%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN510-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:24 AM UTC 2025
% Result : Unsatisfiable 0.61s 0.77s
% Output : Proof 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN510-1 : TPTP v9.0.0. Released v2.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.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
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:37:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.61/0.77 % SZS status Unsatisfiable
% 0.61/0.77 % SZS output start Proof
% 0.61/0.77 tff(c2_1_type, type, (
% 0.61/0.77 c2_1: $i > $o)).
% 0.61/0.77 tff(a576_type, type, (
% 0.61/0.77 a576: $i)).
% 0.61/0.77 tff(c0_1_type, type, (
% 0.61/0.77 c0_1: $i > $o)).
% 0.61/0.77 tff(a582_type, type, (
% 0.61/0.77 a582: $i)).
% 0.61/0.77 tff(c1_1_type, type, (
% 0.61/0.77 c1_1: $i > $o)).
% 0.61/0.77 tff(c3_1_type, type, (
% 0.61/0.77 c3_1: $i > $o)).
% 0.61/0.77 tff(ndr1_0_type, type, (
% 0.61/0.77 ndr1_0: $o)).
% 0.61/0.77 tff(hskp21_type, type, (
% 0.61/0.77 hskp21: $o)).
% 0.61/0.77 tff(a546_type, type, (
% 0.61/0.77 a546: $i)).
% 0.61/0.77 tff(hskp6_type, type, (
% 0.61/0.77 hskp6: $o)).
% 0.61/0.77 tff(hskp0_type, type, (
% 0.61/0.77 hskp0: $o)).
% 0.61/0.77 tff(a536_type, type, (
% 0.61/0.77 a536: $i)).
% 0.61/0.77 tff(a564_type, type, (
% 0.61/0.77 a564: $i)).
% 0.61/0.77 tff(hskp12_type, type, (
% 0.61/0.77 hskp12: $o)).
% 0.61/0.77 tff(hskp31_type, type, (
% 0.61/0.77 hskp31: $o)).
% 0.61/0.77 tff(hskp14_type, type, (
% 0.61/0.77 hskp14: $o)).
% 0.61/0.77 tff(a565_type, type, (
% 0.61/0.77 a565: $i)).
% 0.61/0.77 tff(hskp13_type, type, (
% 0.61/0.77 hskp13: $o)).
% 0.61/0.77 tff(a537_type, type, (
% 0.61/0.77 a537: $i)).
% 0.61/0.77 tff(hskp1_type, type, (
% 0.61/0.77 hskp1: $o)).
% 0.61/0.77 tff(a566_type, type, (
% 0.61/0.77 a566: $i)).
% 0.61/0.77 tff(a551_type, type, (
% 0.61/0.77 a551: $i)).
% 0.61/0.77 tff(a590_type, type, (
% 0.61/0.77 a590: $i)).
% 0.61/0.77 tff(hskp24_type, type, (
% 0.61/0.77 hskp24: $o)).
% 0.61/0.77 tff(hskp10_type, type, (
% 0.61/0.77 hskp10: $o)).
% 0.61/0.77 tff(hskp19_type, type, (
% 0.61/0.77 hskp19: $o)).
% 0.61/0.77 tff(a580_type, type, (
% 0.61/0.77 a580: $i)).
% 0.61/0.77 tff(hskp20_type, type, (
% 0.61/0.77 hskp20: $o)).
% 0.61/0.77 tff(a552_type, type, (
% 0.61/0.77 a552: $i)).
% 0.61/0.77 tff(hskp29_type, type, (
% 0.61/0.77 hskp29: $o)).
% 0.61/0.77 tff(a563_type, type, (
% 0.61/0.77 a563: $i)).
% 0.61/0.77 tff(a584_type, type, (
% 0.61/0.77 a584: $i)).
% 0.61/0.77 tff(a567_type, type, (
% 0.61/0.77 a567: $i)).
% 0.61/0.77 tff(hskp15_type, type, (
% 0.61/0.77 hskp15: $o)).
% 0.61/0.77 tff(hskp22_type, type, (
% 0.61/0.77 hskp22: $o)).
% 0.61/0.77 tff(a539_type, type, (
% 0.61/0.77 a539: $i)).
% 0.61/0.77 tff(hskp3_type, type, (
% 0.61/0.77 hskp3: $o)).
% 0.61/0.77 tff(1,assumption,(~c0_1(a582)), introduced(assumption)).
% 0.61/0.77 tff(2,plain,
% 0.61/0.77 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(3,plain,
% 0.61/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[2])).
% 0.61/0.77 tff(4,plain,
% 0.61/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(5,plain,
% 0.61/0.77 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(6,plain,
% 0.61/0.77 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[5])).
% 0.61/0.77 tff(7,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause203')).
% 0.61/0.77 tff(8,plain,
% 0.61/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.61/0.77 tff(9,plain,
% 0.61/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.61/0.77 tff(10,plain,(
% 0.61/0.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.61/0.77 inference(skolemize,[status(sab)],[9])).
% 0.61/0.77 tff(11,plain,
% 0.61/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.61/0.77 tff(12,assumption,(~hskp21), introduced(assumption)).
% 0.61/0.77 tff(13,plain,
% 0.61/0.77 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(14,plain,
% 0.61/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[13])).
% 0.61/0.77 tff(15,plain,
% 0.61/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(16,plain,
% 0.61/0.77 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(17,plain,
% 0.61/0.77 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[16])).
% 0.61/0.77 tff(18,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause207')).
% 0.61/0.77 tff(19,plain,
% 0.61/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.61/0.77 tff(20,plain,
% 0.61/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.61/0.77 tff(21,plain,(
% 0.61/0.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.61/0.77 inference(skolemize,[status(sab)],[20])).
% 0.61/0.77 tff(22,plain,
% 0.61/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.61/0.77 tff(23,assumption,(hskp0), introduced(assumption)).
% 0.61/0.77 tff(24,plain,
% 0.61/0.77 (((~hskp0) | (~c3_1(a536))) <=> ((~hskp0) | (~c3_1(a536)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(25,plain,
% 0.61/0.77 (((~c3_1(a536)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a536)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(26,axiom,((~c3_1(a536)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 0.61/0.77 tff(27,plain,
% 0.61/0.77 ((~hskp0) | (~c3_1(a536))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.61/0.77 tff(28,plain,
% 0.61/0.77 ((~hskp0) | (~c3_1(a536))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.61/0.77 tff(29,plain,
% 0.61/0.77 (~c3_1(a536)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[28, 23])).
% 0.61/0.77 tff(30,plain,
% 0.61/0.77 (^[U: $i] : refl((hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(31,plain,
% 0.61/0.77 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[30])).
% 0.61/0.77 tff(32,plain,
% 0.61/0.77 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(33,plain,
% 0.61/0.77 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp21) <=> ((hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp21))), rewrite(((hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp21) <=> (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp21) <=> (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(34,plain,
% 0.61/0.77 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp21) <=> ![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[33])).
% 0.61/0.77 tff(35,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 0.61/0.77 tff(36,plain,
% 0.61/0.77 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.61/0.77 tff(37,plain,
% 0.61/0.77 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.61/0.77 tff(38,plain,(
% 0.61/0.77 ![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.77 inference(skolemize,[status(sab)],[37])).
% 0.61/0.77 tff(39,plain,
% 0.61/0.77 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.61/0.77 tff(40,plain,
% 0.61/0.77 (((~hskp0) | c2_1(a536)) <=> ((~hskp0) | c2_1(a536))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(41,axiom,((~hskp0) | c2_1(a536)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.61/0.77 tff(42,plain,
% 0.61/0.77 ((~hskp0) | c2_1(a536)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.61/0.77 tff(43,plain,
% 0.61/0.77 ((~hskp0) | c2_1(a536)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[42, 40])).
% 0.61/0.77 tff(44,plain,
% 0.61/0.77 ((~hskp0) | c2_1(a536)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.61/0.77 tff(45,plain,
% 0.61/0.77 ((~hskp0) | c2_1(a536)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.61/0.77 tff(46,plain,
% 0.61/0.77 ((~hskp0) | c2_1(a536)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.61/0.77 tff(47,plain,
% 0.61/0.77 (c2_1(a536)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[46, 23])).
% 0.61/0.77 tff(48,plain,
% 0.61/0.77 (((~hskp0) | c0_1(a536)) <=> ((~hskp0) | c0_1(a536))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(49,axiom,((~hskp0) | c0_1(a536)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.61/0.77 tff(50,plain,
% 0.61/0.77 ((~hskp0) | c0_1(a536)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.61/0.77 tff(51,plain,
% 0.61/0.77 ((~hskp0) | c0_1(a536)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[50, 48])).
% 0.61/0.77 tff(52,plain,
% 0.61/0.77 ((~hskp0) | c0_1(a536)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[51, 48])).
% 0.61/0.77 tff(53,plain,
% 0.61/0.77 ((~hskp0) | c0_1(a536)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.61/0.77 tff(54,plain,
% 0.61/0.77 ((~hskp0) | c0_1(a536)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[53, 48])).
% 0.61/0.77 tff(55,plain,
% 0.61/0.77 (c0_1(a536)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[54, 23])).
% 0.61/0.77 tff(56,assumption,(~ndr1_0), introduced(assumption)).
% 0.61/0.77 tff(57,plain,
% 0.61/0.77 ((ndr1_0 | (~hskp12)) <=> (ndr1_0 | (~hskp12))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(58,plain,
% 0.61/0.77 (((~hskp12) | ndr1_0) <=> (ndr1_0 | (~hskp12))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(59,axiom,((~hskp12) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause20')).
% 0.61/0.77 tff(60,plain,
% 0.61/0.77 (ndr1_0 | (~hskp12)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.61/0.77 tff(61,plain,
% 0.61/0.77 (ndr1_0 | (~hskp12)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[60, 57])).
% 0.61/0.77 tff(62,plain,
% 0.61/0.77 (~hskp12),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[61, 56])).
% 0.61/0.77 tff(63,assumption,(~hskp12), introduced(assumption)).
% 0.61/0.77 tff(64,plain,
% 0.61/0.77 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(65,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.61/0.77 tff(66,plain,
% 0.61/0.77 ((~hskp31) | ndr1_0),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.61/0.77 tff(67,plain,
% 0.61/0.77 ((~hskp31) | ndr1_0),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[66, 64])).
% 0.61/0.77 tff(68,plain,
% 0.61/0.77 ((~hskp31) | ndr1_0),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[67, 64])).
% 0.61/0.77 tff(69,plain,
% 0.61/0.77 ((~hskp31) | ndr1_0),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.61/0.77 tff(70,plain,
% 0.61/0.77 ((~hskp31) | ndr1_0),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[69, 64])).
% 0.61/0.77 tff(71,plain,
% 0.61/0.77 (~hskp31),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[70, 56])).
% 0.61/0.77 tff(72,plain,
% 0.61/0.77 ((ndr1_0 | (~hskp14)) <=> (ndr1_0 | (~hskp14))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(73,plain,
% 0.61/0.77 (((~hskp14) | ndr1_0) <=> (ndr1_0 | (~hskp14))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(74,axiom,((~hskp14) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause18')).
% 0.61/0.77 tff(75,plain,
% 0.61/0.77 (ndr1_0 | (~hskp14)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.61/0.77 tff(76,plain,
% 0.61/0.77 (ndr1_0 | (~hskp14)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[75, 72])).
% 0.61/0.77 tff(77,plain,
% 0.61/0.77 (~hskp14),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[76, 56])).
% 0.61/0.77 tff(78,plain,
% 0.61/0.77 ((hskp31 | hskp14 | hskp12) <=> (hskp31 | hskp14 | hskp12)),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(79,plain,
% 0.61/0.77 (((hskp31 | hskp12) | hskp14) <=> (hskp31 | hskp14 | hskp12)),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(80,plain,
% 0.61/0.77 ((hskp31 | hskp12) <=> (hskp31 | hskp12)),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(81,plain,
% 0.61/0.77 (((hskp31 | hskp12) | hskp14) <=> ((hskp31 | hskp12) | hskp14)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[80])).
% 0.61/0.77 tff(82,plain,
% 0.61/0.77 (((hskp31 | hskp12) | hskp14) <=> (hskp31 | hskp14 | hskp12)),
% 0.61/0.77 inference(transitivity,[status(thm)],[81, 79])).
% 0.61/0.77 tff(83,axiom,((hskp31 | hskp12) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 0.61/0.77 tff(84,plain,
% 0.61/0.77 (hskp31 | hskp14 | hskp12),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.61/0.77 tff(85,plain,
% 0.61/0.77 (hskp31 | hskp14 | hskp12),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[84, 78])).
% 0.61/0.77 tff(86,plain,
% 0.61/0.77 (hskp31 | hskp14 | hskp12),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.61/0.78 tff(87,plain,
% 0.61/0.78 (hskp31 | hskp14 | hskp12),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[86, 78])).
% 0.61/0.78 tff(88,plain,
% 0.61/0.78 (hskp31 | hskp14 | hskp12),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[87, 78])).
% 0.61/0.78 tff(89,plain,
% 0.61/0.78 ($false),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[88, 77, 71, 63])).
% 0.61/0.78 tff(90,plain,(ndr1_0 | hskp12), inference(lemma,lemma(discharge,[]))).
% 0.61/0.78 tff(91,plain,
% 0.61/0.78 ($false),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[90, 62, 56])).
% 0.61/0.78 tff(92,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.61/0.78 tff(93,plain,
% 0.61/0.78 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp21 | hskp12 | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(94,plain,
% 0.61/0.78 ((hskp21 | hskp12 | (~ndr1_0) | c3_1(a536) | (~c0_1(a536)) | (~c2_1(a536))) <=> (hskp21 | hskp12 | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(95,plain,
% 0.61/0.78 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c3_1(a536) | (~c0_1(a536)) | (~c2_1(a536)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp21 | hskp12 | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536))))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[94])).
% 0.61/0.78 tff(96,plain,
% 0.61/0.78 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c3_1(a536) | (~c0_1(a536)) | (~c2_1(a536)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)))),
% 0.61/0.78 inference(transitivity,[status(thm)],[95, 93])).
% 0.61/0.78 tff(97,plain,
% 0.61/0.78 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c3_1(a536) | (~c0_1(a536)) | (~c2_1(a536)))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(98,plain,
% 0.61/0.78 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.61/0.78 tff(99,plain,
% 0.61/0.78 (hskp12),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[98, 92, 12, 55, 47, 29, 39])).
% 0.61/0.78 tff(100,plain,
% 0.61/0.78 (((~hskp12) | (~c1_1(a564))) <=> ((~hskp12) | (~c1_1(a564)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(101,plain,
% 0.61/0.78 (((~c1_1(a564)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a564)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(102,axiom,((~c1_1(a564)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.61/0.78 tff(103,plain,
% 0.61/0.78 ((~hskp12) | (~c1_1(a564))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.61/0.78 tff(104,plain,
% 0.61/0.78 ((~hskp12) | (~c1_1(a564))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[103, 100])).
% 0.61/0.78 tff(105,plain,
% 0.61/0.78 (~c1_1(a564)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[104, 99])).
% 0.61/0.78 tff(106,assumption,(~hskp13), introduced(assumption)).
% 0.61/0.78 tff(107,assumption,(~hskp6), introduced(assumption)).
% 0.61/0.78 tff(108,plain,
% 0.61/0.78 ((hskp24 | hskp13 | hskp6) <=> (hskp24 | hskp13 | hskp6)),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(109,plain,
% 0.61/0.78 (((hskp13 | hskp24) | hskp6) <=> (hskp24 | hskp13 | hskp6)),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(110,axiom,((hskp13 | hskp24) | hskp6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.61/0.78 tff(111,plain,
% 0.61/0.78 (hskp24 | hskp13 | hskp6),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.61/0.78 tff(112,plain,
% 0.61/0.78 (hskp24 | hskp13 | hskp6),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[111, 108])).
% 0.61/0.78 tff(113,plain,
% 0.61/0.78 (hskp24 | hskp13 | hskp6),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.61/0.78 tff(114,plain,
% 0.61/0.78 (hskp24 | hskp13 | hskp6),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[113, 108])).
% 0.61/0.78 tff(115,plain,
% 0.61/0.78 (hskp24 | hskp13 | hskp6),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[114, 108])).
% 0.61/0.78 tff(116,plain,
% 0.61/0.78 (hskp24),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[115, 107, 106])).
% 0.61/0.78 tff(117,plain,
% 0.61/0.78 (((~hskp24) | (~c2_1(a590))) <=> ((~hskp24) | (~c2_1(a590)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(118,plain,
% 0.61/0.78 (((~c2_1(a590)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a590)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(119,axiom,((~c2_1(a590)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 0.61/0.78 tff(120,plain,
% 0.61/0.78 ((~hskp24) | (~c2_1(a590))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.61/0.78 tff(121,plain,
% 0.61/0.78 ((~hskp24) | (~c2_1(a590))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[120, 117])).
% 0.61/0.78 tff(122,plain,
% 0.61/0.78 (~c2_1(a590)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[121, 116])).
