%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN512-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:39:25 AM UTC 2025
% Result : Unsatisfiable 0.62s 0.81s
% Output : Proof 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN512-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:37:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.62/0.81 % SZS status Unsatisfiable
% 0.62/0.81 % SZS output start Proof
% 0.62/0.81 tff(c1_1_type, type, (
% 0.62/0.81 c1_1: $i > $o)).
% 0.62/0.81 tff(a833_type, type, (
% 0.62/0.81 a833: $i)).
% 0.62/0.81 tff(c0_1_type, type, (
% 0.62/0.81 c0_1: $i > $o)).
% 0.62/0.81 tff(hskp5_type, type, (
% 0.62/0.81 hskp5: $o)).
% 0.62/0.81 tff(hskp4_type, type, (
% 0.62/0.81 hskp4: $o)).
% 0.62/0.81 tff(c2_1_type, type, (
% 0.62/0.81 c2_1: $i > $o)).
% 0.62/0.81 tff(c3_1_type, type, (
% 0.62/0.81 c3_1: $i > $o)).
% 0.62/0.81 tff(ndr1_0_type, type, (
% 0.62/0.81 ndr1_0: $o)).
% 0.62/0.81 tff(hskp17_type, type, (
% 0.62/0.81 hskp17: $o)).
% 0.62/0.81 tff(a830_type, type, (
% 0.62/0.81 a830: $i)).
% 0.62/0.81 tff(hskp2_type, type, (
% 0.62/0.81 hskp2: $o)).
% 0.62/0.81 tff(a859_type, type, (
% 0.62/0.81 a859: $i)).
% 0.62/0.81 tff(a844_type, type, (
% 0.62/0.81 a844: $i)).
% 0.62/0.81 tff(hskp11_type, type, (
% 0.62/0.81 hskp11: $o)).
% 0.62/0.81 tff(a832_type, type, (
% 0.62/0.81 a832: $i)).
% 0.62/0.81 tff(a884_type, type, (
% 0.62/0.81 a884: $i)).
% 0.62/0.81 tff(hskp31_type, type, (
% 0.62/0.81 hskp31: $o)).
% 0.62/0.81 tff(a846_type, type, (
% 0.62/0.81 a846: $i)).
% 0.62/0.81 tff(hskp13_type, type, (
% 0.62/0.81 hskp13: $o)).
% 0.62/0.81 tff(a841_type, type, (
% 0.62/0.81 a841: $i)).
% 0.62/0.81 tff(a863_type, type, (
% 0.62/0.81 a863: $i)).
% 0.62/0.81 tff(a858_type, type, (
% 0.62/0.81 a858: $i)).
% 0.62/0.81 tff(hskp16_type, type, (
% 0.62/0.81 hskp16: $o)).
% 0.62/0.81 tff(hskp3_type, type, (
% 0.62/0.81 hskp3: $o)).
% 0.62/0.81 tff(a835_type, type, (
% 0.62/0.81 a835: $i)).
% 0.62/0.81 tff(hskp8_type, type, (
% 0.62/0.81 hskp8: $o)).
% 0.62/0.81 tff(hskp6_type, type, (
% 0.62/0.81 hskp6: $o)).
% 0.62/0.81 tff(a851_type, type, (
% 0.62/0.81 a851: $i)).
% 0.62/0.81 tff(hskp14_type, type, (
% 0.62/0.81 hskp14: $o)).
% 0.62/0.81 tff(a831_type, type, (
% 0.62/0.81 a831: $i)).
% 0.62/0.81 tff(a875_type, type, (
% 0.62/0.81 a875: $i)).
% 0.62/0.81 tff(hskp19_type, type, (
% 0.62/0.81 hskp19: $o)).
% 0.62/0.81 tff(a838_type, type, (
% 0.62/0.81 a838: $i)).
% 0.62/0.81 tff(hskp24_type, type, (
% 0.62/0.81 hskp24: $o)).
% 0.62/0.81 tff(a828_type, type, (
% 0.62/0.81 a828: $i)).
% 0.62/0.81 tff(hskp0_type, type, (
% 0.62/0.81 hskp0: $o)).
% 0.62/0.81 tff(a857_type, type, (
% 0.62/0.81 a857: $i)).
% 0.62/0.81 tff(hskp30_type, type, (
% 0.62/0.81 hskp30: $o)).
% 0.62/0.81 tff(a861_type, type, (
% 0.62/0.81 a861: $i)).
% 0.62/0.81 tff(hskp18_type, type, (
% 0.62/0.81 hskp18: $o)).
% 0.62/0.81 tff(a890_type, type, (
% 0.62/0.81 a890: $i)).
% 0.62/0.81 tff(hskp25_type, type, (
% 0.62/0.81 hskp25: $o)).
% 0.62/0.81 tff(a864_type, type, (
% 0.62/0.81 a864: $i)).
% 0.62/0.81 tff(hskp20_type, type, (
% 0.62/0.81 hskp20: $o)).
% 0.62/0.81 tff(hskp9_type, type, (
% 0.62/0.81 hskp9: $o)).
% 0.62/0.81 tff(a845_type, type, (
% 0.62/0.81 a845: $i)).
% 0.62/0.81 tff(hskp12_type, type, (
% 0.62/0.81 hskp12: $o)).
% 0.62/0.81 tff(a829_type, type, (
% 0.62/0.81 a829: $i)).
% 0.62/0.81 tff(hskp1_type, type, (
% 0.62/0.81 hskp1: $o)).
% 0.62/0.81 tff(a866_type, type, (
% 0.62/0.81 a866: $i)).
% 0.62/0.81 tff(hskp22_type, type, (
% 0.62/0.81 hskp22: $o)).
% 0.62/0.81 tff(a849_type, type, (
% 0.62/0.81 a849: $i)).
% 0.62/0.81 tff(hskp29_type, type, (
% 0.62/0.81 hskp29: $o)).
% 0.62/0.81 tff(1,plain,
% 0.62/0.81 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(2,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[1])).
% 0.62/0.81 tff(3,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(4,plain,
% 0.62/0.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(5,plain,
% 0.62/0.81 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[4])).
% 0.62/0.81 tff(6,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.62/0.81 tff(7,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.62/0.81 tff(8,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.62/0.81 tff(9,plain,(
% 0.62/0.81 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.81 inference(skolemize,[status(sab)],[8])).
% 0.62/0.81 tff(10,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.62/0.81 tff(11,assumption,(~hskp4), introduced(assumption)).
% 0.62/0.81 tff(12,assumption,(~c3_1(a859)), introduced(assumption)).
% 0.62/0.81 tff(13,plain,
% 0.62/0.81 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(14,plain,
% 0.62/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[13])).
% 0.62/0.81 tff(15,plain,
% 0.62/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(16,plain,
% 0.62/0.81 (^[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))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(17,plain,
% 0.62/0.81 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[16])).
% 0.62/0.81 tff(18,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 0.62/0.81 tff(19,plain,
% 0.62/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.62/0.81 tff(20,plain,
% 0.62/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.62/0.81 tff(21,plain,(
% 0.62/0.81 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.81 inference(skolemize,[status(sab)],[20])).
% 0.62/0.81 tff(22,plain,
% 0.62/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.62/0.81 tff(23,assumption,(~c1_1(a859)), introduced(assumption)).
% 0.62/0.81 tff(24,assumption,(~c0_1(a859)), introduced(assumption)).
% 0.62/0.81 tff(25,plain,
% 0.62/0.81 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(26,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[25])).
% 0.62/0.81 tff(27,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(28,plain,
% 0.62/0.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(29,plain,
% 0.62/0.81 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[28])).
% 0.62/0.81 tff(30,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.62/0.81 tff(31,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.62/0.81 tff(32,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.62/0.81 tff(33,plain,(
% 0.62/0.81 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.81 inference(skolemize,[status(sab)],[32])).
% 0.62/0.81 tff(34,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.62/0.81 tff(35,assumption,(~hskp16), introduced(assumption)).
% 0.62/0.81 tff(36,assumption,(~hskp17), introduced(assumption)).
% 0.62/0.81 tff(37,plain,
% 0.62/0.81 ((hskp17 | hskp16 | hskp2) <=> (hskp17 | hskp16 | hskp2)),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(38,plain,
% 0.62/0.81 (((hskp17 | hskp2) | hskp16) <=> (hskp17 | hskp16 | hskp2)),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(39,plain,
% 0.62/0.81 ((hskp2 | hskp17) <=> (hskp17 | hskp2)),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(40,plain,
% 0.62/0.81 (((hskp2 | hskp17) | hskp16) <=> ((hskp17 | hskp2) | hskp16)),
% 0.62/0.81 inference(monotonicity,[status(thm)],[39])).
% 0.62/0.81 tff(41,plain,
% 0.62/0.81 (((hskp2 | hskp17) | hskp16) <=> (hskp17 | hskp16 | hskp2)),
% 0.62/0.81 inference(transitivity,[status(thm)],[40, 38])).
% 0.62/0.81 tff(42,axiom,((hskp2 | hskp17) | hskp16), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.62/0.81 tff(43,plain,
% 0.62/0.81 (hskp17 | hskp16 | hskp2),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.62/0.81 tff(44,plain,
% 0.62/0.81 (hskp17 | hskp16 | hskp2),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[43, 37])).
% 0.62/0.81 tff(45,plain,
% 0.62/0.81 (hskp17 | hskp16 | hskp2),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.62/0.81 tff(46,plain,
% 0.62/0.81 (hskp17 | hskp16 | hskp2),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[45, 37])).
% 0.62/0.81 tff(47,plain,
% 0.62/0.81 (hskp17 | hskp16 | hskp2),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[46, 37])).
% 0.62/0.81 tff(48,plain,
% 0.62/0.81 (hskp2),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[47, 36, 35])).
% 0.62/0.81 tff(49,plain,
% 0.62/0.81 (((~hskp2) | (~c2_1(a830))) <=> ((~hskp2) | (~c2_1(a830)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(50,plain,
% 0.62/0.81 (((~c2_1(a830)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a830)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(51,axiom,((~c2_1(a830)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.62/0.81 tff(52,plain,
% 0.62/0.81 ((~hskp2) | (~c2_1(a830))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.62/0.81 tff(53,plain,
% 0.62/0.81 ((~hskp2) | (~c2_1(a830))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.62/0.81 tff(54,plain,
% 0.62/0.81 (~c2_1(a830)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[53, 48])).
% 0.62/0.81 tff(55,plain,
% 0.62/0.81 (((~hskp2) | (~c1_1(a830))) <=> ((~hskp2) | (~c1_1(a830)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(56,plain,
% 0.62/0.81 (((~c1_1(a830)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a830)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(57,axiom,((~c1_1(a830)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 0.62/0.81 tff(58,plain,
% 0.62/0.81 ((~hskp2) | (~c1_1(a830))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.62/0.81 tff(59,plain,
% 0.62/0.81 ((~hskp2) | (~c1_1(a830))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.62/0.81 tff(60,plain,
% 0.62/0.81 (~c1_1(a830)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[59, 48])).
