[3223, 3221])).
% 1.63/1.79 tff(3225,plain,
% 1.63/1.79 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(3226,plain,
% 1.63/1.79 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3225, 3224])).
% 1.63/1.79 tff(3227,plain,
% 1.63/1.79 (hskp7 | c1_1(a697)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3226, 206, 12, 458, 474, 3220])).
% 1.63/1.79 tff(3228,plain,
% 1.63/1.79 (hskp7),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3227, 3210])).
% 1.63/1.79 tff(3229,plain,
% 1.63/1.79 (~c3_1(a708)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3009, 3228])).
% 1.63/1.79 tff(3230,plain,
% 1.63/1.79 (c2_1(a708)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3017, 3228])).
% 1.63/1.79 tff(3231,plain,
% 1.63/1.79 (c1_1(a708)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3025, 3228])).
% 1.63/1.79 tff(3232,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | c3_1(a708) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)) | (~c1_1(a708)) | (~c2_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c3_1(a708) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)) | (~c1_1(a708)) | (~c2_1(a708)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3233,plain,
% 1.63/1.79 ((hskp16 | (~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697))) <=> (hskp16 | c3_1(a708) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)) | (~c1_1(a708)) | (~c2_1(a708)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3234,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | c3_1(a708) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)) | (~c1_1(a708)) | (~c2_1(a708))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[3233])).
% 1.63/1.79 tff(3235,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c3_1(a708) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)) | (~c1_1(a708)) | (~c2_1(a708)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[3234, 3232])).
% 1.63/1.79 tff(3236,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(3237,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c3_1(a708) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)) | (~c1_1(a708)) | (~c2_1(a708))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3236, 3235])).
% 1.63/1.79 tff(3238,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3237, 206, 12, 3231, 3230, 458, 474, 3229, 22, 3210])).
% 1.63/1.79 tff(3239,plain,((~hskp3) | hskp16 | c0_1(a725) | c3_1(a725) | c2_1(a725) | (~c3_1(a695))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(3240,plain,
% 1.63/1.79 (~hskp3),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3239, 2921, 524, 968, 12, 3163])).
% 1.63/1.79 tff(3241,assumption,(hskp2), introduced(assumption)).
% 1.63/1.79 tff(3242,plain,
% 1.63/1.79 (~c2_1(a696)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1884, 3241])).
% 1.63/1.79 tff(3243,plain,
% 1.63/1.79 (c1_1(a696)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1907, 3241])).
% 1.63/1.79 tff(3244,plain,
% 1.63/1.79 (c0_1(a696)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[1892, 3241])).
% 1.63/1.79 tff(3245,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | c2_1(a725))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | c2_1(a725))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3246,plain,
% 1.63/1.79 ((hskp3 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c3_1(a725) | c1_1(a725) | c2_1(a725)) <=> (hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | c2_1(a725))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3247,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c3_1(a725) | c1_1(a725) | c2_1(a725))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | c2_1(a725)))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[3246])).
% 1.63/1.79 tff(3248,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c3_1(a725) | c1_1(a725) | c2_1(a725))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | c2_1(a725))),
% 1.63/1.79 inference(transitivity,[status(thm)],[3247, 3245])).
% 1.63/1.79 tff(3249,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c3_1(a725) | c1_1(a725) | c2_1(a725))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(3250,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | c2_1(a725)),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3249, 3248])).
% 1.63/1.79 tff(3251,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3250, 206, 2134, 3244, 3243, 523, 968, 3242, 1602, 2921])).
% 1.63/1.79 tff(3252,plain,((~hskp2) | hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a725)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(3253,plain,
% 1.63/1.79 ($false),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3252, 3240, 3202, 523, 968, 2921])).
% 1.63/1.79 tff(3254,plain,(c2_1(a725) | c1_1(a725) | c3_1(a725) | c0_1(a725) | hskp16 | (~c3_1(a695)) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.63/1.79 tff(3255,plain,
% 1.63/1.79 (c2_1(a725)),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3254, 3044, 2923, 2924, 3184, 3162, 3176])).
% 1.63/1.79 tff(3256,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c2_1(a725)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3257,plain,
% 1.63/1.79 ((hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725))) <=> (hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c2_1(a725)))),
% 1.63/1.79 inference(rewrite,[status(thm)],[])).
% 1.63/1.79 tff(3258,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c2_1(a725))))),
% 1.63/1.79 inference(monotonicity,[status(thm)],[3257])).
% 1.63/1.79 tff(3259,plain,
% 1.63/1.79 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c2_1(a725)))),
% 1.63/1.79 inference(transitivity,[status(thm)],[3258, 3256])).
% 1.63/1.79 tff(3260,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))),
% 1.63/1.79 inference(quant_inst,[status(thm)],[])).
% 1.63/1.79 tff(3261,plain,
% 1.63/1.79 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c2_1(a725))),
% 1.63/1.79 inference(modus_ponens,[status(thm)],[3260, 3259])).
% 1.63/1.79 tff(3262,plain,
% 1.63/1.79 (hskp14 | (~c3_1(a695)) | (~c2_1(a725))),
% 1.63/1.79 inference(unit_resolution,[status(thm)],[3261, 206, 2685, 2649, 3044, 2923, 1545])).
% 1.63/1.79 tff(3263,plain,
% 1.63/1.80 (hskp14),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3262, 3255, 3162])).
% 1.63/1.80 tff(3264,plain,
% 1.63/1.80 (~c3_1(a730)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[438, 3263])).
% 1.63/1.80 tff(3265,plain,
% 1.63/1.80 (c0_1(a730)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[424, 3263])).
% 1.63/1.80 tff(3266,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c3_1(a730) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a730)) | c2_1(a730) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a730) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a730)) | c2_1(a730) | (~c0_1(a763)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3267,plain,
% 1.63/1.80 (((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (c1_1(a763) | c2_1(a763) | c3_1(a730) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a730)) | c2_1(a730) | (~c0_1(a763)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3268,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c3_1(a730) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a730)) | c2_1(a730) | (~c0_1(a763))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[3267])).
% 1.63/1.80 tff(3269,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a730) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a730)) | c2_1(a730) | (~c0_1(a763)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[3268, 3266])).
% 1.63/1.80 tff(3270,plain,
% 1.63/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(3271,plain,
% 1.63/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a730) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a730)) | c2_1(a730) | (~c0_1(a763))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3270, 3269])).
% 1.63/1.80 tff(3272,plain,
% 1.63/1.80 (c2_1(a730)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3271, 206, 1731, 3265, 372, 1728, 3264, 2924, 2923, 2340, 3255])).
% 1.63/1.80 tff(3273,plain,
% 1.63/1.80 (c1_1(a730)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[416, 3263])).
% 1.63/1.80 tff(3274,plain,
% 1.63/1.80 ((hskp29 | hskp13 | hskp7) <=> (hskp29 | hskp13 | hskp7)),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3275,plain,
% 1.63/1.80 (((hskp29 | hskp7) | hskp13) <=> (hskp29 | hskp13 | hskp7)),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3276,axiom,((hskp29 | hskp7) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 1.63/1.80 tff(3277,plain,
% 1.63/1.80 (hskp29 | hskp13 | hskp7),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3276, 3275])).
% 1.63/1.80 tff(3278,plain,
% 1.63/1.80 (hskp29 | hskp13 | hskp7),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3277, 3274])).
% 1.63/1.80 tff(3279,plain,
% 1.63/1.80 (hskp29 | hskp13 | hskp7),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3278, 3274])).
% 1.63/1.80 tff(3280,plain,
% 1.63/1.80 (hskp29 | hskp13 | hskp7),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3279, 3274])).
% 1.63/1.80 tff(3281,plain,
% 1.63/1.80 (hskp29 | hskp13 | hskp7),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3280, 3274])).
% 1.63/1.80 tff(3282,plain,
% 1.63/1.80 (hskp29),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3281, 3176, 2920])).
% 1.63/1.80 tff(3283,plain,
% 1.63/1.80 (((~hskp29) | c3_1(a713)) <=> ((~hskp29) | c3_1(a713))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3284,axiom,((~hskp29) | c3_1(a713)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.63/1.80 tff(3285,plain,
% 1.63/1.80 ((~hskp29) | c3_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3284, 3283])).
% 1.63/1.80 tff(3286,plain,
% 1.63/1.80 ((~hskp29) | c3_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3285, 3283])).
% 1.63/1.80 tff(3287,plain,
% 1.63/1.80 ((~hskp29) | c3_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3286, 3283])).
% 1.63/1.80 tff(3288,plain,
% 1.63/1.80 ((~hskp29) | c3_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3287, 3283])).
% 1.63/1.80 tff(3289,plain,
% 1.63/1.80 ((~hskp29) | c3_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3288, 3283])).
% 1.63/1.80 tff(3290,plain,
% 1.63/1.80 (c3_1(a713)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3289, 3282])).
% 1.63/1.80 tff(3291,plain,
% 1.63/1.80 (((~hskp29) | c2_1(a713)) <=> ((~hskp29) | c2_1(a713))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3292,axiom,((~hskp29) | c2_1(a713)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.63/1.80 tff(3293,plain,
% 1.63/1.80 ((~hskp29) | c2_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3292, 3291])).
% 1.63/1.80 tff(3294,plain,
% 1.63/1.80 ((~hskp29) | c2_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3293, 3291])).
% 1.63/1.80 tff(3295,plain,
% 1.63/1.80 ((~hskp29) | c2_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3294, 3291])).
% 1.63/1.80 tff(3296,plain,
% 1.63/1.80 ((~hskp29) | c2_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3295, 3291])).
% 1.63/1.80 tff(3297,plain,
% 1.63/1.80 ((~hskp29) | c2_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3296, 3291])).
% 1.63/1.80 tff(3298,plain,
% 1.63/1.80 (c2_1(a713)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3297, 3282])).
% 1.63/1.80 tff(3299,plain,
% 1.63/1.80 (((~hskp29) | c0_1(a713)) <=> ((~hskp29) | c0_1(a713))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3300,axiom,((~hskp29) | c0_1(a713)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.63/1.80 tff(3301,plain,
% 1.63/1.80 ((~hskp29) | c0_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3300, 3299])).
% 1.63/1.80 tff(3302,plain,
% 1.63/1.80 ((~hskp29) | c0_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3301, 3299])).
% 1.63/1.80 tff(3303,plain,
% 1.63/1.80 ((~hskp29) | c0_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3302, 3299])).
% 1.63/1.80 tff(3304,plain,
% 1.63/1.80 ((~hskp29) | c0_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3303, 3299])).
% 1.63/1.80 tff(3305,plain,
% 1.63/1.80 ((~hskp29) | c0_1(a713)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3304, 3299])).
% 1.63/1.80 tff(3306,plain,
% 1.63/1.80 (c0_1(a713)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3305, 3282])).
% 1.63/1.80 tff(3307,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a730) | (~ndr1_0) | (~c1_1(a730)) | (~c2_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a730) | (~ndr1_0) | (~c1_1(a730)) | (~c2_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3308,plain,
% 1.63/1.80 ((hskp20 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730))) <=> (hskp20 | c3_1(a730) | (~ndr1_0) | (~c1_1(a730)) | (~c2_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3309,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a730) | (~ndr1_0) | (~c1_1(a730)) | (~c2_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[3308])).
% 1.63/1.80 tff(3310,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a730) | (~ndr1_0) | (~c1_1(a730)) | (~c2_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[3309, 3307])).
% 1.63/1.80 tff(3311,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(3312,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a730) | (~ndr1_0) | (~c1_1(a730)) | (~c2_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3311, 3310])).
% 1.63/1.80 tff(3313,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3312, 206, 250, 3306, 3298, 3290, 3273, 3264, 2002, 3272])).
% 1.63/1.80 tff(3314,plain,(hskp13 | hskp20 | (~c0_1(a763)) | c2_1(a763) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a733)) | (~hskp23)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(3315,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3314, 380, 360, 2920, 366, 2919, 1677, 1678, 2157, 2156, 2155, 250])).
% 1.63/1.80 tff(3316,plain,((~hskp23) | hskp13 | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a733)) | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(3317,plain,
% 1.63/1.80 (~hskp23),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3316, 2915, 2918, 2917, 2916, 2879, 2880, 2878, 250])).
% 1.63/1.80 tff(3318,plain,
% 1.63/1.80 ((hskp23 | hskp13 | hskp11) <=> (hskp23 | hskp13 | hskp11)),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3319,plain,
% 1.63/1.80 (((hskp11 | hskp23) | hskp13) <=> (hskp23 | hskp13 | hskp11)),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3320,axiom,((hskp11 | hskp23) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 1.63/1.80 tff(3321,plain,
% 1.63/1.80 (hskp23 | hskp13 | hskp11),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3320, 3319])).
% 1.63/1.80 tff(3322,plain,
% 1.63/1.80 (hskp23 | hskp13 | hskp11),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3321, 3318])).
% 1.63/1.80 tff(3323,plain,
% 1.63/1.80 (hskp23 | hskp13 | hskp11),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3322, 3318])).
% 1.63/1.80 tff(3324,plain,
% 1.63/1.80 (hskp23 | hskp13 | hskp11),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3323, 3318])).
% 1.63/1.80 tff(3325,plain,
% 1.63/1.80 (hskp23 | hskp13 | hskp11),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3324, 3318])).
% 1.63/1.80 tff(3326,plain,
% 1.63/1.80 (hskp11),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3325, 3317, 2915])).
% 1.63/1.80 tff(3327,plain,
% 1.63/1.80 (~c1_1(a722)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2092, 3326])).
% 1.63/1.80 tff(3328,plain,
% 1.63/1.80 (c3_1(a722)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2281, 3326])).
% 1.63/1.80 tff(3329,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3330,plain,
% 1.63/1.80 ((hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695))) <=> (hskp20 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3331,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[3330])).
% 1.63/1.80 tff(3332,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[3331, 3329])).
% 1.63/1.80 tff(3333,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(3334,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3333, 3332])).
% 1.63/1.80 tff(3335,plain,
% 1.63/1.80 (~c0_1(a733)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3334, 206, 250, 2880, 2878, 2657, 2649, 2002, 11])).
% 1.63/1.80 tff(3336,plain,
% 1.63/1.80 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.63/1.80 inference(bind,[status(th)],[])).
% 1.63/1.80 tff(3337,plain,
% 1.63/1.80 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.63/1.80 inference(quant_intro,[status(thm)],[3336])).
% 1.63/1.80 tff(3338,plain,
% 1.63/1.80 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3339,plain,
% 1.63/1.80 (^[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)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp8) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.63/1.80 inference(bind,[status(th)],[])).
% 1.63/1.80 tff(3340,plain,
% 1.63/1.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.63/1.80 inference(quant_intro,[status(thm)],[3339])).
% 1.63/1.80 tff(3341,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 1.63/1.80 tff(3342,plain,
% 1.63/1.80 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3341, 3340])).
% 1.63/1.80 tff(3343,plain,
% 1.63/1.80 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3342, 3338])).
% 1.63/1.80 tff(3344,plain,(
% 1.63/1.80 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.63/1.80 inference(skolemize,[status(sab)],[3343])).
% 1.63/1.80 tff(3345,plain,
% 1.63/1.80 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3344, 3337])).
% 1.63/1.80 tff(3346,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3347,plain,
% 1.63/1.80 ((hskp8 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733))) <=> (hskp8 | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3348,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[3347])).
% 1.63/1.80 tff(3349,plain,
% 1.63/1.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[3348, 3346])).
% 1.63/1.80 tff(3350,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(3351,plain,
% 1.63/1.80 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[3350, 3349])).
% 1.65/1.80 tff(3352,plain,
% 1.65/1.80 (hskp8),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3351, 206, 2880, 2878, 2916, 2918, 2917, 3345, 3335])).
% 1.65/1.80 tff(3353,plain,
% 1.65/1.80 (~c0_1(a710)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1797, 3352])).
% 1.65/1.80 tff(3354,plain,
% 1.65/1.80 (hskp11),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3325, 426, 2915])).
% 1.65/1.80 tff(3355,plain,
% 1.65/1.80 (~c1_1(a722)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2092, 3354])).
% 1.65/1.80 tff(3356,plain,
% 1.65/1.80 (hskp24),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2767, 426])).
% 1.65/1.80 tff(3357,plain,
% 1.65/1.80 (~c3_1(a764)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[277, 3356])).
% 1.65/1.80 tff(3358,plain,
% 1.65/1.80 (~c2_1(a764)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[283, 3356])).
% 1.65/1.80 tff(3359,plain,
% 1.65/1.80 (c3_1(a710)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1805, 3352])).
% 1.65/1.80 tff(3360,plain,
% 1.65/1.80 (c2_1(a710)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1871, 3352])).
% 1.65/1.80 tff(3361,plain,
% 1.65/1.80 (c3_1(a722)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2281, 3354])).
% 1.65/1.80 tff(3362,plain,
% 1.65/1.80 (c1_1(a764)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[291, 3356])).
% 1.65/1.80 tff(3363,plain,
% 1.65/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c1_1(a722) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c1_1(a722) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a764)))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(3364,plain,
% 1.65/1.80 (((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710))) <=> (c2_1(a764) | c3_1(a764) | c1_1(a722) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a764)))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(3365,plain,
% 1.65/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c1_1(a722) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a764))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[3364])).
% 1.65/1.80 tff(3366,plain,
% 1.65/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c1_1(a722) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a764)))),
% 1.65/1.80 inference(transitivity,[status(thm)],[3365, 3363])).
% 1.65/1.80 tff(3367,plain,
% 1.65/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))),
% 1.65/1.80 inference(quant_inst,[status(thm)],[])).
% 1.65/1.80 tff(3368,plain,
% 1.65/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c1_1(a722) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a764))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[3367, 3366])).
% 1.65/1.80 tff(3369,plain,
% 1.65/1.80 (~c2_1(a722)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3368, 206, 3362, 3361, 3360, 3359, 3358, 3357, 3355, 3353, 10])).
% 1.65/1.80 tff(3370,plain,
% 1.65/1.80 (c0_1(a764)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[298, 206, 162, 3362, 3358, 3357, 271])).
% 1.65/1.80 tff(3371,plain,
% 1.65/1.80 (hskp12),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1967, 2915, 250])).
% 1.65/1.80 tff(3372,plain,
% 1.65/1.80 (~c3_1(a725)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[124, 3371])).