% 0.61/0.78 tff(123,plain,
% 0.61/0.78 (((~hskp24) | (~c0_1(a590))) <=> ((~hskp24) | (~c0_1(a590)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(124,plain,
% 0.61/0.78 (((~c0_1(a590)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a590)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(125,axiom,((~c0_1(a590)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.61/0.78 tff(126,plain,
% 0.61/0.78 ((~hskp24) | (~c0_1(a590))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.61/0.78 tff(127,plain,
% 0.61/0.78 ((~hskp24) | (~c0_1(a590))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[126, 123])).
% 0.61/0.78 tff(128,plain,
% 0.61/0.78 (~c0_1(a590)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[127, 116])).
% 0.61/0.78 tff(129,plain,
% 0.61/0.78 ((hskp14 | hskp13 | hskp6) <=> (hskp14 | hskp13 | hskp6)),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(130,plain,
% 0.61/0.78 (((hskp13 | hskp14) | hskp6) <=> (hskp14 | hskp13 | hskp6)),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(131,axiom,((hskp13 | hskp14) | hskp6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 0.61/0.78 tff(132,plain,
% 0.61/0.78 (hskp14 | hskp13 | hskp6),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.61/0.78 tff(133,plain,
% 0.61/0.78 (hskp14 | hskp13 | hskp6),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[132, 129])).
% 0.61/0.78 tff(134,plain,
% 0.61/0.78 (hskp14 | hskp13 | hskp6),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.61/0.78 tff(135,plain,
% 0.61/0.78 (hskp14 | hskp13 | hskp6),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[134, 129])).
% 0.61/0.78 tff(136,plain,
% 0.61/0.78 (hskp14 | hskp13 | hskp6),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[135, 129])).
% 0.61/0.78 tff(137,plain,
% 0.61/0.78 (hskp14),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[136, 107, 106])).
% 0.61/0.78 tff(138,plain,
% 0.61/0.78 (((~hskp14) | (~c0_1(a566))) <=> ((~hskp14) | (~c0_1(a566)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(139,plain,
% 0.61/0.78 (((~c0_1(a566)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a566)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(140,axiom,((~c0_1(a566)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.61/0.78 tff(141,plain,
% 0.61/0.78 ((~hskp14) | (~c0_1(a566))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.61/0.78 tff(142,plain,
% 0.61/0.78 ((~hskp14) | (~c0_1(a566))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[141, 138])).
% 0.61/0.78 tff(143,plain,
% 0.61/0.78 (~c0_1(a566)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[142, 137])).
% 0.61/0.78 tff(144,plain,
% 0.61/0.78 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(145,plain,
% 0.61/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[144])).
% 0.61/0.78 tff(146,plain,
% 0.61/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(147,plain,
% 0.61/0.78 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(148,plain,
% 0.61/0.78 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_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)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[147])).
% 0.61/0.78 tff(149,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause206')).
% 0.61/0.78 tff(150,plain,
% 0.61/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.61/0.78 tff(151,plain,
% 0.61/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.61/0.78 tff(152,plain,(
% 0.61/0.78 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.78 inference(skolemize,[status(sab)],[151])).
% 0.61/0.78 tff(153,plain,
% 0.61/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.61/0.78 tff(154,assumption,(~c0_1(a566)), introduced(assumption)).
% 0.61/0.78 tff(155,assumption,(~c2_1(a590)), introduced(assumption)).
% 0.61/0.78 tff(156,assumption,(~c0_1(a590)), introduced(assumption)).
% 0.61/0.78 tff(157,plain,
% 0.61/0.78 (hskp14),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[136, 106, 107])).
% 0.61/0.78 tff(158,plain,
% 0.61/0.78 (((~hskp14) | c3_1(a566)) <=> ((~hskp14) | c3_1(a566))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(159,axiom,((~hskp14) | c3_1(a566)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.61/0.78 tff(160,plain,
% 0.61/0.78 ((~hskp14) | c3_1(a566)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.61/0.78 tff(161,plain,
% 0.61/0.78 ((~hskp14) | c3_1(a566)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[160, 158])).
% 0.61/0.78 tff(162,plain,
% 0.61/0.78 ((~hskp14) | c3_1(a566)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[161, 158])).
% 0.61/0.78 tff(163,plain,
% 0.61/0.78 ((~hskp14) | c3_1(a566)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.61/0.78 tff(164,plain,
% 0.61/0.78 ((~hskp14) | c3_1(a566)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[163, 158])).
% 0.61/0.78 tff(165,plain,
% 0.61/0.78 (c3_1(a566)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[164, 157])).
% 0.61/0.78 tff(166,plain,
% 0.61/0.78 (((~hskp14) | c2_1(a566)) <=> ((~hskp14) | c2_1(a566))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(167,axiom,((~hskp14) | c2_1(a566)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.61/0.78 tff(168,plain,
% 0.61/0.78 ((~hskp14) | c2_1(a566)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.61/0.78 tff(169,plain,
% 0.61/0.78 ((~hskp14) | c2_1(a566)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[168, 166])).
% 0.61/0.78 tff(170,plain,
% 0.61/0.78 ((~hskp14) | c2_1(a566)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[169, 166])).
% 0.61/0.78 tff(171,plain,
% 0.61/0.78 ((~hskp14) | c2_1(a566)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.61/0.78 tff(172,plain,
% 0.61/0.78 ((~hskp14) | c2_1(a566)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[171, 166])).
% 0.61/0.78 tff(173,plain,
% 0.61/0.78 (c2_1(a566)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[172, 157])).
% 0.61/0.78 tff(174,plain,
% 0.61/0.78 (hskp24),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[115, 106, 107])).
% 0.61/0.78 tff(175,plain,
% 0.61/0.78 (((~hskp24) | c1_1(a590)) <=> ((~hskp24) | c1_1(a590))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(176,axiom,((~hskp24) | c1_1(a590)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 0.61/0.78 tff(177,plain,
% 0.61/0.78 ((~hskp24) | c1_1(a590)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.61/0.78 tff(178,plain,
% 0.61/0.78 ((~hskp24) | c1_1(a590)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[177, 175])).
% 0.61/0.78 tff(179,plain,
% 0.61/0.78 ((~hskp24) | c1_1(a590)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[178, 175])).
% 0.61/0.78 tff(180,plain,
% 0.61/0.78 ((~hskp24) | c1_1(a590)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.61/0.78 tff(181,plain,
% 0.61/0.78 ((~hskp24) | c1_1(a590)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[180, 175])).
% 0.61/0.78 tff(182,plain,
% 0.61/0.78 (c1_1(a590)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[181, 174])).
% 0.61/0.78 tff(183,assumption,(ndr1_0), introduced(assumption)).
% 0.61/0.78 tff(184,plain,
% 0.61/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a590) | c2_1(a590) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c1_1(a566)) | (~c1_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a590) | c2_1(a590) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c1_1(a566)) | (~c1_1(a590)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(185,plain,
% 0.61/0.78 (((~ndr1_0) | (~c3_1(a566)) | (~c1_1(a566)) | (~c2_1(a566)) | c0_1(a566) | (~c2_1(a566)) | (~c3_1(a566)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590))) <=> (c0_1(a590) | c2_1(a590) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c1_1(a566)) | (~c1_1(a590)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(186,plain,
% 0.61/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a566)) | (~c1_1(a566)) | (~c2_1(a566)) | c0_1(a566) | (~c2_1(a566)) | (~c3_1(a566)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a590) | c2_1(a590) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c1_1(a566)) | (~c1_1(a590))))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[185])).
% 0.61/0.78 tff(187,plain,
% 0.61/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a566)) | (~c1_1(a566)) | (~c2_1(a566)) | c0_1(a566) | (~c2_1(a566)) | (~c3_1(a566)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a590) | c2_1(a590) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c1_1(a566)) | (~c1_1(a590)))),
% 0.61/0.78 inference(transitivity,[status(thm)],[186, 184])).
% 0.61/0.78 tff(188,plain,
% 0.61/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a566)) | (~c1_1(a566)) | (~c2_1(a566)) | c0_1(a566) | (~c2_1(a566)) | (~c3_1(a566)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(189,plain,
% 0.61/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a590) | c2_1(a590) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c1_1(a566)) | (~c1_1(a590))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.61/0.78 tff(190,plain,
% 0.61/0.78 (~c1_1(a566)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[189, 183, 182, 173, 165, 156, 155, 154, 153])).
% 0.61/0.78 tff(191,plain,
% 0.61/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | c1_1(a566))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | c1_1(a566))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(192,plain,
% 0.61/0.78 (((~ndr1_0) | c0_1(a566) | (~c3_1(a566)) | (~c2_1(a566)) | c1_1(a566) | c0_1(a566) | (~c3_1(a566)) | c1_1(a566) | c0_1(a566) | (~c2_1(a566))) <=> (c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | c1_1(a566))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(193,plain,
% 0.61/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a566) | (~c3_1(a566)) | (~c2_1(a566)) | c1_1(a566) | c0_1(a566) | (~c3_1(a566)) | c1_1(a566) | c0_1(a566) | (~c2_1(a566)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | c1_1(a566)))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[192])).
% 0.61/0.78 tff(194,plain,
% 0.61/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a566) | (~c3_1(a566)) | (~c2_1(a566)) | c1_1(a566) | c0_1(a566) | (~c3_1(a566)) | c1_1(a566) | c0_1(a566) | (~c2_1(a566)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | c1_1(a566))),
% 0.61/0.78 inference(transitivity,[status(thm)],[193, 191])).
% 0.61/0.78 tff(195,plain,
% 0.61/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a566) | (~c3_1(a566)) | (~c2_1(a566)) | c1_1(a566) | c0_1(a566) | (~c3_1(a566)) | c1_1(a566) | c0_1(a566) | (~c2_1(a566)))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(196,plain,
% 0.61/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | c1_1(a566)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.61/0.78 tff(197,plain,
% 0.61/0.78 ($false),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[196, 183, 173, 165, 154, 11, 190])).
% 0.61/0.78 tff(198,plain,(hskp13 | (~ndr1_0) | c0_1(a566) | c0_1(a590) | c2_1(a590) | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.61/0.78 tff(199,plain,
% 0.61/0.78 (hskp13 | c0_1(a566) | c0_1(a590) | c2_1(a590) | hskp6),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[198, 92])).
% 0.61/0.78 tff(200,plain,
% 0.61/0.78 ($false),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[199, 143, 128, 106, 107, 122])).
% 0.61/0.78 tff(201,plain,(hskp6 | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.61/0.78 tff(202,plain,
% 0.61/0.78 (hskp6),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[201, 106])).
% 0.61/0.78 tff(203,plain,
% 0.61/0.78 (((~hskp6) | (~c1_1(a546))) <=> ((~hskp6) | (~c1_1(a546)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(204,plain,
% 0.61/0.78 (((~c1_1(a546)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a546)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(205,axiom,((~c1_1(a546)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.61/0.78 tff(206,plain,
% 0.61/0.78 ((~hskp6) | (~c1_1(a546))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.61/0.78 tff(207,plain,
% 0.61/0.78 ((~hskp6) | (~c1_1(a546))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[206, 203])).
% 0.61/0.78 tff(208,plain,
% 0.61/0.78 (~c1_1(a546)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[207, 202])).
% 0.61/0.78 tff(209,plain,
% 0.61/0.78 (((~hskp6) | (~c0_1(a546))) <=> ((~hskp6) | (~c0_1(a546)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(210,plain,
% 0.61/0.78 (((~c0_1(a546)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a546)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(211,axiom,((~c0_1(a546)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.61/0.78 tff(212,plain,
% 0.61/0.78 ((~hskp6) | (~c0_1(a546))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.61/0.78 tff(213,plain,
% 0.61/0.78 ((~hskp6) | (~c0_1(a546))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[212, 209])).
% 0.61/0.78 tff(214,plain,
% 0.61/0.78 (~c0_1(a546)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[213, 202])).
% 0.61/0.78 tff(215,plain,
% 0.61/0.78 (((~hskp6) | c3_1(a546)) <=> ((~hskp6) | c3_1(a546))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(216,axiom,((~hskp6) | c3_1(a546)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.61/0.78 tff(217,plain,
% 0.61/0.78 ((~hskp6) | c3_1(a546)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.61/0.78 tff(218,plain,
% 0.61/0.78 ((~hskp6) | c3_1(a546)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[217, 215])).
% 0.61/0.78 tff(219,plain,
% 0.61/0.78 ((~hskp6) | c3_1(a546)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[218, 215])).
% 0.61/0.78 tff(220,plain,
% 0.61/0.78 ((~hskp6) | c3_1(a546)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.61/0.78 tff(221,plain,
% 0.61/0.78 ((~hskp6) | c3_1(a546)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[220, 215])).
% 0.61/0.78 tff(222,plain,
% 0.61/0.78 (c3_1(a546)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[221, 202])).
% 0.61/0.78 tff(223,plain,
% 0.61/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a546) | c1_1(a546) | (~ndr1_0) | (~c3_1(a546)) | (~c2_1(a546)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | (~c3_1(a546)) | (~c2_1(a546)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(224,plain,
% 0.61/0.78 (((~ndr1_0) | c0_1(a546) | (~c3_1(a546)) | (~c2_1(a546)) | c1_1(a546) | c0_1(a546) | (~c3_1(a546)) | c1_1(a546) | c0_1(a546) | (~c2_1(a546))) <=> (c0_1(a546) | c1_1(a546) | (~ndr1_0) | (~c3_1(a546)) | (~c2_1(a546)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(225,plain,
% 0.61/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a546) | (~c3_1(a546)) | (~c2_1(a546)) | c1_1(a546) | c0_1(a546) | (~c3_1(a546)) | c1_1(a546) | c0_1(a546) | (~c2_1(a546)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a546) | c1_1(a546) | (~ndr1_0) | (~c3_1(a546)) | (~c2_1(a546))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[224])).
% 0.61/0.79 tff(226,plain,
% 0.61/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a546) | (~c3_1(a546)) | (~c2_1(a546)) | c1_1(a546) | c0_1(a546) | (~c3_1(a546)) | c1_1(a546) | c0_1(a546) | (~c2_1(a546)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | (~c3_1(a546)) | (~c2_1(a546)))),
% 0.61/0.79 inference(transitivity,[status(thm)],[225, 223])).
% 0.61/0.79 tff(227,plain,
% 0.61/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a546) | (~c3_1(a546)) | (~c2_1(a546)) | c1_1(a546) | c0_1(a546) | (~c3_1(a546)) | c1_1(a546) | c0_1(a546) | (~c2_1(a546)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(228,plain,
% 0.61/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | (~c3_1(a546)) | (~c2_1(a546))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.61/0.79 tff(229,plain,
% 0.61/0.79 (~c2_1(a546)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[228, 92, 222, 214, 208, 11])).
% 0.61/0.79 tff(230,plain,
% 0.61/0.79 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(231,plain,
% 0.61/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[230])).
% 0.61/0.79 tff(232,plain,
% 0.61/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(233,plain,
% 0.61/0.79 (^[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)) | (~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(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(234,plain,
% 0.61/0.79 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_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) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[233])).
% 0.61/0.79 tff(235,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause202')).
% 0.61/0.79 tff(236,plain,
% 0.61/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.61/0.79 tff(237,plain,
% 0.61/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[236, 232])).
% 0.61/0.79 tff(238,plain,(
% 0.61/0.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.79 inference(skolemize,[status(sab)],[237])).
% 0.61/0.79 tff(239,plain,
% 0.61/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[238, 231])).
% 0.61/0.79 tff(240,plain,
% 0.61/0.79 (^[U: $i] : refl((hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(241,plain,
% 0.61/0.79 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[240])).
% 0.61/0.79 tff(242,plain,
% 0.61/0.79 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(243,plain,
% 0.61/0.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp13))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp14) <=> ((hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp14))), rewrite(((hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp14) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp14) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(244,plain,
% 0.61/0.79 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp14) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[243])).
% 0.61/0.79 tff(245,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.61/0.79 tff(246,plain,
% 0.61/0.79 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.61/0.79 tff(247,plain,
% 0.61/0.79 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[246, 242])).
% 0.61/0.79 tff(248,plain,(
% 0.61/0.79 ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(skolemize,[status(sab)],[247])).
% 0.61/0.79 tff(249,plain,
% 0.61/0.79 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[248, 241])).
% 0.61/0.79 tff(250,assumption,(~hskp14), introduced(assumption)).
% 0.61/0.79 tff(251,plain,
% 0.61/0.79 (^[U: $i] : refl((hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(252,plain,
% 0.61/0.79 (![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[251])).
% 0.61/0.79 tff(253,plain,
% 0.61/0.79 (![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(254,plain,
% 0.61/0.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp21) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp21))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp21) <=> (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp21) <=> (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(255,plain,
% 0.61/0.79 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp21) <=> ![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[254])).
% 0.61/0.79 tff(256,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 0.61/0.79 tff(257,plain,
% 0.61/0.79 (![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.61/0.79 tff(258,plain,
% 0.61/0.79 (![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[257, 253])).
% 0.61/0.79 tff(259,plain,(
% 0.61/0.79 ![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(skolemize,[status(sab)],[258])).
% 0.61/0.79 tff(260,plain,
% 0.61/0.79 (![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[259, 252])).
% 0.61/0.79 tff(261,plain,
% 0.61/0.79 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(262,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[261])).
% 0.61/0.79 tff(263,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(264,plain,
% 0.61/0.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(265,plain,
% 0.61/0.79 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[264])).