% 0.62/0.81 tff(61,assumption,(hskp5), introduced(assumption)).
% 0.62/0.81 tff(62,plain,
% 0.62/0.81 (((~hskp5) | (~c3_1(a833))) <=> ((~hskp5) | (~c3_1(a833)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(63,plain,
% 0.62/0.81 (((~c3_1(a833)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a833)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(64,axiom,((~c3_1(a833)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.62/0.81 tff(65,plain,
% 0.62/0.81 ((~hskp5) | (~c3_1(a833))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.62/0.81 tff(66,plain,
% 0.62/0.81 ((~hskp5) | (~c3_1(a833))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[65, 62])).
% 0.62/0.81 tff(67,plain,
% 0.62/0.81 (~c3_1(a833)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[66, 61])).
% 0.62/0.81 tff(68,plain,
% 0.62/0.81 (((~hskp2) | c0_1(a830)) <=> ((~hskp2) | c0_1(a830))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(69,axiom,((~hskp2) | c0_1(a830)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.62/0.81 tff(70,plain,
% 0.62/0.81 ((~hskp2) | c0_1(a830)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.62/0.81 tff(71,plain,
% 0.62/0.81 ((~hskp2) | c0_1(a830)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[70, 68])).
% 0.62/0.81 tff(72,plain,
% 0.62/0.81 ((~hskp2) | c0_1(a830)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[71, 68])).
% 0.62/0.81 tff(73,plain,
% 0.62/0.81 ((~hskp2) | c0_1(a830)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.62/0.81 tff(74,plain,
% 0.62/0.81 ((~hskp2) | c0_1(a830)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[73, 68])).
% 0.62/0.81 tff(75,plain,
% 0.62/0.81 (c0_1(a830)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[74, 48])).
% 0.62/0.81 tff(76,plain,
% 0.62/0.81 (((~hskp5) | c0_1(a833)) <=> ((~hskp5) | c0_1(a833))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(77,axiom,((~hskp5) | c0_1(a833)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.62/0.81 tff(78,plain,
% 0.62/0.81 ((~hskp5) | c0_1(a833)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.62/0.81 tff(79,plain,
% 0.62/0.81 ((~hskp5) | c0_1(a833)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[78, 76])).
% 0.62/0.81 tff(80,plain,
% 0.62/0.81 ((~hskp5) | c0_1(a833)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.62/0.81 tff(81,plain,
% 0.62/0.81 ((~hskp5) | c0_1(a833)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.62/0.81 tff(82,plain,
% 0.62/0.81 ((~hskp5) | c0_1(a833)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[81, 76])).
% 0.62/0.81 tff(83,plain,
% 0.62/0.81 (c0_1(a833)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[82, 61])).
% 0.62/0.81 tff(84,assumption,(~ndr1_0), introduced(assumption)).
% 0.62/0.81 tff(85,plain,
% 0.62/0.81 ((ndr1_0 | (~hskp8)) <=> (ndr1_0 | (~hskp8))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(86,plain,
% 0.62/0.81 (((~hskp8) | ndr1_0) <=> (ndr1_0 | (~hskp8))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(87,axiom,((~hskp8) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause27')).
% 0.62/0.81 tff(88,plain,
% 0.62/0.81 (ndr1_0 | (~hskp8)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.62/0.81 tff(89,plain,
% 0.62/0.81 (ndr1_0 | (~hskp8)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.62/0.81 tff(90,plain,
% 0.62/0.81 (~hskp8),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[89, 84])).
% 0.62/0.81 tff(91,plain,
% 0.62/0.81 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(92,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.62/0.81 tff(93,plain,
% 0.62/0.81 ((~hskp31) | ndr1_0),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.62/0.81 tff(94,plain,
% 0.62/0.81 ((~hskp31) | ndr1_0),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[93, 91])).
% 0.62/0.81 tff(95,plain,
% 0.62/0.81 ((~hskp31) | ndr1_0),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[94, 91])).
% 0.62/0.81 tff(96,plain,
% 0.62/0.81 ((~hskp31) | ndr1_0),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.62/0.81 tff(97,plain,
% 0.62/0.81 ((~hskp31) | ndr1_0),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[96, 91])).
% 0.62/0.81 tff(98,plain,
% 0.62/0.81 (~hskp31),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[97, 84])).
% 0.62/0.81 tff(99,plain,
% 0.62/0.81 ((ndr1_0 | (~hskp16)) <=> (ndr1_0 | (~hskp16))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(100,plain,
% 0.62/0.81 (((~hskp16) | ndr1_0) <=> (ndr1_0 | (~hskp16))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(101,axiom,((~hskp16) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause19')).
% 0.62/0.81 tff(102,plain,
% 0.62/0.81 (ndr1_0 | (~hskp16)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.62/0.81 tff(103,plain,
% 0.62/0.81 (ndr1_0 | (~hskp16)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.62/0.81 tff(104,plain,
% 0.62/0.81 (~hskp16),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[103, 84])).
% 0.62/0.81 tff(105,plain,
% 0.62/0.81 ((hskp31 | hskp16 | hskp8) <=> (hskp31 | hskp16 | hskp8)),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(106,plain,
% 0.62/0.81 (((hskp31 | hskp8) | hskp16) <=> (hskp31 | hskp16 | hskp8)),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(107,axiom,((hskp31 | hskp8) | hskp16), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.62/0.81 tff(108,plain,
% 0.62/0.81 (hskp31 | hskp16 | hskp8),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.62/0.81 tff(109,plain,
% 0.62/0.81 (hskp31 | hskp16 | hskp8),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[108, 105])).
% 0.62/0.81 tff(110,plain,
% 0.62/0.81 (hskp31 | hskp16 | hskp8),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.62/0.81 tff(111,plain,
% 0.62/0.81 (hskp31 | hskp16 | hskp8),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[110, 105])).
% 0.62/0.81 tff(112,plain,
% 0.62/0.81 (hskp31 | hskp16 | hskp8),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[111, 105])).
% 0.62/0.81 tff(113,plain,
% 0.62/0.81 ($false),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[112, 104, 98, 90])).
% 0.62/0.81 tff(114,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.62/0.81 tff(115,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c3_1(a833) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c3_1(a833) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a833)) | (~c1_1(a833)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(116,plain,
% 0.62/0.81 ((hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830))) <=> (hskp17 | c3_1(a833) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a833)) | (~c1_1(a833)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(117,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c3_1(a833) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a833)) | (~c1_1(a833))))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[116])).
% 0.62/0.81 tff(118,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c3_1(a833) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a833)) | (~c1_1(a833)))),
% 0.62/0.81 inference(transitivity,[status(thm)],[117, 115])).
% 0.62/0.81 tff(119,plain,
% 0.62/0.81 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(120,plain,
% 0.62/0.81 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c3_1(a833) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a833)) | (~c1_1(a833))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.62/0.82 tff(121,plain,
% 0.62/0.82 (~c1_1(a833)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[120, 114, 36, 83, 75, 67, 60, 54, 10])).
% 0.62/0.82 tff(122,plain,
% 0.62/0.82 (^[U: $i] : refl((hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(123,plain,
% 0.62/0.82 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[122])).
% 0.62/0.82 tff(124,plain,
% 0.62/0.82 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(125,plain,
% 0.62/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp6) <=> ((hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp6))), rewrite(((hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp6) <=> (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(126,plain,
% 0.62/0.82 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp6) <=> ![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[125])).
% 0.62/0.82 tff(127,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 0.62/0.82 tff(128,plain,
% 0.62/0.82 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.62/0.82 tff(129,plain,
% 0.62/0.82 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.62/0.82 tff(130,plain,(
% 0.62/0.82 ![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(skolemize,[status(sab)],[129])).
% 0.62/0.82 tff(131,plain,
% 0.62/0.82 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.62/0.82 tff(132,plain,
% 0.62/0.82 (((~hskp5) | c2_1(a833)) <=> ((~hskp5) | c2_1(a833))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(133,axiom,((~hskp5) | c2_1(a833)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.62/0.82 tff(134,plain,
% 0.62/0.82 ((~hskp5) | c2_1(a833)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.62/0.82 tff(135,plain,
% 0.62/0.82 ((~hskp5) | c2_1(a833)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[134, 132])).
% 0.62/0.82 tff(136,plain,
% 0.62/0.82 ((~hskp5) | c2_1(a833)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[135, 132])).
% 0.62/0.82 tff(137,plain,
% 0.62/0.82 ((~hskp5) | c2_1(a833)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.62/0.82 tff(138,plain,
% 0.62/0.82 ((~hskp5) | c2_1(a833)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[137, 132])).
% 0.62/0.82 tff(139,plain,
% 0.62/0.82 (c2_1(a833)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[138, 61])).
% 0.62/0.82 tff(140,plain,
% 0.62/0.82 (((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)))) <=> ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp6 | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(141,plain,
% 0.62/0.82 ((hskp16 | hskp6 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833))) <=> (hskp16 | hskp6 | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(142,plain,
% 0.62/0.82 (((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)))) <=> ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[141])).
% 0.62/0.82 tff(143,plain,
% 0.62/0.82 (((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)))) <=> ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp6 | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[142, 140])).
% 0.62/0.82 tff(144,plain,
% 0.62/0.82 ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(145,plain,
% 0.62/0.82 ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp6 | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.62/0.82 tff(146,plain,
% 0.62/0.82 (hskp6),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[145, 114, 35, 83, 139, 67, 131])).
% 0.62/0.82 tff(147,plain,
% 0.62/0.82 (((~hskp6) | (~c3_1(a835))) <=> ((~hskp6) | (~c3_1(a835)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(148,plain,
% 0.62/0.82 (((~c3_1(a835)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a835)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(149,axiom,((~c3_1(a835)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.62/0.82 tff(150,plain,
% 0.62/0.82 ((~hskp6) | (~c3_1(a835))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.62/0.82 tff(151,plain,
% 0.62/0.82 ((~hskp6) | (~c3_1(a835))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[150, 147])).
% 0.62/0.82 tff(152,plain,
% 0.62/0.82 (~c3_1(a835)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[151, 146])).
% 0.62/0.82 tff(153,plain,
% 0.62/0.82 (((~hskp6) | (~c2_1(a835))) <=> ((~hskp6) | (~c2_1(a835)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(154,plain,
% 0.62/0.82 (((~c2_1(a835)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a835)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(155,axiom,((~c2_1(a835)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.62/0.82 tff(156,plain,
% 0.62/0.82 ((~hskp6) | (~c2_1(a835))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.62/0.82 tff(157,plain,
% 0.62/0.82 ((~hskp6) | (~c2_1(a835))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[156, 153])).
% 0.62/0.82 tff(158,plain,
% 0.62/0.82 (~c2_1(a835)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[157, 146])).