% 1.65/1.80 tff(3373,plain,
% 1.65/1.80 (~c0_1(a725)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[136, 3371])).
% 1.65/1.80 tff(3374,plain,
% 1.65/1.80 (~c2_1(a725)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2741, 206, 162, 3362, 3358, 3357, 3373, 3372, 89])).
% 1.65/1.80 tff(3375,plain,
% 1.65/1.80 (~c2_1(a691)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2932, 3374, 2917, 3373, 3372, 2916, 11])).
% 1.65/1.80 tff(3376,plain,
% 1.65/1.80 (hskp20 | hskp16 | c2_1(a691)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2949, 206, 2918, 2917, 2943])).
% 1.65/1.80 tff(3377,plain,
% 1.65/1.80 (hskp16),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3376, 3375, 250])).
% 1.65/1.80 tff(3378,plain,
% 1.65/1.80 (~c1_1(a738)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2989, 3377])).
% 1.65/1.80 tff(3379,plain,
% 1.65/1.80 (c3_1(a738)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2958, 3377])).
% 1.65/1.80 tff(3380,plain,
% 1.65/1.80 (c2_1(a738)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2966, 3377])).
% 1.65/1.80 tff(3381,plain,
% 1.65/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a764) | c1_1(a738) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a764) | c1_1(a738) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(3382,plain,
% 1.65/1.80 (((~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a722) | (~c3_1(a722)) | c1_1(a722)) <=> (c3_1(a764) | c1_1(a738) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(3383,plain,
% 1.65/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a722) | (~c3_1(a722)) | c1_1(a722))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a764) | c1_1(a738) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a764)) | (~c1_1(a764))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[3382])).
% 1.65/1.80 tff(3384,plain,
% 1.65/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a722) | (~c3_1(a722)) | c1_1(a722))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a764) | c1_1(a738) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.65/1.80 inference(transitivity,[status(thm)],[3383, 3381])).
% 1.65/1.80 tff(3385,plain,
% 1.65/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a722) | (~c3_1(a722)) | c1_1(a722))),
% 1.65/1.80 inference(quant_inst,[status(thm)],[])).
% 1.65/1.80 tff(3386,plain,
% 1.65/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a764) | c1_1(a738) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a764)) | (~c1_1(a764))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[3385, 3384])).
% 1.65/1.80 tff(3387,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3386, 206, 3362, 3380, 3379, 3361, 3357, 3378, 3355, 2984, 3370, 3369])).
% 1.65/1.80 tff(3388,plain,(hskp23 | hskp20 | c3_1(a695) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(3389,plain,
% 1.65/1.80 (c3_1(a695)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3388, 3317, 250, 162])).
% 1.65/1.80 tff(3390,plain,
% 1.65/1.80 (~hskp7),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3175, 3389, 250])).
% 1.65/1.80 tff(3391,plain,
% 1.65/1.80 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c3_1(a722)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c3_1(a722)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3392,plain,
% 1.65/1.81 ((hskp13 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722))) <=> (hskp13 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c3_1(a722)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3393,plain,
% 1.65/1.81 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c3_1(a722))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[3392])).
% 1.65/1.81 tff(3394,plain,
% 1.65/1.81 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c3_1(a722)))),
% 1.65/1.81 inference(transitivity,[status(thm)],[3393, 3391])).
% 1.65/1.81 tff(3395,plain,
% 1.65/1.81 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(3396,plain,
% 1.65/1.81 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c3_1(a722))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[3395, 3394])).
% 1.65/1.81 tff(3397,plain,
% 1.65/1.81 (~c2_1(a722)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3396, 206, 2915, 3390, 3328, 3327, 2725])).
% 1.65/1.81 tff(3398,plain,
% 1.65/1.81 (~c1_1(a725)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[130, 3371])).
% 1.65/1.81 tff(3399,plain,
% 1.65/1.81 (~hskp16),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3183, 3390, 2915])).
% 1.65/1.81 tff(3400,plain,
% 1.65/1.81 (c2_1(a725)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3254, 3399, 3372, 3373, 3398, 3389, 3390])).
% 1.65/1.81 tff(3401,plain,
% 1.65/1.81 (hskp14 | (~c3_1(a695)) | (~c2_1(a725))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3261, 206, 2685, 2649, 3398, 3372, 1545])).
% 1.65/1.81 tff(3402,plain,
% 1.65/1.81 (hskp14),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3401, 3400, 3389])).
% 1.65/1.81 tff(3403,plain,
% 1.65/1.81 (~c3_1(a730)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[438, 3402])).
% 1.65/1.81 tff(3404,plain,
% 1.65/1.81 (hskp24),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2767, 3317])).
% 1.65/1.81 tff(3405,plain,
% 1.65/1.81 (~c3_1(a764)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[277, 3404])).
% 1.65/1.81 tff(3406,plain,
% 1.65/1.81 (~c2_1(a764)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[283, 3404])).
% 1.65/1.81 tff(3407,plain,
% 1.65/1.81 (c1_1(a730)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[416, 3402])).
% 1.65/1.81 tff(3408,plain,
% 1.65/1.81 (c0_1(a730)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[424, 3402])).
% 1.65/1.81 tff(3409,plain,
% 1.65/1.81 (hskp29),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3281, 3390, 2915])).
% 1.65/1.81 tff(3410,plain,
% 1.65/1.81 (c3_1(a713)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3289, 3409])).
% 1.65/1.81 tff(3411,plain,
% 1.65/1.81 (c2_1(a713)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3297, 3409])).
% 1.65/1.81 tff(3412,plain,
% 1.65/1.81 (c0_1(a713)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3305, 3409])).
% 1.65/1.81 tff(3413,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a764) | c3_1(a764) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a764) | c3_1(a764) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3414,plain,
% 1.65/1.81 (((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a764) | c2_1(a764) | c0_1(a764)) <=> (c2_1(a764) | c3_1(a764) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3415,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a764) | c2_1(a764) | c0_1(a764))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a764) | c3_1(a764) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764)))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[3414])).
% 1.65/1.81 tff(3416,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a764) | c2_1(a764) | c0_1(a764))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a764) | c3_1(a764) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))),
% 1.65/1.81 inference(transitivity,[status(thm)],[3415, 3413])).
% 1.65/1.81 tff(3417,plain,
% 1.65/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a764) | c2_1(a764) | c0_1(a764))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(3418,plain,
% 1.65/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a764) | c3_1(a764) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764)),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[3417, 3416])).
% 1.65/1.81 tff(3419,plain,
% 1.65/1.81 (c0_1(a764)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3418, 206, 3412, 3411, 3410, 3408, 3407, 3406, 3405, 3403, 1699])).
% 1.65/1.81 tff(3420,plain,
% 1.65/1.81 (c0_1(a722)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2100, 3326])).
% 1.65/1.81 tff(3421,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c0_1(a722)) | (~c2_1(a725)) | (~c0_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c0_1(a722)) | (~c2_1(a725)) | (~c0_1(a764)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3422,plain,
% 1.65/1.81 (((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c0_1(a722)) | (~c2_1(a725)) | (~c0_1(a764)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3423,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c0_1(a722)) | (~c2_1(a725)) | (~c0_1(a764))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[3422])).
% 1.65/1.81 tff(3424,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c0_1(a722)) | (~c2_1(a725)) | (~c0_1(a764)))),
% 1.65/1.81 inference(transitivity,[status(thm)],[3423, 3421])).
% 1.65/1.81 tff(3425,plain,
% 1.65/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(3426,plain,
% 1.65/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c0_1(a722)) | (~c2_1(a725)) | (~c0_1(a764))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[3425, 3424])).
% 1.65/1.81 tff(3427,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3426, 206, 3420, 3406, 3405, 3373, 3372, 3327, 2340, 3400, 3419, 3397])).
% 1.65/1.81 tff(3428,plain,(hskp20 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(3429,plain,
% 1.65/1.81 (hskp20),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3428, 162])).
% 1.65/1.81 tff(3430,plain,
% 1.65/1.81 (~c3_1(a754)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[614, 3429])).
% 1.65/1.81 tff(3431,plain,
% 1.65/1.81 (~c0_1(a754)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[541, 3429])).
% 1.65/1.81 tff(3432,plain,
% 1.65/1.81 (c2_1(a754)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[172, 3429])).
% 1.65/1.81 tff(3433,plain,
% 1.65/1.81 (~hskp24),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1557, 3431, 162, 3432, 3430])).
% 1.65/1.81 tff(3434,plain,
% 1.65/1.81 (hskp23),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2767, 3433])).
% 1.65/1.81 tff(3435,plain,
% 1.65/1.81 (~c2_1(a763)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[365, 3434])).
% 1.65/1.81 tff(3436,plain,
% 1.65/1.81 (~c1_1(a763)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[371, 3434])).
% 1.65/1.81 tff(3437,plain,
% 1.65/1.81 (c0_1(a763)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[379, 3434])).
% 1.65/1.81 tff(3438,assumption,(~c3_1(a763)), introduced(assumption)).
% 1.65/1.81 tff(3439,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3440,plain,
% 1.65/1.81 (((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3441,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[3440])).
% 1.65/1.81 tff(3442,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))),
% 1.65/1.81 inference(transitivity,[status(thm)],[3441, 3439])).
% 1.65/1.81 tff(3443,plain,
% 1.65/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(3444,plain,
% 1.65/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[3443, 3442])).
% 1.65/1.81 tff(3445,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3444, 206, 1731, 348, 1729, 1728, 164, 163, 2340, 3438])).
% 1.65/1.81 tff(3446,plain,(c3_1(a763) | (~c0_1(a763)) | (~c2_1(a754)) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(3447,plain,
% 1.65/1.81 (c3_1(a763)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3446, 3437, 3432, 3436, 3435, 3431, 3430])).
% 1.65/1.81 tff(3448,plain,
% 1.65/1.81 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a760) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c3_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c3_1(a760)) | (~c1_1(a760)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3449,plain,
% 1.65/1.81 ((hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp10 | c0_1(a760) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c3_1(a760)) | (~c1_1(a760)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3450,plain,
% 1.65/1.81 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a760) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c3_1(a760)) | (~c1_1(a760))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[3449])).
% 1.65/1.81 tff(3451,plain,
% 1.65/1.81 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c3_1(a760)) | (~c1_1(a760)))),
% 1.65/1.81 inference(transitivity,[status(thm)],[3450, 3448])).
% 1.65/1.81 tff(3452,plain,
% 1.65/1.81 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(3453,plain,
% 1.65/1.81 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c3_1(a760)) | (~c1_1(a760))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[3452, 3451])).
% 1.65/1.81 tff(3454,plain,
% 1.65/1.81 (hskp10),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3453, 206, 3056, 3055, 3432, 3054, 3431, 3430, 1671])).
% 1.65/1.81 tff(3455,plain,
% 1.65/1.81 (~c2_1(a717)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1812, 3454])).
% 1.65/1.81 tff(3456,plain,
% 1.65/1.81 (c1_1(a717)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2897, 3454])).
% 1.65/1.81 tff(3457,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a717) | (~c1_1(a717)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3458,plain,
% 1.65/1.81 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717))) <=> (c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a717) | (~c1_1(a717)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3459,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a717) | (~c1_1(a717))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[3458])).
% 1.65/1.81 tff(3460,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a717) | (~c1_1(a717)))),
% 1.65/1.81 inference(transitivity,[status(thm)],[3459, 3457])).
% 1.65/1.81 tff(3461,plain,
% 1.65/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(3462,plain,
% 1.65/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a717) | (~c1_1(a717))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 1.65/1.81 tff(3463,plain,
% 1.65/1.81 (c0_1(a717)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3462, 206, 2685, 2657, 2649, 3456, 3455, 756, 11])).
% 1.65/1.81 tff(3464,plain,
% 1.65/1.81 (hskp4),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2820, 2705, 3434])).
% 1.65/1.81 tff(3465,plain,
% 1.65/1.81 (~c3_1(a698)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[976, 3464])).
% 1.65/1.81 tff(3466,plain,
% 1.65/1.81 (~c2_1(a698)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[854, 3464])).
% 1.65/1.81 tff(3467,plain,
% 1.65/1.81 (~c0_1(a698)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[848, 3464])).
% 1.65/1.81 tff(3468,plain,
% 1.65/1.81 (c3_1(a717)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1820, 3454])).
% 1.65/1.81 tff(3469,plain,
% 1.65/1.81 (hskp0),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3085, 206, 3468, 3455, 3467, 3466, 3465, 2715, 3463])).
% 1.65/1.81 tff(3470,plain,
% 1.65/1.81 (~c1_1(a692)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[787, 3469])).
% 1.65/1.81 tff(3471,plain,
% 1.65/1.81 (~c0_1(a692)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[793, 3469])).
% 1.65/1.81 tff(3472,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3473,plain,
% 1.65/1.81 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a698) | c0_1(a698) | (~c1_1(a698))) <=> (c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3474,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a698) | c0_1(a698) | (~c1_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[3473])).
% 1.65/1.81 tff(3475,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a698) | c0_1(a698) | (~c1_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 1.65/1.81 inference(transitivity,[status(thm)],[3474, 3472])).
% 1.65/1.81 tff(3476,plain,
% 1.65/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a698) | c0_1(a698) | (~c1_1(a698)))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(3477,plain,
% 1.65/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[3476, 3475])).
% 1.65/1.81 tff(3478,plain,
% 1.65/1.81 (~c1_1(a698)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3477, 206, 2685, 2657, 2649, 3467, 3466, 756, 11])).
% 1.65/1.81 tff(3479,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a760) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | c2_1(a760) | (~c1_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a760) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | c2_1(a760) | (~c1_1(a760)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3480,plain,
% 1.65/1.81 (((~ndr1_0) | c0_1(a760) | c2_1(a760) | (~c1_1(a760)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698)) <=> (c0_1(a760) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | c2_1(a760) | (~c1_1(a760)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3481,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a760) | c2_1(a760) | (~c1_1(a760)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a760) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | c2_1(a760) | (~c1_1(a760))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[3480])).
% 1.65/1.81 tff(3482,plain,
% 1.65/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a760) | c2_1(a760) | (~c1_1(a760)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a760) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | c2_1(a760) | (~c1_1(a760)))),
% 1.65/1.81 inference(transitivity,[status(thm)],[3481, 3479])).
% 1.65/1.81 tff(3483,plain,
% 1.65/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a760) | c2_1(a760) | (~c1_1(a760)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(3484,plain,
% 1.65/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a760) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | c2_1(a760) | (~c1_1(a760))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[3483, 3482])).
% 1.65/1.81 tff(3485,plain,
% 1.65/1.81 (c2_1(a760)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3484, 206, 3056, 3054, 3467, 3466, 3465, 110, 3478])).
% 1.65/1.81 tff(3486,plain,
% 1.65/1.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3487,plain,
% 1.65/1.81 ((hskp3 | (~ndr1_0) | (~c2_1(a760)) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695))) <=> (hskp3 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(3488,plain,
% 1.65/1.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a760)) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a760))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[3487])).
% 1.65/1.82 tff(3489,plain,
% 1.65/1.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a760)) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 1.65/1.82 inference(transitivity,[status(thm)],[3488, 3486])).
% 1.65/1.82 tff(3490,plain,
% 1.65/1.82 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a760)) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(3491,plain,
% 1.65/1.82 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a760))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[3490, 3489])).
% 1.65/1.82 tff(3492,plain,
% 1.65/1.82 (hskp3),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[3491, 206, 2685, 2649, 3056, 3055, 2132, 11, 3485])).
% 1.65/1.82 tff(3493,plain,
% 1.65/1.82 (~c3_1(a697)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1286, 3492])).
% 1.65/1.82 tff(3494,plain,
% 1.65/1.82 (c2_1(a692)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[803, 3469])).
% 1.65/1.82 tff(3495,plain,
% 1.65/1.82 (c0_1(a697)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[457, 3492])).
% 1.65/1.82 tff(3496,plain,
% 1.65/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(3497,plain,
% 1.65/1.82 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692)) <=> (c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(3498,plain,
% 1.65/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697)))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[3497])).
% 1.65/1.82 tff(3499,plain,
% 1.65/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697))),
% 1.65/1.82 inference(transitivity,[status(thm)],[3498, 3496])).
% 1.65/1.82 tff(3500,plain,
% 1.65/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(3501,plain,
% 1.65/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697)),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[3500, 3499])).
% 1.65/1.82 tff(3502,plain,
% 1.65/1.82 (c1_1(a697)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[3501, 206, 2657, 2649, 3495, 3494, 3493, 3471, 3470, 512, 11])).
% 1.65/1.82 tff(3503,plain,
% 1.65/1.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c3_1(a717)) | (~c1_1(a717)))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(3504,plain,
% 1.65/1.82 ((hskp17 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717))) <=> (hskp17 | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c3_1(a717)) | (~c1_1(a717)))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(3505,plain,
% 1.65/1.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c3_1(a717)) | (~c1_1(a717))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[3504])).
% 1.65/1.82 tff(3506,plain,
% 1.65/1.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c3_1(a717)) | (~c1_1(a717)))),
% 1.65/1.82 inference(transitivity,[status(thm)],[3505, 3503])).
% 1.65/1.82 tff(3507,plain,
% 1.65/1.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(3508,plain,
% 1.65/1.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c3_1(a717)) | (~c1_1(a717))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[3507, 3506])).
% 1.65/1.82 tff(3509,plain,
% 1.65/1.82 (hskp17),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[3508, 206, 2685, 2657, 3456, 3468, 3455, 3098, 11])).
% 1.65/1.82 tff(3510,plain,
% 1.65/1.82 (~c3_1(a744)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[3110, 3509])).
% 1.65/1.82 tff(3511,plain,
% 1.65/1.82 (~c1_1(a744)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[3116, 3509])).
% 1.65/1.82 tff(3512,plain,
% 1.65/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a744) | c3_1(a744) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a744) | c3_1(a744) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a744)))),
% 1.67/1.82 inference(rewrite,[status(thm)],[])).
% 1.67/1.82 tff(3513,plain,
% 1.67/1.82 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692)) <=> (c1_1(a744) | c3_1(a744) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a744)))),
% 1.67/1.82 inference(rewrite,[status(thm)],[])).
% 1.67/1.82 tff(3514,plain,
% 1.67/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a744) | c3_1(a744) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a744))))),
% 1.67/1.82 inference(monotonicity,[status(thm)],[3513])).