% 0.61/0.79 tff(266,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.61/0.79 tff(267,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.61/0.79 tff(268,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[267, 263])).
% 0.61/0.79 tff(269,plain,(
% 0.61/0.79 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.79 inference(skolemize,[status(sab)],[268])).
% 0.61/0.79 tff(270,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[269, 262])).
% 0.61/0.79 tff(271,plain,
% 0.61/0.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a546) | c1_1(a546) | (~ndr1_0) | (~c3_1(a546)) | c2_1(a546))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a546) | c1_1(a546) | (~ndr1_0) | (~c3_1(a546)) | c2_1(a546))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(272,plain,
% 0.61/0.79 ((hskp0 | (~ndr1_0) | c1_1(a546) | c0_1(a546) | (~c3_1(a546)) | c2_1(a546) | c1_1(a546) | c0_1(a546)) <=> (hskp0 | c0_1(a546) | c1_1(a546) | (~ndr1_0) | (~c3_1(a546)) | c2_1(a546))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(273,plain,
% 0.61/0.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a546) | c0_1(a546) | (~c3_1(a546)) | c2_1(a546) | c1_1(a546) | c0_1(a546))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a546) | c1_1(a546) | (~ndr1_0) | (~c3_1(a546)) | c2_1(a546)))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[272])).
% 0.61/0.79 tff(274,plain,
% 0.61/0.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a546) | c0_1(a546) | (~c3_1(a546)) | c2_1(a546) | c1_1(a546) | c0_1(a546))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a546) | c1_1(a546) | (~ndr1_0) | (~c3_1(a546)) | c2_1(a546))),
% 0.61/0.79 inference(transitivity,[status(thm)],[273, 271])).
% 0.61/0.79 tff(275,plain,
% 0.61/0.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a546) | c0_1(a546) | (~c3_1(a546)) | c2_1(a546) | c1_1(a546) | c0_1(a546))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(276,plain,
% 0.61/0.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a546) | c1_1(a546) | (~ndr1_0) | (~c3_1(a546)) | c2_1(a546)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.61/0.79 tff(277,plain,
% 0.61/0.79 (hskp0),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[276, 92, 222, 214, 208, 270, 229])).
% 0.61/0.79 tff(278,plain,
% 0.61/0.79 (~c3_1(a536)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[28, 277])).
% 0.61/0.79 tff(279,plain,
% 0.61/0.79 (c2_1(a536)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[46, 277])).
% 0.61/0.79 tff(280,plain,
% 0.61/0.79 (c0_1(a536)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[54, 277])).
% 0.61/0.79 tff(281,plain,
% 0.61/0.79 (((~![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp21 | hskp14 | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)))) <=> ((~![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp21 | hskp14 | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(282,plain,
% 0.61/0.79 ((hskp21 | hskp14 | (~ndr1_0) | c3_1(a536) | (~c0_1(a536)) | (~c2_1(a536))) <=> (hskp21 | hskp14 | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(283,plain,
% 0.61/0.79 (((~![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp21 | hskp14 | (~ndr1_0) | c3_1(a536) | (~c0_1(a536)) | (~c2_1(a536)))) <=> ((~![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp21 | hskp14 | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[282])).
% 0.61/0.79 tff(284,plain,
% 0.61/0.79 (((~![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp21 | hskp14 | (~ndr1_0) | c3_1(a536) | (~c0_1(a536)) | (~c2_1(a536)))) <=> ((~![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp21 | hskp14 | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)))),
% 0.61/0.79 inference(transitivity,[status(thm)],[283, 281])).
% 0.61/0.79 tff(285,plain,
% 0.61/0.79 ((~![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp21 | hskp14 | (~ndr1_0) | c3_1(a536) | (~c0_1(a536)) | (~c2_1(a536)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(286,plain,
% 0.61/0.79 ((~![U: $i] : (hskp21 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp21 | hskp14 | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.61/0.79 tff(287,plain,
% 0.61/0.79 (hskp21 | hskp14),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[286, 92, 280, 279, 278, 260])).
% 0.61/0.79 tff(288,plain,
% 0.61/0.79 (hskp21),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[287, 250])).
% 0.61/0.79 tff(289,plain,
% 0.61/0.79 (((~hskp21) | c3_1(a582)) <=> ((~hskp21) | c3_1(a582))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(290,axiom,((~hskp21) | c3_1(a582)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 0.61/0.79 tff(291,plain,
% 0.61/0.79 ((~hskp21) | c3_1(a582)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.61/0.79 tff(292,plain,
% 0.61/0.79 ((~hskp21) | c3_1(a582)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[291, 289])).
% 0.61/0.79 tff(293,plain,
% 0.61/0.79 ((~hskp21) | c3_1(a582)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[292, 289])).
% 0.61/0.79 tff(294,plain,
% 0.61/0.79 ((~hskp21) | c3_1(a582)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.61/0.79 tff(295,plain,
% 0.61/0.79 ((~hskp21) | c3_1(a582)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[294, 289])).
% 0.61/0.79 tff(296,plain,
% 0.61/0.79 (c3_1(a582)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[295, 288])).
% 0.61/0.79 tff(297,plain,
% 0.61/0.79 (((~hskp21) | c2_1(a582)) <=> ((~hskp21) | c2_1(a582))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(298,axiom,((~hskp21) | c2_1(a582)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 0.61/0.79 tff(299,plain,
% 0.61/0.79 ((~hskp21) | c2_1(a582)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.61/0.79 tff(300,plain,
% 0.61/0.79 ((~hskp21) | c2_1(a582)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[299, 297])).
% 0.61/0.79 tff(301,plain,
% 0.61/0.79 ((~hskp21) | c2_1(a582)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[300, 297])).
% 0.61/0.79 tff(302,plain,
% 0.61/0.79 ((~hskp21) | c2_1(a582)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[301, 297])).
% 0.61/0.79 tff(303,plain,
% 0.61/0.79 ((~hskp21) | c2_1(a582)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[302, 297])).
% 0.61/0.79 tff(304,plain,
% 0.61/0.79 (c2_1(a582)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[303, 288])).
% 0.61/0.79 tff(305,plain,
% 0.61/0.79 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp13 | (~ndr1_0) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(306,plain,
% 0.61/0.79 ((hskp14 | hskp13 | (~ndr1_0) | c0_1(a582) | (~c3_1(a582)) | (~c2_1(a582))) <=> (hskp14 | hskp13 | (~ndr1_0) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(307,plain,
% 0.61/0.79 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a582) | (~c3_1(a582)) | (~c2_1(a582)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[306])).
% 0.61/0.79 tff(308,plain,
% 0.61/0.79 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a582) | (~c3_1(a582)) | (~c2_1(a582)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp13 | (~ndr1_0) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582)))),
% 0.61/0.79 inference(transitivity,[status(thm)],[307, 305])).
% 0.61/0.79 tff(309,plain,
% 0.61/0.79 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a582) | (~c3_1(a582)) | (~c2_1(a582)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(310,plain,
% 0.61/0.79 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp13 | (~ndr1_0) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.61/0.79 tff(311,plain,
% 0.61/0.79 (c0_1(a582)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[310, 92, 250, 106, 304, 296, 249])).
% 0.61/0.79 tff(312,plain,
% 0.61/0.79 (^[U: $i] : refl((hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(313,plain,
% 0.61/0.79 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[312])).
% 0.61/0.80 tff(314,plain,
% 0.61/0.80 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(315,plain,
% 0.61/0.80 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp10))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp14) <=> ((hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp14))), rewrite(((hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp14) <=> (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp14) <=> (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(316,plain,
% 0.61/0.80 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp14) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[315])).
% 0.61/0.80 tff(317,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.61/0.80 tff(318,plain,
% 0.61/0.80 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.61/0.80 tff(319,plain,
% 0.61/0.80 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[318, 314])).
% 0.61/0.80 tff(320,plain,(
% 0.61/0.80 ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.80 inference(skolemize,[status(sab)],[319])).
% 0.61/0.80 tff(321,plain,
% 0.61/0.80 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[320, 313])).
% 0.61/0.80 tff(322,plain,
% 0.61/0.80 (((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)))) <=> ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp14 | hskp10 | (~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(323,plain,
% 0.61/0.80 ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(324,plain,
% 0.61/0.80 ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp14 | hskp10 | (~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.61/0.80 tff(325,plain,
% 0.61/0.80 (hskp10 | (~c0_1(a582))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[324, 92, 250, 304, 296, 321])).
% 0.61/0.80 tff(326,plain,
% 0.61/0.80 (hskp10),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[325, 311])).
% 0.61/0.80 tff(327,plain,
% 0.61/0.80 (((~hskp10) | (~c0_1(a551))) <=> ((~hskp10) | (~c0_1(a551)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(328,plain,
% 0.61/0.80 (((~c0_1(a551)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a551)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(329,axiom,((~c0_1(a551)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.61/0.80 tff(330,plain,
% 0.61/0.80 ((~hskp10) | (~c0_1(a551))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.61/0.80 tff(331,plain,
% 0.61/0.80 ((~hskp10) | (~c0_1(a551))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[330, 327])).
% 0.61/0.80 tff(332,plain,
% 0.61/0.80 (~c0_1(a551)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[331, 326])).
% 0.61/0.80 tff(333,plain,
% 0.61/0.80 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(334,plain,
% 0.61/0.80 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[333])).
% 0.61/0.80 tff(335,plain,
% 0.61/0.80 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(336,plain,
% 0.61/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(337,plain,
% 0.61/0.80 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[336])).
% 0.61/0.80 tff(338,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 0.61/0.80 tff(339,plain,
% 0.61/0.80 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.61/0.80 tff(340,plain,
% 0.61/0.80 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[339, 335])).
% 0.61/0.80 tff(341,plain,(
% 0.61/0.80 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.61/0.80 inference(skolemize,[status(sab)],[340])).
% 0.61/0.80 tff(342,plain,
% 0.61/0.80 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[341, 334])).
% 0.61/0.80 tff(343,plain,
% 0.61/0.80 (((~hskp21) | (~c1_1(a582))) <=> ((~hskp21) | (~c1_1(a582)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(344,plain,
% 0.61/0.80 (((~c1_1(a582)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a582)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(345,axiom,((~c1_1(a582)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.61/0.80 tff(346,plain,
% 0.61/0.80 ((~hskp21) | (~c1_1(a582))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.61/0.80 tff(347,plain,
% 0.61/0.80 ((~hskp21) | (~c1_1(a582))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[346, 343])).
% 0.61/0.80 tff(348,plain,
% 0.61/0.80 (~c1_1(a582)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[347, 288])).
% 0.61/0.80 tff(349,plain,
% 0.61/0.80 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a582) | (~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a582) | (~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(350,plain,
% 0.61/0.80 ((hskp19 | (~ndr1_0) | c1_1(a582) | (~c3_1(a582)) | (~c2_1(a582)) | c1_1(a582) | (~c0_1(a582)) | (~c2_1(a582))) <=> (hskp19 | c1_1(a582) | (~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(351,plain,
% 0.61/0.80 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a582) | (~c3_1(a582)) | (~c2_1(a582)) | c1_1(a582) | (~c0_1(a582)) | (~c2_1(a582)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a582) | (~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[350])).
% 0.61/0.80 tff(352,plain,
% 0.61/0.80 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a582) | (~c3_1(a582)) | (~c2_1(a582)) | c1_1(a582) | (~c0_1(a582)) | (~c2_1(a582)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a582) | (~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)))),
% 0.61/0.80 inference(transitivity,[status(thm)],[351, 349])).
% 0.61/0.80 tff(353,plain,
% 0.61/0.80 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a582) | (~c3_1(a582)) | (~c2_1(a582)) | c1_1(a582) | (~c0_1(a582)) | (~c2_1(a582)))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(354,plain,
% 0.61/0.80 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a582) | (~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.65/0.80 tff(355,plain,
% 0.65/0.80 (hskp19),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[354, 92, 304, 296, 348, 342, 311])).
% 0.65/0.80 tff(356,plain,
% 0.65/0.80 (((~hskp19) | (~c3_1(a576))) <=> ((~hskp19) | (~c3_1(a576)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(357,plain,
% 0.65/0.80 (((~c3_1(a576)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a576)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(358,axiom,((~c3_1(a576)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.65/0.80 tff(359,plain,
% 0.65/0.80 ((~hskp19) | (~c3_1(a576))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.65/0.80 tff(360,plain,
% 0.65/0.80 ((~hskp19) | (~c3_1(a576))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[359, 356])).
% 0.65/0.80 tff(361,plain,
% 0.65/0.80 (~c3_1(a576)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[360, 355])).
% 0.65/0.80 tff(362,plain,
% 0.65/0.80 (((~hskp19) | (~c1_1(a576))) <=> ((~hskp19) | (~c1_1(a576)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(363,plain,
% 0.65/0.80 (((~c1_1(a576)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a576)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(364,axiom,((~c1_1(a576)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 0.65/0.80 tff(365,plain,
% 0.65/0.80 ((~hskp19) | (~c1_1(a576))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.65/0.80 tff(366,plain,
% 0.65/0.80 ((~hskp19) | (~c1_1(a576))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[365, 362])).
% 0.65/0.80 tff(367,plain,
% 0.65/0.80 (~c1_1(a576)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[366, 355])).
% 0.65/0.80 tff(368,plain,
% 0.65/0.80 (((~hskp10) | c1_1(a551)) <=> ((~hskp10) | c1_1(a551))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(369,axiom,((~hskp10) | c1_1(a551)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.65/0.80 tff(370,plain,
% 0.65/0.80 ((~hskp10) | c1_1(a551)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.65/0.80 tff(371,plain,
% 0.65/0.80 ((~hskp10) | c1_1(a551)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[370, 368])).
% 0.65/0.80 tff(372,plain,
% 0.65/0.80 ((~hskp10) | c1_1(a551)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[371, 368])).
% 0.65/0.80 tff(373,plain,
% 0.65/0.80 ((~hskp10) | c1_1(a551)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[372, 368])).
% 0.65/0.80 tff(374,plain,
% 0.65/0.80 ((~hskp10) | c1_1(a551)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[373, 368])).
% 0.65/0.80 tff(375,plain,
% 0.65/0.80 (c1_1(a551)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[374, 326])).
% 0.65/0.80 tff(376,plain,
% 0.65/0.80 (((~hskp19) | c0_1(a576)) <=> ((~hskp19) | c0_1(a576))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(377,axiom,((~hskp19) | c0_1(a576)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.65/0.80 tff(378,plain,
% 0.65/0.80 ((~hskp19) | c0_1(a576)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.65/0.80 tff(379,plain,
% 0.65/0.80 ((~hskp19) | c0_1(a576)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[378, 376])).
% 0.65/0.80 tff(380,plain,
% 0.65/0.80 ((~hskp19) | c0_1(a576)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[379, 376])).
% 0.65/0.80 tff(381,plain,
% 0.65/0.80 ((~hskp19) | c0_1(a576)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[380, 376])).
% 0.65/0.80 tff(382,plain,
% 0.65/0.80 ((~hskp19) | c0_1(a576)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[381, 376])).
% 0.65/0.80 tff(383,plain,
% 0.65/0.80 (c0_1(a576)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[382, 355])).
% 0.65/0.80 tff(384,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c1_1(a576) | c3_1(a576) | c0_1(a551) | c0_1(a546) | (~ndr1_0) | (~c3_1(a546)) | c2_1(a546) | c2_1(a551) | (~c1_1(a551)) | (~c0_1(a576)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c1_1(a576) | c3_1(a576) | c0_1(a551) | c0_1(a546) | (~ndr1_0) | (~c3_1(a546)) | c2_1(a546) | c2_1(a551) | (~c1_1(a551)) | (~c0_1(a576)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(385,plain,
% 0.65/0.80 (((~ndr1_0) | c3_1(a576) | c1_1(a576) | (~c0_1(a576)) | c2_1(a546) | c0_1(a546) | (~c3_1(a546)) | c0_1(a551) | c2_1(a551) | (~c1_1(a551))) <=> (c1_1(a576) | c3_1(a576) | c0_1(a551) | c0_1(a546) | (~ndr1_0) | (~c3_1(a546)) | c2_1(a546) | c2_1(a551) | (~c1_1(a551)) | (~c0_1(a576)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(386,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a576) | c1_1(a576) | (~c0_1(a576)) | c2_1(a546) | c0_1(a546) | (~c3_1(a546)) | c0_1(a551) | c2_1(a551) | (~c1_1(a551)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c1_1(a576) | c3_1(a576) | c0_1(a551) | c0_1(a546) | (~ndr1_0) | (~c3_1(a546)) | c2_1(a546) | c2_1(a551) | (~c1_1(a551)) | (~c0_1(a576))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[385])).
% 0.65/0.80 tff(387,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a576) | c1_1(a576) | (~c0_1(a576)) | c2_1(a546) | c0_1(a546) | (~c3_1(a546)) | c0_1(a551) | c2_1(a551) | (~c1_1(a551)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c1_1(a576) | c3_1(a576) | c0_1(a551) | c0_1(a546) | (~ndr1_0) | (~c3_1(a546)) | c2_1(a546) | c2_1(a551) | (~c1_1(a551)) | (~c0_1(a576)))),
% 0.65/0.80 inference(transitivity,[status(thm)],[386, 384])).