% 0.62/0.82 tff(159,plain,
% 0.62/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a835) | c3_1(a835) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | c1_1(a835))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a835) | c3_1(a835) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | c1_1(a835))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(160,plain,
% 0.62/0.82 (((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c3_1(a835) | c2_1(a835) | c1_1(a835)) <=> (c2_1(a835) | c3_1(a835) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | c1_1(a835))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(161,plain,
% 0.62/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c3_1(a835) | c2_1(a835) | c1_1(a835))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a835) | c3_1(a835) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | c1_1(a835)))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[160])).
% 0.62/0.82 tff(162,plain,
% 0.62/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c3_1(a835) | c2_1(a835) | c1_1(a835))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a835) | c3_1(a835) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | c1_1(a835))),
% 0.62/0.82 inference(transitivity,[status(thm)],[161, 159])).
% 0.62/0.82 tff(163,plain,
% 0.62/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c3_1(a835) | c2_1(a835) | c1_1(a835))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(164,plain,
% 0.62/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a835) | c3_1(a835) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | c1_1(a835)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.62/0.82 tff(165,plain,
% 0.62/0.82 (c1_1(a835)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[164, 114, 83, 139, 158, 152, 67, 22, 121])).
% 0.62/0.82 tff(166,plain,
% 0.62/0.82 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(167,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[166])).
% 0.62/0.82 tff(168,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(169,plain,
% 0.62/0.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(170,plain,
% 0.62/0.82 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[169])).
% 0.62/0.82 tff(171,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.62/0.82 tff(172,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.62/0.82 tff(173,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.62/0.82 tff(174,plain,(
% 0.62/0.82 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.62/0.82 inference(skolemize,[status(sab)],[173])).
% 0.62/0.82 tff(175,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.62/0.82 tff(176,plain,
% 0.62/0.82 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(177,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[176])).
% 0.62/0.82 tff(178,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(179,plain,
% 0.62/0.82 (^[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) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(180,plain,
% 0.62/0.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[179])).
% 0.62/0.82 tff(181,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 0.62/0.82 tff(182,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.62/0.82 tff(183,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.62/0.82 tff(184,plain,(
% 0.62/0.82 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.82 inference(skolemize,[status(sab)],[183])).
% 0.62/0.82 tff(185,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[184, 177])).
% 0.62/0.82 tff(186,plain,
% 0.62/0.82 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a833) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c2_1(a833)) | (~c0_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a833) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c2_1(a833)) | (~c0_1(a833)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(187,plain,
% 0.62/0.82 ((hskp14 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830))) <=> (hskp14 | c3_1(a833) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c2_1(a833)) | (~c0_1(a833)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(188,plain,
% 0.62/0.82 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a833) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c2_1(a833)) | (~c0_1(a833))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[187])).
% 0.62/0.82 tff(189,plain,
% 0.62/0.82 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a833) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c2_1(a833)) | (~c0_1(a833)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[188, 186])).
% 0.62/0.82 tff(190,plain,
% 0.62/0.82 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(191,plain,
% 0.62/0.82 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a833) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c2_1(a833)) | (~c0_1(a833))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.62/0.82 tff(192,plain,
% 0.62/0.82 (hskp14),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[191, 114, 83, 139, 75, 67, 60, 54, 185])).
% 0.62/0.82 tff(193,plain,
% 0.62/0.82 (((~hskp14) | (~c3_1(a851))) <=> ((~hskp14) | (~c3_1(a851)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(194,plain,
% 0.62/0.82 (((~c3_1(a851)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a851)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(195,axiom,((~c3_1(a851)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.62/0.82 tff(196,plain,
% 0.62/0.82 ((~hskp14) | (~c3_1(a851))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.62/0.82 tff(197,plain,
% 0.62/0.82 ((~hskp14) | (~c3_1(a851))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[196, 193])).
% 0.62/0.82 tff(198,plain,
% 0.62/0.82 (~c3_1(a851)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[197, 192])).
% 0.62/0.82 tff(199,plain,
% 0.62/0.82 (((~hskp14) | c2_1(a851)) <=> ((~hskp14) | c2_1(a851))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(200,axiom,((~hskp14) | c2_1(a851)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.62/0.82 tff(201,plain,
% 0.62/0.82 ((~hskp14) | c2_1(a851)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.62/0.82 tff(202,plain,
% 0.62/0.82 ((~hskp14) | c2_1(a851)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[201, 199])).
% 0.62/0.82 tff(203,plain,
% 0.62/0.82 ((~hskp14) | c2_1(a851)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[202, 199])).
% 0.62/0.82 tff(204,plain,
% 0.62/0.82 ((~hskp14) | c2_1(a851)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.62/0.82 tff(205,plain,
% 0.62/0.82 ((~hskp14) | c2_1(a851)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[204, 199])).
% 0.62/0.82 tff(206,plain,
% 0.62/0.82 (c2_1(a851)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[205, 192])).
% 0.62/0.82 tff(207,plain,
% 0.62/0.82 (((~hskp14) | c1_1(a851)) <=> ((~hskp14) | c1_1(a851))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(208,axiom,((~hskp14) | c1_1(a851)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.62/0.82 tff(209,plain,
% 0.62/0.82 ((~hskp14) | c1_1(a851)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.62/0.82 tff(210,plain,
% 0.62/0.82 ((~hskp14) | c1_1(a851)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[209, 207])).
% 0.62/0.82 tff(211,plain,
% 0.62/0.82 ((~hskp14) | c1_1(a851)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[210, 207])).
% 0.62/0.82 tff(212,plain,
% 0.62/0.82 ((~hskp14) | c1_1(a851)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.62/0.82 tff(213,plain,
% 0.62/0.82 ((~hskp14) | c1_1(a851)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[212, 207])).
% 0.62/0.82 tff(214,plain,
% 0.62/0.82 (c1_1(a851)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[213, 192])).
% 0.62/0.82 tff(215,plain,
% 0.62/0.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c3_1(a851) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a835)) | (~c2_1(a851)) | (~c1_1(a851)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a851) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a835)) | (~c2_1(a851)) | (~c1_1(a851)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(216,plain,
% 0.62/0.83 ((hskp17 | (~ndr1_0) | c3_1(a851) | (~c2_1(a851)) | (~c1_1(a851)) | c2_1(a835) | c3_1(a835) | (~c1_1(a835))) <=> (hskp17 | c3_1(a851) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a835)) | (~c2_1(a851)) | (~c1_1(a851)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(217,plain,
% 0.62/0.83 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a851) | (~c2_1(a851)) | (~c1_1(a851)) | c2_1(a835) | c3_1(a835) | (~c1_1(a835)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c3_1(a851) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a835)) | (~c2_1(a851)) | (~c1_1(a851))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[216])).
% 0.62/0.83 tff(218,plain,
% 0.62/0.83 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a851) | (~c2_1(a851)) | (~c1_1(a851)) | c2_1(a835) | c3_1(a835) | (~c1_1(a835)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a851) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a835)) | (~c2_1(a851)) | (~c1_1(a851)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[217, 215])).
% 0.62/0.83 tff(219,plain,
% 0.62/0.83 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a851) | (~c2_1(a851)) | (~c1_1(a851)) | c2_1(a835) | c3_1(a835) | (~c1_1(a835)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(220,plain,
% 0.62/0.83 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a851) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a835)) | (~c2_1(a851)) | (~c1_1(a851))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.62/0.83 tff(221,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[220, 114, 36, 214, 206, 198, 158, 152, 175, 165])).
% 0.62/0.83 tff(222,plain,((~hskp5) | hskp17 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(223,plain,
% 0.62/0.83 (~hskp5),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[222, 36, 35])).
% 0.62/0.83 tff(224,plain,
% 0.62/0.83 (^[U: $i] : refl((hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(225,plain,
% 0.62/0.83 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[224])).
% 0.62/0.83 tff(226,plain,
% 0.62/0.83 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(227,plain,
% 0.62/0.83 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp5) | hskp16) <=> ((hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp16))), rewrite(((hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp16) <=> (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp5) | hskp16) <=> (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(228,plain,
% 0.62/0.83 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp5) | hskp16) <=> ![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[227])).
% 0.62/0.83 tff(229,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp5) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 0.62/0.83 tff(230,plain,
% 0.62/0.83 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.62/0.83 tff(231,plain,
% 0.62/0.83 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.62/0.83 tff(232,plain,(
% 0.62/0.83 ![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.83 inference(skolemize,[status(sab)],[231])).
% 0.62/0.83 tff(233,plain,
% 0.62/0.83 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[232, 225])).
% 0.62/0.83 tff(234,assumption,(hskp3), introduced(assumption)).
% 0.62/0.83 tff(235,plain,
% 0.62/0.83 (((~hskp3) | (~c1_1(a831))) <=> ((~hskp3) | (~c1_1(a831)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(236,plain,
% 0.62/0.83 (((~c1_1(a831)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a831)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(237,axiom,((~c1_1(a831)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.62/0.83 tff(238,plain,
% 0.62/0.83 ((~hskp3) | (~c1_1(a831))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.62/0.83 tff(239,plain,
% 0.62/0.83 ((~hskp3) | (~c1_1(a831))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[238, 235])).
% 0.62/0.83 tff(240,plain,
% 0.62/0.83 (~c1_1(a831)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[239, 234])).
% 0.62/0.83 tff(241,plain,
% 0.62/0.83 (((~hskp3) | c3_1(a831)) <=> ((~hskp3) | c3_1(a831))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(242,axiom,((~hskp3) | c3_1(a831)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.62/0.83 tff(243,plain,
% 0.62/0.83 ((~hskp3) | c3_1(a831)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.62/0.83 tff(244,plain,
% 0.62/0.83 ((~hskp3) | c3_1(a831)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[243, 241])).
% 0.62/0.83 tff(245,plain,
% 0.62/0.83 ((~hskp3) | c3_1(a831)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[244, 241])).
% 0.62/0.83 tff(246,plain,
% 0.62/0.83 ((~hskp3) | c3_1(a831)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[245, 241])).
% 0.62/0.83 tff(247,plain,
% 0.62/0.83 ((~hskp3) | c3_1(a831)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[246, 241])).
% 0.62/0.83 tff(248,plain,
% 0.62/0.83 (c3_1(a831)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[247, 234])).
% 0.62/0.83 tff(249,plain,
% 0.62/0.83 (((~hskp3) | c2_1(a831)) <=> ((~hskp3) | c2_1(a831))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(250,axiom,((~hskp3) | c2_1(a831)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.62/0.83 tff(251,plain,
% 0.62/0.83 ((~hskp3) | c2_1(a831)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.62/0.83 tff(252,plain,
% 0.62/0.83 ((~hskp3) | c2_1(a831)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[251, 249])).
% 0.62/0.83 tff(253,plain,
% 0.62/0.83 ((~hskp3) | c2_1(a831)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[252, 249])).
% 0.62/0.83 tff(254,plain,
% 0.62/0.83 ((~hskp3) | c2_1(a831)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.62/0.83 tff(255,plain,
% 0.62/0.83 ((~hskp3) | c2_1(a831)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[254, 249])).
% 0.62/0.83 tff(256,plain,
% 0.62/0.83 (c2_1(a831)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[255, 234])).