% 1.67/1.82 tff(3515,plain,
% 1.67/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a744) | c3_1(a744) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a744)))),
% 1.67/1.82 inference(transitivity,[status(thm)],[3514, 3512])).
% 1.67/1.82 tff(3516,plain,
% 1.67/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))),
% 1.67/1.82 inference(quant_inst,[status(thm)],[])).
% 1.67/1.82 tff(3517,plain,
% 1.67/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a744) | c3_1(a744) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a744))),
% 1.67/1.82 inference(modus_ponens,[status(thm)],[3516, 3515])).
% 1.67/1.82 tff(3518,plain,
% 1.67/1.82 (~c0_1(a744)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[3517, 206, 2657, 2649, 3494, 3511, 3510, 3471, 3470, 512, 11])).
% 1.67/1.82 tff(3519,plain,
% 1.67/1.82 (~c2_1(a744)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[3130, 3509])).
% 1.67/1.82 tff(3520,plain,
% 1.67/1.82 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 1.67/1.82 inference(bind,[status(th)],[])).
% 1.67/1.82 tff(3521,plain,
% 1.67/1.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.67/1.82 inference(quant_intro,[status(thm)],[3520])).
% 1.67/1.82 tff(3522,plain,
% 1.67/1.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.67/1.82 inference(rewrite,[status(thm)],[])).
% 1.67/1.82 tff(3523,plain,
% 1.67/1.82 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 1.67/1.82 inference(bind,[status(th)],[])).
% 1.67/1.82 tff(3524,plain,
% 1.67/1.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.67/1.82 inference(quant_intro,[status(thm)],[3523])).
% 1.67/1.82 tff(3525,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.67/1.82 tff(3526,plain,
% 1.67/1.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.67/1.82 inference(modus_ponens,[status(thm)],[3525, 3524])).
% 1.67/1.82 tff(3527,plain,
% 1.67/1.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.67/1.82 inference(modus_ponens,[status(thm)],[3526, 3522])).
% 1.67/1.82 tff(3528,plain,(
% 1.67/1.82 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.67/1.82 inference(skolemize,[status(sab)],[3527])).
% 1.67/1.82 tff(3529,plain,
% 1.67/1.82 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.67/1.82 inference(modus_ponens,[status(thm)],[3528, 3521])).
% 1.67/1.82 tff(3530,plain,
% 1.67/1.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a760) | c2_1(a717) | (~ndr1_0) | (~c1_1(a717)) | (~c0_1(a717)) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a760) | c2_1(a717) | (~ndr1_0) | (~c1_1(a717)) | (~c0_1(a717)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 1.67/1.82 inference(rewrite,[status(thm)],[])).
% 1.67/1.82 tff(3531,plain,
% 1.67/1.82 ((hskp5 | (~ndr1_0) | c2_1(a717) | (~c0_1(a717)) | (~c1_1(a717)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760))) <=> (hskp5 | c0_1(a760) | c2_1(a717) | (~ndr1_0) | (~c1_1(a717)) | (~c0_1(a717)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 1.67/1.82 inference(rewrite,[status(thm)],[])).
% 1.67/1.82 tff(3532,plain,
% 1.67/1.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a717) | (~c0_1(a717)) | (~c1_1(a717)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a760) | c2_1(a717) | (~ndr1_0) | (~c1_1(a717)) | (~c0_1(a717)) | (~c2_1(a760)) | (~c1_1(a760))))),
% 1.67/1.82 inference(monotonicity,[status(thm)],[3531])).
% 1.67/1.82 tff(3533,plain,
% 1.67/1.82 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a717) | (~c0_1(a717)) | (~c1_1(a717)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a760) | c2_1(a717) | (~ndr1_0) | (~c1_1(a717)) | (~c0_1(a717)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 1.67/1.82 inference(transitivity,[status(thm)],[3532, 3530])).
% 1.67/1.82 tff(3534,plain,
% 1.67/1.82 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a717) | (~c0_1(a717)) | (~c1_1(a717)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))),
% 1.67/1.82 inference(quant_inst,[status(thm)],[])).
% 1.67/1.82 tff(3535,plain,
% 1.67/1.82 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a760) | c2_1(a717) | (~ndr1_0) | (~c1_1(a717)) | (~c0_1(a717)) | (~c2_1(a760)) | (~c1_1(a760))),
% 1.67/1.82 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 1.67/1.82 tff(3536,plain,
% 1.67/1.82 (hskp5),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[3535, 206, 3056, 3456, 3054, 3455, 3529, 3485, 3463])).
% 1.67/1.82 tff(3537,plain,
% 1.67/1.82 (c2_1(a701)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[36, 3536])).
% 1.67/1.82 tff(3538,plain,
% 1.67/1.82 (c0_1(a701)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[44, 3536])).
% 1.67/1.82 tff(3539,plain,
% 1.67/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c0_1(a744))),
% 1.67/1.82 inference(rewrite,[status(thm)],[])).
% 1.67/1.82 tff(3540,plain,
% 1.67/1.82 (((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744)) <=> (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c0_1(a744))),
% 1.67/1.82 inference(rewrite,[status(thm)],[])).
% 1.67/1.82 tff(3541,plain,
% 1.67/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c0_1(a744)))),
% 1.67/1.82 inference(monotonicity,[status(thm)],[3540])).
% 1.67/1.82 tff(3542,plain,
% 1.67/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c0_1(a744))),
% 1.67/1.82 inference(transitivity,[status(thm)],[3541, 3539])).
% 1.67/1.82 tff(3543,plain,
% 1.67/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))),
% 1.67/1.82 inference(quant_inst,[status(thm)],[])).
% 1.67/1.82 tff(3544,plain,
% 1.67/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c0_1(a744)),
% 1.67/1.82 inference(modus_ponens,[status(thm)],[3543, 3542])).
% 1.67/1.82 tff(3545,plain,
% 1.67/1.82 (~c3_1(a701)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[3544, 206, 3538, 3537, 3495, 3519, 3510, 3493, 1699, 3518, 3502])).
% 1.67/1.82 tff(3546,plain,
% 1.67/1.82 (~c1_1(a754)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[1391, 206, 162, 3431, 3430, 3467, 3466, 3465, 271])).
% 1.67/1.82 tff(3547,plain,
% 1.67/1.82 (~c1_1(a701)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[28, 3536])).
% 1.67/1.82 tff(3548,plain,
% 1.67/1.82 (c2_1(a697)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[473, 3492])).
% 1.67/1.82 tff(3549,plain,
% 1.67/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c0_1(a754) | c1_1(a701) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a754) | c1_1(a701) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))),
% 1.67/1.82 inference(rewrite,[status(thm)],[])).
% 1.67/1.82 tff(3550,plain,
% 1.67/1.82 (((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754)) <=> (c0_1(a754) | c1_1(a701) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))),
% 1.67/1.82 inference(rewrite,[status(thm)],[])).
% 1.67/1.82 tff(3551,plain,
% 1.67/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c0_1(a754) | c1_1(a701) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754))))),
% 1.67/1.82 inference(monotonicity,[status(thm)],[3550])).
% 1.67/1.82 tff(3552,plain,
% 1.67/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a754) | c1_1(a701) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))),
% 1.67/1.82 inference(transitivity,[status(thm)],[3551, 3549])).
% 1.67/1.82 tff(3553,plain,
% 1.67/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754))),
% 1.67/1.82 inference(quant_inst,[status(thm)],[])).
% 1.67/1.82 tff(3554,plain,
% 1.67/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a754) | c1_1(a701) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754))),
% 1.67/1.82 inference(modus_ponens,[status(thm)],[3553, 3552])).
% 1.67/1.82 tff(3555,plain,
% 1.67/1.82 ($false),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[3554, 206, 3432, 3538, 3548, 3431, 3547, 3493, 512, 3546, 3502, 3545])).
% 1.67/1.82 tff(3556,plain,(c3_1(a695) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.67/1.82 tff(3557,plain,
% 1.67/1.82 (c3_1(a695)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[3556, 162])).
% 1.67/1.82 tff(3558,plain,
% 1.67/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a763)) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a763)) | (~c0_1(a763)))),
% 1.67/1.82 inference(rewrite,[status(thm)],[])).
% 1.67/1.82 tff(3559,plain,
% 1.67/1.82 (((~ndr1_0) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754))) <=> (c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a763)) | (~c0_1(a763)))),
% 1.67/1.82 inference(rewrite,[status(thm)],[])).
% 1.67/1.82 tff(3560,plain,
% 1.67/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a763)) | (~c0_1(a763))))),
% 1.67/1.82 inference(monotonicity,[status(thm)],[3559])).
% 1.67/1.82 tff(3561,plain,
% 1.67/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a763)) | (~c0_1(a763)))),
% 1.67/1.82 inference(transitivity,[status(thm)],[3560, 3558])).
% 1.67/1.82 tff(3562,plain,
% 1.67/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))),
% 1.67/1.82 inference(quant_inst,[status(thm)],[])).
% 1.67/1.82 tff(3563,plain,
% 1.67/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a763)) | (~c0_1(a763))),
% 1.67/1.82 inference(modus_ponens,[status(thm)],[3562, 3561])).
% 1.67/1.82 tff(3564,plain,
% 1.67/1.82 ((~c1_1(a754)) | (~c3_1(a763))),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[3563, 206, 3437, 3432, 3435, 3431, 3430, 159])).
% 1.67/1.82 tff(3565,plain,
% 1.67/1.82 (~c1_1(a754)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[3564, 3447])).
% 1.67/1.82 tff(3566,plain,
% 1.67/1.82 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a754) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a754) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c1_1(a754) | (~c2_1(a754)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3567,plain,
% 1.67/1.83 ((hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754))) <=> (hskp14 | c3_1(a754) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c1_1(a754) | (~c2_1(a754)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3568,plain,
% 1.67/1.83 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a754) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c1_1(a754) | (~c2_1(a754))))),
% 1.67/1.83 inference(monotonicity,[status(thm)],[3567])).
% 1.67/1.83 tff(3569,plain,
% 1.67/1.83 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a754) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c1_1(a754) | (~c2_1(a754)))),
% 1.67/1.83 inference(transitivity,[status(thm)],[3568, 3566])).
% 1.67/1.83 tff(3570,plain,
% 1.67/1.83 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))),
% 1.67/1.83 inference(quant_inst,[status(thm)],[])).
% 1.67/1.83 tff(3571,plain,
% 1.67/1.83 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a754) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c1_1(a754) | (~c2_1(a754))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3570, 3569])).
% 1.67/1.83 tff(3572,plain,
% 1.67/1.83 (hskp14 | (~c3_1(a695)) | c1_1(a754)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3571, 206, 2685, 2649, 3432, 3430, 1545])).
% 1.67/1.83 tff(3573,plain,
% 1.67/1.83 (hskp14),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3572, 3565, 3557])).
% 1.67/1.83 tff(3574,plain,
% 1.67/1.83 (~c3_1(a730)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[438, 3573])).
% 1.67/1.83 tff(3575,plain,
% 1.67/1.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a754)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3576,plain,
% 1.67/1.83 ((hskp8 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a754)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3577,plain,
% 1.67/1.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a754))))),
% 1.67/1.83 inference(monotonicity,[status(thm)],[3576])).
% 1.67/1.83 tff(3578,plain,
% 1.67/1.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a754)))),
% 1.67/1.83 inference(transitivity,[status(thm)],[3577, 3575])).
% 1.67/1.83 tff(3579,plain,
% 1.67/1.83 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.67/1.83 inference(quant_inst,[status(thm)],[])).
% 1.67/1.83 tff(3580,plain,
% 1.67/1.83 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a754))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3579, 3578])).
% 1.67/1.83 tff(3581,plain,
% 1.67/1.83 (hskp8 | (~c3_1(a695))),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3580, 206, 2657, 2649, 3432, 3431, 3430, 1784])).
% 1.67/1.83 tff(3582,plain,
% 1.67/1.83 (hskp8),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3581, 3557])).
% 1.67/1.83 tff(3583,plain,
% 1.67/1.83 (c2_1(a710)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[1871, 3582])).
% 1.67/1.83 tff(3584,plain,
% 1.67/1.83 (~c0_1(a710)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[1797, 3582])).
% 1.67/1.83 tff(3585,plain,
% 1.67/1.83 (c3_1(a710)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[1805, 3582])).
% 1.67/1.83 tff(3586,plain,
% 1.67/1.83 (^[U: $i] : refl((hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 1.67/1.83 inference(bind,[status(th)],[])).
% 1.67/1.83 tff(3587,plain,
% 1.67/1.83 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.67/1.83 inference(quant_intro,[status(thm)],[3586])).
% 1.67/1.83 tff(3588,plain,
% 1.67/1.83 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3589,plain,
% 1.67/1.83 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp15) <=> ((hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp15))), rewrite(((hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp15) <=> (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.67/1.83 inference(bind,[status(th)],[])).
% 1.67/1.83 tff(3590,plain,
% 1.67/1.83 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp15) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.67/1.83 inference(quant_intro,[status(thm)],[3589])).
% 1.67/1.83 tff(3591,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 1.67/1.83 tff(3592,plain,
% 1.67/1.83 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3591, 3590])).
% 1.67/1.83 tff(3593,plain,
% 1.67/1.83 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3592, 3588])).
% 1.67/1.83 tff(3594,plain,(
% 1.67/1.83 ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.67/1.83 inference(skolemize,[status(sab)],[3593])).
% 1.67/1.83 tff(3595,plain,
% 1.67/1.83 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3594, 3587])).
% 1.67/1.83 tff(3596,plain,
% 1.67/1.83 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3597,plain,
% 1.67/1.83 ((hskp16 | hskp15 | (~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730))) <=> (hskp16 | hskp15 | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3598,plain,
% 1.67/1.83 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730))))),
% 1.67/1.83 inference(monotonicity,[status(thm)],[3597])).
% 1.67/1.83 tff(3599,plain,
% 1.67/1.83 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)))),
% 1.67/1.83 inference(transitivity,[status(thm)],[3598, 3596])).
% 1.67/1.83 tff(3600,plain,
% 1.67/1.83 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)))),
% 1.67/1.83 inference(quant_inst,[status(thm)],[])).
% 1.67/1.83 tff(3601,plain,
% 1.67/1.83 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3600, 3599])).
% 1.67/1.83 tff(3602,plain,
% 1.67/1.83 (hskp15),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3601, 206, 12, 425, 417, 439, 3595])).
% 1.67/1.83 tff(3603,plain,
% 1.67/1.83 (((~hskp15) | (~c2_1(a734))) <=> ((~hskp15) | (~c2_1(a734)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3604,plain,
% 1.67/1.83 (((~c2_1(a734)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a734)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3605,axiom,((~c2_1(a734)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.67/1.83 tff(3606,plain,
% 1.67/1.83 ((~hskp15) | (~c2_1(a734))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3605, 3604])).
% 1.67/1.83 tff(3607,plain,
% 1.67/1.83 ((~hskp15) | (~c2_1(a734))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3606, 3603])).
% 1.67/1.83 tff(3608,plain,
% 1.67/1.83 (~c2_1(a734)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3607, 3602])).
% 1.67/1.83 tff(3609,plain,
% 1.67/1.83 (((~hskp15) | (~c1_1(a734))) <=> ((~hskp15) | (~c1_1(a734)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3610,plain,
% 1.67/1.83 (((~c1_1(a734)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a734)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3611,axiom,((~c1_1(a734)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.67/1.83 tff(3612,plain,
% 1.67/1.83 ((~hskp15) | (~c1_1(a734))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3611, 3610])).
% 1.67/1.83 tff(3613,plain,
% 1.67/1.83 ((~hskp15) | (~c1_1(a734))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3612, 3609])).
% 1.67/1.83 tff(3614,plain,
% 1.67/1.83 (~c1_1(a734)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3613, 3602])).
% 1.67/1.83 tff(3615,assumption,(c3_1(a710)), introduced(assumption)).
% 1.67/1.83 tff(3616,assumption,(c2_1(a710)), introduced(assumption)).
% 1.67/1.83 tff(3617,plain,
% 1.67/1.83 (((~hskp15) | c3_1(a734)) <=> ((~hskp15) | c3_1(a734))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3618,axiom,((~hskp15) | c3_1(a734)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.67/1.83 tff(3619,plain,
% 1.67/1.83 ((~hskp15) | c3_1(a734)),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3618, 3617])).
% 1.67/1.83 tff(3620,plain,
% 1.67/1.83 ((~hskp15) | c3_1(a734)),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3619, 3617])).
% 1.67/1.83 tff(3621,plain,
% 1.67/1.83 ((~hskp15) | c3_1(a734)),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3620, 3617])).
% 1.67/1.83 tff(3622,plain,
% 1.67/1.83 ((~hskp15) | c3_1(a734)),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3621, 3617])).
% 1.67/1.83 tff(3623,plain,
% 1.67/1.83 ((~hskp15) | c3_1(a734)),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3622, 3617])).
% 1.67/1.83 tff(3624,plain,
% 1.67/1.83 (c3_1(a734)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3623, 3602])).
% 1.67/1.83 tff(3625,assumption,(~c1_1(a710)), introduced(assumption)).
% 1.67/1.83 tff(3626,assumption,(~c3_1(a730)), introduced(assumption)).
% 1.67/1.83 tff(3627,assumption,(~c2_1(a734)), introduced(assumption)).
% 1.67/1.83 tff(3628,assumption,(~c1_1(a734)), introduced(assumption)).
% 1.67/1.83 tff(3629,assumption,(c1_1(a730)), introduced(assumption)).
% 1.67/1.83 tff(3630,assumption,(c0_1(a730)), introduced(assumption)).
% 1.67/1.83 tff(3631,assumption,(c3_1(a734)), introduced(assumption)).
% 1.67/1.83 tff(3632,plain,
% 1.67/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a734) | c2_1(a734) | c3_1(a730) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710) | (~c0_1(a730)) | (~c1_1(a730)) | (~c3_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a734) | c2_1(a734) | c3_1(a730) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710) | (~c0_1(a730)) | (~c1_1(a730)) | (~c3_1(a734)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3633,plain,
% 1.67/1.83 (((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c2_1(a734) | (~c3_1(a734)) | c1_1(a734)) <=> (c1_1(a734) | c2_1(a734) | c3_1(a730) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710) | (~c0_1(a730)) | (~c1_1(a730)) | (~c3_1(a734)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3634,plain,
% 1.67/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c2_1(a734) | (~c3_1(a734)) | c1_1(a734))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a734) | c2_1(a734) | c3_1(a730) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710) | (~c0_1(a730)) | (~c1_1(a730)) | (~c3_1(a734))))),
% 1.67/1.83 inference(monotonicity,[status(thm)],[3633])).