% 0.65/0.80 tff(388,plain,
% 0.65/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a576) | c1_1(a576) | (~c0_1(a576)) | c2_1(a546) | c0_1(a546) | (~c3_1(a546)) | c0_1(a551) | c2_1(a551) | (~c1_1(a551)))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(389,plain,
% 0.65/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c1_1(a576) | c3_1(a576) | c0_1(a551) | c0_1(a546) | (~ndr1_0) | (~c3_1(a546)) | c2_1(a546) | c2_1(a551) | (~c1_1(a551)) | (~c0_1(a576))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.65/0.80 tff(390,plain,
% 0.65/0.80 (c2_1(a551)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[389, 92, 383, 375, 222, 367, 361, 332, 214, 239, 229])).
% 0.65/0.80 tff(391,plain,
% 0.65/0.80 (((~hskp10) | c3_1(a551)) <=> ((~hskp10) | c3_1(a551))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(392,axiom,((~hskp10) | c3_1(a551)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.65/0.80 tff(393,plain,
% 0.65/0.80 ((~hskp10) | c3_1(a551)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.65/0.80 tff(394,plain,
% 0.65/0.80 ((~hskp10) | c3_1(a551)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[393, 391])).
% 0.65/0.80 tff(395,plain,
% 0.65/0.80 ((~hskp10) | c3_1(a551)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[394, 391])).
% 0.65/0.80 tff(396,plain,
% 0.65/0.80 ((~hskp10) | c3_1(a551)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[395, 391])).
% 0.65/0.80 tff(397,plain,
% 0.65/0.80 ((~hskp10) | c3_1(a551)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[396, 391])).
% 0.65/0.80 tff(398,plain,
% 0.65/0.80 (c3_1(a551)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[397, 326])).
% 0.65/0.80 tff(399,plain,
% 0.65/0.80 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp13 | c0_1(a551) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a551) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(400,plain,
% 0.65/0.80 ((hskp14 | hskp13 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c2_1(a551))) <=> (hskp14 | hskp13 | c0_1(a551) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(401,plain,
% 0.65/0.80 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c2_1(a551)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp13 | c0_1(a551) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[400])).
% 0.65/0.80 tff(402,plain,
% 0.65/0.80 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c2_1(a551)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a551) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551)))),
% 0.65/0.80 inference(transitivity,[status(thm)],[401, 399])).
% 0.65/0.80 tff(403,plain,
% 0.65/0.80 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a551) | (~c3_1(a551)) | (~c2_1(a551)))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(404,plain,
% 0.65/0.80 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a551) | (~ndr1_0) | (~c2_1(a551)) | (~c3_1(a551))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[403, 402])).
% 0.65/0.80 tff(405,plain,
% 0.65/0.80 ($false),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[404, 92, 250, 106, 398, 332, 249, 390])).
% 0.65/0.80 tff(406,plain,(hskp14 | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.65/0.80 tff(407,plain,
% 0.65/0.80 (hskp14),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[406, 106])).
% 0.65/0.80 tff(408,plain,
% 0.65/0.80 (~c0_1(a566)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[142, 407])).
% 0.65/0.80 tff(409,plain,
% 0.65/0.80 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(410,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[409])).
% 0.65/0.80 tff(411,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(412,plain,
% 0.65/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(413,plain,
% 0.65/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[412])).
% 0.65/0.80 tff(414,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 0.65/0.80 tff(415,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.65/0.80 tff(416,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[415, 411])).
% 0.65/0.80 tff(417,plain,(
% 0.65/0.80 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.80 inference(skolemize,[status(sab)],[416])).
% 0.65/0.80 tff(418,plain,
% 0.65/0.80 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[417, 410])).
% 0.65/0.80 tff(419,plain,
% 0.65/0.80 (hskp21 | hskp12),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[98, 92, 280, 279, 278, 39])).
% 0.65/0.80 tff(420,plain,
% 0.65/0.80 (hskp12),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[419, 12])).
% 0.65/0.80 tff(421,plain,
% 0.65/0.80 (~c1_1(a564)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[104, 420])).
% 0.65/0.80 tff(422,plain,
% 0.65/0.80 (((~hskp12) | c3_1(a564)) <=> ((~hskp12) | c3_1(a564))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(423,axiom,((~hskp12) | c3_1(a564)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.65/0.80 tff(424,plain,
% 0.65/0.80 ((~hskp12) | c3_1(a564)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.65/0.80 tff(425,plain,
% 0.65/0.80 ((~hskp12) | c3_1(a564)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[424, 422])).
% 0.65/0.80 tff(426,plain,
% 0.65/0.80 ((~hskp12) | c3_1(a564)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[425, 422])).
% 0.65/0.80 tff(427,plain,
% 0.65/0.80 ((~hskp12) | c3_1(a564)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[426, 422])).
% 0.65/0.80 tff(428,plain,
% 0.65/0.80 ((~hskp12) | c3_1(a564)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[427, 422])).
% 0.65/0.80 tff(429,plain,
% 0.65/0.80 (c3_1(a564)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[428, 420])).
% 0.65/0.80 tff(430,plain,
% 0.65/0.80 (((~hskp12) | c0_1(a564)) <=> ((~hskp12) | c0_1(a564))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(431,axiom,((~hskp12) | c0_1(a564)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.65/0.80 tff(432,plain,
% 0.65/0.80 ((~hskp12) | c0_1(a564)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.65/0.80 tff(433,plain,
% 0.65/0.80 ((~hskp12) | c0_1(a564)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[432, 430])).
% 0.65/0.80 tff(434,plain,
% 0.65/0.80 ((~hskp12) | c0_1(a564)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[433, 430])).
% 0.65/0.80 tff(435,plain,
% 0.65/0.80 ((~hskp12) | c0_1(a564)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[434, 430])).
% 0.65/0.80 tff(436,plain,
% 0.65/0.80 ((~hskp12) | c0_1(a564)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[435, 430])).
% 0.65/0.80 tff(437,plain,
% 0.65/0.80 (c0_1(a564)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[436, 420])).
% 0.65/0.80 tff(438,plain,
% 0.65/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a564) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | c2_1(a546) | (~c3_1(a564)) | (~c0_1(a564)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a564) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | c2_1(a546) | (~c3_1(a564)) | (~c0_1(a564)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(439,plain,
% 0.65/0.80 ((hskp1 | (~ndr1_0) | c1_1(a564) | (~c3_1(a564)) | (~c0_1(a564)) | c2_1(a546) | c1_1(a546) | c0_1(a546)) <=> (hskp1 | c1_1(a564) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | c2_1(a546) | (~c3_1(a564)) | (~c0_1(a564)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(440,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a564) | (~c3_1(a564)) | (~c0_1(a564)) | c2_1(a546) | c1_1(a546) | c0_1(a546))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a564) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | c2_1(a546) | (~c3_1(a564)) | (~c0_1(a564))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[439])).
% 0.65/0.81 tff(441,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a564) | (~c3_1(a564)) | (~c0_1(a564)) | c2_1(a546) | c1_1(a546) | c0_1(a546))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a564) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | c2_1(a546) | (~c3_1(a564)) | (~c0_1(a564)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[440, 438])).
% 0.65/0.81 tff(442,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a564) | (~c3_1(a564)) | (~c0_1(a564)) | c2_1(a546) | c1_1(a546) | c0_1(a546))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(443,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a564) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | c2_1(a546) | (~c3_1(a564)) | (~c0_1(a564))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.65/0.81 tff(444,plain,
% 0.65/0.81 (hskp1),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[443, 92, 437, 429, 421, 214, 208, 418, 229])).
% 0.65/0.81 tff(445,plain,
% 0.65/0.81 (((~hskp1) | (~c3_1(a537))) <=> ((~hskp1) | (~c3_1(a537)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(446,plain,
% 0.65/0.81 (((~c3_1(a537)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a537)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(447,axiom,((~c3_1(a537)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 0.65/0.81 tff(448,plain,
% 0.65/0.81 ((~hskp1) | (~c3_1(a537))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.65/0.81 tff(449,plain,
% 0.65/0.81 ((~hskp1) | (~c3_1(a537))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[448, 445])).
% 0.65/0.81 tff(450,plain,
% 0.65/0.81 (~c3_1(a537)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[449, 444])).
% 0.65/0.81 tff(451,plain,
% 0.65/0.81 (((~hskp1) | (~c1_1(a537))) <=> ((~hskp1) | (~c1_1(a537)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(452,plain,
% 0.65/0.81 (((~c1_1(a537)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a537)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(453,axiom,((~c1_1(a537)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 0.65/0.81 tff(454,plain,
% 0.65/0.81 ((~hskp1) | (~c1_1(a537))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.65/0.81 tff(455,plain,
% 0.65/0.81 ((~hskp1) | (~c1_1(a537))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[454, 451])).
% 0.65/0.81 tff(456,plain,
% 0.65/0.81 (~c1_1(a537)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[455, 444])).
% 0.65/0.81 tff(457,plain,
% 0.65/0.81 (((~hskp1) | c2_1(a537)) <=> ((~hskp1) | c2_1(a537))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(458,axiom,((~hskp1) | c2_1(a537)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 0.65/0.81 tff(459,plain,
% 0.65/0.81 ((~hskp1) | c2_1(a537)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.65/0.81 tff(460,plain,
% 0.65/0.81 ((~hskp1) | c2_1(a537)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[459, 457])).
% 0.65/0.81 tff(461,plain,
% 0.65/0.81 ((~hskp1) | c2_1(a537)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[460, 457])).
% 0.65/0.81 tff(462,plain,
% 0.65/0.81 ((~hskp1) | c2_1(a537)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[461, 457])).
% 0.65/0.81 tff(463,plain,
% 0.65/0.81 ((~hskp1) | c2_1(a537)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[462, 457])).
% 0.65/0.81 tff(464,plain,
% 0.65/0.81 (c2_1(a537)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[463, 444])).
% 0.65/0.81 tff(465,plain,
% 0.65/0.81 (c3_1(a566)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[164, 407])).
% 0.65/0.81 tff(466,plain,
% 0.65/0.81 (c2_1(a566)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[172, 407])).
% 0.65/0.81 tff(467,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a566) | c0_1(a546) | c1_1(a546) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | c0_1(a537) | (~c3_1(a546)) | (~c2_1(a566)) | (~c3_1(a566)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a566) | c0_1(a546) | c1_1(a546) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | c0_1(a537) | (~c3_1(a546)) | (~c2_1(a566)) | (~c3_1(a566)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(468,plain,
% 0.65/0.81 (((~ndr1_0) | c0_1(a566) | (~c3_1(a566)) | (~c2_1(a566)) | c1_1(a546) | c0_1(a546) | (~c3_1(a546)) | c1_1(a537) | c0_1(a537) | (~c2_1(a537))) <=> (c0_1(a566) | c0_1(a546) | c1_1(a546) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | c0_1(a537) | (~c3_1(a546)) | (~c2_1(a566)) | (~c3_1(a566)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(469,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a566) | (~c3_1(a566)) | (~c2_1(a566)) | c1_1(a546) | c0_1(a546) | (~c3_1(a546)) | c1_1(a537) | c0_1(a537) | (~c2_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a566) | c0_1(a546) | c1_1(a546) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | c0_1(a537) | (~c3_1(a546)) | (~c2_1(a566)) | (~c3_1(a566))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[468])).
% 0.65/0.81 tff(470,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a566) | (~c3_1(a566)) | (~c2_1(a566)) | c1_1(a546) | c0_1(a546) | (~c3_1(a546)) | c1_1(a537) | c0_1(a537) | (~c2_1(a537)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a566) | c0_1(a546) | c1_1(a546) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | c0_1(a537) | (~c3_1(a546)) | (~c2_1(a566)) | (~c3_1(a566)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[469, 467])).
% 0.65/0.81 tff(471,plain,
% 0.65/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a566) | (~c3_1(a566)) | (~c2_1(a566)) | c1_1(a546) | c0_1(a546) | (~c3_1(a546)) | c1_1(a537) | c0_1(a537) | (~c2_1(a537)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(472,plain,
% 0.65/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a566) | c0_1(a546) | c1_1(a546) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | c0_1(a537) | (~c3_1(a546)) | (~c2_1(a566)) | (~c3_1(a566))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.65/0.81 tff(473,plain,
% 0.65/0.81 (c0_1(a537)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[472, 92, 466, 465, 222, 464, 408, 214, 208, 456, 11])).
% 0.65/0.81 tff(474,plain,
% 0.65/0.81 (^[U: $i] : refl((hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(475,plain,
% 0.65/0.81 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[474])).
% 0.65/0.81 tff(476,plain,
% 0.65/0.81 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(477,plain,
% 0.65/0.81 (^[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)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) | hskp20) <=> ((hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp20))), rewrite(((hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp20) <=> (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) | hskp20) <=> (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(478,plain,
% 0.65/0.81 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) | hskp20) <=> ![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[477])).
% 0.65/0.81 tff(479,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 0.65/0.81 tff(480,plain,
% 0.65/0.81 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.65/0.81 tff(481,plain,
% 0.65/0.81 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[480, 476])).
% 0.65/0.81 tff(482,plain,(
% 0.65/0.81 ![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.81 inference(skolemize,[status(sab)],[481])).
% 0.65/0.81 tff(483,plain,
% 0.65/0.81 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[482, 475])).
% 0.65/0.81 tff(484,plain,
% 0.65/0.81 (((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp13 | c1_1(a537) | c3_1(a537) | (~ndr1_0) | (~c0_1(a537)))) <=> ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp13 | c1_1(a537) | c3_1(a537) | (~ndr1_0) | (~c0_1(a537)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(485,plain,
% 0.65/0.81 ((hskp20 | hskp13 | (~ndr1_0) | c3_1(a537) | c1_1(a537) | (~c0_1(a537))) <=> (hskp20 | hskp13 | c1_1(a537) | c3_1(a537) | (~ndr1_0) | (~c0_1(a537)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(486,plain,
% 0.65/0.81 (((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | c3_1(a537) | c1_1(a537) | (~c0_1(a537)))) <=> ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp13 | c1_1(a537) | c3_1(a537) | (~ndr1_0) | (~c0_1(a537))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[485])).
% 0.65/0.81 tff(487,plain,
% 0.65/0.81 (((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | c3_1(a537) | c1_1(a537) | (~c0_1(a537)))) <=> ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp13 | c1_1(a537) | c3_1(a537) | (~ndr1_0) | (~c0_1(a537)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[486, 484])).
% 0.65/0.81 tff(488,plain,
% 0.65/0.81 ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | c3_1(a537) | c1_1(a537) | (~c0_1(a537)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(489,plain,
% 0.65/0.81 ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp13 | c1_1(a537) | c3_1(a537) | (~ndr1_0) | (~c0_1(a537))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.65/0.81 tff(490,plain,
% 0.65/0.81 (hskp20),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[489, 92, 106, 456, 450, 483, 473])).
% 0.65/0.81 tff(491,plain,
% 0.65/0.81 (((~hskp20) | (~c0_1(a580))) <=> ((~hskp20) | (~c0_1(a580)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(492,plain,
% 0.65/0.81 (((~c0_1(a580)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a580)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(493,axiom,((~c0_1(a580)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.65/0.81 tff(494,plain,
% 0.65/0.81 ((~hskp20) | (~c0_1(a580))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[493, 492])).
% 0.65/0.81 tff(495,plain,
% 0.65/0.81 ((~hskp20) | (~c0_1(a580))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[494, 491])).
% 0.65/0.81 tff(496,plain,
% 0.65/0.81 (~c0_1(a580)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[495, 490])).
% 0.65/0.81 tff(497,plain,
% 0.65/0.81 (((~hskp20) | (~c3_1(a580))) <=> ((~hskp20) | (~c3_1(a580)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(498,plain,
% 0.65/0.81 (((~c3_1(a580)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a580)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(499,axiom,((~c3_1(a580)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.65/0.81 tff(500,plain,
% 0.65/0.81 ((~hskp20) | (~c3_1(a580))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.65/0.81 tff(501,plain,
% 0.65/0.81 ((~hskp20) | (~c3_1(a580))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[500, 497])).
% 0.65/0.81 tff(502,plain,
% 0.65/0.81 (~c3_1(a580)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[501, 490])).
% 0.65/0.81 tff(503,plain,
% 0.65/0.81 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(504,plain,
% 0.65/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[503])).
% 0.65/0.81 tff(505,plain,
% 0.65/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(506,plain,
% 0.65/0.81 (^[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))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(507,plain,
% 0.65/0.81 (![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))) | (~c1_1(W))) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[506])).
% 0.65/0.81 tff(508,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))) | (~c1_1(W))) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause208')).
% 0.65/0.81 tff(509,plain,
% 0.65/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[508, 507])).
% 0.65/0.81 tff(510,plain,
% 0.65/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[509, 505])).
% 0.65/0.81 tff(511,plain,(
% 0.65/0.81 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.65/0.81 inference(skolemize,[status(sab)],[510])).
% 0.65/0.81 tff(512,plain,
% 0.65/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[511, 504])).
% 0.65/0.81 tff(513,assumption,(~c3_1(a580)), introduced(assumption)).
% 0.65/0.81 tff(514,assumption,(~c0_1(a580)), introduced(assumption)).
% 0.65/0.81 tff(515,assumption,(~c1_1(a537)), introduced(assumption)).