% 0.62/0.83 tff(257,assumption,(~hskp5), introduced(assumption)).
% 0.62/0.83 tff(258,plain,
% 0.62/0.83 (((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c2_1(a831)))) <=> ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp16 | hskp5 | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c2_1(a831)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(259,plain,
% 0.62/0.83 ((hskp16 | hskp5 | (~ndr1_0) | c1_1(a831) | (~c2_1(a831)) | (~c3_1(a831))) <=> (hskp16 | hskp5 | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c2_1(a831)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(260,plain,
% 0.62/0.83 (((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | c1_1(a831) | (~c2_1(a831)) | (~c3_1(a831)))) <=> ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c2_1(a831))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[259])).
% 0.62/0.83 tff(261,plain,
% 0.62/0.83 (((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | c1_1(a831) | (~c2_1(a831)) | (~c3_1(a831)))) <=> ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp16 | hskp5 | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c2_1(a831)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[260, 258])).
% 0.62/0.83 tff(262,plain,
% 0.62/0.83 ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | c1_1(a831) | (~c2_1(a831)) | (~c3_1(a831)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(263,plain,
% 0.62/0.83 ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp16 | hskp5 | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c2_1(a831))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.62/0.83 tff(264,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[263, 114, 35, 257, 256, 248, 240, 233])).
% 0.62/0.83 tff(265,plain,((~hskp3) | hskp16 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(266,plain,
% 0.62/0.83 (~hskp3),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[265, 223, 35])).
% 0.62/0.83 tff(267,plain,
% 0.62/0.83 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(268,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[267])).
% 0.62/0.83 tff(269,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(270,plain,
% 0.62/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_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)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_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)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(271,plain,
% 0.62/0.83 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[270])).
% 0.62/0.83 tff(272,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 0.62/0.83 tff(273,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.62/0.83 tff(274,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[273, 269])).
% 0.62/0.83 tff(275,plain,(
% 0.62/0.83 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(skolemize,[status(sab)],[274])).
% 0.62/0.83 tff(276,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[275, 268])).
% 0.62/0.83 tff(277,plain,
% 0.62/0.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c0_1(a830)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(278,plain,
% 0.62/0.83 ((hskp3 | (~ndr1_0) | c2_1(a830) | (~c3_1(a830)) | (~c0_1(a830)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830))) <=> (hskp3 | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c0_1(a830)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(279,plain,
% 0.62/0.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a830) | (~c3_1(a830)) | (~c0_1(a830)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c0_1(a830))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[278])).
% 0.62/0.83 tff(280,plain,
% 0.62/0.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a830) | (~c3_1(a830)) | (~c0_1(a830)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c0_1(a830)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[279, 277])).
% 0.62/0.83 tff(281,plain,
% 0.62/0.83 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a830) | (~c3_1(a830)) | (~c0_1(a830)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(282,plain,
% 0.62/0.83 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c0_1(a830))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.62/0.83 tff(283,plain,
% 0.62/0.83 (hskp3 | (~c3_1(a830))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[282, 114, 75, 60, 54, 276])).
% 0.62/0.83 tff(284,plain,
% 0.62/0.83 (~c3_1(a830)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[283, 266])).
% 0.62/0.83 tff(285,assumption,(~hskp31), introduced(assumption)).
% 0.62/0.83 tff(286,plain,
% 0.62/0.83 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(287,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[286])).
% 0.62/0.83 tff(288,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(289,plain,
% 0.62/0.83 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp31) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp31))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp31) <=> (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(290,plain,
% 0.62/0.83 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[289])).
% 0.62/0.83 tff(291,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.62/0.83 tff(292,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.62/0.83 tff(293,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[292, 288])).
% 0.62/0.83 tff(294,plain,(
% 0.62/0.83 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(skolemize,[status(sab)],[293])).
% 0.62/0.83 tff(295,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[294, 287])).
% 0.62/0.83 tff(296,assumption,(hskp17), introduced(assumption)).
% 0.62/0.83 tff(297,plain,
% 0.62/0.83 (((~hskp17) | (~c3_1(a859))) <=> ((~hskp17) | (~c3_1(a859)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(298,plain,
% 0.62/0.83 (((~c3_1(a859)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a859)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(299,axiom,((~c3_1(a859)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.62/0.83 tff(300,plain,
% 0.62/0.83 ((~hskp17) | (~c3_1(a859))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.62/0.83 tff(301,plain,
% 0.62/0.83 ((~hskp17) | (~c3_1(a859))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[300, 297])).
% 0.62/0.83 tff(302,plain,
% 0.62/0.83 (~c3_1(a859)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[301, 296])).
% 0.62/0.83 tff(303,plain,
% 0.62/0.83 (((~hskp17) | (~c1_1(a859))) <=> ((~hskp17) | (~c1_1(a859)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(304,plain,
% 0.62/0.83 (((~c1_1(a859)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a859)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(305,axiom,((~c1_1(a859)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.62/0.83 tff(306,plain,
% 0.62/0.83 ((~hskp17) | (~c1_1(a859))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.62/0.83 tff(307,plain,
% 0.62/0.83 ((~hskp17) | (~c1_1(a859))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[306, 303])).
% 0.62/0.83 tff(308,plain,
% 0.62/0.83 (~c1_1(a859)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[307, 296])).
% 0.62/0.83 tff(309,plain,
% 0.62/0.83 (hskp8),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[112, 285, 35])).
% 0.62/0.83 tff(310,plain,
% 0.62/0.83 (((~hskp8) | (~c3_1(a838))) <=> ((~hskp8) | (~c3_1(a838)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(311,plain,
% 0.62/0.83 (((~c3_1(a838)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a838)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(312,axiom,((~c3_1(a838)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.62/0.83 tff(313,plain,
% 0.62/0.83 ((~hskp8) | (~c3_1(a838))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.62/0.83 tff(314,plain,
% 0.62/0.83 ((~hskp8) | (~c3_1(a838))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[313, 310])).
% 0.62/0.83 tff(315,plain,
% 0.62/0.83 (~c3_1(a838)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[314, 309])).
% 0.62/0.83 tff(316,plain,
% 0.62/0.83 (((~hskp8) | (~c2_1(a838))) <=> ((~hskp8) | (~c2_1(a838)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(317,plain,
% 0.62/0.83 (((~c2_1(a838)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a838)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(318,axiom,((~c2_1(a838)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.62/0.83 tff(319,plain,
% 0.62/0.83 ((~hskp8) | (~c2_1(a838))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.62/0.83 tff(320,plain,
% 0.62/0.83 ((~hskp8) | (~c2_1(a838))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[319, 316])).
% 0.62/0.83 tff(321,plain,
% 0.62/0.83 (~c2_1(a838)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[320, 309])).
% 0.62/0.83 tff(322,plain,
% 0.62/0.83 (((~hskp8) | c1_1(a838)) <=> ((~hskp8) | c1_1(a838))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(323,axiom,((~hskp8) | c1_1(a838)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.62/0.83 tff(324,plain,
% 0.62/0.83 ((~hskp8) | c1_1(a838)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.62/0.83 tff(325,plain,
% 0.62/0.83 ((~hskp8) | c1_1(a838)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[324, 322])).
% 0.62/0.83 tff(326,plain,
% 0.62/0.83 ((~hskp8) | c1_1(a838)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[325, 322])).
% 0.62/0.83 tff(327,plain,
% 0.62/0.83 ((~hskp8) | c1_1(a838)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[326, 322])).
% 0.62/0.83 tff(328,plain,
% 0.62/0.83 ((~hskp8) | c1_1(a838)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[327, 322])).
% 0.62/0.83 tff(329,plain,
% 0.62/0.83 (c1_1(a838)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[328, 309])).
% 0.62/0.83 tff(330,plain,
% 0.62/0.83 (((~hskp17) | c0_1(a859)) <=> ((~hskp17) | c0_1(a859))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(331,axiom,((~hskp17) | c0_1(a859)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.62/0.83 tff(332,plain,
% 0.62/0.83 ((~hskp17) | c0_1(a859)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.62/0.83 tff(333,plain,
% 0.62/0.83 ((~hskp17) | c0_1(a859)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[332, 330])).
% 0.62/0.83 tff(334,plain,
% 0.62/0.83 ((~hskp17) | c0_1(a859)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[333, 330])).
% 0.62/0.83 tff(335,plain,
% 0.62/0.83 ((~hskp17) | c0_1(a859)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[334, 330])).
% 0.62/0.83 tff(336,plain,
% 0.62/0.83 ((~hskp17) | c0_1(a859)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[335, 330])).
% 0.62/0.83 tff(337,plain,
% 0.62/0.83 (c0_1(a859)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[336, 296])).
% 0.62/0.83 tff(338,plain,
% 0.62/0.83 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c1_1(a859) | c3_1(a859) | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | (~c1_1(a838)) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c1_1(a859) | c3_1(a859) | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | (~c1_1(a838)) | (~c0_1(a859)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(339,plain,
% 0.62/0.83 ((hskp31 | (~ndr1_0) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859))) <=> (hskp31 | c1_1(a859) | c3_1(a859) | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | (~c1_1(a838)) | (~c0_1(a859)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(340,plain,
% 0.62/0.83 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c1_1(a859) | c3_1(a859) | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | (~c1_1(a838)) | (~c0_1(a859))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[339])).
% 0.62/0.83 tff(341,plain,
% 0.62/0.83 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c1_1(a859) | c3_1(a859) | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | (~c1_1(a838)) | (~c0_1(a859)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[340, 338])).
% 0.62/0.83 tff(342,plain,
% 0.62/0.83 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(343,plain,
% 0.62/0.84 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c1_1(a859) | c3_1(a859) | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | (~c1_1(a838)) | (~c0_1(a859))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.62/0.84 tff(344,plain,
% 0.62/0.84 (~c0_1(a838)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[343, 285, 114, 337, 329, 308, 302, 321, 295])).
% 0.62/0.84 tff(345,assumption,(~hskp19), introduced(assumption)).
% 0.62/0.84 tff(346,plain,
% 0.62/0.84 (^[U: $i] : refl((hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(347,plain,
% 0.62/0.84 (![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[346])).
% 0.62/0.84 tff(348,plain,
% 0.62/0.84 (![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(349,plain,
% 0.62/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | 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))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | 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) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp31) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp31))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp31) <=> (hskp31 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp31) <=> (hskp31 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp31) | hskp19) <=> ((hskp31 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp19))), rewrite(((hskp31 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp19) <=> (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp31) | hskp19) <=> (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(350,plain,
% 0.62/0.84 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp31) | hskp19) <=> ![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[349])).
% 0.62/0.84 tff(351,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp31) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.62/0.84 tff(352,plain,
% 0.62/0.84 (![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.62/0.84 tff(353,plain,
% 0.62/0.84 (![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[352, 348])).
% 0.62/0.84 tff(354,plain,(
% 0.62/0.84 ![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.62/0.84 inference(skolemize,[status(sab)],[353])).
% 0.62/0.84 tff(355,plain,
% 0.62/0.84 (![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[354, 347])).