% 1.67/1.83 tff(3635,plain,
% 1.67/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c2_1(a734) | (~c3_1(a734)) | c1_1(a734))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a734) | c2_1(a734) | c3_1(a730) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710) | (~c0_1(a730)) | (~c1_1(a730)) | (~c3_1(a734)))),
% 1.67/1.83 inference(transitivity,[status(thm)],[3634, 3632])).
% 1.67/1.83 tff(3636,plain,
% 1.67/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c2_1(a734) | (~c3_1(a734)) | c1_1(a734))),
% 1.67/1.83 inference(quant_inst,[status(thm)],[])).
% 1.67/1.83 tff(3637,plain,
% 1.67/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a734) | c2_1(a734) | c3_1(a730) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710) | (~c0_1(a730)) | (~c1_1(a730)) | (~c3_1(a734))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3636, 3635])).
% 1.67/1.83 tff(3638,plain,
% 1.67/1.83 ($false),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3637, 206, 3631, 3630, 3629, 3616, 3615, 3628, 3627, 3626, 2984, 3625])).
% 1.67/1.83 tff(3639,plain,(c1_1(a710) | (~c3_1(a734)) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a710)) | (~c3_1(a710)) | c1_1(a734) | c2_1(a734) | c3_1(a730)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.83 tff(3640,plain,
% 1.67/1.83 (c1_1(a710)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3639, 3624, 425, 417, 3616, 3615, 3614, 3608, 439])).
% 1.67/1.83 tff(3641,assumption,(~c0_1(a710)), introduced(assumption)).
% 1.67/1.83 tff(3642,plain,
% 1.67/1.83 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c0_1(a763)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3643,plain,
% 1.67/1.83 ((hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710))) <=> (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c0_1(a763)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3644,plain,
% 1.67/1.83 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c0_1(a763))))),
% 1.67/1.83 inference(monotonicity,[status(thm)],[3643])).
% 1.67/1.83 tff(3645,plain,
% 1.67/1.83 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c0_1(a763)))),
% 1.67/1.83 inference(transitivity,[status(thm)],[3644, 3642])).
% 1.67/1.83 tff(3646,plain,
% 1.67/1.83 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)))),
% 1.67/1.83 inference(quant_inst,[status(thm)],[])).
% 1.67/1.83 tff(3647,plain,
% 1.67/1.83 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c0_1(a763))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3646, 3645])).
% 1.67/1.83 tff(3648,plain,
% 1.67/1.83 (hskp4 | (~c1_1(a710))),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3647, 206, 1731, 3615, 1729, 1728, 3641, 2070])).
% 1.67/1.83 tff(3649,plain,
% 1.67/1.83 (hskp4),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3648, 3640])).
% 1.67/1.83 tff(3650,plain,
% 1.67/1.83 (~c3_1(a698)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[976, 3649])).
% 1.67/1.83 tff(3651,plain,
% 1.67/1.83 (~c2_1(a698)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[854, 3649])).
% 1.67/1.83 tff(3652,plain,
% 1.67/1.83 (~c0_1(a698)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[848, 3649])).
% 1.67/1.83 tff(3653,plain,
% 1.67/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a730) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a730)) | (~c1_1(a730)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a730) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a730)) | (~c1_1(a730)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3654,plain,
% 1.67/1.83 (((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a698) | c2_1(a698) | c0_1(a698)) <=> (c3_1(a730) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a730)) | (~c1_1(a730)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3655,plain,
% 1.67/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a730) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a730)) | (~c1_1(a730))))),
% 1.67/1.83 inference(monotonicity,[status(thm)],[3654])).
% 1.67/1.83 tff(3656,plain,
% 1.67/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a730) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a730)) | (~c1_1(a730)))),
% 1.67/1.83 inference(transitivity,[status(thm)],[3655, 3653])).
% 1.67/1.83 tff(3657,plain,
% 1.67/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a698) | c2_1(a698) | c0_1(a698))),
% 1.67/1.83 inference(quant_inst,[status(thm)],[])).
% 1.67/1.83 tff(3658,plain,
% 1.67/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a730) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a730)) | (~c1_1(a730))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3657, 3656])).
% 1.67/1.83 tff(3659,plain,
% 1.67/1.83 ($false),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3658, 206, 2685, 2649, 425, 417, 439, 3652, 3651, 3650, 1699, 3163])).
% 1.67/1.83 tff(3660,plain,((~hskp14) | (~c3_1(a695)) | (~c0_1(a763)) | (~c3_1(a710)) | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~c2_1(a710)) | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.67/1.83 tff(3661,plain,
% 1.67/1.83 (hskp16),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3660, 3573, 3437, 3585, 3436, 3435, 3584, 3583, 3557])).
% 1.67/1.83 tff(3662,plain,
% 1.67/1.83 (~c1_1(a738)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[2989, 3661])).
% 1.67/1.83 tff(3663,plain,
% 1.67/1.83 (c1_1(a730)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[416, 3573])).
% 1.67/1.83 tff(3664,plain,
% 1.67/1.83 (c0_1(a730)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[424, 3573])).
% 1.67/1.83 tff(3665,plain,
% 1.67/1.83 (c3_1(a738)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[2958, 3661])).
% 1.67/1.83 tff(3666,plain,
% 1.67/1.83 (c2_1(a738)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[2966, 3661])).
% 1.67/1.83 tff(3667,plain,
% 1.67/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3668,plain,
% 1.67/1.83 (((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763)) <=> (c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3669,plain,
% 1.67/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763))))),
% 1.67/1.83 inference(monotonicity,[status(thm)],[3668])).
% 1.67/1.83 tff(3670,plain,
% 1.67/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 1.67/1.83 inference(transitivity,[status(thm)],[3669, 3667])).
% 1.67/1.83 tff(3671,plain,
% 1.67/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))),
% 1.67/1.83 inference(quant_inst,[status(thm)],[])).
% 1.67/1.83 tff(3672,plain,
% 1.67/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763))),
% 1.67/1.83 inference(modus_ponens,[status(thm)],[3671, 3670])).
% 1.67/1.83 tff(3673,plain,
% 1.67/1.83 ($false),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[3672, 206, 3666, 3665, 3664, 3663, 3436, 3435, 3662, 3574, 2984, 3447])).
% 1.67/1.83 tff(3674,plain,(hskp6), inference(lemma,lemma(discharge,[]))).
% 1.67/1.83 tff(3675,plain,
% 1.67/1.83 (~c2_1(a702)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[62, 3674])).
% 1.67/1.83 tff(3676,plain,
% 1.67/1.83 (c3_1(a702)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[70, 3674])).
% 1.67/1.83 tff(3677,plain,
% 1.67/1.83 (c0_1(a702)),
% 1.67/1.83 inference(unit_resolution,[status(thm)],[78, 3674])).
% 1.67/1.83 tff(3678,plain,
% 1.67/1.83 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c2_1(a702) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a702) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3679,plain,
% 1.67/1.83 ((hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp0 | c2_1(a702) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.67/1.83 inference(rewrite,[status(thm)],[])).
% 1.67/1.83 tff(3680,plain,
% 1.67/1.83 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c2_1(a702) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702))))),
% 1.67/1.84 inference(monotonicity,[status(thm)],[3679])).
% 1.67/1.84 tff(3681,plain,
% 1.67/1.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a702) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.67/1.84 inference(transitivity,[status(thm)],[3680, 3678])).
% 1.67/1.84 tff(3682,plain,
% 1.67/1.84 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 1.67/1.84 inference(quant_inst,[status(thm)],[])).
% 1.67/1.84 tff(3683,plain,
% 1.67/1.84 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a702) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702))),
% 1.67/1.84 inference(modus_ponens,[status(thm)],[3682, 3681])).
% 1.67/1.84 tff(3684,plain,
% 1.67/1.84 (hskp0),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3683, 206, 3677, 3676, 3675, 1291, 1290, 1289, 2715])).
% 1.67/1.84 tff(3685,plain,
% 1.67/1.84 (~c1_1(a692)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[787, 3684])).
% 1.67/1.84 tff(3686,plain,
% 1.67/1.84 (~c0_1(a692)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[793, 3684])).
% 1.67/1.84 tff(3687,plain,
% 1.67/1.84 (~c1_1(a698)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3477, 206, 2685, 2657, 2649, 1291, 1290, 756, 11])).
% 1.67/1.84 tff(3688,plain,
% 1.67/1.84 (c2_1(a760)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3484, 206, 3056, 3054, 1291, 1290, 1289, 110, 3687])).
% 1.67/1.84 tff(3689,plain,
% 1.67/1.84 (hskp3),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3491, 206, 2685, 2649, 3056, 3055, 2132, 11, 3688])).
% 1.67/1.84 tff(3690,plain,
% 1.67/1.84 (~c3_1(a697)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[1286, 3689])).
% 1.67/1.84 tff(3691,plain,
% 1.67/1.84 (c2_1(a692)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[803, 3684])).
% 1.67/1.84 tff(3692,plain,
% 1.67/1.84 (c0_1(a697)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[457, 3689])).
% 1.67/1.84 tff(3693,plain,
% 1.67/1.84 (c1_1(a697)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3501, 206, 2657, 2649, 3692, 3691, 3690, 3686, 3685, 512, 11])).
% 1.67/1.84 tff(3694,assumption,(~c1_1(a692)), introduced(assumption)).
% 1.67/1.84 tff(3695,assumption,(~c0_1(a692)), introduced(assumption)).
% 1.67/1.84 tff(3696,assumption,(c2_1(a760)), introduced(assumption)).
% 1.67/1.84 tff(3697,plain,
% 1.67/1.84 (hskp3),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3491, 206, 2685, 2649, 3056, 3055, 2132, 11, 3696])).
% 1.67/1.84 tff(3698,plain,
% 1.67/1.84 (~c3_1(a697)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[1286, 3697])).
% 1.67/1.84 tff(3699,assumption,(c2_1(a692)), introduced(assumption)).
% 1.67/1.84 tff(3700,plain,
% 1.67/1.84 (c0_1(a697)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[457, 3697])).
% 1.67/1.84 tff(3701,plain,
% 1.67/1.84 (c1_1(a697)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3501, 206, 2657, 2649, 3700, 3699, 3698, 3695, 3694, 512, 11])).
% 1.67/1.84 tff(3702,assumption,(~hskp5), introduced(assumption)).
% 1.67/1.84 tff(3703,plain,
% 1.67/1.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a760) | c2_1(a702) | (~ndr1_0) | (~c1_1(a702)) | (~c0_1(a702)) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a760) | c2_1(a702) | (~ndr1_0) | (~c1_1(a702)) | (~c0_1(a702)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3704,plain,
% 1.67/1.84 ((hskp5 | (~ndr1_0) | c2_1(a702) | (~c0_1(a702)) | (~c1_1(a702)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760))) <=> (hskp5 | c0_1(a760) | c2_1(a702) | (~ndr1_0) | (~c1_1(a702)) | (~c0_1(a702)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3705,plain,
% 1.67/1.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a702) | (~c0_1(a702)) | (~c1_1(a702)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a760) | c2_1(a702) | (~ndr1_0) | (~c1_1(a702)) | (~c0_1(a702)) | (~c2_1(a760)) | (~c1_1(a760))))),
% 1.67/1.84 inference(monotonicity,[status(thm)],[3704])).
% 1.67/1.84 tff(3706,plain,
% 1.67/1.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a702) | (~c0_1(a702)) | (~c1_1(a702)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a760) | c2_1(a702) | (~ndr1_0) | (~c1_1(a702)) | (~c0_1(a702)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 1.67/1.84 inference(transitivity,[status(thm)],[3705, 3703])).
% 1.67/1.84 tff(3707,plain,
% 1.67/1.84 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a702) | (~c0_1(a702)) | (~c1_1(a702)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))),
% 1.67/1.84 inference(quant_inst,[status(thm)],[])).
% 1.67/1.84 tff(3708,plain,
% 1.67/1.84 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a760) | c2_1(a702) | (~ndr1_0) | (~c1_1(a702)) | (~c0_1(a702)) | (~c2_1(a760)) | (~c1_1(a760))),
% 1.67/1.84 inference(modus_ponens,[status(thm)],[3707, 3706])).
% 1.67/1.84 tff(3709,plain,
% 1.67/1.84 (hskp5 | (~c1_1(a702)) | (~c2_1(a760))),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3708, 206, 3056, 3677, 3054, 3675, 3529])).
% 1.67/1.84 tff(3710,plain,
% 1.67/1.84 (~c1_1(a702)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3709, 3702, 3696])).
% 1.67/1.84 tff(3711,plain,
% 1.67/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c2_1(a702) | c1_1(a692) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c3_1(a692)) | (~c3_1(a702)) | c1_1(a702))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c2_1(a702) | c1_1(a692) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c3_1(a692)) | (~c3_1(a702)) | c1_1(a702))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3712,plain,
% 1.67/1.84 (((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a692) | (~c2_1(a692)) | (~c3_1(a692)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702)) <=> (c2_1(a702) | c1_1(a692) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c3_1(a692)) | (~c3_1(a702)) | c1_1(a702))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3713,plain,
% 1.67/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a692) | (~c2_1(a692)) | (~c3_1(a692)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c2_1(a702) | c1_1(a692) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c3_1(a692)) | (~c3_1(a702)) | c1_1(a702)))),
% 1.67/1.84 inference(monotonicity,[status(thm)],[3712])).
% 1.67/1.84 tff(3714,plain,
% 1.67/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a692) | (~c2_1(a692)) | (~c3_1(a692)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c2_1(a702) | c1_1(a692) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c3_1(a692)) | (~c3_1(a702)) | c1_1(a702))),
% 1.67/1.84 inference(transitivity,[status(thm)],[3713, 3711])).
% 1.67/1.84 tff(3715,plain,
% 1.67/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a692) | (~c2_1(a692)) | (~c3_1(a692)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702))),
% 1.67/1.84 inference(quant_inst,[status(thm)],[])).
% 1.67/1.84 tff(3716,plain,
% 1.67/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c2_1(a702) | c1_1(a692) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c3_1(a692)) | (~c3_1(a702)) | c1_1(a702)),
% 1.67/1.84 inference(modus_ponens,[status(thm)],[3715, 3714])).
% 1.67/1.84 tff(3717,plain,
% 1.67/1.84 ((~c3_1(a692)) | c1_1(a702)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3716, 206, 2685, 2657, 3676, 3699, 3675, 3694, 2984, 11])).
% 1.67/1.84 tff(3718,plain,
% 1.67/1.84 (~c3_1(a692)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3717, 3710])).
% 1.67/1.84 tff(3719,plain,
% 1.67/1.84 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a760) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a760)) | (~c1_1(a760)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3720,plain,
% 1.67/1.84 ((hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692))) <=> (hskp10 | c0_1(a760) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a760)) | (~c1_1(a760)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3721,plain,
% 1.67/1.84 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a760) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a760)) | (~c1_1(a760))))),
% 1.67/1.84 inference(monotonicity,[status(thm)],[3720])).
% 1.67/1.84 tff(3722,plain,
% 1.67/1.84 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a760)) | (~c1_1(a760)))),
% 1.67/1.84 inference(transitivity,[status(thm)],[3721, 3719])).
% 1.67/1.84 tff(3723,plain,
% 1.67/1.84 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)))),
% 1.67/1.84 inference(quant_inst,[status(thm)],[])).
% 1.67/1.84 tff(3724,plain,
% 1.67/1.84 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a760)) | (~c1_1(a760))),
% 1.67/1.84 inference(modus_ponens,[status(thm)],[3723, 3722])).
% 1.67/1.84 tff(3725,plain,
% 1.67/1.84 (hskp10),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3724, 206, 3056, 3055, 3699, 3054, 3695, 1671, 3718])).
% 1.67/1.84 tff(3726,plain,
% 1.67/1.84 (~c2_1(a717)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[1812, 3725])).
% 1.67/1.84 tff(3727,plain,
% 1.67/1.84 (c2_1(a697)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[473, 3697])).
% 1.67/1.84 tff(3728,plain,
% 1.67/1.84 (c1_1(a717)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[2897, 3725])).
% 1.67/1.84 tff(3729,plain,
% 1.67/1.84 (c0_1(a717)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3073, 206, 3728, 3700, 3727, 3726, 3698, 756, 3701])).
% 1.67/1.84 tff(3730,plain,
% 1.67/1.84 ($false),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3535, 206, 3702, 3056, 3728, 3054, 3726, 3529, 3696, 3729])).
% 1.67/1.84 tff(3731,plain,(hskp5 | (~c2_1(a760)) | (~c2_1(a692)) | c0_1(a692) | c1_1(a692) | c3_1(a695)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.84 tff(3732,plain,
% 1.67/1.84 (hskp5),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3731, 3688, 3691, 3686, 3685, 11])).
% 1.67/1.84 tff(3733,plain,
% 1.67/1.84 (c2_1(a701)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[36, 3732])).
% 1.67/1.84 tff(3734,plain,
% 1.67/1.84 (c0_1(a701)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[44, 3732])).
% 1.67/1.84 tff(3735,plain,
% 1.67/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a698) | c2_1(a698) | c3_1(a698) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a698) | c2_1(a698) | c3_1(a698) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3736,plain,
% 1.67/1.84 (((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a698) | c2_1(a698) | c0_1(a698)) <=> (c0_1(a698) | c2_1(a698) | c3_1(a698) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3737,plain,
% 1.67/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a698) | c2_1(a698) | c3_1(a698) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701))))),
% 1.67/1.84 inference(monotonicity,[status(thm)],[3736])).
% 1.67/1.84 tff(3738,plain,
% 1.67/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a698) | c2_1(a698) | c3_1(a698) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)))),
% 1.67/1.84 inference(transitivity,[status(thm)],[3737, 3735])).
% 1.67/1.84 tff(3739,plain,
% 1.67/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a698) | c2_1(a698) | c0_1(a698))),
% 1.67/1.84 inference(quant_inst,[status(thm)],[])).