% 0.65/0.81 tff(516,assumption,(c2_1(a536)), introduced(assumption)).
% 0.65/0.81 tff(517,assumption,(c0_1(a536)), introduced(assumption)).
% 0.65/0.81 tff(518,assumption,(~c3_1(a536)), introduced(assumption)).
% 0.65/0.81 tff(519,plain,
% 0.65/0.81 (hskp21 | hskp14 | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[286, 518, 260])).
% 0.65/0.81 tff(520,plain,
% 0.65/0.81 (hskp14),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[519, 12, 183, 517, 516])).
% 0.65/0.81 tff(521,plain,
% 0.65/0.81 (c2_1(a566)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[172, 520])).
% 0.65/0.81 tff(522,assumption,(c2_1(a537)), introduced(assumption)).
% 0.65/0.81 tff(523,assumption,(c3_1(a546)), introduced(assumption)).
% 0.65/0.81 tff(524,plain,
% 0.65/0.81 (c3_1(a566)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[164, 520])).
% 0.65/0.81 tff(525,assumption,(~c1_1(a546)), introduced(assumption)).
% 0.65/0.81 tff(526,assumption,(~c0_1(a546)), introduced(assumption)).
% 0.65/0.81 tff(527,plain,
% 0.65/0.81 ((~ndr1_0) | (~c2_1(a537)) | c0_1(a537) | (~c3_1(a546)) | (~c2_1(a566)) | (~c3_1(a566))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[472, 154, 526, 525, 515, 11])).
% 0.65/0.81 tff(528,plain,
% 0.65/0.81 (c0_1(a537)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[527, 524, 183, 523, 522, 521])).
% 0.65/0.81 tff(529,assumption,(~c3_1(a537)), introduced(assumption)).
% 0.65/0.81 tff(530,plain,
% 0.65/0.81 (hskp20 | hskp13 | c1_1(a537) | (~ndr1_0) | (~c0_1(a537))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[489, 529, 483])).
% 0.65/0.81 tff(531,plain,
% 0.65/0.81 (hskp20),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[530, 528, 183, 515, 106])).
% 0.65/0.81 tff(532,plain,
% 0.65/0.81 (((~hskp20) | c1_1(a580)) <=> ((~hskp20) | c1_1(a580))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(533,axiom,((~hskp20) | c1_1(a580)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 0.65/0.81 tff(534,plain,
% 0.65/0.81 ((~hskp20) | c1_1(a580)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.65/0.81 tff(535,plain,
% 0.65/0.81 ((~hskp20) | c1_1(a580)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[534, 532])).
% 0.65/0.81 tff(536,plain,
% 0.65/0.81 ((~hskp20) | c1_1(a580)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[535, 532])).
% 0.65/0.81 tff(537,plain,
% 0.65/0.81 ((~hskp20) | c1_1(a580)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[536, 532])).
% 0.65/0.81 tff(538,plain,
% 0.65/0.81 ((~hskp20) | c1_1(a580)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[537, 532])).
% 0.65/0.81 tff(539,plain,
% 0.65/0.81 (c1_1(a580)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[538, 531])).
% 0.65/0.81 tff(540,plain,
% 0.65/0.81 (^[U: $i] : refl((hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(541,plain,
% 0.65/0.81 (![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[540])).
% 0.65/0.81 tff(542,plain,
% 0.65/0.81 (![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(543,plain,
% 0.65/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) | hskp21) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp21))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp21) <=> (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) | hskp21) <=> (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(544,plain,
% 0.65/0.82 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) | hskp21) <=> ![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[543])).
% 0.65/0.82 tff(545,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.65/0.82 tff(546,plain,
% 0.65/0.82 (![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.65/0.82 tff(547,plain,
% 0.65/0.82 (![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[546, 542])).
% 0.65/0.82 tff(548,plain,(
% 0.65/0.82 ![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[547])).
% 0.65/0.82 tff(549,plain,
% 0.65/0.82 (![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[548, 541])).
% 0.65/0.82 tff(550,plain,
% 0.65/0.82 (((~![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp29 | hskp21 | c1_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a537)))) <=> ((~![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp29 | hskp21 | c1_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a537)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(551,plain,
% 0.65/0.82 ((hskp29 | hskp21 | (~ndr1_0) | c3_1(a537) | c1_1(a537) | (~c2_1(a537))) <=> (hskp29 | hskp21 | c1_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a537)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(552,plain,
% 0.65/0.82 (((~![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp29 | hskp21 | (~ndr1_0) | c3_1(a537) | c1_1(a537) | (~c2_1(a537)))) <=> ((~![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp29 | hskp21 | c1_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a537))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[551])).
% 0.65/0.82 tff(553,plain,
% 0.65/0.82 (((~![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp29 | hskp21 | (~ndr1_0) | c3_1(a537) | c1_1(a537) | (~c2_1(a537)))) <=> ((~![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp29 | hskp21 | c1_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a537)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[552, 550])).
% 0.65/0.82 tff(554,plain,
% 0.65/0.82 ((~![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp29 | hskp21 | (~ndr1_0) | c3_1(a537) | c1_1(a537) | (~c2_1(a537)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(555,plain,
% 0.65/0.82 ((~![U: $i] : (hskp29 | hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp29 | hskp21 | c1_1(a537) | c3_1(a537) | (~ndr1_0) | (~c2_1(a537))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[554, 553])).
% 0.65/0.82 tff(556,plain,
% 0.65/0.82 (hskp29 | hskp21 | c1_1(a537) | (~ndr1_0) | (~c2_1(a537))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[555, 529, 549])).
% 0.65/0.82 tff(557,plain,
% 0.65/0.82 (hskp29),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[556, 12, 183, 522, 515])).
% 0.65/0.82 tff(558,plain,
% 0.65/0.82 (((~hskp29) | c3_1(a552)) <=> ((~hskp29) | c3_1(a552))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(559,axiom,((~hskp29) | c3_1(a552)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.65/0.82 tff(560,plain,
% 0.65/0.82 ((~hskp29) | c3_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.65/0.82 tff(561,plain,
% 0.65/0.82 ((~hskp29) | c3_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[560, 558])).
% 0.65/0.82 tff(562,plain,
% 0.65/0.82 ((~hskp29) | c3_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[561, 558])).
% 0.65/0.82 tff(563,plain,
% 0.65/0.82 ((~hskp29) | c3_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[562, 558])).
% 0.65/0.82 tff(564,plain,
% 0.65/0.82 ((~hskp29) | c3_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[563, 558])).
% 0.65/0.82 tff(565,plain,
% 0.65/0.82 (c3_1(a552)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[564, 557])).
% 0.65/0.82 tff(566,plain,
% 0.65/0.82 (((~hskp29) | c2_1(a552)) <=> ((~hskp29) | c2_1(a552))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(567,axiom,((~hskp29) | c2_1(a552)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.65/0.82 tff(568,plain,
% 0.65/0.82 ((~hskp29) | c2_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.65/0.82 tff(569,plain,
% 0.65/0.82 ((~hskp29) | c2_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[568, 566])).
% 0.65/0.82 tff(570,plain,
% 0.65/0.82 ((~hskp29) | c2_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[569, 566])).
% 0.65/0.82 tff(571,plain,
% 0.65/0.82 ((~hskp29) | c2_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[570, 566])).
% 0.65/0.82 tff(572,plain,
% 0.65/0.82 ((~hskp29) | c2_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[571, 566])).
% 0.65/0.82 tff(573,plain,
% 0.65/0.82 (c2_1(a552)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[572, 557])).
% 0.65/0.82 tff(574,plain,
% 0.65/0.82 (((~hskp29) | c0_1(a552)) <=> ((~hskp29) | c0_1(a552))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(575,axiom,((~hskp29) | c0_1(a552)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.65/0.82 tff(576,plain,
% 0.65/0.82 ((~hskp29) | c0_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.65/0.82 tff(577,plain,
% 0.65/0.82 ((~hskp29) | c0_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[576, 574])).
% 0.65/0.82 tff(578,plain,
% 0.65/0.82 ((~hskp29) | c0_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[577, 574])).
% 0.65/0.82 tff(579,plain,
% 0.65/0.82 ((~hskp29) | c0_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[578, 574])).
% 0.65/0.82 tff(580,plain,
% 0.65/0.82 ((~hskp29) | c0_1(a552)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[579, 574])).
% 0.65/0.82 tff(581,plain,
% 0.65/0.82 (c0_1(a552)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[580, 557])).
% 0.65/0.82 tff(582,plain,
% 0.65/0.82 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(583,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[582])).
% 0.65/0.82 tff(584,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(585,plain,
% 0.65/0.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp31) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp31))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp31) <=> (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(586,plain,
% 0.65/0.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[585])).
% 0.65/0.82 tff(587,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 0.65/0.82 tff(588,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.65/0.82 tff(589,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[588, 584])).
% 0.65/0.82 tff(590,plain,(
% 0.65/0.82 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[589])).
% 0.65/0.82 tff(591,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[590, 583])).
% 0.65/0.82 tff(592,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp31 | c0_1(a566) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c2_1(a566)) | (~c3_1(a566)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp31 | c0_1(a566) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c2_1(a566)) | (~c3_1(a566)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(593,plain,
% 0.65/0.82 ((hskp31 | (~ndr1_0) | c1_1(a537) | (~c0_1(a537)) | (~c2_1(a537)) | c0_1(a566) | (~c2_1(a566)) | (~c3_1(a566))) <=> (hskp31 | c0_1(a566) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c2_1(a566)) | (~c3_1(a566)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(594,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp31 | (~ndr1_0) | c1_1(a537) | (~c0_1(a537)) | (~c2_1(a537)) | c0_1(a566) | (~c2_1(a566)) | (~c3_1(a566)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp31 | c0_1(a566) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c2_1(a566)) | (~c3_1(a566))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[593])).
% 0.65/0.82 tff(595,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp31 | (~ndr1_0) | c1_1(a537) | (~c0_1(a537)) | (~c2_1(a537)) | c0_1(a566) | (~c2_1(a566)) | (~c3_1(a566)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp31 | c0_1(a566) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c2_1(a566)) | (~c3_1(a566)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[594, 592])).
% 0.65/0.82 tff(596,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp31 | (~ndr1_0) | c1_1(a537) | (~c0_1(a537)) | (~c2_1(a537)) | c0_1(a566) | (~c2_1(a566)) | (~c3_1(a566)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(597,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp31 | c0_1(a566) | c1_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c2_1(a566)) | (~c3_1(a566))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.65/0.82 tff(598,plain,
% 0.65/0.82 (hskp31 | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c2_1(a566)) | (~c3_1(a566))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[597, 154, 515, 591])).
% 0.65/0.82 tff(599,plain,
% 0.65/0.82 (hskp31),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[598, 528, 183, 522, 521, 524])).
% 0.65/0.82 tff(600,plain,
% 0.65/0.82 (((~hskp31) | c3_1(a563)) <=> ((~hskp31) | c3_1(a563))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(601,axiom,((~hskp31) | c3_1(a563)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.65/0.82 tff(602,plain,
% 0.65/0.82 ((~hskp31) | c3_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.65/0.82 tff(603,plain,
% 0.65/0.82 ((~hskp31) | c3_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[602, 600])).
% 0.65/0.82 tff(604,plain,
% 0.65/0.82 ((~hskp31) | c3_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[603, 600])).
% 0.65/0.82 tff(605,plain,
% 0.65/0.82 ((~hskp31) | c3_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[604, 600])).
% 0.65/0.82 tff(606,plain,
% 0.65/0.82 ((~hskp31) | c3_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[605, 600])).
% 0.65/0.82 tff(607,plain,
% 0.65/0.82 (c3_1(a563)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[606, 599])).
% 0.65/0.82 tff(608,plain,
% 0.65/0.82 (((~hskp31) | c1_1(a563)) <=> ((~hskp31) | c1_1(a563))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(609,axiom,((~hskp31) | c1_1(a563)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 0.65/0.82 tff(610,plain,
% 0.65/0.82 ((~hskp31) | c1_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[609, 608])).
% 0.65/0.82 tff(611,plain,
% 0.65/0.82 ((~hskp31) | c1_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[610, 608])).
% 0.65/0.82 tff(612,plain,
% 0.65/0.82 ((~hskp31) | c1_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[611, 608])).
% 0.65/0.82 tff(613,plain,
% 0.65/0.82 ((~hskp31) | c1_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[612, 608])).
% 0.65/0.82 tff(614,plain,
% 0.65/0.82 ((~hskp31) | c1_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[613, 608])).
% 0.65/0.82 tff(615,plain,
% 0.65/0.82 (c1_1(a563)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[614, 599])).
% 0.65/0.82 tff(616,plain,
% 0.65/0.82 (((~hskp31) | c0_1(a563)) <=> ((~hskp31) | c0_1(a563))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(617,axiom,((~hskp31) | c0_1(a563)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.65/0.82 tff(618,plain,
% 0.65/0.82 ((~hskp31) | c0_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[617, 616])).
% 0.65/0.82 tff(619,plain,
% 0.65/0.82 ((~hskp31) | c0_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[618, 616])).
% 0.65/0.82 tff(620,plain,
% 0.65/0.82 ((~hskp31) | c0_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[619, 616])).
% 0.65/0.82 tff(621,plain,
% 0.65/0.82 ((~hskp31) | c0_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[620, 616])).
% 0.65/0.82 tff(622,plain,
% 0.65/0.82 ((~hskp31) | c0_1(a563)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[621, 616])).
% 0.65/0.82 tff(623,plain,
% 0.65/0.82 (c0_1(a563)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[622, 599])).
% 0.65/0.82 tff(624,plain,
% 0.65/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a580) | c3_1(a580) | (~ndr1_0) | (~c1_1(a580)) | (~c3_1(a552)) | (~c2_1(a552)) | (~c0_1(a552)) | (~c1_1(a563)) | (~c0_1(a563)) | (~c3_1(a563)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a580) | c3_1(a580) | (~ndr1_0) | (~c1_1(a580)) | (~c3_1(a552)) | (~c2_1(a552)) | (~c0_1(a552)) | (~c1_1(a563)) | (~c0_1(a563)) | (~c3_1(a563)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(625,plain,
% 0.65/0.82 (((~ndr1_0) | (~c3_1(a552)) | (~c0_1(a552)) | (~c2_1(a552)) | (~c0_1(a563)) | (~c3_1(a563)) | (~c1_1(a563)) | c3_1(a580) | c0_1(a580) | (~c1_1(a580))) <=> (c0_1(a580) | c3_1(a580) | (~ndr1_0) | (~c1_1(a580)) | (~c3_1(a552)) | (~c2_1(a552)) | (~c0_1(a552)) | (~c1_1(a563)) | (~c0_1(a563)) | (~c3_1(a563)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(626,plain,
% 0.65/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a552)) | (~c0_1(a552)) | (~c2_1(a552)) | (~c0_1(a563)) | (~c3_1(a563)) | (~c1_1(a563)) | c3_1(a580) | c0_1(a580) | (~c1_1(a580)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a580) | c3_1(a580) | (~ndr1_0) | (~c1_1(a580)) | (~c3_1(a552)) | (~c2_1(a552)) | (~c0_1(a552)) | (~c1_1(a563)) | (~c0_1(a563)) | (~c3_1(a563))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[625])).
% 0.65/0.82 tff(627,plain,
% 0.65/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a552)) | (~c0_1(a552)) | (~c2_1(a552)) | (~c0_1(a563)) | (~c3_1(a563)) | (~c1_1(a563)) | c3_1(a580) | c0_1(a580) | (~c1_1(a580)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a580) | c3_1(a580) | (~ndr1_0) | (~c1_1(a580)) | (~c3_1(a552)) | (~c2_1(a552)) | (~c0_1(a552)) | (~c1_1(a563)) | (~c0_1(a563)) | (~c3_1(a563)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[626, 624])).
% 0.65/0.82 tff(628,plain,
% 0.65/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a552)) | (~c0_1(a552)) | (~c2_1(a552)) | (~c0_1(a563)) | (~c3_1(a563)) | (~c1_1(a563)) | c3_1(a580) | c0_1(a580) | (~c1_1(a580)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(629,plain,
% 0.65/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a580) | c3_1(a580) | (~ndr1_0) | (~c1_1(a580)) | (~c3_1(a552)) | (~c2_1(a552)) | (~c0_1(a552)) | (~c1_1(a563)) | (~c0_1(a563)) | (~c3_1(a563))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[628, 627])).
% 0.65/0.82 tff(630,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[629, 183, 623, 615, 607, 581, 573, 565, 539, 514, 513, 512])).
% 0.65/0.82 tff(631,plain,(hskp21 | (~ndr1_0) | c0_1(a580) | c3_1(a580) | (~c2_1(a537)) | c0_1(a566) | c1_1(a537) | hskp13 | c3_1(a537) | (~c3_1(a546)) | c0_1(a546) | c1_1(a546) | (~c0_1(a536)) | (~c2_1(a536)) | c3_1(a536)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(632,plain,
% 0.65/0.82 (hskp21 | c0_1(a580) | c3_1(a580) | (~c2_1(a537)) | c0_1(a566) | c1_1(a537) | hskp13 | c3_1(a537) | (~c3_1(a546)) | c0_1(a546) | c1_1(a546) | (~c0_1(a536)) | (~c2_1(a536)) | c3_1(a536)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[631, 92])).