% 0.62/0.84 tff(356,plain,
% 0.62/0.84 (((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | c1_1(a859) | c3_1(a859) | (~ndr1_0) | c2_1(a859))) <=> ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp31 | hskp19 | c1_1(a859) | c3_1(a859) | (~ndr1_0) | c2_1(a859))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(357,plain,
% 0.62/0.84 ((hskp31 | hskp19 | (~ndr1_0) | c2_1(a859) | c1_1(a859) | c3_1(a859)) <=> (hskp31 | hskp19 | c1_1(a859) | c3_1(a859) | (~ndr1_0) | c2_1(a859))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(358,plain,
% 0.62/0.84 (((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | (~ndr1_0) | c2_1(a859) | c1_1(a859) | c3_1(a859))) <=> ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | c1_1(a859) | c3_1(a859) | (~ndr1_0) | c2_1(a859)))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[357])).
% 0.62/0.84 tff(359,plain,
% 0.62/0.84 (((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | (~ndr1_0) | c2_1(a859) | c1_1(a859) | c3_1(a859))) <=> ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp31 | hskp19 | c1_1(a859) | c3_1(a859) | (~ndr1_0) | c2_1(a859))),
% 0.62/0.84 inference(transitivity,[status(thm)],[358, 356])).
% 0.62/0.84 tff(360,plain,
% 0.62/0.84 ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | (~ndr1_0) | c2_1(a859) | c1_1(a859) | c3_1(a859))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(361,plain,
% 0.62/0.84 ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp31 | hskp19 | c1_1(a859) | c3_1(a859) | (~ndr1_0) | c2_1(a859)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.62/0.84 tff(362,plain,
% 0.62/0.84 (hskp19 | c2_1(a859)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[361, 285, 114, 23, 12, 355])).
% 0.62/0.84 tff(363,plain,
% 0.62/0.84 (c2_1(a859)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[362, 345])).
% 0.62/0.84 tff(364,plain,
% 0.62/0.84 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(365,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[364])).
% 0.62/0.84 tff(366,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(367,plain,
% 0.62/0.84 (^[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) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(368,plain,
% 0.62/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[367])).
% 0.62/0.84 tff(369,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 0.62/0.84 tff(370,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.62/0.84 tff(371,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[370, 366])).
% 0.62/0.84 tff(372,plain,(
% 0.62/0.84 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(skolemize,[status(sab)],[371])).
% 0.62/0.84 tff(373,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[372, 365])).
% 0.62/0.84 tff(374,plain,
% 0.62/0.84 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(375,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[374])).
% 0.62/0.84 tff(376,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(377,plain,
% 0.62/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(378,plain,
% 0.62/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[377])).
% 0.62/0.84 tff(379,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.62/0.84 tff(380,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.62/0.84 tff(381,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[380, 376])).
% 0.62/0.84 tff(382,plain,(
% 0.62/0.84 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(skolemize,[status(sab)],[381])).
% 0.62/0.84 tff(383,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[382, 375])).
% 0.62/0.84 tff(384,assumption,(~c0_1(a838)), introduced(assumption)).
% 0.62/0.84 tff(385,assumption,(hskp4), introduced(assumption)).
% 0.62/0.84 tff(386,plain,
% 0.62/0.84 (((~hskp4) | (~c3_1(a832))) <=> ((~hskp4) | (~c3_1(a832)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(387,plain,
% 0.62/0.84 (((~c3_1(a832)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a832)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(388,axiom,((~c3_1(a832)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.62/0.84 tff(389,plain,
% 0.62/0.84 ((~hskp4) | (~c3_1(a832))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.62/0.84 tff(390,plain,
% 0.62/0.84 ((~hskp4) | (~c3_1(a832))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[389, 386])).
% 0.62/0.84 tff(391,plain,
% 0.62/0.84 (~c3_1(a832)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[390, 385])).
% 0.62/0.84 tff(392,plain,
% 0.62/0.84 (((~hskp4) | (~c2_1(a832))) <=> ((~hskp4) | (~c2_1(a832)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(393,plain,
% 0.62/0.84 (((~c2_1(a832)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a832)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(394,axiom,((~c2_1(a832)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.62/0.84 tff(395,plain,
% 0.62/0.84 ((~hskp4) | (~c2_1(a832))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.62/0.84 tff(396,plain,
% 0.62/0.84 ((~hskp4) | (~c2_1(a832))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[395, 392])).
% 0.62/0.84 tff(397,plain,
% 0.62/0.84 (~c2_1(a832)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[396, 385])).
% 0.62/0.84 tff(398,plain,
% 0.62/0.84 (((~hskp4) | (~c1_1(a832))) <=> ((~hskp4) | (~c1_1(a832)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(399,plain,
% 0.62/0.84 (((~c1_1(a832)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a832)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(400,axiom,((~c1_1(a832)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.62/0.84 tff(401,plain,
% 0.62/0.84 ((~hskp4) | (~c1_1(a832))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.62/0.84 tff(402,plain,
% 0.62/0.84 ((~hskp4) | (~c1_1(a832))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[401, 398])).
% 0.62/0.84 tff(403,plain,
% 0.62/0.84 (~c1_1(a832)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[402, 385])).
% 0.62/0.84 tff(404,plain,
% 0.62/0.84 (((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0))) <=> ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp31 | hskp19 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(405,plain,
% 0.62/0.84 ((hskp31 | hskp19 | (~ndr1_0) | c2_1(a832) | c1_1(a832) | c3_1(a832)) <=> (hskp31 | hskp19 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(406,plain,
% 0.62/0.84 (((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | (~ndr1_0) | c2_1(a832) | c1_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0)))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[405])).
% 0.62/0.84 tff(407,plain,
% 0.62/0.84 (((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | (~ndr1_0) | c2_1(a832) | c1_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp31 | hskp19 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0))),
% 0.62/0.84 inference(transitivity,[status(thm)],[406, 404])).
% 0.62/0.84 tff(408,plain,
% 0.62/0.84 ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | (~ndr1_0) | c2_1(a832) | c1_1(a832) | c3_1(a832))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(409,plain,
% 0.62/0.84 ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp31 | hskp19 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.62/0.84 tff(410,plain,
% 0.62/0.84 ($false),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[409, 285, 114, 345, 403, 397, 391, 355])).
% 0.62/0.84 tff(411,plain,((~hskp4) | hskp31 | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.62/0.84 tff(412,plain,
% 0.62/0.84 (~hskp4),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[411, 345, 285])).
% 0.62/0.84 tff(413,plain,
% 0.62/0.84 (^[U: $i] : refl((hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(414,plain,
% 0.62/0.84 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[413])).
% 0.62/0.84 tff(415,plain,
% 0.62/0.84 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(416,plain,
% 0.62/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp4) <=> ((hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp4))), rewrite(((hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp4) <=> (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp4) <=> (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(417,plain,
% 0.62/0.84 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp4) <=> ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[416])).
% 0.62/0.84 tff(418,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.62/0.84 tff(419,plain,
% 0.62/0.84 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.62/0.84 tff(420,plain,
% 0.62/0.84 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[419, 415])).
% 0.62/0.84 tff(421,plain,(
% 0.62/0.84 ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.62/0.84 inference(skolemize,[status(sab)],[420])).
% 0.62/0.84 tff(422,plain,
% 0.62/0.84 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[421, 414])).
% 0.62/0.84 tff(423,assumption,(~c3_1(a838)), introduced(assumption)).
% 0.62/0.84 tff(424,assumption,(~c2_1(a838)), introduced(assumption)).
% 0.62/0.84 tff(425,plain,
% 0.62/0.84 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | c2_1(a838) | c3_1(a838) | (~ndr1_0) | c0_1(a838))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp11 | hskp4 | c2_1(a838) | c3_1(a838) | (~ndr1_0) | c0_1(a838))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(426,plain,
% 0.62/0.84 ((hskp11 | hskp4 | (~ndr1_0) | c2_1(a838) | c0_1(a838) | c3_1(a838)) <=> (hskp11 | hskp4 | c2_1(a838) | c3_1(a838) | (~ndr1_0) | c0_1(a838))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(427,plain,
% 0.62/0.84 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | (~ndr1_0) | c2_1(a838) | c0_1(a838) | c3_1(a838))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | c2_1(a838) | c3_1(a838) | (~ndr1_0) | c0_1(a838)))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[426])).
% 0.62/0.84 tff(428,plain,
% 0.62/0.84 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | (~ndr1_0) | c2_1(a838) | c0_1(a838) | c3_1(a838))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp11 | hskp4 | c2_1(a838) | c3_1(a838) | (~ndr1_0) | c0_1(a838))),
% 0.62/0.84 inference(transitivity,[status(thm)],[427, 425])).
% 0.62/0.84 tff(429,plain,
% 0.62/0.84 ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | (~ndr1_0) | c2_1(a838) | c0_1(a838) | c3_1(a838))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(430,plain,
% 0.62/0.84 ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp11 | hskp4 | c2_1(a838) | c3_1(a838) | (~ndr1_0) | c0_1(a838)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.62/0.84 tff(431,plain,
% 0.62/0.84 (hskp11 | hskp4 | c0_1(a838)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[430, 114, 424, 423, 422])).
% 0.62/0.84 tff(432,plain,
% 0.62/0.84 (hskp11),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[431, 412, 384])).
% 0.62/0.84 tff(433,plain,
% 0.62/0.84 (((~hskp11) | (~c2_1(a844))) <=> ((~hskp11) | (~c2_1(a844)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(434,plain,
% 0.62/0.84 (((~c2_1(a844)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a844)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(435,axiom,((~c2_1(a844)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.62/0.84 tff(436,plain,
% 0.62/0.84 ((~hskp11) | (~c2_1(a844))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.62/0.84 tff(437,plain,
% 0.62/0.84 ((~hskp11) | (~c2_1(a844))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[436, 433])).
% 0.62/0.84 tff(438,plain,
% 0.62/0.84 (~c2_1(a844)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[437, 432])).
% 0.62/0.84 tff(439,plain,
% 0.62/0.84 (((~hskp11) | (~c1_1(a844))) <=> ((~hskp11) | (~c1_1(a844)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(440,plain,
% 0.62/0.84 (((~c1_1(a844)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a844)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(441,axiom,((~c1_1(a844)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.62/0.84 tff(442,plain,
% 0.62/0.84 ((~hskp11) | (~c1_1(a844))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.62/0.84 tff(443,plain,
% 0.62/0.84 ((~hskp11) | (~c1_1(a844))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[442, 439])).
% 0.62/0.84 tff(444,plain,
% 0.62/0.84 (~c1_1(a844)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[443, 432])).
% 0.62/0.84 tff(445,plain,
% 0.62/0.84 (((~hskp11) | c3_1(a844)) <=> ((~hskp11) | c3_1(a844))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(446,axiom,((~hskp11) | c3_1(a844)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.62/0.84 tff(447,plain,
% 0.62/0.84 ((~hskp11) | c3_1(a844)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.62/0.84 tff(448,plain,
% 0.62/0.84 ((~hskp11) | c3_1(a844)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[447, 445])).