% 1.67/1.84 tff(3740,plain,
% 1.67/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a698) | c2_1(a698) | c3_1(a698) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701))),
% 1.67/1.84 inference(modus_ponens,[status(thm)],[3739, 3738])).
% 1.67/1.84 tff(3741,plain,
% 1.67/1.84 (~c3_1(a701)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3740, 206, 3734, 3733, 3692, 1291, 1290, 1289, 3690, 1699, 3693])).
% 1.67/1.84 tff(3742,plain,
% 1.67/1.84 (~c1_1(a701)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[28, 3732])).
% 1.67/1.84 tff(3743,plain,
% 1.67/1.84 (c2_1(a697)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[473, 3689])).
% 1.67/1.84 tff(3744,plain,
% 1.67/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a701) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a701) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3745,plain,
% 1.67/1.84 (((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692)) <=> (c1_1(a701) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3746,plain,
% 1.67/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a701) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701))))),
% 1.67/1.84 inference(monotonicity,[status(thm)],[3745])).
% 1.67/1.84 tff(3747,plain,
% 1.67/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a701) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)))),
% 1.67/1.84 inference(transitivity,[status(thm)],[3746, 3744])).
% 1.67/1.84 tff(3748,plain,
% 1.67/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))),
% 1.67/1.84 inference(quant_inst,[status(thm)],[])).
% 1.67/1.84 tff(3749,plain,
% 1.67/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a701) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701))),
% 1.67/1.84 inference(modus_ponens,[status(thm)],[3748, 3747])).
% 1.67/1.84 tff(3750,plain,
% 1.67/1.84 ($false),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3749, 206, 3734, 3743, 3691, 3742, 3690, 3686, 3685, 512, 3693, 3741])).
% 1.67/1.84 tff(3751,plain,((~hskp4) | c3_1(a695)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.84 tff(3752,plain,
% 1.67/1.84 (~hskp4),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3751, 11])).
% 1.67/1.84 tff(3753,plain,
% 1.67/1.84 (~hskp23),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[2820, 3752, 2705])).
% 1.67/1.84 tff(3754,plain,
% 1.67/1.84 (hskp24),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[2767, 3753])).
% 1.67/1.84 tff(3755,plain,
% 1.67/1.84 (~c2_1(a764)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[283, 3754])).
% 1.67/1.84 tff(3756,plain,
% 1.67/1.84 (c1_1(a764)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[291, 3754])).
% 1.67/1.84 tff(3757,plain,
% 1.67/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a764) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a764) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a764) | (~c1_1(a764)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3758,plain,
% 1.67/1.84 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a764) | c0_1(a764) | (~c1_1(a764))) <=> (c2_1(a764) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a764) | (~c1_1(a764)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3759,plain,
% 1.67/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a764) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a764) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a764) | (~c1_1(a764))))),
% 1.67/1.84 inference(monotonicity,[status(thm)],[3758])).
% 1.67/1.84 tff(3760,plain,
% 1.67/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a764) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a764) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a764) | (~c1_1(a764)))),
% 1.67/1.84 inference(transitivity,[status(thm)],[3759, 3757])).
% 1.67/1.84 tff(3761,plain,
% 1.67/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a764) | c0_1(a764) | (~c1_1(a764)))),
% 1.67/1.84 inference(quant_inst,[status(thm)],[])).
% 1.67/1.84 tff(3762,plain,
% 1.67/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a764) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a764) | (~c1_1(a764))),
% 1.67/1.84 inference(modus_ponens,[status(thm)],[3761, 3760])).
% 1.67/1.84 tff(3763,plain,
% 1.67/1.84 (c0_1(a764)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3762, 206, 2685, 2657, 2649, 3756, 3755, 756, 11])).
% 1.67/1.84 tff(3764,plain,
% 1.67/1.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | c2_1(a764) | c0_1(a760) | (~ndr1_0) | (~c2_1(a760)) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c2_1(a764) | c0_1(a760) | (~ndr1_0) | (~c2_1(a760)) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3765,plain,
% 1.67/1.84 ((hskp5 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760))) <=> (hskp5 | c2_1(a764) | c0_1(a760) | (~ndr1_0) | (~c2_1(a760)) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3766,plain,
% 1.67/1.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | c2_1(a764) | c0_1(a760) | (~ndr1_0) | (~c2_1(a760)) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764))))),
% 1.67/1.84 inference(monotonicity,[status(thm)],[3765])).
% 1.67/1.84 tff(3767,plain,
% 1.67/1.84 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c2_1(a764) | c0_1(a760) | (~ndr1_0) | (~c2_1(a760)) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.84 inference(transitivity,[status(thm)],[3766, 3764])).
% 1.67/1.84 tff(3768,plain,
% 1.67/1.84 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))),
% 1.67/1.84 inference(quant_inst,[status(thm)],[])).
% 1.67/1.84 tff(3769,plain,
% 1.67/1.84 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c2_1(a764) | c0_1(a760) | (~ndr1_0) | (~c2_1(a760)) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764))),
% 1.67/1.84 inference(modus_ponens,[status(thm)],[3768, 3767])).
% 1.67/1.84 tff(3770,plain,
% 1.67/1.84 (hskp5 | (~c2_1(a760))),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3769, 206, 3756, 3056, 3755, 3054, 3529, 3763])).
% 1.67/1.84 tff(3771,plain,
% 1.67/1.84 (~c2_1(a760)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3770, 2666])).
% 1.67/1.84 tff(3772,plain,
% 1.67/1.84 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | c2_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp5 | hskp1 | c2_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3773,plain,
% 1.67/1.84 ((hskp5 | hskp1 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764))) <=> (hskp5 | hskp1 | c2_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3774,plain,
% 1.67/1.84 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | c2_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764))))),
% 1.67/1.84 inference(monotonicity,[status(thm)],[3773])).
% 1.67/1.84 tff(3775,plain,
% 1.67/1.84 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp5 | hskp1 | c2_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.84 inference(transitivity,[status(thm)],[3774, 3772])).
% 1.67/1.84 tff(3776,plain,
% 1.67/1.84 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.84 inference(quant_inst,[status(thm)],[])).
% 1.67/1.84 tff(3777,plain,
% 1.67/1.84 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp5 | hskp1 | c2_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764))),
% 1.67/1.84 inference(modus_ponens,[status(thm)],[3776, 3775])).
% 1.67/1.84 tff(3778,plain,
% 1.67/1.84 (hskp5 | hskp1 | (~c0_1(a764))),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3777, 206, 3756, 3755, 1516])).
% 1.67/1.84 tff(3779,plain,
% 1.67/1.84 (hskp1),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[3778, 2666, 3763])).
% 1.67/1.84 tff(3780,plain,
% 1.67/1.84 (~c3_1(a693)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[1484, 3779])).
% 1.67/1.84 tff(3781,plain,
% 1.67/1.84 (~c1_1(a693)),
% 1.67/1.84 inference(unit_resolution,[status(thm)],[1354, 3779])).
% 1.67/1.84 tff(3782,plain,
% 1.67/1.84 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3783,plain,
% 1.67/1.84 ((hskp16 | hskp15 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695))) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)))),
% 1.67/1.84 inference(rewrite,[status(thm)],[])).
% 1.67/1.84 tff(3784,plain,
% 1.67/1.84 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695))))),
% 1.67/1.85 inference(monotonicity,[status(thm)],[3783])).
% 1.67/1.85 tff(3785,plain,
% 1.67/1.85 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)))),
% 1.67/1.85 inference(transitivity,[status(thm)],[3784, 3782])).
% 1.67/1.85 tff(3786,plain,
% 1.67/1.85 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)))),
% 1.67/1.85 inference(quant_inst,[status(thm)],[])).
% 1.67/1.85 tff(3787,plain,
% 1.67/1.85 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695))),
% 1.67/1.85 inference(modus_ponens,[status(thm)],[3786, 3785])).
% 1.67/1.85 tff(3788,plain,
% 1.67/1.85 (hskp16 | hskp15 | c3_1(a695)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3787, 206, 2685, 2657, 3595])).
% 1.67/1.85 tff(3789,plain,
% 1.67/1.85 (hskp15),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3788, 12, 11])).
% 1.67/1.85 tff(3790,plain,
% 1.67/1.85 (~c2_1(a734)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3607, 3789])).
% 1.67/1.85 tff(3791,plain,
% 1.67/1.85 (~c1_1(a734)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3613, 3789])).
% 1.67/1.85 tff(3792,plain,
% 1.67/1.85 (c2_1(a693)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[344, 3779])).
% 1.67/1.85 tff(3793,plain,
% 1.67/1.85 (c3_1(a734)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3623, 3789])).
% 1.67/1.85 tff(3794,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a760) | c1_1(a734) | c2_1(a734) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a734)) | (~c3_1(a760)) | c2_1(a760))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a760) | c1_1(a734) | c2_1(a734) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a734)) | (~c3_1(a760)) | c2_1(a760))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3795,plain,
% 1.67/1.85 (((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a760) | c0_1(a760) | (~c3_1(a760))) <=> (c0_1(a760) | c1_1(a734) | c2_1(a734) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a734)) | (~c3_1(a760)) | c2_1(a760))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3796,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a760) | c0_1(a760) | (~c3_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a760) | c1_1(a734) | c2_1(a734) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a734)) | (~c3_1(a760)) | c2_1(a760)))),
% 1.67/1.85 inference(monotonicity,[status(thm)],[3795])).
% 1.67/1.85 tff(3797,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a760) | c0_1(a760) | (~c3_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a760) | c1_1(a734) | c2_1(a734) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a734)) | (~c3_1(a760)) | c2_1(a760))),
% 1.67/1.85 inference(transitivity,[status(thm)],[3796, 3794])).
% 1.67/1.85 tff(3798,plain,
% 1.67/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a760) | c0_1(a760) | (~c3_1(a760)))),
% 1.67/1.85 inference(quant_inst,[status(thm)],[])).
% 1.67/1.85 tff(3799,plain,
% 1.67/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a760) | c1_1(a734) | c2_1(a734) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a734)) | (~c3_1(a760)) | c2_1(a760)),
% 1.67/1.85 inference(modus_ponens,[status(thm)],[3798, 3797])).
% 1.67/1.85 tff(3800,plain,
% 1.67/1.85 ($false),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3799, 206, 3055, 3793, 3792, 3054, 3791, 3790, 3781, 3780, 879, 3771])).
% 1.67/1.85 tff(3801,plain,(hskp16 | c3_1(a695)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.85 tff(3802,plain,
% 1.67/1.85 (hskp16),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3801, 11])).
% 1.67/1.85 tff(3803,plain,
% 1.67/1.85 (~c1_1(a738)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[2989, 3802])).
% 1.67/1.85 tff(3804,plain,
% 1.67/1.85 (~c3_1(a764)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[277, 3754])).
% 1.67/1.85 tff(3805,plain,
% 1.67/1.85 (c3_1(a738)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[2958, 3802])).
% 1.67/1.85 tff(3806,plain,
% 1.67/1.85 (c2_1(a738)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[2966, 3802])).
% 1.67/1.85 tff(3807,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a760) | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a760) | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a764)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3808,plain,
% 1.67/1.85 (((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a760) | (~c3_1(a760)) | (~c2_1(a760))) <=> (c2_1(a764) | c3_1(a764) | c0_1(a760) | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a764)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3809,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a760) | (~c3_1(a760)) | (~c2_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a760) | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a764))))),
% 1.67/1.85 inference(monotonicity,[status(thm)],[3808])).
% 1.67/1.85 tff(3810,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a760) | (~c3_1(a760)) | (~c2_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a760) | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a764)))),
% 1.67/1.85 inference(transitivity,[status(thm)],[3809, 3807])).
% 1.67/1.85 tff(3811,plain,
% 1.67/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a760) | (~c3_1(a760)) | (~c2_1(a760)))),
% 1.67/1.85 inference(quant_inst,[status(thm)],[])).
% 1.67/1.85 tff(3812,plain,
% 1.67/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a760) | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a764))),
% 1.67/1.85 inference(modus_ponens,[status(thm)],[3811, 3810])).
% 1.67/1.85 tff(3813,plain,
% 1.67/1.85 (~c2_1(a760)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3812, 206, 3756, 3055, 3806, 3805, 3755, 3804, 3054, 3803, 10])).
% 1.67/1.85 tff(3814,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a764) | c0_1(a760) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c2_1(a760) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a760) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c2_1(a760) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3815,plain,
% 1.67/1.85 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c2_1(a760) | c0_1(a760) | (~c1_1(a760))) <=> (c3_1(a764) | c0_1(a760) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c2_1(a760) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3816,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c2_1(a760) | c0_1(a760) | (~c1_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a764) | c0_1(a760) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c2_1(a760) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764))))),
% 1.67/1.85 inference(monotonicity,[status(thm)],[3815])).
% 1.67/1.85 tff(3817,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c2_1(a760) | c0_1(a760) | (~c1_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a760) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c2_1(a760) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.85 inference(transitivity,[status(thm)],[3816, 3814])).
% 1.67/1.85 tff(3818,plain,
% 1.67/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c2_1(a760) | c0_1(a760) | (~c1_1(a760)))),
% 1.67/1.85 inference(quant_inst,[status(thm)],[])).
% 1.67/1.85 tff(3819,plain,
% 1.67/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a760) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c2_1(a760) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764))),
% 1.67/1.85 inference(modus_ponens,[status(thm)],[3818, 3817])).
% 1.67/1.85 tff(3820,plain,
% 1.67/1.85 ($false),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3819, 206, 2657, 2649, 3756, 3056, 3804, 3054, 756, 3763, 11, 3813])).
% 1.67/1.85 tff(3821,plain,(c3_1(a695)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.85 tff(3822,plain,
% 1.67/1.85 (~hskp7),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3175, 250, 3821])).
% 1.67/1.85 tff(3823,plain,
% 1.67/1.85 (hskp29),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3281, 2920, 3822])).
% 1.67/1.85 tff(3824,plain,
% 1.67/1.85 (c2_1(a713)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3297, 3823])).
% 1.67/1.85 tff(3825,plain,
% 1.67/1.85 (c0_1(a713)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3305, 3823])).
% 1.67/1.85 tff(3826,plain,
% 1.67/1.85 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a713)) | (~c2_1(a713)) | c1_1(a713))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a713)) | (~c2_1(a713)) | c1_1(a713))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3827,plain,
% 1.67/1.85 ((hskp16 | hskp7 | (~ndr1_0) | c1_1(a713) | (~c2_1(a713)) | (~c0_1(a713))) <=> (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a713)) | (~c2_1(a713)) | c1_1(a713))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3828,plain,
% 1.67/1.85 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a713) | (~c2_1(a713)) | (~c0_1(a713)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a713)) | (~c2_1(a713)) | c1_1(a713)))),
% 1.67/1.85 inference(monotonicity,[status(thm)],[3827])).
% 1.67/1.85 tff(3829,plain,
% 1.67/1.85 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a713) | (~c2_1(a713)) | (~c0_1(a713)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a713)) | (~c2_1(a713)) | c1_1(a713))),
% 1.67/1.85 inference(transitivity,[status(thm)],[3828, 3826])).
% 1.67/1.85 tff(3830,plain,
% 1.67/1.85 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a713) | (~c2_1(a713)) | (~c0_1(a713)))),
% 1.67/1.85 inference(quant_inst,[status(thm)],[])).
% 1.67/1.85 tff(3831,plain,
% 1.67/1.85 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a713)) | (~c2_1(a713)) | c1_1(a713)),
% 1.67/1.85 inference(modus_ponens,[status(thm)],[3830, 3829])).
% 1.67/1.85 tff(3832,plain,
% 1.67/1.85 (c1_1(a713)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3831, 206, 12, 3822, 3825, 3824, 3220])).
% 1.67/1.85 tff(3833,plain,
% 1.67/1.85 (c2_1(a725)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3254, 2923, 3821, 3822, 12, 2924, 3044])).
% 1.67/1.85 tff(3834,plain,
% 1.67/1.85 (c3_1(a713)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3289, 3823])).
% 1.67/1.85 tff(3835,plain,
% 1.67/1.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c2_1(a713)) | (~c1_1(a713)) | (~c3_1(a713)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c2_1(a713)) | (~c1_1(a713)) | (~c3_1(a713)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3836,plain,
% 1.67/1.85 ((hskp8 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c1_1(a713)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp8 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c2_1(a713)) | (~c1_1(a713)) | (~c3_1(a713)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3837,plain,
% 1.67/1.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c1_1(a713)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c2_1(a713)) | (~c1_1(a713)) | (~c3_1(a713))))),
% 1.67/1.85 inference(monotonicity,[status(thm)],[3836])).
% 1.67/1.85 tff(3838,plain,
% 1.67/1.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c1_1(a713)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c2_1(a713)) | (~c1_1(a713)) | (~c3_1(a713)))),
% 1.67/1.85 inference(transitivity,[status(thm)],[3837, 3835])).
% 1.67/1.85 tff(3839,plain,
% 1.67/1.85 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c1_1(a713)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.67/1.85 inference(quant_inst,[status(thm)],[])).
% 1.67/1.85 tff(3840,plain,
% 1.67/1.85 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c2_1(a713)) | (~c1_1(a713)) | (~c3_1(a713))),
% 1.67/1.85 inference(modus_ponens,[status(thm)],[3839, 3838])).
% 1.67/1.85 tff(3841,plain,
% 1.67/1.85 (hskp8),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3840, 206, 3824, 3834, 2924, 2923, 1784, 3833, 3832])).
% 1.67/1.85 tff(3842,plain,
% 1.67/1.85 (c3_1(a710)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[1805, 3841])).
% 1.67/1.85 tff(3843,plain,
% 1.67/1.85 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3844,plain,
% 1.67/1.85 ((hskp14 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725))) <=> (hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3845,plain,
% 1.67/1.85 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713))))),
% 1.67/1.85 inference(monotonicity,[status(thm)],[3844])).
% 1.67/1.85 tff(3846,plain,
% 1.67/1.85 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))),
% 1.67/1.85 inference(transitivity,[status(thm)],[3845, 3843])).
% 1.67/1.85 tff(3847,plain,
% 1.67/1.85 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))),
% 1.67/1.85 inference(quant_inst,[status(thm)],[])).
% 1.67/1.85 tff(3848,plain,
% 1.67/1.85 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713))),
% 1.67/1.85 inference(modus_ponens,[status(thm)],[3847, 3846])).