% 0.65/0.82 tff(633,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[632, 502, 496, 12, 464, 408, 456, 106, 450, 222, 214, 208, 280, 279, 278])).
% 0.65/0.82 tff(634,plain,(hskp21 | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(635,plain,
% 0.65/0.82 (hskp21),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[634, 106])).
% 0.65/0.82 tff(636,plain,
% 0.65/0.82 (~c1_1(a582)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[347, 635])).
% 0.65/0.82 tff(637,plain,
% 0.65/0.82 (c3_1(a582)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[295, 635])).
% 0.65/0.82 tff(638,plain,
% 0.65/0.82 (c2_1(a582)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[303, 635])).
% 0.65/0.82 tff(639,plain,
% 0.65/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a582) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a582) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(640,plain,
% 0.65/0.82 (((~ndr1_0) | c0_1(a566) | (~c3_1(a566)) | (~c2_1(a566)) | c1_1(a582) | c0_1(a582) | (~c3_1(a582)) | c1_1(a582) | c0_1(a582) | (~c2_1(a582))) <=> (c1_1(a582) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(641,plain,
% 0.65/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a566) | (~c3_1(a566)) | (~c2_1(a566)) | c1_1(a582) | c0_1(a582) | (~c3_1(a582)) | c1_1(a582) | c0_1(a582) | (~c2_1(a582)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a582) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[640])).
% 0.65/0.82 tff(642,plain,
% 0.65/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a566) | (~c3_1(a566)) | (~c2_1(a566)) | c1_1(a582) | c0_1(a582) | (~c3_1(a582)) | c1_1(a582) | c0_1(a582) | (~c2_1(a582)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a582) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[641, 639])).
% 0.65/0.82 tff(643,plain,
% 0.65/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a566) | (~c3_1(a566)) | (~c2_1(a566)) | c1_1(a582) | c0_1(a582) | (~c3_1(a582)) | c1_1(a582) | c0_1(a582) | (~c2_1(a582)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(644,plain,
% 0.65/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a582) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[643, 642])).
% 0.65/0.82 tff(645,plain,
% 0.65/0.82 (c0_1(a582)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[644, 92, 638, 637, 466, 465, 636, 408, 11])).
% 0.65/0.82 tff(646,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a582) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | c2_1(a546) | (~c3_1(a582)) | (~c0_1(a582)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a582) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | c2_1(a546) | (~c3_1(a582)) | (~c0_1(a582)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(647,plain,
% 0.65/0.82 ((hskp1 | (~ndr1_0) | c1_1(a582) | (~c3_1(a582)) | (~c0_1(a582)) | c2_1(a546) | c1_1(a546) | c0_1(a546)) <=> (hskp1 | c1_1(a582) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | c2_1(a546) | (~c3_1(a582)) | (~c0_1(a582)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(648,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a582) | (~c3_1(a582)) | (~c0_1(a582)) | c2_1(a546) | c1_1(a546) | c0_1(a546))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a582) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | c2_1(a546) | (~c3_1(a582)) | (~c0_1(a582))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[647])).
% 0.65/0.83 tff(649,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a582) | (~c3_1(a582)) | (~c0_1(a582)) | c2_1(a546) | c1_1(a546) | c0_1(a546))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a582) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | c2_1(a546) | (~c3_1(a582)) | (~c0_1(a582)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[648, 646])).
% 0.65/0.83 tff(650,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a582) | (~c3_1(a582)) | (~c0_1(a582)) | c2_1(a546) | c1_1(a546) | c0_1(a546))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(651,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a582) | c0_1(a546) | c1_1(a546) | (~ndr1_0) | c2_1(a546) | (~c3_1(a582)) | (~c0_1(a582))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[650, 649])).
% 0.65/0.83 tff(652,plain,
% 0.65/0.83 (hskp1),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[651, 92, 637, 636, 214, 208, 418, 229, 645])).
% 0.65/0.83 tff(653,plain,
% 0.65/0.83 (~c1_1(a537)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[455, 652])).
% 0.65/0.83 tff(654,plain,
% 0.65/0.83 (c2_1(a537)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[463, 652])).
% 0.65/0.83 tff(655,plain,
% 0.65/0.83 (c0_1(a537)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[472, 92, 466, 465, 222, 654, 408, 214, 208, 653, 11])).
% 0.65/0.83 tff(656,plain,
% 0.65/0.83 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(657,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[656])).
% 0.65/0.83 tff(658,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(659,plain,
% 0.65/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp13))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(660,plain,
% 0.65/0.83 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[659])).
% 0.65/0.83 tff(661,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 0.65/0.83 tff(662,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.65/0.83 tff(663,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[662, 658])).
% 0.65/0.83 tff(664,plain,(
% 0.65/0.83 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(skolemize,[status(sab)],[663])).
% 0.65/0.83 tff(665,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[664, 657])).
% 0.65/0.83 tff(666,plain,
% 0.65/0.83 (hskp19),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[354, 92, 638, 637, 636, 342, 645])).
% 0.65/0.83 tff(667,plain,
% 0.65/0.83 (~c3_1(a576)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[360, 666])).
% 0.65/0.83 tff(668,plain,
% 0.65/0.83 (~c1_1(a576)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[366, 666])).
% 0.65/0.83 tff(669,plain,
% 0.65/0.83 (c0_1(a576)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[382, 666])).
% 0.65/0.83 tff(670,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp31 | c1_1(a582) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c0_1(a582)) | (~c2_1(a582)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp31 | c1_1(a582) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c0_1(a582)) | (~c2_1(a582)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(671,plain,
% 0.65/0.83 ((hskp31 | (~ndr1_0) | c1_1(a582) | (~c0_1(a582)) | (~c2_1(a582)) | c0_1(a566) | (~c2_1(a566)) | (~c3_1(a566))) <=> (hskp31 | c1_1(a582) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c0_1(a582)) | (~c2_1(a582)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(672,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp31 | (~ndr1_0) | c1_1(a582) | (~c0_1(a582)) | (~c2_1(a582)) | c0_1(a566) | (~c2_1(a566)) | (~c3_1(a566)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp31 | c1_1(a582) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c0_1(a582)) | (~c2_1(a582))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[671])).
% 0.65/0.83 tff(673,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp31 | (~ndr1_0) | c1_1(a582) | (~c0_1(a582)) | (~c2_1(a582)) | c0_1(a566) | (~c2_1(a566)) | (~c3_1(a566)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp31 | c1_1(a582) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c0_1(a582)) | (~c2_1(a582)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[672, 670])).
% 0.65/0.83 tff(674,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp31 | (~ndr1_0) | c1_1(a582) | (~c0_1(a582)) | (~c2_1(a582)) | c0_1(a566) | (~c2_1(a566)) | (~c3_1(a566)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(675,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp31 | c1_1(a582) | c0_1(a566) | (~ndr1_0) | (~c2_1(a566)) | (~c3_1(a566)) | (~c0_1(a582)) | (~c2_1(a582))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.65/0.83 tff(676,plain,
% 0.65/0.83 (hskp31),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[675, 92, 638, 466, 465, 636, 408, 591, 645])).
% 0.65/0.83 tff(677,plain,
% 0.65/0.83 (c1_1(a563)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[614, 676])).
% 0.65/0.83 tff(678,plain,
% 0.65/0.83 (c0_1(a563)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[622, 676])).
% 0.65/0.83 tff(679,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a576) | c3_1(a576) | (~ndr1_0) | (~c0_1(a576)) | (~c1_1(a563)) | (~c0_1(a563)) | (~c2_1(a563)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a576) | c3_1(a576) | (~ndr1_0) | (~c0_1(a576)) | (~c1_1(a563)) | (~c0_1(a563)) | (~c2_1(a563)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(680,plain,
% 0.65/0.83 ((hskp13 | (~ndr1_0) | (~c1_1(a563)) | (~c0_1(a563)) | (~c2_1(a563)) | c1_1(a576) | c3_1(a576) | (~c0_1(a576))) <=> (hskp13 | c1_1(a576) | c3_1(a576) | (~ndr1_0) | (~c0_1(a576)) | (~c1_1(a563)) | (~c0_1(a563)) | (~c2_1(a563)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(681,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a563)) | (~c0_1(a563)) | (~c2_1(a563)) | c1_1(a576) | c3_1(a576) | (~c0_1(a576)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp13 | c1_1(a576) | c3_1(a576) | (~ndr1_0) | (~c0_1(a576)) | (~c1_1(a563)) | (~c0_1(a563)) | (~c2_1(a563))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[680])).
% 0.65/0.83 tff(682,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a563)) | (~c0_1(a563)) | (~c2_1(a563)) | c1_1(a576) | c3_1(a576) | (~c0_1(a576)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a576) | c3_1(a576) | (~ndr1_0) | (~c0_1(a576)) | (~c1_1(a563)) | (~c0_1(a563)) | (~c2_1(a563)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[681, 679])).
% 0.65/0.83 tff(683,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a563)) | (~c0_1(a563)) | (~c2_1(a563)) | c1_1(a576) | c3_1(a576) | (~c0_1(a576)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(684,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp13 | c1_1(a576) | c3_1(a576) | (~ndr1_0) | (~c0_1(a576)) | (~c1_1(a563)) | (~c0_1(a563)) | (~c2_1(a563))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.65/0.83 tff(685,plain,
% 0.65/0.83 (~c2_1(a563)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[684, 92, 106, 678, 677, 669, 668, 667, 665])).
% 0.65/0.83 tff(686,plain,
% 0.65/0.83 (~c3_1(a537)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[449, 652])).
% 0.65/0.83 tff(687,plain,
% 0.65/0.83 (c3_1(a563)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[606, 676])).
% 0.65/0.83 tff(688,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a582) | c3_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c3_1(a582)) | (~c0_1(a582)) | (~c0_1(a563)) | c2_1(a563) | (~c3_1(a563)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a582) | c3_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c3_1(a582)) | (~c0_1(a582)) | (~c0_1(a563)) | c2_1(a563) | (~c3_1(a563)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(689,plain,
% 0.65/0.83 (((~ndr1_0) | c3_1(a537) | (~c0_1(a537)) | (~c2_1(a537)) | c2_1(a563) | (~c0_1(a563)) | (~c3_1(a563)) | c1_1(a582) | (~c3_1(a582)) | (~c0_1(a582))) <=> (c1_1(a582) | c3_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c3_1(a582)) | (~c0_1(a582)) | (~c0_1(a563)) | c2_1(a563) | (~c3_1(a563)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(690,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a537) | (~c0_1(a537)) | (~c2_1(a537)) | c2_1(a563) | (~c0_1(a563)) | (~c3_1(a563)) | c1_1(a582) | (~c3_1(a582)) | (~c0_1(a582)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a582) | c3_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c3_1(a582)) | (~c0_1(a582)) | (~c0_1(a563)) | c2_1(a563) | (~c3_1(a563))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[689])).
% 0.65/0.83 tff(691,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a537) | (~c0_1(a537)) | (~c2_1(a537)) | c2_1(a563) | (~c0_1(a563)) | (~c3_1(a563)) | c1_1(a582) | (~c3_1(a582)) | (~c0_1(a582)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a582) | c3_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c3_1(a582)) | (~c0_1(a582)) | (~c0_1(a563)) | c2_1(a563) | (~c3_1(a563)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[690, 688])).
% 0.65/0.83 tff(692,plain,
% 0.65/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a537) | (~c0_1(a537)) | (~c2_1(a537)) | c2_1(a563) | (~c0_1(a563)) | (~c3_1(a563)) | c1_1(a582) | (~c3_1(a582)) | (~c0_1(a582)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(693,plain,
% 0.65/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a582) | c3_1(a537) | (~ndr1_0) | (~c2_1(a537)) | (~c0_1(a537)) | (~c3_1(a582)) | (~c0_1(a582)) | (~c0_1(a563)) | c2_1(a563) | (~c3_1(a563))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[692, 691])).
% 0.65/0.83 tff(694,plain,
% 0.65/0.83 ($false),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[693, 92, 678, 687, 637, 654, 636, 686, 22, 645, 685, 655])).
% 0.65/0.83 tff(695,plain,(hskp13), inference(lemma,lemma(discharge,[]))).
% 0.65/0.83 tff(696,plain,
% 0.65/0.83 (((~hskp13) | (~c2_1(a565))) <=> ((~hskp13) | (~c2_1(a565)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(697,plain,
% 0.65/0.83 (((~c2_1(a565)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a565)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(698,axiom,((~c2_1(a565)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.65/0.83 tff(699,plain,
% 0.65/0.83 ((~hskp13) | (~c2_1(a565))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[698, 697])).
% 0.65/0.83 tff(700,plain,
% 0.65/0.83 ((~hskp13) | (~c2_1(a565))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[699, 696])).
% 0.65/0.83 tff(701,plain,
% 0.65/0.83 (~c2_1(a565)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[700, 695])).
% 0.65/0.83 tff(702,plain,
% 0.65/0.83 (c3_1(a564)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[428, 99])).
% 0.65/0.83 tff(703,plain,
% 0.65/0.83 (c0_1(a564)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[436, 99])).
% 0.65/0.83 tff(704,plain,
% 0.65/0.83 (((~hskp13) | c3_1(a565)) <=> ((~hskp13) | c3_1(a565))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(705,axiom,((~hskp13) | c3_1(a565)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.65/0.83 tff(706,plain,
% 0.65/0.83 ((~hskp13) | c3_1(a565)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.65/0.83 tff(707,plain,
% 0.65/0.83 ((~hskp13) | c3_1(a565)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[706, 704])).
% 0.65/0.83 tff(708,plain,
% 0.65/0.83 ((~hskp13) | c3_1(a565)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[707, 704])).
% 0.65/0.83 tff(709,plain,
% 0.65/0.83 ((~hskp13) | c3_1(a565)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[708, 704])).
% 0.65/0.83 tff(710,plain,
% 0.65/0.83 ((~hskp13) | c3_1(a565)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[709, 704])).
% 0.65/0.83 tff(711,plain,
% 0.65/0.83 (c3_1(a565)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[710, 695])).
% 0.65/0.83 tff(712,plain,
% 0.65/0.83 (((~hskp13) | c0_1(a565)) <=> ((~hskp13) | c0_1(a565))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(713,axiom,((~hskp13) | c0_1(a565)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.65/0.83 tff(714,plain,
% 0.65/0.83 ((~hskp13) | c0_1(a565)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[713, 712])).
% 0.65/0.83 tff(715,plain,
% 0.65/0.83 ((~hskp13) | c0_1(a565)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[714, 712])).
% 0.65/0.83 tff(716,plain,
% 0.65/0.83 ((~hskp13) | c0_1(a565)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[715, 712])).
% 0.65/0.83 tff(717,plain,
% 0.65/0.83 ((~hskp13) | c0_1(a565)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[716, 712])).
% 0.65/0.83 tff(718,plain,
% 0.65/0.83 ((~hskp13) | c0_1(a565)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[717, 712])).
% 0.65/0.83 tff(719,plain,
% 0.65/0.83 (c0_1(a565)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[718, 695])).
% 0.65/0.83 tff(720,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c2_1(a565) | c1_1(a564) | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c3_1(a564)) | (~c0_1(a564)) | (~c0_1(a565)) | (~c3_1(a565)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a565) | c1_1(a564) | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c3_1(a564)) | (~c0_1(a564)) | (~c0_1(a565)) | (~c3_1(a565)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(721,plain,
% 0.65/0.83 (((~ndr1_0) | c3_1(a536) | (~c0_1(a536)) | (~c2_1(a536)) | c2_1(a565) | (~c0_1(a565)) | (~c3_1(a565)) | c1_1(a564) | (~c3_1(a564)) | (~c0_1(a564))) <=> (c2_1(a565) | c1_1(a564) | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c3_1(a564)) | (~c0_1(a564)) | (~c0_1(a565)) | (~c3_1(a565)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(722,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a536) | (~c0_1(a536)) | (~c2_1(a536)) | c2_1(a565) | (~c0_1(a565)) | (~c3_1(a565)) | c1_1(a564) | (~c3_1(a564)) | (~c0_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c2_1(a565) | c1_1(a564) | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c3_1(a564)) | (~c0_1(a564)) | (~c0_1(a565)) | (~c3_1(a565))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[721])).
% 0.65/0.83 tff(723,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a536) | (~c0_1(a536)) | (~c2_1(a536)) | c2_1(a565) | (~c0_1(a565)) | (~c3_1(a565)) | c1_1(a564) | (~c3_1(a564)) | (~c0_1(a564)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a565) | c1_1(a564) | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c3_1(a564)) | (~c0_1(a564)) | (~c0_1(a565)) | (~c3_1(a565)))),
% 0.68/0.83 inference(transitivity,[status(thm)],[722, 720])).
% 0.68/0.83 tff(724,plain,
% 0.68/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a536) | (~c0_1(a536)) | (~c2_1(a536)) | c2_1(a565) | (~c0_1(a565)) | (~c3_1(a565)) | c1_1(a564) | (~c3_1(a564)) | (~c0_1(a564)))),
% 0.68/0.83 inference(quant_inst,[status(thm)],[])).