% 0.62/0.84 tff(449,plain,
% 0.62/0.84 ((~hskp11) | c3_1(a844)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[448, 445])).
% 0.62/0.84 tff(450,plain,
% 0.62/0.84 ((~hskp11) | c3_1(a844)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[449, 445])).
% 0.62/0.84 tff(451,plain,
% 0.62/0.84 ((~hskp11) | c3_1(a844)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[450, 445])).
% 0.62/0.84 tff(452,plain,
% 0.62/0.84 (c3_1(a844)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[451, 432])).
% 0.62/0.84 tff(453,assumption,(c0_1(a859)), introduced(assumption)).
% 0.62/0.84 tff(454,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a859)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(455,plain,
% 0.62/0.84 ((hskp13 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a844) | c1_1(a844) | (~c3_1(a844))) <=> (hskp13 | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a859)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(456,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a844) | c1_1(a844) | (~c3_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a859))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[455])).
% 0.62/0.84 tff(457,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a844) | c1_1(a844) | (~c3_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a859)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[456, 454])).
% 0.62/0.84 tff(458,plain,
% 0.62/0.84 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a844) | c1_1(a844) | (~c3_1(a844)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(459,plain,
% 0.62/0.84 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a859))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.62/0.84 tff(460,plain,
% 0.62/0.84 (hskp13),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[459, 114, 453, 452, 23, 12, 444, 438, 383])).
% 0.62/0.84 tff(461,plain,
% 0.62/0.84 (((~hskp13) | (~c2_1(a846))) <=> ((~hskp13) | (~c2_1(a846)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(462,plain,
% 0.62/0.84 (((~c2_1(a846)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a846)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(463,axiom,((~c2_1(a846)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.62/0.84 tff(464,plain,
% 0.62/0.84 ((~hskp13) | (~c2_1(a846))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.62/0.84 tff(465,plain,
% 0.62/0.84 ((~hskp13) | (~c2_1(a846))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[464, 461])).
% 0.62/0.84 tff(466,plain,
% 0.62/0.84 (~c2_1(a846)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[465, 460])).
% 0.62/0.84 tff(467,plain,
% 0.62/0.84 (((~hskp13) | (~c0_1(a846))) <=> ((~hskp13) | (~c0_1(a846)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(468,plain,
% 0.62/0.84 (((~c0_1(a846)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a846)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(469,axiom,((~c0_1(a846)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.62/0.84 tff(470,plain,
% 0.62/0.84 ((~hskp13) | (~c0_1(a846))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.62/0.84 tff(471,plain,
% 0.62/0.84 ((~hskp13) | (~c0_1(a846))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[470, 467])).
% 0.62/0.84 tff(472,plain,
% 0.62/0.84 (~c0_1(a846)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[471, 460])).
% 0.62/0.84 tff(473,plain,
% 0.62/0.84 (((~hskp13) | c3_1(a846)) <=> ((~hskp13) | c3_1(a846))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(474,axiom,((~hskp13) | c3_1(a846)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.62/0.84 tff(475,plain,
% 0.62/0.84 ((~hskp13) | c3_1(a846)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.62/0.84 tff(476,plain,
% 0.62/0.84 ((~hskp13) | c3_1(a846)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[475, 473])).
% 0.62/0.84 tff(477,plain,
% 0.62/0.84 ((~hskp13) | c3_1(a846)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[476, 473])).
% 0.62/0.84 tff(478,plain,
% 0.62/0.84 ((~hskp13) | c3_1(a846)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[477, 473])).
% 0.62/0.84 tff(479,plain,
% 0.62/0.84 ((~hskp13) | c3_1(a846)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[478, 473])).
% 0.62/0.84 tff(480,plain,
% 0.62/0.84 (c3_1(a846)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[479, 460])).
% 0.62/0.84 tff(481,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c3_1(a859) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c3_1(a846)) | (~c2_1(a859)) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c3_1(a859) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c3_1(a846)) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(482,plain,
% 0.62/0.84 ((hskp4 | (~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846))) <=> (hskp4 | c3_1(a859) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c3_1(a846)) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(483,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c3_1(a859) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c3_1(a846)) | (~c2_1(a859)) | (~c0_1(a859))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[482])).
% 0.62/0.84 tff(484,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c3_1(a859) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c3_1(a846)) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[483, 481])).
% 0.62/0.85 tff(485,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(486,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c3_1(a859) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c3_1(a846)) | (~c2_1(a859)) | (~c0_1(a859))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.62/0.85 tff(487,plain,
% 0.62/0.85 ($false),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[486, 114, 412, 453, 480, 12, 472, 466, 373, 363])).
% 0.62/0.85 tff(488,plain,(hskp19 | (~c0_1(a859)) | c3_1(a859) | c1_1(a859) | c0_1(a838) | c2_1(a838) | c3_1(a838) | hskp31), inference(lemma,lemma(discharge,[]))).
% 0.62/0.85 tff(489,plain,
% 0.62/0.85 (hskp19),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[488, 337, 302, 308, 344, 321, 315, 285])).
% 0.62/0.85 tff(490,plain,
% 0.62/0.85 (((~hskp19) | (~c2_1(a863))) <=> ((~hskp19) | (~c2_1(a863)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(491,plain,
% 0.62/0.85 (((~c2_1(a863)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a863)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(492,axiom,((~c2_1(a863)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.62/0.85 tff(493,plain,
% 0.62/0.85 ((~hskp19) | (~c2_1(a863))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.62/0.85 tff(494,plain,
% 0.62/0.85 ((~hskp19) | (~c2_1(a863))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[493, 490])).
% 0.62/0.85 tff(495,plain,
% 0.62/0.85 (~c2_1(a863)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[494, 489])).
% 0.62/0.85 tff(496,plain,
% 0.62/0.85 (((~hskp19) | c0_1(a863)) <=> ((~hskp19) | c0_1(a863))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(497,axiom,((~hskp19) | c0_1(a863)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.62/0.85 tff(498,plain,
% 0.62/0.85 ((~hskp19) | c0_1(a863)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.62/0.85 tff(499,plain,
% 0.62/0.85 ((~hskp19) | c0_1(a863)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[498, 496])).
% 0.62/0.85 tff(500,plain,
% 0.62/0.85 ((~hskp19) | c0_1(a863)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[499, 496])).
% 0.62/0.85 tff(501,plain,
% 0.62/0.85 ((~hskp19) | c0_1(a863)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[500, 496])).
% 0.62/0.85 tff(502,plain,
% 0.62/0.85 ((~hskp19) | c0_1(a863)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[501, 496])).
% 0.62/0.85 tff(503,plain,
% 0.62/0.85 (c0_1(a863)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[502, 489])).
% 0.62/0.85 tff(504,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | (~c1_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | (~c1_1(a863)) | (~c0_1(a863)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(505,plain,
% 0.62/0.85 ((hskp31 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c0_1(a863)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859))) <=> (hskp31 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | (~c1_1(a863)) | (~c0_1(a863)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(506,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c0_1(a863)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | (~c1_1(a863)) | (~c0_1(a863))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[505])).
% 0.62/0.85 tff(507,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c0_1(a863)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | (~c1_1(a863)) | (~c0_1(a863)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[506, 504])).
% 0.62/0.85 tff(508,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c0_1(a863)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(509,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | (~c1_1(a863)) | (~c0_1(a863))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[508, 507])).
% 0.62/0.85 tff(510,plain,
% 0.62/0.85 (~c1_1(a863)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[509, 285, 114, 503, 337, 495, 308, 302, 295])).
% 0.62/0.85 tff(511,plain,
% 0.62/0.85 (((~hskp19) | c3_1(a863)) <=> ((~hskp19) | c3_1(a863))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(512,axiom,((~hskp19) | c3_1(a863)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.62/0.85 tff(513,plain,
% 0.62/0.85 ((~hskp19) | c3_1(a863)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.62/0.85 tff(514,plain,
% 0.62/0.85 ((~hskp19) | c3_1(a863)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[513, 511])).
% 0.62/0.85 tff(515,plain,
% 0.62/0.85 ((~hskp19) | c3_1(a863)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[514, 511])).
% 0.62/0.85 tff(516,plain,
% 0.62/0.85 ((~hskp19) | c3_1(a863)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[515, 511])).
% 0.62/0.85 tff(517,plain,
% 0.62/0.85 ((~hskp19) | c3_1(a863)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[516, 511])).
% 0.62/0.85 tff(518,plain,
% 0.62/0.85 (c3_1(a863)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[517, 489])).
% 0.62/0.85 tff(519,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | c1_1(a863) | (~c3_1(a863)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(520,plain,
% 0.62/0.85 ((hskp13 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863))) <=> (hskp13 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | c1_1(a863) | (~c3_1(a863)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(521,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | c1_1(a863) | (~c3_1(a863))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[520])).
% 0.62/0.85 tff(522,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | c1_1(a863) | (~c3_1(a863)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[521, 519])).
% 0.62/0.85 tff(523,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(524,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | c1_1(a863) | (~c3_1(a863))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.62/0.85 tff(525,plain,
% 0.62/0.85 (hskp13),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[524, 114, 518, 337, 495, 308, 302, 383, 510])).
% 0.62/0.85 tff(526,plain,
% 0.62/0.85 (~c2_1(a846)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[465, 525])).
% 0.62/0.85 tff(527,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a863) | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a863) | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(528,plain,
% 0.62/0.85 ((hskp3 | (~ndr1_0) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863))) <=> (hskp3 | c2_1(a863) | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(529,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a863) | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[528])).
% 0.62/0.85 tff(530,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a863) | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[529, 527])).
% 0.62/0.85 tff(531,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(532,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a863) | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.62/0.85 tff(533,plain,
% 0.62/0.85 (hskp3),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[532, 114, 503, 518, 495, 276, 510])).
% 0.62/0.85 tff(534,plain,
% 0.62/0.85 (~c1_1(a831)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[239, 533])).
% 0.62/0.85 tff(535,plain,
% 0.62/0.85 (c3_1(a831)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[247, 533])).
% 0.62/0.85 tff(536,plain,
% 0.62/0.85 (c2_1(a831)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[255, 533])).
% 0.62/0.85 tff(537,plain,
% 0.62/0.85 (hskp5),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[263, 114, 35, 536, 535, 534, 233])).
% 0.62/0.85 tff(538,plain,
% 0.62/0.85 (~c3_1(a833)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[66, 537])).
% 0.62/0.85 tff(539,plain,
% 0.62/0.85 (c2_1(a833)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[138, 537])).
% 0.62/0.85 tff(540,plain,
% 0.62/0.85 (c0_1(a833)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[82, 537])).
% 0.62/0.85 tff(541,plain,
% 0.62/0.85 (hskp6),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[145, 114, 35, 540, 539, 538, 131])).
% 0.62/0.85 tff(542,plain,
% 0.62/0.85 (~c3_1(a835)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[151, 541])).