% 1.67/1.85 tff(3849,plain,
% 1.67/1.85 (hskp14),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3848, 206, 3825, 3824, 3834, 3044, 2923, 1545, 3833])).
% 1.67/1.85 tff(3850,assumption,(hskp20), introduced(assumption)).
% 1.67/1.85 tff(3851,plain,
% 1.67/1.85 (~c3_1(a754)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[614, 3850])).
% 1.67/1.85 tff(3852,plain,
% 1.67/1.85 (~c0_1(a754)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[541, 3850])).
% 1.67/1.85 tff(3853,plain,
% 1.67/1.85 (c2_1(a754)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[172, 3850])).
% 1.67/1.85 tff(3854,plain,
% 1.67/1.85 (c0_1(a764)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[1087, 206, 1921, 3853, 3677, 3676, 1919, 3852, 3851, 3675, 159])).
% 1.67/1.85 tff(3855,plain,
% 1.67/1.85 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | c3_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | c3_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3856,plain,
% 1.67/1.85 ((hskp16 | hskp15 | (~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764))) <=> (hskp16 | hskp15 | c3_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3857,plain,
% 1.67/1.85 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | c3_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764))))),
% 1.67/1.85 inference(monotonicity,[status(thm)],[3856])).
% 1.67/1.85 tff(3858,plain,
% 1.67/1.85 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | c3_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.85 inference(transitivity,[status(thm)],[3857, 3855])).
% 1.67/1.85 tff(3859,plain,
% 1.67/1.85 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.85 inference(quant_inst,[status(thm)],[])).
% 1.67/1.85 tff(3860,plain,
% 1.67/1.85 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | c3_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764))),
% 1.67/1.85 inference(modus_ponens,[status(thm)],[3859, 3858])).
% 1.67/1.85 tff(3861,plain,
% 1.67/1.85 (hskp15 | (~c0_1(a764))),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3860, 206, 12, 1921, 1919, 3595])).
% 1.67/1.85 tff(3862,plain,
% 1.67/1.85 (hskp15),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3861, 3854])).
% 1.67/1.85 tff(3863,plain,
% 1.67/1.85 (~c2_1(a734)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3607, 3862])).
% 1.67/1.85 tff(3864,plain,
% 1.67/1.85 (~c1_1(a734)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3613, 3862])).
% 1.67/1.85 tff(3865,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c0_1(a734)) | (~c2_1(a754)) | (~c0_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c0_1(a734)) | (~c2_1(a754)) | (~c0_1(a764)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3866,plain,
% 1.67/1.85 (((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c0_1(a734)) | (~c2_1(a754)) | (~c0_1(a764)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3867,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c0_1(a734)) | (~c2_1(a754)) | (~c0_1(a764))))),
% 1.67/1.85 inference(monotonicity,[status(thm)],[3866])).
% 1.67/1.85 tff(3868,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c0_1(a734)) | (~c2_1(a754)) | (~c0_1(a764)))),
% 1.67/1.85 inference(transitivity,[status(thm)],[3867, 3865])).
% 1.67/1.85 tff(3869,plain,
% 1.67/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.67/1.85 inference(quant_inst,[status(thm)],[])).
% 1.67/1.85 tff(3870,plain,
% 1.67/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c0_1(a734)) | (~c2_1(a754)) | (~c0_1(a764))),
% 1.67/1.85 inference(modus_ponens,[status(thm)],[3869, 3868])).
% 1.67/1.85 tff(3871,plain,
% 1.67/1.85 (~c0_1(a734)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3870, 206, 3853, 1920, 1919, 3852, 3851, 3864, 3863, 2340, 3854])).
% 1.67/1.85 tff(3872,plain,
% 1.67/1.85 (~c1_1(a754)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[1050, 206, 3853, 3677, 3676, 3852, 3851, 3675, 159])).
% 1.67/1.85 tff(3873,plain,
% 1.67/1.85 (c3_1(a734)),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3623, 3862])).
% 1.67/1.85 tff(3874,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c3_1(a734)) | c0_1(a734) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c3_1(a734)) | c0_1(a734) | c1_1(a754) | (~c2_1(a754)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3875,plain,
% 1.67/1.85 (((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734))) <=> (c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c3_1(a734)) | c0_1(a734) | c1_1(a754) | (~c2_1(a754)))),
% 1.67/1.85 inference(rewrite,[status(thm)],[])).
% 1.67/1.85 tff(3876,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c3_1(a734)) | c0_1(a734) | c1_1(a754) | (~c2_1(a754))))),
% 1.67/1.85 inference(monotonicity,[status(thm)],[3875])).
% 1.67/1.85 tff(3877,plain,
% 1.67/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c3_1(a734)) | c0_1(a734) | c1_1(a754) | (~c2_1(a754)))),
% 1.67/1.85 inference(transitivity,[status(thm)],[3876, 3874])).
% 1.67/1.85 tff(3878,plain,
% 1.67/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))),
% 1.67/1.85 inference(quant_inst,[status(thm)],[])).
% 1.67/1.85 tff(3879,plain,
% 1.67/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c3_1(a734)) | c0_1(a734) | c1_1(a754) | (~c2_1(a754))),
% 1.67/1.85 inference(modus_ponens,[status(thm)],[3878, 3877])).
% 1.67/1.85 tff(3880,plain,
% 1.67/1.85 ($false),
% 1.67/1.85 inference(unit_resolution,[status(thm)],[3879, 206, 3853, 3873, 3851, 3864, 3863, 879, 3872, 3871])).
% 1.67/1.85 tff(3881,plain,((~hskp20) | c2_1(a764) | c3_1(a764) | hskp16 | (~c1_1(a764))), inference(lemma,lemma(discharge,[]))).
% 1.67/1.86 tff(3882,plain,
% 1.67/1.86 (~hskp20),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3881, 3358, 3357, 12, 3362])).
% 1.67/1.86 tff(3883,plain,
% 1.67/1.86 (hskp11),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3325, 2920, 426])).
% 1.67/1.86 tff(3884,plain,
% 1.67/1.86 (c3_1(a722)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[2281, 3883])).
% 1.67/1.86 tff(3885,plain,
% 1.67/1.86 (c0_1(a722)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[2100, 3883])).
% 1.67/1.86 tff(3886,plain,
% 1.67/1.86 (~c1_1(a722)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[2092, 3883])).
% 1.67/1.86 tff(3887,assumption,(~c1_1(a722)), introduced(assumption)).
% 1.67/1.86 tff(3888,assumption,(c0_1(a722)), introduced(assumption)).
% 1.67/1.86 tff(3889,plain,
% 1.67/1.86 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c0_1(a722)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c0_1(a722)))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3890,plain,
% 1.67/1.86 ((hskp16 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c0_1(a722))) <=> (hskp16 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c0_1(a722)))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3891,plain,
% 1.67/1.86 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c0_1(a722)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c0_1(a722))))),
% 1.67/1.86 inference(monotonicity,[status(thm)],[3890])).
% 1.67/1.86 tff(3892,plain,
% 1.67/1.86 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c0_1(a722)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c0_1(a722)))),
% 1.67/1.86 inference(transitivity,[status(thm)],[3891, 3889])).
% 1.67/1.86 tff(3893,plain,
% 1.67/1.86 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c0_1(a722)))),
% 1.67/1.86 inference(quant_inst,[status(thm)],[])).
% 1.67/1.86 tff(3894,plain,
% 1.67/1.86 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c0_1(a722))),
% 1.67/1.86 inference(modus_ponens,[status(thm)],[3893, 3892])).
% 1.67/1.86 tff(3895,plain,
% 1.67/1.86 (hskp7 | (~c2_1(a722))),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3894, 206, 12, 3888, 3887, 3220])).
% 1.67/1.86 tff(3896,plain,
% 1.67/1.86 (~c2_1(a722)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3895, 3822])).
% 1.67/1.86 tff(3897,plain,
% 1.67/1.86 (hskp12),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[1967, 250, 2920])).
% 1.67/1.86 tff(3898,plain,
% 1.67/1.86 (~c1_1(a725)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[130, 3897])).
% 1.67/1.86 tff(3899,plain,
% 1.67/1.86 (~c0_1(a725)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[136, 3897])).
% 1.67/1.86 tff(3900,plain,
% 1.67/1.86 (~c3_1(a725)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[124, 3897])).
% 1.67/1.86 tff(3901,plain,
% 1.67/1.86 (c2_1(a725)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3254, 3900, 3821, 3822, 12, 3899, 3898])).
% 1.67/1.86 tff(3902,assumption,(c3_1(a722)), introduced(assumption)).
% 1.67/1.86 tff(3903,plain,
% 1.67/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | (~c2_1(a725)) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | (~c2_1(a725)) | c0_1(a764) | (~c1_1(a764)))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3904,plain,
% 1.67/1.86 (((~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764))) <=> (c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | (~c2_1(a725)) | c0_1(a764) | (~c1_1(a764)))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3905,plain,
% 1.67/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | (~c2_1(a725)) | c0_1(a764) | (~c1_1(a764))))),
% 1.67/1.86 inference(monotonicity,[status(thm)],[3904])).
% 1.67/1.86 tff(3906,plain,
% 1.67/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | (~c2_1(a725)) | c0_1(a764) | (~c1_1(a764)))),
% 1.67/1.86 inference(transitivity,[status(thm)],[3905, 3903])).
% 1.67/1.86 tff(3907,plain,
% 1.67/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)))),
% 1.67/1.86 inference(quant_inst,[status(thm)],[])).
% 1.67/1.86 tff(3908,plain,
% 1.67/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | (~c2_1(a725)) | c0_1(a764) | (~c1_1(a764))),
% 1.67/1.86 inference(modus_ponens,[status(thm)],[3907, 3906])).
% 1.67/1.86 tff(3909,plain,
% 1.67/1.86 (c0_1(a764)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3908, 206, 1921, 3888, 3902, 1919, 3899, 3900, 159, 3901, 3896])).
% 1.67/1.86 tff(3910,plain,
% 1.67/1.86 ($false),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3426, 206, 3888, 1920, 1919, 3899, 3900, 3887, 2340, 3901, 3909, 3896])).
% 1.67/1.86 tff(3911,plain,(hskp20 | (~c0_1(a722)) | c2_1(a764) | c3_1(a764) | c1_1(a722) | (~c1_1(a764)) | (~c3_1(a722)) | hskp16 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.67/1.86 tff(3912,plain,
% 1.67/1.86 ($false),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3911, 3886, 3885, 3358, 3357, 3882, 3362, 3884, 12, 2920])).
% 1.67/1.86 tff(3913,plain,(hskp13 | hskp16 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.67/1.86 tff(3914,plain,
% 1.67/1.86 (hskp13),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3913, 426, 12])).
% 1.67/1.86 tff(3915,plain,
% 1.67/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3916,plain,
% 1.67/1.86 (((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726)) <=> (c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3917,plain,
% 1.67/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764))))),
% 1.67/1.86 inference(monotonicity,[status(thm)],[3916])).
% 1.67/1.86 tff(3918,plain,
% 1.67/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)))),
% 1.67/1.86 inference(transitivity,[status(thm)],[3917, 3915])).
% 1.67/1.86 tff(3919,plain,
% 1.67/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726))),
% 1.67/1.86 inference(quant_inst,[status(thm)],[])).
% 1.67/1.86 tff(3920,plain,
% 1.67/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764))),
% 1.67/1.86 inference(modus_ponens,[status(thm)],[3919, 3918])).
% 1.67/1.86 tff(3921,plain,
% 1.67/1.86 (c2_1(a726)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3920, 206, 2685, 2649, 1921, 1919, 1935, 1929, 1699, 1985, 3163])).
% 1.67/1.86 tff(3922,plain,
% 1.67/1.86 ($false),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[2732, 206, 250, 2685, 2649, 1950, 1929, 2002, 3163, 3921])).
% 1.67/1.86 tff(3923,plain,((~hskp13) | hskp20 | (~c3_1(a695)) | (~c1_1(a764)) | c3_1(a764) | (~c0_1(a764))), inference(lemma,lemma(discharge,[]))).
% 1.67/1.86 tff(3924,plain,
% 1.67/1.86 (~c0_1(a764)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3923, 3914, 3362, 3821, 3357, 3882])).
% 1.67/1.86 tff(3925,plain,
% 1.67/1.86 (~hskp7),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3175, 3882, 3821])).
% 1.67/1.86 tff(3926,plain,
% 1.67/1.86 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3927,plain,
% 1.67/1.86 ((hskp7 | hskp2 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | c2_1(a764)) <=> (hskp7 | hskp2 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3928,plain,
% 1.67/1.86 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | c2_1(a764))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764)))),
% 1.67/1.86 inference(monotonicity,[status(thm)],[3927])).
% 1.67/1.86 tff(3929,plain,
% 1.67/1.86 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | c2_1(a764))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764))),
% 1.67/1.86 inference(transitivity,[status(thm)],[3928, 3926])).
% 1.67/1.86 tff(3930,plain,
% 1.67/1.86 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | c2_1(a764))),
% 1.67/1.86 inference(quant_inst,[status(thm)],[])).
% 1.67/1.86 tff(3931,plain,
% 1.67/1.86 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764)),
% 1.67/1.86 inference(modus_ponens,[status(thm)],[3930, 3929])).
% 1.67/1.86 tff(3932,plain,
% 1.67/1.86 (hskp7 | hskp2 | c0_1(a764)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3931, 206, 3358, 3357, 3194])).
% 1.67/1.86 tff(3933,plain,
% 1.67/1.86 (hskp2),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3932, 3924, 3925])).
% 1.67/1.86 tff(3934,plain,
% 1.67/1.86 (~c2_1(a696)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[1884, 3933])).
% 1.67/1.86 tff(3935,plain,
% 1.67/1.86 (c1_1(a696)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[1907, 3933])).
% 1.67/1.86 tff(3936,plain,
% 1.67/1.86 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | c2_1(a696) | (~ndr1_0) | (~c3_1(a696)) | (~c1_1(a696)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a696) | (~ndr1_0) | (~c3_1(a696)) | (~c1_1(a696)))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3937,plain,
% 1.67/1.86 ((hskp20 | hskp16 | (~ndr1_0) | c2_1(a696) | (~c3_1(a696)) | (~c1_1(a696))) <=> (hskp20 | hskp16 | c2_1(a696) | (~ndr1_0) | (~c3_1(a696)) | (~c1_1(a696)))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3938,plain,
% 1.67/1.86 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a696) | (~c3_1(a696)) | (~c1_1(a696)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | c2_1(a696) | (~ndr1_0) | (~c3_1(a696)) | (~c1_1(a696))))),
% 1.67/1.86 inference(monotonicity,[status(thm)],[3937])).
% 1.67/1.86 tff(3939,plain,
% 1.67/1.86 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a696) | (~c3_1(a696)) | (~c1_1(a696)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a696) | (~ndr1_0) | (~c3_1(a696)) | (~c1_1(a696)))),
% 1.67/1.86 inference(transitivity,[status(thm)],[3938, 3936])).
% 1.67/1.86 tff(3940,plain,
% 1.67/1.86 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a696) | (~c3_1(a696)) | (~c1_1(a696)))),
% 1.67/1.86 inference(quant_inst,[status(thm)],[])).
% 1.67/1.86 tff(3941,plain,
% 1.67/1.86 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a696) | (~ndr1_0) | (~c3_1(a696)) | (~c1_1(a696))),
% 1.67/1.86 inference(modus_ponens,[status(thm)],[3940, 3939])).
% 1.67/1.86 tff(3942,plain,
% 1.67/1.86 (~c3_1(a696)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3941, 206, 3882, 12, 3935, 3934, 2943])).
% 1.67/1.86 tff(3943,plain,
% 1.67/1.86 (c0_1(a696)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[1892, 3933])).
% 1.67/1.86 tff(3944,plain,
% 1.67/1.86 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3945,plain,
% 1.67/1.86 ((hskp20 | hskp16 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702))) <=> (hskp20 | hskp16 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3946,plain,
% 1.67/1.86 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702))))),
% 1.67/1.86 inference(monotonicity,[status(thm)],[3945])).
% 1.67/1.86 tff(3947,plain,
% 1.67/1.86 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)))),
% 1.67/1.86 inference(transitivity,[status(thm)],[3946, 3944])).
% 1.67/1.86 tff(3948,plain,
% 1.67/1.86 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702)))),
% 1.67/1.86 inference(quant_inst,[status(thm)],[])).
% 1.67/1.86 tff(3949,plain,
% 1.67/1.86 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702))),
% 1.67/1.86 inference(modus_ponens,[status(thm)],[3948, 3947])).
% 1.67/1.86 tff(3950,plain,
% 1.67/1.86 (hskp20 | hskp16 | (~c1_1(a702))),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3949, 206, 3676, 3675, 2943])).
% 1.67/1.86 tff(3951,plain,
% 1.67/1.86 (~c1_1(a702)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3950, 3882, 12])).
% 1.67/1.86 tff(3952,plain,
% 1.67/1.86 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.67/1.86 inference(bind,[status(th)],[])).
% 1.67/1.86 tff(3953,plain,
% 1.67/1.86 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.67/1.86 inference(quant_intro,[status(thm)],[3952])).
% 1.67/1.86 tff(3954,plain,
% 1.67/1.86 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3955,plain,
% 1.67/1.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp29))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.67/1.86 inference(bind,[status(th)],[])).
% 1.67/1.86 tff(3956,plain,
% 1.67/1.86 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.67/1.86 inference(quant_intro,[status(thm)],[3955])).
% 1.67/1.86 tff(3957,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 1.67/1.86 tff(3958,plain,
% 1.67/1.86 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.67/1.86 inference(modus_ponens,[status(thm)],[3957, 3956])).
% 1.67/1.86 tff(3959,plain,
% 1.67/1.86 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.67/1.86 inference(modus_ponens,[status(thm)],[3958, 3954])).
% 1.67/1.86 tff(3960,plain,(
% 1.67/1.86 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.67/1.86 inference(skolemize,[status(sab)],[3959])).
% 1.67/1.86 tff(3961,plain,
% 1.67/1.86 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.67/1.86 inference(modus_ponens,[status(thm)],[3960, 3953])).