% 0.68/0.83 tff(725,plain,
% 0.68/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a565) | c1_1(a564) | c3_1(a536) | (~ndr1_0) | (~c2_1(a536)) | (~c0_1(a536)) | (~c3_1(a564)) | (~c0_1(a564)) | (~c0_1(a565)) | (~c3_1(a565))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.68/0.83 tff(726,plain,
% 0.68/0.83 ($false),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[725, 92, 719, 711, 703, 702, 55, 47, 701, 105, 29, 22])).
% 0.68/0.83 tff(727,plain,((~hskp0) | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.68/0.83 tff(728,plain,
% 0.68/0.83 (~hskp0),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[727, 12])).
% 0.68/0.83 tff(729,plain,
% 0.68/0.83 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.68/0.83 inference(bind,[status(th)],[])).
% 0.68/0.83 tff(730,plain,
% 0.68/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.68/0.83 inference(quant_intro,[status(thm)],[729])).
% 0.68/0.83 tff(731,plain,
% 0.68/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.68/0.83 inference(rewrite,[status(thm)],[])).
% 0.68/0.83 tff(732,plain,
% 0.68/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.68/0.83 inference(bind,[status(th)],[])).
% 0.68/0.83 tff(733,plain,
% 0.68/0.83 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.68/0.83 inference(quant_intro,[status(thm)],[732])).
% 0.68/0.83 tff(734,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 0.68/0.83 tff(735,plain,
% 0.68/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[734, 733])).
% 0.68/0.83 tff(736,plain,
% 0.68/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[735, 731])).
% 0.68/0.83 tff(737,plain,(
% 0.68/0.83 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.68/0.83 inference(skolemize,[status(sab)],[736])).
% 0.68/0.83 tff(738,plain,
% 0.68/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[737, 730])).
% 0.68/0.83 tff(739,assumption,(~hskp0), introduced(assumption)).
% 0.68/0.83 tff(740,plain,
% 0.68/0.83 (^[U: $i] : refl((hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.68/0.83 inference(bind,[status(th)],[])).
% 0.68/0.83 tff(741,plain,
% 0.68/0.83 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.68/0.83 inference(quant_intro,[status(thm)],[740])).
% 0.68/0.83 tff(742,plain,
% 0.68/0.83 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.68/0.83 inference(rewrite,[status(thm)],[])).
% 0.68/0.83 tff(743,plain,
% 0.68/0.83 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp0) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp0))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp0) <=> (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.68/0.83 inference(bind,[status(th)],[])).
% 0.68/0.83 tff(744,plain,
% 0.68/0.83 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp0) <=> ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.68/0.83 inference(quant_intro,[status(thm)],[743])).
% 0.68/0.83 tff(745,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 0.68/0.83 tff(746,plain,
% 0.68/0.83 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[745, 744])).
% 0.68/0.83 tff(747,plain,
% 0.68/0.83 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[746, 742])).
% 0.68/0.83 tff(748,plain,(
% 0.68/0.83 ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.68/0.83 inference(skolemize,[status(sab)],[747])).
% 0.68/0.83 tff(749,plain,
% 0.68/0.83 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[748, 741])).
% 0.68/0.83 tff(750,plain,
% 0.68/0.83 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp0 | c2_1(a565) | (~ndr1_0) | (~c0_1(a565)) | (~c3_1(a565)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp0 | c2_1(a565) | (~ndr1_0) | (~c0_1(a565)) | (~c3_1(a565)))),
% 0.68/0.83 inference(rewrite,[status(thm)],[])).
% 0.68/0.83 tff(751,plain,
% 0.68/0.83 ((hskp15 | hskp0 | (~ndr1_0) | c2_1(a565) | (~c3_1(a565)) | (~c0_1(a565))) <=> (hskp15 | hskp0 | c2_1(a565) | (~ndr1_0) | (~c0_1(a565)) | (~c3_1(a565)))),
% 0.68/0.83 inference(rewrite,[status(thm)],[])).
% 0.68/0.83 tff(752,plain,
% 0.68/0.83 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp0 | (~ndr1_0) | c2_1(a565) | (~c3_1(a565)) | (~c0_1(a565)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp0 | c2_1(a565) | (~ndr1_0) | (~c0_1(a565)) | (~c3_1(a565))))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[751])).
% 0.68/0.83 tff(753,plain,
% 0.68/0.83 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp0 | (~ndr1_0) | c2_1(a565) | (~c3_1(a565)) | (~c0_1(a565)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp0 | c2_1(a565) | (~ndr1_0) | (~c0_1(a565)) | (~c3_1(a565)))),
% 0.68/0.83 inference(transitivity,[status(thm)],[752, 750])).
% 0.68/0.83 tff(754,plain,
% 0.68/0.83 ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp0 | (~ndr1_0) | c2_1(a565) | (~c3_1(a565)) | (~c0_1(a565)))),
% 0.68/0.83 inference(quant_inst,[status(thm)],[])).
% 0.68/0.83 tff(755,plain,
% 0.68/0.83 ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp0 | c2_1(a565) | (~ndr1_0) | (~c0_1(a565)) | (~c3_1(a565))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[754, 753])).
% 0.68/0.84 tff(756,plain,
% 0.68/0.84 (hskp15 | hskp0),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[755, 92, 719, 711, 701, 749])).
% 0.68/0.84 tff(757,plain,
% 0.68/0.84 (hskp15),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[756, 739])).
% 0.68/0.84 tff(758,plain,
% 0.68/0.84 (((~hskp15) | (~c2_1(a567))) <=> ((~hskp15) | (~c2_1(a567)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(759,plain,
% 0.68/0.84 (((~c2_1(a567)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a567)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(760,axiom,((~c2_1(a567)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.68/0.84 tff(761,plain,
% 0.68/0.84 ((~hskp15) | (~c2_1(a567))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[760, 759])).
% 0.68/0.84 tff(762,plain,
% 0.68/0.84 ((~hskp15) | (~c2_1(a567))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[761, 758])).
% 0.68/0.84 tff(763,plain,
% 0.68/0.84 (~c2_1(a567)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[762, 757])).
% 0.68/0.84 tff(764,plain,
% 0.68/0.84 (^[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))))),
% 0.68/0.84 inference(bind,[status(th)],[])).
% 0.68/0.84 tff(765,plain,
% 0.68/0.84 (![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)))),
% 0.68/0.84 inference(quant_intro,[status(thm)],[764])).
% 0.68/0.84 tff(766,plain,
% 0.68/0.84 (![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)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(767,plain,
% 0.68/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | 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)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | 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)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp22) <=> (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.68/0.84 inference(bind,[status(th)],[])).
% 0.68/0.84 tff(768,plain,
% 0.68/0.84 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp22) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.68/0.84 inference(quant_intro,[status(thm)],[767])).
% 0.68/0.84 tff(769,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 0.68/0.84 tff(770,plain,
% 0.68/0.84 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[769, 768])).
% 0.68/0.84 tff(771,plain,
% 0.68/0.84 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[770, 766])).
% 0.68/0.84 tff(772,plain,(
% 0.68/0.84 ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.68/0.84 inference(skolemize,[status(sab)],[771])).
% 0.68/0.84 tff(773,plain,
% 0.68/0.84 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[772, 765])).
% 0.68/0.84 tff(774,plain,
% 0.68/0.84 (((~hskp15) | c1_1(a567)) <=> ((~hskp15) | c1_1(a567))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(775,axiom,((~hskp15) | c1_1(a567)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.68/0.84 tff(776,plain,
% 0.68/0.84 ((~hskp15) | c1_1(a567)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.68/0.84 tff(777,plain,
% 0.68/0.84 ((~hskp15) | c1_1(a567)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[776, 774])).
% 0.68/0.84 tff(778,plain,
% 0.68/0.84 ((~hskp15) | c1_1(a567)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[777, 774])).
% 0.68/0.84 tff(779,plain,
% 0.68/0.84 ((~hskp15) | c1_1(a567)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[778, 774])).
% 0.68/0.84 tff(780,plain,
% 0.68/0.84 ((~hskp15) | c1_1(a567)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[779, 774])).
% 0.68/0.84 tff(781,plain,
% 0.68/0.84 (c1_1(a567)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[780, 757])).
% 0.68/0.84 tff(782,assumption,(~hskp3), introduced(assumption)).
% 0.68/0.84 tff(783,plain,
% 0.68/0.84 (^[U: $i] : refl((hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.68/0.84 inference(bind,[status(th)],[])).
% 0.68/0.84 tff(784,plain,
% 0.68/0.84 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.84 inference(quant_intro,[status(thm)],[783])).
% 0.68/0.84 tff(785,plain,
% 0.68/0.84 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(786,plain,
% 0.68/0.84 (^[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)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp6) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp6))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp6) <=> (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.68/0.84 inference(bind,[status(th)],[])).
% 0.68/0.84 tff(787,plain,
% 0.68/0.84 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp6) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.84 inference(quant_intro,[status(thm)],[786])).
% 0.68/0.84 tff(788,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 0.68/0.84 tff(789,plain,
% 0.68/0.84 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[788, 787])).
% 0.68/0.84 tff(790,plain,
% 0.68/0.84 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[789, 785])).
% 0.68/0.84 tff(791,plain,(
% 0.68/0.84 ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.84 inference(skolemize,[status(sab)],[790])).
% 0.68/0.84 tff(792,plain,
% 0.68/0.84 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[791, 784])).
% 0.68/0.84 tff(793,assumption,(~c2_1(a567)), introduced(assumption)).
% 0.68/0.84 tff(794,assumption,(c1_1(a567)), introduced(assumption)).
% 0.68/0.84 tff(795,plain,
% 0.68/0.84 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | c2_1(a567) | (~ndr1_0) | (~c3_1(a567)) | (~c1_1(a567)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c2_1(a567) | (~ndr1_0) | (~c3_1(a567)) | (~c1_1(a567)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(796,plain,
% 0.68/0.84 ((hskp6 | hskp3 | (~ndr1_0) | c2_1(a567) | (~c3_1(a567)) | (~c1_1(a567))) <=> (hskp6 | hskp3 | c2_1(a567) | (~ndr1_0) | (~c3_1(a567)) | (~c1_1(a567)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(797,plain,
% 0.68/0.84 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c2_1(a567) | (~c3_1(a567)) | (~c1_1(a567)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | c2_1(a567) | (~ndr1_0) | (~c3_1(a567)) | (~c1_1(a567))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[796])).
% 0.68/0.84 tff(798,plain,
% 0.68/0.84 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c2_1(a567) | (~c3_1(a567)) | (~c1_1(a567)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c2_1(a567) | (~ndr1_0) | (~c3_1(a567)) | (~c1_1(a567)))),
% 0.68/0.84 inference(transitivity,[status(thm)],[797, 795])).
% 0.68/0.84 tff(799,plain,
% 0.68/0.84 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c2_1(a567) | (~c3_1(a567)) | (~c1_1(a567)))),
% 0.68/0.84 inference(quant_inst,[status(thm)],[])).
% 0.68/0.84 tff(800,plain,
% 0.68/0.84 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c2_1(a567) | (~ndr1_0) | (~c3_1(a567)) | (~c1_1(a567))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.68/0.84 tff(801,plain,
% 0.68/0.84 (hskp3 | (~c3_1(a567))),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[800, 92, 107, 794, 793, 792])).
% 0.68/0.84 tff(802,plain,
% 0.68/0.84 (~c3_1(a567)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[801, 782])).
% 0.68/0.84 tff(803,plain,
% 0.68/0.84 (^[U: $i] : refl((hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))),
% 0.68/0.84 inference(bind,[status(th)],[])).
% 0.68/0.84 tff(804,plain,
% 0.68/0.84 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.68/0.84 inference(quant_intro,[status(thm)],[803])).
% 0.68/0.84 tff(805,plain,
% 0.68/0.84 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(806,plain,
% 0.68/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp6) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp6))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp6) <=> (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp6) <=> (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))))),
% 0.68/0.84 inference(bind,[status(th)],[])).
% 0.68/0.84 tff(807,plain,
% 0.68/0.84 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp6) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.68/0.84 inference(quant_intro,[status(thm)],[806])).
% 0.68/0.84 tff(808,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 0.68/0.84 tff(809,plain,
% 0.68/0.84 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[808, 807])).
% 0.68/0.84 tff(810,plain,
% 0.68/0.84 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[809, 805])).
% 0.68/0.84 tff(811,plain,(
% 0.68/0.84 ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.68/0.84 inference(skolemize,[status(sab)],[810])).
% 0.68/0.84 tff(812,plain,
% 0.68/0.84 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[811, 804])).
% 0.68/0.84 tff(813,plain,
% 0.68/0.84 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp3 | c2_1(a567) | (~ndr1_0) | c3_1(a567) | (~c1_1(a567)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp3 | c2_1(a567) | (~ndr1_0) | c3_1(a567) | (~c1_1(a567)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(814,plain,
% 0.68/0.84 ((hskp6 | hskp3 | (~ndr1_0) | c3_1(a567) | c2_1(a567) | (~c1_1(a567))) <=> (hskp6 | hskp3 | c2_1(a567) | (~ndr1_0) | c3_1(a567) | (~c1_1(a567)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(815,plain,
% 0.68/0.84 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a567) | c2_1(a567) | (~c1_1(a567)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp3 | c2_1(a567) | (~ndr1_0) | c3_1(a567) | (~c1_1(a567))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[814])).
% 0.68/0.84 tff(816,plain,
% 0.68/0.84 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a567) | c2_1(a567) | (~c1_1(a567)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp3 | c2_1(a567) | (~ndr1_0) | c3_1(a567) | (~c1_1(a567)))),
% 0.68/0.84 inference(transitivity,[status(thm)],[815, 813])).
% 0.68/0.84 tff(817,plain,
% 0.68/0.84 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a567) | c2_1(a567) | (~c1_1(a567)))),
% 0.68/0.84 inference(quant_inst,[status(thm)],[])).
% 0.68/0.84 tff(818,plain,
% 0.68/0.84 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp3 | c2_1(a567) | (~ndr1_0) | c3_1(a567) | (~c1_1(a567))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[817, 816])).
% 0.68/0.84 tff(819,plain,
% 0.68/0.84 (hskp3 | c3_1(a567)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[818, 92, 107, 794, 793, 812])).
% 0.68/0.84 tff(820,plain,
% 0.68/0.84 ($false),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[819, 802, 782])).
% 0.68/0.84 tff(821,plain,(hskp3 | hskp6 | (~c1_1(a567)) | c2_1(a567)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.84 tff(822,plain,
% 0.68/0.84 (hskp3),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[821, 781, 107, 763])).
% 0.68/0.84 tff(823,plain,
% 0.68/0.84 (((~hskp3) | (~c3_1(a539))) <=> ((~hskp3) | (~c3_1(a539)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(824,plain,
% 0.68/0.84 (((~c3_1(a539)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a539)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(825,axiom,((~c3_1(a539)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 0.68/0.84 tff(826,plain,
% 0.68/0.84 ((~hskp3) | (~c3_1(a539))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[825, 824])).
% 0.68/0.84 tff(827,plain,
% 0.68/0.84 ((~hskp3) | (~c3_1(a539))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[826, 823])).
% 0.68/0.84 tff(828,plain,
% 0.68/0.84 (~c3_1(a539)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[827, 822])).
% 0.68/0.84 tff(829,plain,
% 0.68/0.84 (((~hskp3) | (~c2_1(a539))) <=> ((~hskp3) | (~c2_1(a539)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(830,plain,
% 0.68/0.84 (((~c2_1(a539)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a539)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(831,axiom,((~c2_1(a539)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 0.68/0.84 tff(832,plain,
% 0.68/0.84 ((~hskp3) | (~c2_1(a539))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[831, 830])).
% 0.68/0.84 tff(833,plain,
% 0.68/0.84 ((~hskp3) | (~c2_1(a539))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[832, 829])).
% 0.68/0.84 tff(834,plain,
% 0.68/0.84 (~c2_1(a539)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[833, 822])).
% 0.68/0.84 tff(835,plain,
% 0.68/0.84 (((~hskp3) | c0_1(a539)) <=> ((~hskp3) | c0_1(a539))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(836,axiom,((~hskp3) | c0_1(a539)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.68/0.84 tff(837,plain,
% 0.68/0.84 ((~hskp3) | c0_1(a539)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.68/0.84 tff(838,plain,
% 0.68/0.84 ((~hskp3) | c0_1(a539)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[837, 835])).
% 0.68/0.84 tff(839,plain,
% 0.68/0.84 ((~hskp3) | c0_1(a539)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[838, 835])).
% 0.68/0.84 tff(840,plain,
% 0.68/0.84 ((~hskp3) | c0_1(a539)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[839, 835])).
% 0.68/0.84 tff(841,plain,
% 0.68/0.84 ((~hskp3) | c0_1(a539)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[840, 835])).
% 0.68/0.84 tff(842,plain,
% 0.68/0.84 (c0_1(a539)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[841, 822])).