% 0.62/0.85 tff(543,plain,
% 0.62/0.85 (~c2_1(a835)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[157, 541])).
% 0.62/0.85 tff(544,plain,
% 0.62/0.85 (((~hskp6) | (~c0_1(a835))) <=> ((~hskp6) | (~c0_1(a835)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(545,plain,
% 0.62/0.85 (((~c0_1(a835)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a835)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(546,axiom,((~c0_1(a835)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.62/0.85 tff(547,plain,
% 0.62/0.85 ((~hskp6) | (~c0_1(a835))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.62/0.85 tff(548,plain,
% 0.62/0.85 ((~hskp6) | (~c0_1(a835))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[547, 544])).
% 0.62/0.85 tff(549,plain,
% 0.62/0.85 (~c0_1(a835)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[548, 541])).
% 0.62/0.85 tff(550,plain,
% 0.62/0.85 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.62/0.85 inference(bind,[status(th)],[])).
% 0.62/0.85 tff(551,plain,
% 0.62/0.85 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.85 inference(quant_intro,[status(thm)],[550])).
% 0.62/0.85 tff(552,plain,
% 0.62/0.85 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(553,plain,
% 0.62/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp24) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp24))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.62/0.85 inference(bind,[status(th)],[])).
% 0.62/0.85 tff(554,plain,
% 0.62/0.85 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.85 inference(quant_intro,[status(thm)],[553])).
% 0.62/0.85 tff(555,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.62/0.85 tff(556,plain,
% 0.62/0.85 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.62/0.85 tff(557,plain,
% 0.62/0.85 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[556, 552])).
% 0.62/0.85 tff(558,plain,(
% 0.62/0.85 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.85 inference(skolemize,[status(sab)],[557])).
% 0.62/0.85 tff(559,plain,
% 0.62/0.85 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[558, 551])).
% 0.62/0.85 tff(560,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp24 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | c1_1(a863) | (~c3_1(a863)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(561,plain,
% 0.62/0.85 ((hskp24 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863))) <=> (hskp24 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | c1_1(a863) | (~c3_1(a863)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(562,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | c1_1(a863) | (~c3_1(a863))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[561])).
% 0.62/0.85 tff(563,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp24 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | c1_1(a863) | (~c3_1(a863)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[562, 560])).
% 0.62/0.85 tff(564,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(565,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp24 | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | c1_1(a863) | (~c3_1(a863))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[564, 563])).
% 0.62/0.85 tff(566,plain,
% 0.62/0.85 (hskp24),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[565, 114, 518, 337, 495, 308, 302, 559, 510])).
% 0.62/0.85 tff(567,plain,
% 0.62/0.85 (((~hskp24) | (~c2_1(a884))) <=> ((~hskp24) | (~c2_1(a884)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(568,plain,
% 0.62/0.85 (((~c2_1(a884)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a884)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(569,axiom,((~c2_1(a884)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.62/0.85 tff(570,plain,
% 0.62/0.85 ((~hskp24) | (~c2_1(a884))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[569, 568])).
% 0.62/0.85 tff(571,plain,
% 0.62/0.85 ((~hskp24) | (~c2_1(a884))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[570, 567])).
% 0.62/0.85 tff(572,plain,
% 0.62/0.85 (~c2_1(a884)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[571, 566])).
% 0.62/0.85 tff(573,plain,
% 0.62/0.85 (((~hskp24) | c1_1(a884)) <=> ((~hskp24) | c1_1(a884))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(574,axiom,((~hskp24) | c1_1(a884)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.62/0.85 tff(575,plain,
% 0.62/0.85 ((~hskp24) | c1_1(a884)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[574, 573])).
% 0.62/0.85 tff(576,plain,
% 0.62/0.85 ((~hskp24) | c1_1(a884)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[575, 573])).
% 0.62/0.85 tff(577,plain,
% 0.62/0.85 ((~hskp24) | c1_1(a884)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[576, 573])).
% 0.62/0.85 tff(578,plain,
% 0.62/0.85 ((~hskp24) | c1_1(a884)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[577, 573])).
% 0.62/0.85 tff(579,plain,
% 0.62/0.85 ((~hskp24) | c1_1(a884)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[578, 573])).
% 0.62/0.85 tff(580,plain,
% 0.62/0.85 (c1_1(a884)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[579, 566])).
% 0.62/0.85 tff(581,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c2_1(a884) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | (~c1_1(a884)) | (~c0_1(a884)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c2_1(a884) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | (~c1_1(a884)) | (~c0_1(a884)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(582,plain,
% 0.62/0.85 ((hskp31 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c0_1(a884)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859))) <=> (hskp31 | c2_1(a884) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | (~c1_1(a884)) | (~c0_1(a884)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(583,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c0_1(a884)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c2_1(a884) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | (~c1_1(a884)) | (~c0_1(a884))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[582])).
% 0.62/0.85 tff(584,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c0_1(a884)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c2_1(a884) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | (~c1_1(a884)) | (~c0_1(a884)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[583, 581])).
% 0.62/0.85 tff(585,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c0_1(a884)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(586,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c2_1(a884) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)) | (~c1_1(a884)) | (~c0_1(a884))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.62/0.85 tff(587,plain,
% 0.62/0.85 (~c0_1(a884)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[586, 285, 114, 580, 337, 572, 308, 302, 295])).
% 0.62/0.85 tff(588,plain,
% 0.62/0.85 (((~hskp24) | c3_1(a884)) <=> ((~hskp24) | c3_1(a884))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(589,axiom,((~hskp24) | c3_1(a884)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.62/0.85 tff(590,plain,
% 0.62/0.85 ((~hskp24) | c3_1(a884)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[589, 588])).
% 0.62/0.85 tff(591,plain,
% 0.62/0.85 ((~hskp24) | c3_1(a884)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[590, 588])).
% 0.62/0.85 tff(592,plain,
% 0.62/0.85 ((~hskp24) | c3_1(a884)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[591, 588])).
% 0.62/0.85 tff(593,plain,
% 0.62/0.85 ((~hskp24) | c3_1(a884)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[592, 588])).
% 0.62/0.85 tff(594,plain,
% 0.62/0.85 ((~hskp24) | c3_1(a884)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[593, 588])).
% 0.62/0.85 tff(595,plain,
% 0.62/0.85 (c3_1(a884)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[594, 566])).
% 0.62/0.85 tff(596,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a884) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a884)) | c0_1(a884))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a884) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a884)) | c0_1(a884))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(597,plain,
% 0.62/0.85 ((hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a884) | c0_1(a884) | (~c3_1(a884))) <=> (hskp4 | c2_1(a884) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a884)) | c0_1(a884))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(598,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a884) | c0_1(a884) | (~c3_1(a884)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a884) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a884)) | c0_1(a884)))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[597])).
% 0.62/0.85 tff(599,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a884) | c0_1(a884) | (~c3_1(a884)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a884) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a884)) | c0_1(a884))),
% 0.62/0.85 inference(transitivity,[status(thm)],[598, 596])).
% 0.62/0.85 tff(600,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a884) | c0_1(a884) | (~c3_1(a884)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(601,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a884) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a884)) | c0_1(a884)),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.62/0.85 tff(602,plain,
% 0.62/0.85 (hskp4),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[601, 114, 595, 540, 539, 572, 538, 373, 587])).
% 0.62/0.85 tff(603,plain,
% 0.62/0.85 (~c1_1(a832)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[402, 602])).
% 0.62/0.85 tff(604,plain,
% 0.62/0.85 (~c2_1(a832)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[396, 602])).
% 0.62/0.85 tff(605,plain,
% 0.62/0.85 (~c3_1(a832)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[390, 602])).
% 0.62/0.85 tff(606,assumption,(~c3_1(a832)), introduced(assumption)).
% 0.62/0.85 tff(607,assumption,(~c2_1(a832)), introduced(assumption)).
% 0.62/0.85 tff(608,assumption,(~c1_1(a832)), introduced(assumption)).
% 0.62/0.85 tff(609,assumption,(~c1_1(a863)), introduced(assumption)).
% 0.62/0.85 tff(610,plain,
% 0.62/0.85 (hskp19 | c1_1(a832) | c2_1(a832)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[409, 285, 114, 606, 355])).
% 0.62/0.85 tff(611,plain,
% 0.62/0.85 (hskp19),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[610, 608, 607])).
% 0.62/0.85 tff(612,plain,
% 0.62/0.85 (~c2_1(a863)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[494, 611])).
% 0.62/0.85 tff(613,plain,
% 0.62/0.85 (c3_1(a863)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[517, 611])).
% 0.62/0.85 tff(614,plain,
% 0.62/0.85 (c0_1(a863)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[502, 611])).
% 0.62/0.85 tff(615,plain,
% 0.62/0.85 (hskp3 | c1_1(a863)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[532, 114, 614, 613, 612, 276])).
% 0.62/0.85 tff(616,plain,
% 0.62/0.85 (hskp3),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[615, 609])).
% 0.62/0.85 tff(617,plain,
% 0.62/0.85 (c3_1(a831)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[247, 616])).
% 0.62/0.85 tff(618,plain,
% 0.62/0.85 (c2_1(a831)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[255, 616])).
% 0.62/0.85 tff(619,assumption,(~c1_1(a831)), introduced(assumption)).
% 0.62/0.85 tff(620,plain,
% 0.62/0.85 (hskp5 | (~c3_1(a831)) | (~c2_1(a831))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[263, 114, 35, 619, 233])).
% 0.62/0.85 tff(621,plain,
% 0.62/0.85 (hskp5),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[620, 618, 617])).
% 0.62/0.85 tff(622,plain,
% 0.62/0.85 (c2_1(a833)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[138, 621])).
% 0.62/0.85 tff(623,plain,
% 0.62/0.85 (c0_1(a833)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[82, 621])).
% 0.62/0.85 tff(624,assumption,(~c3_1(a833)), introduced(assumption)).
% 0.62/0.85 tff(625,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a863) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a863) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a863) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a863) | (~c0_1(a863)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(626,plain,
% 0.62/0.85 ((hskp14 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863))) <=> (hskp14 | c2_1(a863) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a863) | (~c0_1(a863)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(627,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a863) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a863) | (~c0_1(a863))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[626])).
% 0.62/0.85 tff(628,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a863) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a863) | (~c0_1(a863)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[627, 625])).
% 0.62/0.85 tff(629,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(630,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a863) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a863) | (~c0_1(a863))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.62/0.85 tff(631,plain,
% 0.62/0.85 (hskp14 | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a863)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[630, 114, 614, 612, 624, 185])).
% 0.62/0.85 tff(632,plain,
% 0.62/0.85 (hskp14),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[631, 623, 622, 609])).
% 0.62/0.85 tff(633,plain,
% 0.62/0.85 (~c3_1(a851)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[197, 632])).
% 0.62/0.85 tff(634,plain,
% 0.62/0.85 (c2_1(a851)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[205, 632])).
% 0.62/0.85 tff(635,plain,
% 0.62/0.85 (c1_1(a851)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[213, 632])).