% 1.67/1.86 tff(3962,plain,
% 1.67/1.86 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp29 | c2_1(a764) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp29 | c2_1(a764) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | c0_1(a764) | (~c1_1(a764)))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3963,plain,
% 1.67/1.86 ((hskp29 | (~ndr1_0) | c1_1(a702) | c2_1(a702) | (~c3_1(a702)) | c0_1(a764) | c2_1(a764) | (~c1_1(a764))) <=> (hskp29 | c2_1(a764) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | c0_1(a764) | (~c1_1(a764)))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3964,plain,
% 1.67/1.86 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a702) | c2_1(a702) | (~c3_1(a702)) | c0_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp29 | c2_1(a764) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | c0_1(a764) | (~c1_1(a764))))),
% 1.67/1.86 inference(monotonicity,[status(thm)],[3963])).
% 1.67/1.86 tff(3965,plain,
% 1.67/1.86 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a702) | c2_1(a702) | (~c3_1(a702)) | c0_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp29 | c2_1(a764) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | c0_1(a764) | (~c1_1(a764)))),
% 1.67/1.86 inference(transitivity,[status(thm)],[3964, 3962])).
% 1.67/1.86 tff(3966,plain,
% 1.67/1.86 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a702) | c2_1(a702) | (~c3_1(a702)) | c0_1(a764) | c2_1(a764) | (~c1_1(a764)))),
% 1.67/1.86 inference(quant_inst,[status(thm)],[])).
% 1.67/1.86 tff(3967,plain,
% 1.67/1.86 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp29 | c2_1(a764) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | c0_1(a764) | (~c1_1(a764))),
% 1.67/1.86 inference(modus_ponens,[status(thm)],[3966, 3965])).
% 1.67/1.86 tff(3968,plain,
% 1.67/1.86 (hskp29),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3967, 206, 3362, 3676, 3358, 3675, 3961, 3924, 3951])).
% 1.67/1.86 tff(3969,plain,
% 1.67/1.86 (c3_1(a713)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3289, 3968])).
% 1.67/1.86 tff(3970,plain,
% 1.67/1.86 (c2_1(a713)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3297, 3968])).
% 1.67/1.86 tff(3971,plain,
% 1.67/1.86 (c0_1(a713)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3305, 3968])).
% 1.67/1.86 tff(3972,plain,
% 1.67/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a764) | c3_1(a764) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3973,plain,
% 1.67/1.86 (((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | c3_1(a764) | c2_1(a764) | c0_1(a764)) <=> (c2_1(a764) | c3_1(a764) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))),
% 1.67/1.86 inference(rewrite,[status(thm)],[])).
% 1.67/1.86 tff(3974,plain,
% 1.67/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | c3_1(a764) | c2_1(a764) | c0_1(a764))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a764) | c3_1(a764) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764)))),
% 1.67/1.86 inference(monotonicity,[status(thm)],[3973])).
% 1.67/1.86 tff(3975,plain,
% 1.67/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | c3_1(a764) | c2_1(a764) | c0_1(a764))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))),
% 1.67/1.86 inference(transitivity,[status(thm)],[3974, 3972])).
% 1.67/1.86 tff(3976,plain,
% 1.67/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | c3_1(a764) | c2_1(a764) | c0_1(a764))),
% 1.67/1.86 inference(quant_inst,[status(thm)],[])).
% 1.67/1.86 tff(3977,plain,
% 1.67/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764)),
% 1.67/1.86 inference(modus_ponens,[status(thm)],[3976, 3975])).
% 1.67/1.86 tff(3978,plain,
% 1.67/1.86 ($false),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3977, 206, 3971, 3970, 3969, 3943, 3935, 3358, 3357, 1699, 3942, 3924])).
% 1.67/1.86 tff(3979,plain,(hskp23 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.67/1.86 tff(3980,plain,
% 1.67/1.86 (hskp23),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3979, 12])).
% 1.67/1.86 tff(3981,plain,
% 1.67/1.86 (c0_1(a763)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[379, 3980])).
% 1.67/1.86 tff(3982,plain,
% 1.67/1.86 (~c2_1(a763)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[365, 3980])).
% 1.67/1.86 tff(3983,plain,
% 1.67/1.86 (~c1_1(a763)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[371, 3980])).
% 1.67/1.86 tff(3984,plain,
% 1.67/1.86 (c2_1(a710)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[1871, 3841])).
% 1.67/1.86 tff(3985,plain,
% 1.67/1.86 (~c0_1(a710)),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[1797, 3841])).
% 1.67/1.86 tff(3986,plain,
% 1.67/1.86 ($false),
% 1.67/1.86 inference(unit_resolution,[status(thm)],[3660, 3985, 3984, 3821, 12, 3983, 3982, 3981, 3849, 3842])).
% 1.67/1.87 tff(3987,plain,(hskp13 | hskp16 | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.67/1.87 tff(3988,plain,
% 1.67/1.87 (hskp13),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3987, 250, 12])).
% 1.67/1.87 tff(3989,plain,
% 1.67/1.87 (~c3_1(a726)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[1928, 3988])).
% 1.67/1.87 tff(3990,plain,
% 1.67/1.87 (~c0_1(a726)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[1934, 3988])).
% 1.67/1.87 tff(3991,plain,
% 1.67/1.87 (c1_1(a726)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[1949, 3988])).
% 1.67/1.87 tff(3992,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(3993,plain,
% 1.67/1.87 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726))) <=> (c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(3994,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)) | (~c2_1(a726))))),
% 1.67/1.87 inference(monotonicity,[status(thm)],[3993])).
% 1.67/1.87 tff(3995,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 1.67/1.87 inference(transitivity,[status(thm)],[3994, 3992])).
% 1.67/1.87 tff(3996,plain,
% 1.67/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))),
% 1.67/1.87 inference(quant_inst,[status(thm)],[])).
% 1.67/1.87 tff(3997,plain,
% 1.67/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)) | (~c2_1(a726))),
% 1.67/1.87 inference(modus_ponens,[status(thm)],[3996, 3995])).
% 1.67/1.87 tff(3998,plain,
% 1.67/1.87 (~c2_1(a726)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3997, 206, 3991, 3677, 3676, 3990, 3989, 3675, 159])).
% 1.67/1.87 tff(3999,plain,
% 1.67/1.87 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4000,plain,
% 1.67/1.87 ((hskp7 | hskp2 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726)) <=> (hskp7 | hskp2 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4001,plain,
% 1.67/1.87 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726)))),
% 1.67/1.87 inference(monotonicity,[status(thm)],[4000])).
% 1.67/1.87 tff(4002,plain,
% 1.67/1.87 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))),
% 1.67/1.87 inference(transitivity,[status(thm)],[4001, 3999])).
% 1.67/1.87 tff(4003,plain,
% 1.67/1.87 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726))),
% 1.67/1.87 inference(quant_inst,[status(thm)],[])).
% 1.67/1.87 tff(4004,plain,
% 1.67/1.87 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726)),
% 1.67/1.87 inference(modus_ponens,[status(thm)],[4003, 4002])).
% 1.67/1.87 tff(4005,plain,
% 1.67/1.87 (hskp2 | c2_1(a726)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[4004, 206, 3822, 3990, 3989, 3194])).
% 1.67/1.87 tff(4006,plain,
% 1.67/1.87 (hskp2),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[4005, 3998])).
% 1.67/1.87 tff(4007,plain,
% 1.67/1.87 (~c2_1(a696)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[1884, 4006])).
% 1.67/1.87 tff(4008,plain,
% 1.67/1.87 (c1_1(a696)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[1907, 4006])).
% 1.67/1.87 tff(4009,plain,
% 1.67/1.87 (~c3_1(a696)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3941, 206, 250, 12, 4008, 4007, 2943])).
% 1.67/1.87 tff(4010,plain,
% 1.67/1.87 (c0_1(a696)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[1892, 4006])).
% 1.67/1.87 tff(4011,plain,
% 1.67/1.87 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | c1_1(a763) | c2_1(a763) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a763) | c2_1(a763) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a763)))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4012,plain,
% 1.67/1.87 ((hskp12 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763))) <=> (hskp12 | c1_1(a763) | c2_1(a763) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a763)))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4013,plain,
% 1.67/1.87 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | c1_1(a763) | c2_1(a763) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a763))))),
% 1.67/1.87 inference(monotonicity,[status(thm)],[4012])).
% 1.67/1.87 tff(4014,plain,
% 1.67/1.87 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a763) | c2_1(a763) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a763)))),
% 1.67/1.87 inference(transitivity,[status(thm)],[4013, 4011])).
% 1.67/1.87 tff(4015,plain,
% 1.67/1.87 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)))),
% 1.67/1.87 inference(quant_inst,[status(thm)],[])).
% 1.67/1.87 tff(4016,plain,
% 1.67/1.87 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a763) | c2_1(a763) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a763))),
% 1.67/1.87 inference(modus_ponens,[status(thm)],[4015, 4014])).
% 1.67/1.87 tff(4017,plain,
% 1.67/1.87 (hskp12),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[4016, 206, 3981, 4010, 4008, 3983, 3982, 4007, 2322])).
% 1.67/1.87 tff(4018,plain,
% 1.67/1.87 (~c1_1(a725)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[130, 4017])).
% 1.67/1.87 tff(4019,plain,
% 1.67/1.87 (~c0_1(a725)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[136, 4017])).
% 1.67/1.87 tff(4020,plain,
% 1.67/1.87 (~c3_1(a725)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[124, 4017])).
% 1.67/1.87 tff(4021,plain,
% 1.67/1.87 (c2_1(a725)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3254, 4020, 3821, 3822, 12, 4019, 4018])).
% 1.67/1.87 tff(4022,plain,
% 1.67/1.87 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4023,plain,
% 1.67/1.87 ((hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c1_1(a696))) <=> (hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4024,plain,
% 1.67/1.87 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c1_1(a696)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696))))),
% 1.67/1.87 inference(monotonicity,[status(thm)],[4023])).
% 1.67/1.87 tff(4025,plain,
% 1.67/1.87 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c1_1(a696)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)))),
% 1.67/1.87 inference(transitivity,[status(thm)],[4024, 4022])).
% 1.67/1.87 tff(4026,plain,
% 1.67/1.87 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c1_1(a696)))),
% 1.67/1.87 inference(quant_inst,[status(thm)],[])).
% 1.67/1.87 tff(4027,plain,
% 1.67/1.87 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696))),
% 1.67/1.87 inference(modus_ponens,[status(thm)],[4026, 4025])).
% 1.67/1.87 tff(4028,plain,
% 1.67/1.87 (hskp15),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[4027, 206, 12, 4010, 4008, 3595, 4009])).
% 1.67/1.87 tff(4029,plain,
% 1.67/1.87 (~c2_1(a734)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3607, 4028])).
% 1.67/1.87 tff(4030,plain,
% 1.67/1.87 (~c1_1(a734)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3613, 4028])).
% 1.67/1.87 tff(4031,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a734) | c2_1(a734) | c0_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c2_1(a725)) | (~c0_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a734) | c2_1(a734) | c0_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c2_1(a725)) | (~c0_1(a734)))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4032,plain,
% 1.67/1.87 (((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c0_1(a696)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (c1_1(a734) | c2_1(a734) | c0_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c2_1(a725)) | (~c0_1(a734)))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4033,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c0_1(a696)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a734) | c2_1(a734) | c0_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c2_1(a725)) | (~c0_1(a734))))),
% 1.67/1.87 inference(monotonicity,[status(thm)],[4032])).
% 1.67/1.87 tff(4034,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c0_1(a696)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a734) | c2_1(a734) | c0_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c2_1(a725)) | (~c0_1(a734)))),
% 1.67/1.87 inference(transitivity,[status(thm)],[4033, 4031])).
% 1.67/1.87 tff(4035,plain,
% 1.67/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c0_1(a696)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.67/1.87 inference(quant_inst,[status(thm)],[])).
% 1.67/1.87 tff(4036,plain,
% 1.67/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a734) | c2_1(a734) | c0_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c2_1(a725)) | (~c0_1(a734))),
% 1.67/1.87 inference(modus_ponens,[status(thm)],[4035, 4034])).
% 1.67/1.87 tff(4037,plain,
% 1.67/1.87 (~c0_1(a734)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[4036, 206, 4010, 4030, 4029, 4019, 4020, 4007, 2340, 4021, 4009])).
% 1.67/1.87 tff(4038,plain,
% 1.67/1.87 (c3_1(a734)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3623, 4028])).
% 1.67/1.87 tff(4039,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a734) | c2_1(a734) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a734)) | c0_1(a734))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a734) | c2_1(a734) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a734)) | c0_1(a734))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4040,plain,
% 1.67/1.87 (((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734))) <=> (c1_1(a734) | c2_1(a734) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a734)) | c0_1(a734))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4041,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a734) | c2_1(a734) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a734)) | c0_1(a734)))),
% 1.67/1.87 inference(monotonicity,[status(thm)],[4040])).
% 1.67/1.87 tff(4042,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a734) | c2_1(a734) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a734)) | c0_1(a734))),
% 1.67/1.87 inference(transitivity,[status(thm)],[4041, 4039])).
% 1.67/1.87 tff(4043,plain,
% 1.67/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))),
% 1.67/1.87 inference(quant_inst,[status(thm)],[])).
% 1.67/1.87 tff(4044,plain,
% 1.67/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a734) | c2_1(a734) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a734)) | c0_1(a734)),
% 1.67/1.87 inference(modus_ponens,[status(thm)],[4043, 4042])).
% 1.67/1.87 tff(4045,plain,
% 1.67/1.87 ($false),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[4044, 206, 4038, 4030, 4029, 4018, 4020, 879, 4021, 4037])).
% 1.67/1.87 tff(4046,plain,(hskp20 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.67/1.87 tff(4047,plain,
% 1.67/1.87 (hskp20),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[4046, 12])).
% 1.67/1.87 tff(4048,plain,
% 1.67/1.87 (~c3_1(a754)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[614, 4047])).
% 1.67/1.87 tff(4049,plain,
% 1.67/1.87 (~c0_1(a754)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[541, 4047])).
% 1.67/1.87 tff(4050,plain,
% 1.67/1.87 (c2_1(a754)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[172, 4047])).
% 1.67/1.87 tff(4051,plain,
% 1.67/1.87 (hskp8),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3580, 206, 2657, 2649, 4050, 4049, 4048, 1784, 3821])).
% 1.67/1.87 tff(4052,plain,
% 1.67/1.87 (c3_1(a710)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[1805, 4051])).
% 1.67/1.87 tff(4053,plain,
% 1.67/1.87 (c3_1(a763)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3446, 4049, 3983, 3981, 3982, 4050, 4048])).
% 1.67/1.87 tff(4054,plain,
% 1.67/1.87 (~c1_1(a754)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3563, 206, 3981, 4050, 3982, 4049, 4048, 159, 4053])).
% 1.67/1.87 tff(4055,plain,
% 1.67/1.87 (hskp14),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3571, 206, 2685, 2649, 4050, 4048, 1545, 4054, 3821])).
% 1.67/1.87 tff(4056,plain,
% 1.67/1.87 (c2_1(a710)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[1871, 4051])).
% 1.67/1.87 tff(4057,plain,
% 1.67/1.87 (~c0_1(a710)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[1797, 4051])).
% 1.67/1.87 tff(4058,plain,
% 1.67/1.87 ($false),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3660, 4057, 4056, 3821, 12, 3983, 3982, 3981, 4055, 4052])).
% 1.67/1.87 tff(4059,plain,(hskp16), inference(lemma,lemma(discharge,[]))).
% 1.67/1.87 tff(4060,plain,
% 1.67/1.87 (~c2_1(a726)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3997, 206, 1950, 3677, 3676, 1935, 1929, 3675, 159])).
% 1.67/1.87 tff(4061,plain,
% 1.67/1.87 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c2_1(a726))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c2_1(a726))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4062,plain,
% 1.67/1.87 ((hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | c2_1(a726)) <=> (hskp0 | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c2_1(a726))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4063,plain,
% 1.67/1.87 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c2_1(a726)))),
% 1.67/1.87 inference(monotonicity,[status(thm)],[4062])).
% 1.67/1.87 tff(4064,plain,
% 1.67/1.87 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c2_1(a726))),
% 1.67/1.87 inference(transitivity,[status(thm)],[4063, 4061])).
% 1.67/1.87 tff(4065,plain,
% 1.67/1.87 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | c2_1(a726))),
% 1.67/1.87 inference(quant_inst,[status(thm)],[])).
% 1.67/1.87 tff(4066,plain,
% 1.67/1.87 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c2_1(a726)),
% 1.67/1.87 inference(modus_ponens,[status(thm)],[4065, 4064])).
% 1.67/1.87 tff(4067,plain,
% 1.67/1.87 (hskp0),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[4066, 206, 3677, 3676, 1935, 1929, 3675, 2715, 4060])).
% 1.67/1.87 tff(4068,plain,
% 1.67/1.87 (~c0_1(a692)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[793, 4067])).
% 1.67/1.87 tff(4069,plain,
% 1.67/1.87 (~c1_1(a738)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[2989, 4059])).
% 1.67/1.87 tff(4070,plain,
% 1.67/1.87 (c2_1(a692)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[803, 4067])).
% 1.67/1.87 tff(4071,plain,
% 1.67/1.87 (c3_1(a738)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[2958, 4059])).
% 1.67/1.87 tff(4072,plain,
% 1.67/1.87 (c2_1(a738)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[2966, 4059])).
% 1.67/1.87 tff(4073,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a738) | c3_1(a726) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c3_1(a692)) | (~c1_1(a726)) | c2_1(a726) | (~c2_1(a738)) | (~c3_1(a738)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a738) | c3_1(a726) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c3_1(a692)) | (~c1_1(a726)) | c2_1(a726) | (~c2_1(a738)) | (~c3_1(a738)))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4074,plain,
% 1.67/1.87 (((~ndr1_0) | c3_1(a726) | c2_1(a726) | (~c1_1(a726)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a692) | (~c3_1(a692)) | (~c2_1(a692))) <=> (c1_1(a738) | c3_1(a726) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c3_1(a692)) | (~c1_1(a726)) | c2_1(a726) | (~c2_1(a738)) | (~c3_1(a738)))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4075,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a726) | c2_1(a726) | (~c1_1(a726)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a692) | (~c3_1(a692)) | (~c2_1(a692)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a738) | c3_1(a726) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c3_1(a692)) | (~c1_1(a726)) | c2_1(a726) | (~c2_1(a738)) | (~c3_1(a738))))),
% 1.67/1.87 inference(monotonicity,[status(thm)],[4074])).