% 0.68/0.84 tff(843,plain,
% 0.68/0.84 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | c2_1(a539) | c3_1(a539) | (~ndr1_0) | (~c0_1(a539)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c2_1(a539) | c3_1(a539) | (~ndr1_0) | (~c0_1(a539)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(844,plain,
% 0.68/0.84 ((hskp22 | hskp21 | (~ndr1_0) | c3_1(a539) | c2_1(a539) | (~c0_1(a539))) <=> (hskp22 | hskp21 | c2_1(a539) | c3_1(a539) | (~ndr1_0) | (~c0_1(a539)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(845,plain,
% 0.68/0.84 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a539) | c2_1(a539) | (~c0_1(a539)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | c2_1(a539) | c3_1(a539) | (~ndr1_0) | (~c0_1(a539))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[844])).
% 0.68/0.84 tff(846,plain,
% 0.68/0.84 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a539) | c2_1(a539) | (~c0_1(a539)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c2_1(a539) | c3_1(a539) | (~ndr1_0) | (~c0_1(a539)))),
% 0.68/0.84 inference(transitivity,[status(thm)],[845, 843])).
% 0.68/0.84 tff(847,plain,
% 0.68/0.84 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a539) | c2_1(a539) | (~c0_1(a539)))),
% 0.68/0.84 inference(quant_inst,[status(thm)],[])).
% 0.68/0.84 tff(848,plain,
% 0.68/0.84 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c2_1(a539) | c3_1(a539) | (~ndr1_0) | (~c0_1(a539))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[847, 846])).
% 0.68/0.84 tff(849,plain,
% 0.68/0.84 (hskp22),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[848, 92, 12, 842, 834, 828, 773])).
% 0.68/0.84 tff(850,plain,
% 0.68/0.84 (((~hskp22) | (~c0_1(a584))) <=> ((~hskp22) | (~c0_1(a584)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(851,plain,
% 0.68/0.84 (((~c0_1(a584)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a584)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(852,axiom,((~c0_1(a584)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.68/0.84 tff(853,plain,
% 0.68/0.84 ((~hskp22) | (~c0_1(a584))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.68/0.84 tff(854,plain,
% 0.68/0.84 ((~hskp22) | (~c0_1(a584))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[853, 850])).
% 0.68/0.84 tff(855,plain,
% 0.68/0.84 (~c0_1(a584)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[854, 849])).
% 0.68/0.84 tff(856,plain,
% 0.68/0.84 (((~hskp15) | c0_1(a567)) <=> ((~hskp15) | c0_1(a567))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(857,axiom,((~hskp15) | c0_1(a567)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.68/0.84 tff(858,plain,
% 0.68/0.84 ((~hskp15) | c0_1(a567)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[857, 856])).
% 0.68/0.84 tff(859,plain,
% 0.68/0.84 ((~hskp15) | c0_1(a567)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[858, 856])).
% 0.68/0.84 tff(860,plain,
% 0.68/0.84 ((~hskp15) | c0_1(a567)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[859, 856])).
% 0.68/0.84 tff(861,plain,
% 0.68/0.84 ((~hskp15) | c0_1(a567)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[860, 856])).
% 0.68/0.84 tff(862,plain,
% 0.68/0.84 ((~hskp15) | c0_1(a567)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[861, 856])).
% 0.68/0.84 tff(863,plain,
% 0.68/0.84 (c0_1(a567)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[862, 757])).
% 0.68/0.84 tff(864,plain,
% 0.68/0.84 (((~hskp22) | c3_1(a584)) <=> ((~hskp22) | c3_1(a584))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(865,axiom,((~hskp22) | c3_1(a584)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 0.68/0.84 tff(866,plain,
% 0.68/0.84 ((~hskp22) | c3_1(a584)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[865, 864])).
% 0.68/0.84 tff(867,plain,
% 0.68/0.84 ((~hskp22) | c3_1(a584)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[866, 864])).
% 0.68/0.84 tff(868,plain,
% 0.68/0.84 ((~hskp22) | c3_1(a584)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[867, 864])).
% 0.68/0.84 tff(869,plain,
% 0.68/0.84 ((~hskp22) | c3_1(a584)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[868, 864])).
% 0.68/0.84 tff(870,plain,
% 0.68/0.84 ((~hskp22) | c3_1(a584)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[869, 864])).
% 0.68/0.84 tff(871,plain,
% 0.68/0.84 (c3_1(a584)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[870, 849])).
% 0.68/0.84 tff(872,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp6 | c0_1(a584) | c2_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c1_1(a567)) | (~c3_1(a584)) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp6 | c0_1(a584) | c2_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c1_1(a567)) | (~c3_1(a584)) | (~c1_1(a584)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(873,plain,
% 0.68/0.84 ((hskp6 | (~ndr1_0) | c2_1(a567) | (~c1_1(a567)) | (~c0_1(a567)) | c0_1(a584) | (~c3_1(a584)) | (~c1_1(a584))) <=> (hskp6 | c0_1(a584) | c2_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c1_1(a567)) | (~c3_1(a584)) | (~c1_1(a584)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(874,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a567) | (~c1_1(a567)) | (~c0_1(a567)) | c0_1(a584) | (~c3_1(a584)) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp6 | c0_1(a584) | c2_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c1_1(a567)) | (~c3_1(a584)) | (~c1_1(a584))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[873])).
% 0.68/0.84 tff(875,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a567) | (~c1_1(a567)) | (~c0_1(a567)) | c0_1(a584) | (~c3_1(a584)) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp6 | c0_1(a584) | c2_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c1_1(a567)) | (~c3_1(a584)) | (~c1_1(a584)))),
% 0.68/0.84 inference(transitivity,[status(thm)],[874, 872])).
% 0.68/0.84 tff(876,plain,
% 0.68/0.84 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a567) | (~c1_1(a567)) | (~c0_1(a567)) | c0_1(a584) | (~c3_1(a584)) | (~c1_1(a584)))),
% 0.68/0.84 inference(quant_inst,[status(thm)],[])).
% 0.68/0.84 tff(877,plain,
% 0.68/0.84 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp6 | c0_1(a584) | c2_1(a567) | (~ndr1_0) | (~c0_1(a567)) | (~c1_1(a567)) | (~c3_1(a584)) | (~c1_1(a584))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[876, 875])).
% 0.68/0.84 tff(878,plain,
% 0.68/0.84 (~c1_1(a584)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[877, 92, 107, 871, 863, 781, 855, 763, 738])).
% 0.68/0.84 tff(879,plain,
% 0.68/0.84 (((~hskp22) | (~c2_1(a584))) <=> ((~hskp22) | (~c2_1(a584)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(880,plain,
% 0.68/0.84 (((~c2_1(a584)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a584)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(881,axiom,((~c2_1(a584)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.68/0.84 tff(882,plain,
% 0.68/0.84 ((~hskp22) | (~c2_1(a584))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[881, 880])).
% 0.68/0.84 tff(883,plain,
% 0.68/0.84 ((~hskp22) | (~c2_1(a584))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[882, 879])).
% 0.68/0.84 tff(884,plain,
% 0.68/0.84 (~c2_1(a584)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[883, 849])).
% 0.68/0.84 tff(885,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | c1_1(a584))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | c1_1(a584))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(886,plain,
% 0.68/0.84 ((hskp0 | (~ndr1_0) | c1_1(a584) | c0_1(a584) | (~c3_1(a584)) | c2_1(a584) | c1_1(a584) | c0_1(a584)) <=> (hskp0 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | c1_1(a584))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(887,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a584) | c0_1(a584) | (~c3_1(a584)) | c2_1(a584) | c1_1(a584) | c0_1(a584))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | c1_1(a584)))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[886])).
% 0.68/0.84 tff(888,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a584) | c0_1(a584) | (~c3_1(a584)) | c2_1(a584) | c1_1(a584) | c0_1(a584))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | c1_1(a584))),
% 0.68/0.84 inference(transitivity,[status(thm)],[887, 885])).
% 0.68/0.84 tff(889,plain,
% 0.68/0.84 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a584) | c0_1(a584) | (~c3_1(a584)) | c2_1(a584) | c1_1(a584) | c0_1(a584))),
% 0.68/0.84 inference(quant_inst,[status(thm)],[])).
% 0.68/0.84 tff(890,plain,
% 0.68/0.84 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | c1_1(a584)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[889, 888])).
% 0.68/0.84 tff(891,plain,
% 0.68/0.84 ($false),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[890, 92, 739, 871, 855, 884, 270, 878])).
% 0.68/0.84 tff(892,plain,(hskp0 | hskp6 | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.68/0.84 tff(893,plain,
% 0.68/0.84 (hskp6),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[892, 728, 12])).
% 0.68/0.84 tff(894,plain,
% 0.68/0.84 (~c1_1(a546)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[207, 893])).
% 0.68/0.84 tff(895,plain,
% 0.68/0.84 (~c0_1(a546)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[213, 893])).
% 0.68/0.84 tff(896,plain,
% 0.68/0.84 (c3_1(a546)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[221, 893])).
% 0.68/0.84 tff(897,plain,
% 0.68/0.84 (~c2_1(a546)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[228, 92, 896, 895, 894, 11])).
% 0.68/0.84 tff(898,plain,
% 0.68/0.84 ($false),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[276, 92, 728, 896, 895, 894, 270, 897])).
% 0.68/0.84 tff(899,plain,(hskp21), inference(lemma,lemma(discharge,[]))).
% 0.68/0.84 tff(900,plain,
% 0.68/0.84 (~c1_1(a582)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[347, 899])).
% 0.68/0.84 tff(901,plain,
% 0.68/0.84 (c3_1(a582)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[295, 899])).
% 0.68/0.84 tff(902,plain,
% 0.68/0.84 (c2_1(a582)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[303, 899])).
% 0.68/0.84 tff(903,plain,
% 0.68/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a582) | (~ndr1_0) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a582) | (~ndr1_0) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(904,plain,
% 0.68/0.84 (((~ndr1_0) | c0_1(a582) | (~c3_1(a582)) | (~c2_1(a582)) | c1_1(a582) | c0_1(a582) | (~c3_1(a582)) | c1_1(a582) | c0_1(a582) | (~c2_1(a582))) <=> (c1_1(a582) | (~ndr1_0) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(905,plain,
% 0.68/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a582) | (~c3_1(a582)) | (~c2_1(a582)) | c1_1(a582) | c0_1(a582) | (~c3_1(a582)) | c1_1(a582) | c0_1(a582) | (~c2_1(a582)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a582) | (~ndr1_0) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[904])).
% 0.68/0.84 tff(906,plain,
% 0.68/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a582) | (~c3_1(a582)) | (~c2_1(a582)) | c1_1(a582) | c0_1(a582) | (~c3_1(a582)) | c1_1(a582) | c0_1(a582) | (~c2_1(a582)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a582) | (~ndr1_0) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582)))),
% 0.68/0.85 inference(transitivity,[status(thm)],[905, 903])).
% 0.68/0.85 tff(907,plain,
% 0.68/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a582) | (~c3_1(a582)) | (~c2_1(a582)) | c1_1(a582) | c0_1(a582) | (~c3_1(a582)) | c1_1(a582) | c0_1(a582) | (~c2_1(a582)))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(908,plain,
% 0.68/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a582) | (~ndr1_0) | (~c3_1(a582)) | c0_1(a582) | (~c2_1(a582))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[907, 906])).
% 0.68/0.85 tff(909,plain,
% 0.68/0.85 ($false),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[908, 92, 902, 901, 900, 11, 1])).
% 0.68/0.85 tff(910,plain,(c0_1(a582)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.85 tff(911,plain,
% 0.68/0.85 (hskp19 | (~c0_1(a582))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[354, 92, 902, 901, 900, 342])).
% 0.68/0.85 tff(912,plain,
% 0.68/0.85 (hskp19),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[911, 910])).
% 0.68/0.85 tff(913,plain,
% 0.68/0.85 (~c3_1(a576)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[360, 912])).
% 0.68/0.85 tff(914,plain,
% 0.68/0.85 (c0_1(a576)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[382, 912])).
% 0.68/0.85 tff(915,plain,
% 0.68/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a582) | c3_1(a576) | c2_1(a565) | (~ndr1_0) | (~c0_1(a565)) | (~c3_1(a565)) | (~c0_1(a576)) | (~c2_1(a576)) | (~c3_1(a582)) | (~c0_1(a582)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a582) | c3_1(a576) | c2_1(a565) | (~ndr1_0) | (~c0_1(a565)) | (~c3_1(a565)) | (~c0_1(a576)) | (~c2_1(a576)) | (~c3_1(a582)) | (~c0_1(a582)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(916,plain,
% 0.68/0.85 (((~ndr1_0) | c3_1(a576) | (~c0_1(a576)) | (~c2_1(a576)) | c2_1(a565) | (~c0_1(a565)) | (~c3_1(a565)) | c1_1(a582) | (~c3_1(a582)) | (~c0_1(a582))) <=> (c1_1(a582) | c3_1(a576) | c2_1(a565) | (~ndr1_0) | (~c0_1(a565)) | (~c3_1(a565)) | (~c0_1(a576)) | (~c2_1(a576)) | (~c3_1(a582)) | (~c0_1(a582)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(917,plain,
% 0.68/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a576) | (~c0_1(a576)) | (~c2_1(a576)) | c2_1(a565) | (~c0_1(a565)) | (~c3_1(a565)) | c1_1(a582) | (~c3_1(a582)) | (~c0_1(a582)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a582) | c3_1(a576) | c2_1(a565) | (~ndr1_0) | (~c0_1(a565)) | (~c3_1(a565)) | (~c0_1(a576)) | (~c2_1(a576)) | (~c3_1(a582)) | (~c0_1(a582))))),
% 0.68/0.85 inference(monotonicity,[status(thm)],[916])).
% 0.68/0.85 tff(918,plain,
% 0.68/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a576) | (~c0_1(a576)) | (~c2_1(a576)) | c2_1(a565) | (~c0_1(a565)) | (~c3_1(a565)) | c1_1(a582) | (~c3_1(a582)) | (~c0_1(a582)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a582) | c3_1(a576) | c2_1(a565) | (~ndr1_0) | (~c0_1(a565)) | (~c3_1(a565)) | (~c0_1(a576)) | (~c2_1(a576)) | (~c3_1(a582)) | (~c0_1(a582)))),
% 0.68/0.85 inference(transitivity,[status(thm)],[917, 915])).
% 0.68/0.85 tff(919,plain,
% 0.68/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a576) | (~c0_1(a576)) | (~c2_1(a576)) | c2_1(a565) | (~c0_1(a565)) | (~c3_1(a565)) | c1_1(a582) | (~c3_1(a582)) | (~c0_1(a582)))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(920,plain,
% 0.68/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a582) | c3_1(a576) | c2_1(a565) | (~ndr1_0) | (~c0_1(a565)) | (~c3_1(a565)) | (~c0_1(a576)) | (~c2_1(a576)) | (~c3_1(a582)) | (~c0_1(a582))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[919, 918])).
% 0.68/0.85 tff(921,plain,
% 0.68/0.85 (~c2_1(a576)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[920, 92, 901, 914, 719, 711, 900, 913, 701, 22, 910])).
% 0.68/0.85 tff(922,plain,
% 0.68/0.85 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(923,plain,
% 0.68/0.85 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[922])).
% 0.68/0.85 tff(924,plain,
% 0.68/0.85 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(925,plain,
% 0.68/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(926,plain,
% 0.68/0.85 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[925])).
% 0.68/0.85 tff(927,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 0.68/0.85 tff(928,plain,
% 0.68/0.85 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[927, 926])).
% 0.68/0.85 tff(929,plain,
% 0.68/0.85 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[928, 924])).
% 0.68/0.85 tff(930,plain,(
% 0.68/0.85 ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.68/0.85 inference(skolemize,[status(sab)],[929])).
% 0.68/0.85 tff(931,plain,
% 0.68/0.85 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[930, 923])).
% 0.68/0.85 tff(932,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (c3_1(a576) | (~ndr1_0) | (~c0_1(a576)) | c2_1(a576) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | c3_1(a576) | (~ndr1_0) | (~c0_1(a576)) | c2_1(a576) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(933,plain,
% 0.68/0.85 (((~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)) | c2_1(a576) | c3_1(a576) | (~c0_1(a576))) <=> (c3_1(a576) | (~ndr1_0) | (~c0_1(a576)) | c2_1(a576) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(934,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)) | c2_1(a576) | c3_1(a576) | (~c0_1(a576)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (c3_1(a576) | (~ndr1_0) | (~c0_1(a576)) | c2_1(a576) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582))))),
% 0.68/0.85 inference(monotonicity,[status(thm)],[933])).
% 0.68/0.85 tff(935,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)) | c2_1(a576) | c3_1(a576) | (~c0_1(a576)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | c3_1(a576) | (~ndr1_0) | (~c0_1(a576)) | c2_1(a576) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)))),
% 0.68/0.85 inference(transitivity,[status(thm)],[934, 932])).
% 0.68/0.85 tff(936,plain,
% 0.68/0.85 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582)) | c2_1(a576) | c3_1(a576) | (~c0_1(a576)))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(937,plain,
% 0.68/0.85 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | c3_1(a576) | (~ndr1_0) | (~c0_1(a576)) | c2_1(a576) | (~c3_1(a582)) | (~c0_1(a582)) | (~c2_1(a582))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[936, 935])).
% 0.68/0.85 tff(938,plain,
% 0.68/0.85 ($false),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[937, 92, 902, 901, 914, 913, 931, 910, 921])).
% 0.68/0.85 % SZS output end Proof
% 0.68/0.85 % E exiting
%------------------------------------------------------------------------------