% 1.67/1.87 tff(4076,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a726) | c2_1(a726) | (~c1_1(a726)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a692) | (~c3_1(a692)) | (~c2_1(a692)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a738) | c3_1(a726) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c3_1(a692)) | (~c1_1(a726)) | c2_1(a726) | (~c2_1(a738)) | (~c3_1(a738)))),
% 1.67/1.87 inference(transitivity,[status(thm)],[4075, 4073])).
% 1.67/1.87 tff(4077,plain,
% 1.67/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a726) | c2_1(a726) | (~c1_1(a726)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a692) | (~c3_1(a692)) | (~c2_1(a692)))),
% 1.67/1.87 inference(quant_inst,[status(thm)],[])).
% 1.67/1.87 tff(4078,plain,
% 1.67/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a738) | c3_1(a726) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c3_1(a692)) | (~c1_1(a726)) | c2_1(a726) | (~c2_1(a738)) | (~c3_1(a738))),
% 1.67/1.87 inference(modus_ponens,[status(thm)],[4077, 4076])).
% 1.67/1.87 tff(4079,plain,
% 1.67/1.87 (~c3_1(a692)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[4078, 206, 4072, 4071, 1950, 4070, 4069, 1929, 4068, 10, 4060])).
% 1.67/1.87 tff(4080,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a726) | c3_1(a726) | c2_1(a702) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a702) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4081,plain,
% 1.67/1.87 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726))) <=> (c0_1(a726) | c3_1(a726) | c2_1(a702) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)))),
% 1.67/1.87 inference(rewrite,[status(thm)],[])).
% 1.67/1.87 tff(4082,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a726) | c3_1(a726) | c2_1(a702) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726))))),
% 1.67/1.87 inference(monotonicity,[status(thm)],[4081])).
% 1.67/1.87 tff(4083,plain,
% 1.67/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a702) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)))),
% 1.67/1.87 inference(transitivity,[status(thm)],[4082, 4080])).
% 1.67/1.87 tff(4084,plain,
% 1.67/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))),
% 1.67/1.87 inference(quant_inst,[status(thm)],[])).
% 1.67/1.87 tff(4085,plain,
% 1.67/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a702) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726))),
% 1.67/1.87 inference(modus_ponens,[status(thm)],[4084, 4083])).
% 1.67/1.87 tff(4086,plain,
% 1.67/1.87 ($false),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[4085, 206, 1950, 3677, 3676, 4070, 1935, 1929, 3675, 4068, 159, 4079])).
% 1.67/1.87 tff(4087,plain,(~hskp13), inference(lemma,lemma(discharge,[]))).
% 1.67/1.87 tff(4088,plain,
% 1.67/1.87 (hskp7),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3183, 4087, 4059])).
% 1.67/1.87 tff(4089,plain,
% 1.67/1.87 (hskp20),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3175, 4088, 3821])).
% 1.67/1.87 tff(4090,plain,
% 1.67/1.87 (~c3_1(a754)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[614, 4089])).
% 1.67/1.87 tff(4091,plain,
% 1.67/1.87 (~c0_1(a754)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[541, 4089])).
% 1.67/1.87 tff(4092,plain,
% 1.67/1.87 (c2_1(a754)),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[172, 4089])).
% 1.67/1.87 tff(4093,plain,
% 1.67/1.87 (hskp8),
% 1.67/1.87 inference(unit_resolution,[status(thm)],[3580, 206, 2657, 2649, 4092, 4091, 4090, 1784, 3821])).
% 1.67/1.88 tff(4094,plain,
% 1.67/1.88 (~c0_1(a710)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[1797, 4093])).
% 1.67/1.88 tff(4095,plain,
% 1.67/1.88 (~c1_1(a754)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[1050, 206, 4092, 3677, 3676, 4091, 4090, 3675, 159])).
% 1.67/1.88 tff(4096,plain,
% 1.67/1.88 (hskp14),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[3571, 206, 2685, 2649, 4092, 4090, 1545, 4095, 3821])).
% 1.67/1.88 tff(4097,plain,
% 1.67/1.88 (~c3_1(a730)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[438, 4096])).
% 1.67/1.88 tff(4098,plain,
% 1.67/1.88 (c3_1(a710)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[1805, 4093])).
% 1.67/1.88 tff(4099,plain,
% 1.67/1.88 (c2_1(a710)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[1871, 4093])).
% 1.67/1.88 tff(4100,plain,
% 1.67/1.88 (c1_1(a730)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[416, 4096])).
% 1.67/1.88 tff(4101,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a738) | c3_1(a730) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c1_1(a730)) | c2_1(a730) | (~c2_1(a738)) | (~c3_1(a738)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a738) | c3_1(a730) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c1_1(a730)) | c2_1(a730) | (~c2_1(a738)) | (~c3_1(a738)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4102,plain,
% 1.67/1.88 (((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710))) <=> (c1_1(a738) | c3_1(a730) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c1_1(a730)) | c2_1(a730) | (~c2_1(a738)) | (~c3_1(a738)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4103,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a738) | c3_1(a730) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c1_1(a730)) | c2_1(a730) | (~c2_1(a738)) | (~c3_1(a738))))),
% 1.67/1.88 inference(monotonicity,[status(thm)],[4102])).
% 1.67/1.88 tff(4104,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a738) | c3_1(a730) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c1_1(a730)) | c2_1(a730) | (~c2_1(a738)) | (~c3_1(a738)))),
% 1.67/1.88 inference(transitivity,[status(thm)],[4103, 4101])).
% 1.67/1.88 tff(4105,plain,
% 1.67/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))),
% 1.67/1.88 inference(quant_inst,[status(thm)],[])).
% 1.67/1.88 tff(4106,plain,
% 1.67/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a738) | c3_1(a730) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c1_1(a730)) | c2_1(a730) | (~c2_1(a738)) | (~c3_1(a738))),
% 1.67/1.88 inference(modus_ponens,[status(thm)],[4105, 4104])).
% 1.67/1.88 tff(4107,plain,
% 1.67/1.88 (c2_1(a730)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[4106, 206, 4072, 4071, 4100, 4099, 4098, 4069, 4097, 4094, 10])).
% 1.67/1.88 tff(4108,plain,
% 1.67/1.88 (~c3_1(a708)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[3009, 4088])).
% 1.67/1.88 tff(4109,plain,
% 1.67/1.88 (c1_1(a708)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[3025, 4088])).
% 1.67/1.88 tff(4110,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c0_1(a708) | (~c1_1(a708)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c0_1(a708) | (~c1_1(a708)) | (~c2_1(a754)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4111,plain,
% 1.67/1.88 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a708) | c0_1(a708) | (~c1_1(a708))) <=> (c0_1(a754) | c3_1(a754) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c0_1(a708) | (~c1_1(a708)) | (~c2_1(a754)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4112,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a708) | c0_1(a708) | (~c1_1(a708)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c0_1(a708) | (~c1_1(a708)) | (~c2_1(a754))))),
% 1.67/1.88 inference(monotonicity,[status(thm)],[4111])).
% 1.67/1.88 tff(4113,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a708) | c0_1(a708) | (~c1_1(a708)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c0_1(a708) | (~c1_1(a708)) | (~c2_1(a754)))),
% 1.67/1.88 inference(transitivity,[status(thm)],[4112, 4110])).
% 1.67/1.88 tff(4114,plain,
% 1.67/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a708) | c0_1(a708) | (~c1_1(a708)))),
% 1.67/1.88 inference(quant_inst,[status(thm)],[])).
% 1.67/1.88 tff(4115,plain,
% 1.67/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c0_1(a708) | (~c1_1(a708)) | (~c2_1(a754))),
% 1.67/1.88 inference(modus_ponens,[status(thm)],[4114, 4113])).
% 1.67/1.88 tff(4116,plain,
% 1.67/1.88 (c0_1(a708)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[4115, 206, 4092, 4109, 3677, 3676, 4091, 4090, 4108, 3675, 159])).
% 1.67/1.88 tff(4117,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a738) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | (~c0_1(a708)) | (~c1_1(a708)) | (~c2_1(a738)) | (~c3_1(a738)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a738) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | (~c0_1(a708)) | (~c1_1(a708)) | (~c2_1(a738)) | (~c3_1(a738)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4118,plain,
% 1.67/1.88 (((~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702)) <=> (c1_1(a738) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | (~c0_1(a708)) | (~c1_1(a708)) | (~c2_1(a738)) | (~c3_1(a738)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4119,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a738) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | (~c0_1(a708)) | (~c1_1(a708)) | (~c2_1(a738)) | (~c3_1(a738))))),
% 1.67/1.88 inference(monotonicity,[status(thm)],[4118])).
% 1.67/1.88 tff(4120,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a738) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | (~c0_1(a708)) | (~c1_1(a708)) | (~c2_1(a738)) | (~c3_1(a738)))),
% 1.67/1.88 inference(transitivity,[status(thm)],[4119, 4117])).
% 1.67/1.88 tff(4121,plain,
% 1.67/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702))),
% 1.67/1.88 inference(quant_inst,[status(thm)],[])).
% 1.67/1.88 tff(4122,plain,
% 1.67/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a738) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | (~c0_1(a708)) | (~c1_1(a708)) | (~c2_1(a738)) | (~c3_1(a738))),
% 1.67/1.88 inference(modus_ponens,[status(thm)],[4121, 4120])).
% 1.67/1.88 tff(4123,plain,
% 1.67/1.88 (c1_1(a702) | (~c0_1(a708))),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[4122, 206, 4072, 4071, 4109, 3676, 4069, 4108, 3675, 2984])).
% 1.67/1.88 tff(4124,plain,
% 1.67/1.88 (c1_1(a702)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[4123, 4116])).
% 1.67/1.88 tff(4125,plain,
% 1.67/1.88 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)) | (~c0_1(a708)) | (~c1_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)) | (~c0_1(a708)) | (~c1_1(a708)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4126,plain,
% 1.67/1.88 ((hskp17 | (~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702))) <=> (hskp17 | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)) | (~c0_1(a708)) | (~c1_1(a708)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4127,plain,
% 1.67/1.88 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)) | (~c0_1(a708)) | (~c1_1(a708))))),
% 1.67/1.88 inference(monotonicity,[status(thm)],[4126])).
% 1.67/1.88 tff(4128,plain,
% 1.67/1.88 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)) | (~c0_1(a708)) | (~c1_1(a708)))),
% 1.67/1.88 inference(transitivity,[status(thm)],[4127, 4125])).
% 1.67/1.88 tff(4129,plain,
% 1.67/1.88 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702)))),
% 1.67/1.88 inference(quant_inst,[status(thm)],[])).
% 1.67/1.88 tff(4130,plain,
% 1.67/1.88 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)) | (~c0_1(a708)) | (~c1_1(a708))),
% 1.67/1.88 inference(modus_ponens,[status(thm)],[4129, 4128])).
% 1.67/1.88 tff(4131,plain,
% 1.67/1.88 (hskp17 | (~c1_1(a702))),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[4130, 206, 4109, 3676, 4108, 3675, 3098, 4116])).
% 1.67/1.88 tff(4132,plain,
% 1.67/1.88 (hskp17),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[4131, 4124])).
% 1.67/1.88 tff(4133,plain,
% 1.67/1.88 (~c3_1(a744)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[3110, 4132])).
% 1.67/1.88 tff(4134,plain,
% 1.67/1.88 (~c2_1(a744)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[3130, 4132])).
% 1.67/1.88 tff(4135,plain,
% 1.67/1.88 (~c1_1(a744)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[3116, 4132])).
% 1.67/1.88 tff(4136,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a754) | c3_1(a754) | c1_1(a744) | c2_1(a744) | c3_1(a744) | (~ndr1_0) | (~c0_1(a744)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a754) | c3_1(a754) | c1_1(a744) | c2_1(a744) | c3_1(a744) | (~ndr1_0) | (~c0_1(a744)) | (~c2_1(a754)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4137,plain,
% 1.67/1.88 (((~ndr1_0) | c3_1(a744) | c2_1(a744) | (~c0_1(a744)) | c1_1(a744) | c2_1(a744) | (~c0_1(a744)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (c0_1(a754) | c3_1(a754) | c1_1(a744) | c2_1(a744) | c3_1(a744) | (~ndr1_0) | (~c0_1(a744)) | (~c2_1(a754)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4138,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a744) | c2_1(a744) | (~c0_1(a744)) | c1_1(a744) | c2_1(a744) | (~c0_1(a744)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a754) | c3_1(a754) | c1_1(a744) | c2_1(a744) | c3_1(a744) | (~ndr1_0) | (~c0_1(a744)) | (~c2_1(a754))))),
% 1.67/1.88 inference(monotonicity,[status(thm)],[4137])).
% 1.67/1.88 tff(4139,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a744) | c2_1(a744) | (~c0_1(a744)) | c1_1(a744) | c2_1(a744) | (~c0_1(a744)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a754) | c3_1(a754) | c1_1(a744) | c2_1(a744) | c3_1(a744) | (~ndr1_0) | (~c0_1(a744)) | (~c2_1(a754)))),
% 1.67/1.88 inference(transitivity,[status(thm)],[4138, 4136])).
% 1.67/1.88 tff(4140,plain,
% 1.67/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a744) | c2_1(a744) | (~c0_1(a744)) | c1_1(a744) | c2_1(a744) | (~c0_1(a744)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.67/1.88 inference(quant_inst,[status(thm)],[])).
% 1.67/1.88 tff(4141,plain,
% 1.67/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a754) | c3_1(a754) | c1_1(a744) | c2_1(a744) | c3_1(a744) | (~ndr1_0) | (~c0_1(a744)) | (~c2_1(a754))),
% 1.67/1.88 inference(modus_ponens,[status(thm)],[4140, 4139])).
% 1.67/1.88 tff(4142,plain,
% 1.67/1.88 (~c0_1(a744)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[4141, 206, 4092, 4091, 4090, 4135, 4134, 4133, 2340])).
% 1.67/1.88 tff(4143,plain,
% 1.67/1.88 (c2_1(a708)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[3017, 4088])).
% 1.67/1.88 tff(4144,plain,
% 1.67/1.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a708) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a708)) | (~c2_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a708) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a708)) | (~c2_1(a708)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4145,plain,
% 1.67/1.88 ((hskp3 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c0_1(a708))) <=> (hskp3 | c3_1(a708) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a708)) | (~c2_1(a708)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4146,plain,
% 1.67/1.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c0_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a708) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a708)) | (~c2_1(a708))))),
% 1.67/1.88 inference(monotonicity,[status(thm)],[4145])).
% 1.67/1.88 tff(4147,plain,
% 1.67/1.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c0_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a708) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a708)) | (~c2_1(a708)))),
% 1.67/1.88 inference(transitivity,[status(thm)],[4146, 4144])).
% 1.67/1.88 tff(4148,plain,
% 1.67/1.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c0_1(a708)))),
% 1.67/1.88 inference(quant_inst,[status(thm)],[])).
% 1.67/1.88 tff(4149,plain,
% 1.67/1.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a708) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a708)) | (~c2_1(a708))),
% 1.67/1.88 inference(modus_ponens,[status(thm)],[4148, 4147])).
% 1.67/1.88 tff(4150,plain,
% 1.67/1.88 (hskp3),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[4149, 206, 2657, 2649, 4143, 4108, 2132, 3821, 4116])).
% 1.67/1.88 tff(4151,plain,
% 1.67/1.88 (~c3_1(a697)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[1286, 4150])).
% 1.67/1.88 tff(4152,plain,
% 1.67/1.88 (c0_1(a697)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[457, 4150])).
% 1.67/1.88 tff(4153,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c0_1(a744))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4154,plain,
% 1.67/1.88 (((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744)) <=> (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c0_1(a744))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4155,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c0_1(a744)))),
% 1.67/1.88 inference(monotonicity,[status(thm)],[4154])).
% 1.67/1.88 tff(4156,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c0_1(a744))),
% 1.67/1.88 inference(transitivity,[status(thm)],[4155, 4153])).
% 1.67/1.88 tff(4157,plain,
% 1.67/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))),
% 1.67/1.88 inference(quant_inst,[status(thm)],[])).
% 1.67/1.88 tff(4158,plain,
% 1.67/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c0_1(a744)),
% 1.67/1.88 inference(modus_ponens,[status(thm)],[4157, 4156])).
% 1.67/1.88 tff(4159,plain,
% 1.67/1.88 (~c1_1(a697)),
% 1.67/1.88 inference(unit_resolution,[status(thm)],[4158, 206, 2685, 2649, 4152, 4134, 4133, 4151, 1699, 4142, 3821])).
% 1.67/1.88 tff(4160,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c0_1(a754) | c3_1(a730) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a754) | c3_1(a730) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)) | c1_1(a754) | (~c2_1(a754)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4161,plain,
% 1.67/1.88 (((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754)) <=> (c0_1(a754) | c3_1(a730) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)) | c1_1(a754) | (~c2_1(a754)))),
% 1.67/1.88 inference(rewrite,[status(thm)],[])).
% 1.67/1.88 tff(4162,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c0_1(a754) | c3_1(a730) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)) | c1_1(a754) | (~c2_1(a754))))),
% 1.67/1.88 inference(monotonicity,[status(thm)],[4161])).
% 1.67/1.88 tff(4163,plain,
% 1.67/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a754) | c3_1(a730) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)) | c1_1(a754) | (~c2_1(a754)))),
% 1.67/1.89 inference(transitivity,[status(thm)],[4162, 4160])).
% 1.67/1.89 tff(4164,plain,
% 1.67/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754))),
% 1.67/1.89 inference(quant_inst,[status(thm)],[])).
% 1.67/1.89 tff(4165,plain,
% 1.67/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a754) | c3_1(a730) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)) | c1_1(a754) | (~c2_1(a754))),
% 1.67/1.89 inference(modus_ponens,[status(thm)],[4164, 4163])).
% 1.67/1.89 tff(4166,plain,
% 1.67/1.89 ($false),
% 1.67/1.89 inference(unit_resolution,[status(thm)],[4165, 206, 4092, 4100, 4152, 4091, 4097, 4151, 512, 4095, 4159, 4107])).
% 1.67/1.89 % SZS output end Proof
% 1.67/1.89 % E exiting
%------------------------------------------------------------------------------