% 0.62/0.85 tff(636,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c3_1(a851) | c2_1(a838) | c3_1(a838) | (~ndr1_0) | (~c1_1(a838)) | (~c2_1(a851)) | (~c1_1(a851)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a851) | c2_1(a838) | c3_1(a838) | (~ndr1_0) | (~c1_1(a838)) | (~c2_1(a851)) | (~c1_1(a851)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(637,plain,
% 0.62/0.85 ((hskp17 | (~ndr1_0) | c3_1(a851) | (~c2_1(a851)) | (~c1_1(a851)) | c2_1(a838) | c3_1(a838) | (~c1_1(a838))) <=> (hskp17 | c3_1(a851) | c2_1(a838) | c3_1(a838) | (~ndr1_0) | (~c1_1(a838)) | (~c2_1(a851)) | (~c1_1(a851)))),
% 0.62/0.86 inference(rewrite,[status(thm)],[])).
% 0.62/0.86 tff(638,plain,
% 0.62/0.86 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a851) | (~c2_1(a851)) | (~c1_1(a851)) | c2_1(a838) | c3_1(a838) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c3_1(a851) | c2_1(a838) | c3_1(a838) | (~ndr1_0) | (~c1_1(a838)) | (~c2_1(a851)) | (~c1_1(a851))))),
% 0.62/0.86 inference(monotonicity,[status(thm)],[637])).
% 0.62/0.86 tff(639,plain,
% 0.62/0.86 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a851) | (~c2_1(a851)) | (~c1_1(a851)) | c2_1(a838) | c3_1(a838) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a851) | c2_1(a838) | c3_1(a838) | (~ndr1_0) | (~c1_1(a838)) | (~c2_1(a851)) | (~c1_1(a851)))),
% 0.62/0.86 inference(transitivity,[status(thm)],[638, 636])).
% 0.62/0.86 tff(640,plain,
% 0.62/0.86 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a851) | (~c2_1(a851)) | (~c1_1(a851)) | c2_1(a838) | c3_1(a838) | (~c1_1(a838)))),
% 0.62/0.86 inference(quant_inst,[status(thm)],[])).
% 0.62/0.86 tff(641,plain,
% 0.62/0.86 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a851) | c2_1(a838) | c3_1(a838) | (~ndr1_0) | (~c1_1(a838)) | (~c2_1(a851)) | (~c1_1(a851))),
% 0.62/0.86 inference(modus_ponens,[status(thm)],[640, 639])).
% 0.62/0.86 tff(642,plain,
% 0.62/0.86 (hskp17),
% 0.62/0.86 inference(unit_resolution,[status(thm)],[641, 114, 635, 634, 329, 633, 321, 315, 175])).
% 0.62/0.86 tff(643,plain,
% 0.62/0.86 (~c3_1(a859)),
% 0.62/0.86 inference(unit_resolution,[status(thm)],[301, 642])).
% 0.62/0.86 tff(644,plain,
% 0.62/0.86 (~c1_1(a859)),
% 0.62/0.86 inference(unit_resolution,[status(thm)],[307, 642])).
% 0.62/0.86 tff(645,plain,
% 0.62/0.86 (c0_1(a859)),
% 0.62/0.86 inference(unit_resolution,[status(thm)],[336, 642])).
% 0.62/0.86 tff(646,plain,
% 0.62/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a859) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a859) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.62/0.86 inference(rewrite,[status(thm)],[])).
% 0.62/0.86 tff(647,plain,
% 0.62/0.86 (((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c3_1(a832) | c2_1(a832) | c1_1(a832)) <=> (c1_1(a859) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.62/0.86 inference(rewrite,[status(thm)],[])).
% 0.62/0.86 tff(648,plain,
% 0.62/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a859) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859))))),
% 0.62/0.86 inference(monotonicity,[status(thm)],[647])).
% 0.62/0.86 tff(649,plain,
% 0.62/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a859) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.62/0.86 inference(transitivity,[status(thm)],[648, 646])).
% 0.62/0.86 tff(650,plain,
% 0.62/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c3_1(a832) | c2_1(a832) | c1_1(a832))),
% 0.62/0.86 inference(quant_inst,[status(thm)],[])).
% 0.62/0.86 tff(651,plain,
% 0.62/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a859) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859))),
% 0.62/0.86 inference(modus_ponens,[status(thm)],[650, 649])).
% 0.62/0.86 tff(652,plain,
% 0.62/0.86 (~c2_1(a859)),
% 0.62/0.86 inference(unit_resolution,[status(thm)],[651, 114, 645, 644, 643, 608, 607, 606, 22])).
% 0.62/0.86 tff(653,plain,
% 0.62/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 0.62/0.86 inference(bind,[status(th)],[])).
% 0.62/0.86 tff(654,plain,
% 0.62/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.62/0.86 inference(quant_intro,[status(thm)],[653])).
% 0.62/0.86 tff(655,plain,
% 0.62/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.62/0.86 inference(rewrite,[status(thm)],[])).
% 0.62/0.86 tff(656,plain,
% 0.62/0.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 0.62/0.86 inference(bind,[status(th)],[])).
% 0.62/0.86 tff(657,plain,
% 0.62/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.62/0.86 inference(quant_intro,[status(thm)],[656])).
% 0.62/0.86 tff(658,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause206')).
% 0.62/0.86 tff(659,plain,
% 0.62/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.62/0.86 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.62/0.86 tff(660,plain,
% 0.62/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.62/0.86 inference(modus_ponens,[status(thm)],[659, 655])).
% 0.62/0.86 tff(661,plain,(
% 0.62/0.86 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.62/0.86 inference(skolemize,[status(sab)],[660])).
% 0.62/0.86 tff(662,plain,
% 0.62/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.62/0.86 inference(modus_ponens,[status(thm)],[661, 654])).
% 0.62/0.86 tff(663,assumption,(~c3_1(a835)), introduced(assumption)).
% 0.62/0.86 tff(664,assumption,(~c2_1(a835)), introduced(assumption)).
% 0.62/0.86 tff(665,assumption,(~c0_1(a835)), introduced(assumption)).
% 0.62/0.86 tff(666,assumption,(~c2_1(a846)), introduced(assumption)).
% 0.62/0.86 tff(667,plain,
% 0.62/0.86 (hskp13),
% 0.62/0.86 inference(unit_resolution,[status(thm)],[524, 114, 613, 645, 612, 644, 643, 383, 609])).
% 0.62/0.86 tff(668,plain,
% 0.62/0.86 (~c0_1(a846)),
% 0.62/0.86 inference(unit_resolution,[status(thm)],[471, 667])).
% 0.62/0.86 tff(669,assumption,(~hskp0), introduced(assumption)).
% 0.62/0.86 tff(670,plain,
% 0.62/0.86 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.62/0.86 inference(bind,[status(th)],[])).
% 0.62/0.86 tff(671,plain,
% 0.62/0.86 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.86 inference(quant_intro,[status(thm)],[670])).
% 0.62/0.86 tff(672,plain,
% 0.62/0.86 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.86 inference(rewrite,[status(thm)],[])).
% 0.62/0.86 tff(673,plain,
% 0.62/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c0_1(V))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c0_1(V)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c1_1(V) | c0_1(V))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c1_1(V) | c0_1(V)))), ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.62/0.86 inference(bind,[status(th)],[])).
% 0.62/0.86 tff(674,plain,
% 0.62/0.86 (![V: $i, U: $i] : ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.86 inference(quant_intro,[status(thm)],[673])).
% 0.62/0.86 tff(675,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.70/0.86 tff(676,plain,
% 0.70/0.86 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.70/0.86 tff(677,plain,
% 0.70/0.86 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[676, 672])).
% 0.70/0.86 tff(678,plain,(
% 0.70/0.86 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.70/0.86 inference(skolemize,[status(sab)],[677])).
% 0.70/0.86 tff(679,plain,
% 0.70/0.86 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[678, 671])).
% 0.70/0.86 tff(680,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(681,plain,
% 0.70/0.86 ((hskp0 | (~ndr1_0) | c2_1(a832) | c0_1(a832) | c3_1(a832) | c2_1(a832) | c1_1(a832) | c0_1(a832)) <=> (hskp0 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(682,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a832) | c0_1(a832) | c3_1(a832) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832)))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[681])).
% 0.70/0.86 tff(683,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a832) | c0_1(a832) | c3_1(a832) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 0.70/0.86 inference(transitivity,[status(thm)],[682, 680])).
% 0.70/0.86 tff(684,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a832) | c0_1(a832) | c3_1(a832) | c2_1(a832) | c1_1(a832) | c0_1(a832))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(685,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[684, 683])).
% 0.70/0.86 tff(686,plain,
% 0.70/0.86 (hskp0 | c1_1(a832) | c0_1(a832)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[685, 114, 607, 606, 679])).
% 0.70/0.86 tff(687,plain,
% 0.70/0.86 (c0_1(a832)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[686, 669, 608])).
% 0.70/0.86 tff(688,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c2_1(a863) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c1_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c2_1(a863) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c1_1(a863)) | (~c0_1(a863)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(689,plain,
% 0.70/0.86 ((hskp31 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c0_1(a863)) | c1_1(a832) | c3_1(a832) | (~c0_1(a832))) <=> (hskp31 | c2_1(a863) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c1_1(a863)) | (~c0_1(a863)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(690,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c0_1(a863)) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c2_1(a863) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c1_1(a863)) | (~c0_1(a863))))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[689])).
% 0.70/0.86 tff(691,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c0_1(a863)) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c2_1(a863) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c1_1(a863)) | (~c0_1(a863)))),
% 0.70/0.86 inference(transitivity,[status(thm)],[690, 688])).
% 0.70/0.86 tff(692,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c0_1(a863)) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(693,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c2_1(a863) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c1_1(a863)) | (~c0_1(a863))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[692, 691])).
% 0.70/0.86 tff(694,plain,
% 0.70/0.86 ((~c0_1(a832)) | (~c1_1(a863))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[693, 285, 114, 614, 612, 608, 606, 295])).
% 0.70/0.86 tff(695,plain,
% 0.70/0.86 (~c1_1(a863)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[694, 687])).
% 0.70/0.86 tff(696,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | c2_1(a863) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c2_1(a863) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c1_1(a863) | (~c3_1(a863)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(697,plain,
% 0.70/0.86 ((hskp13 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863))) <=> (hskp13 | c2_1(a863) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c1_1(a863) | (~c3_1(a863)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(698,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | c2_1(a863) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c1_1(a863) | (~c3_1(a863))))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[697])).
% 0.70/0.86 tff(699,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c2_1(a863) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c1_1(a863) | (~c3_1(a863)))),
% 0.70/0.86 inference(transitivity,[status(thm)],[698, 696])).
% 0.70/0.86 tff(700,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(701,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c2_1(a863) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c1_1(a863) | (~c3_1(a863))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.70/0.86 tff(702,plain,
% 0.70/0.86 (hskp13 | (~c0_1(a832)) | c1_1(a863)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[701, 114, 613, 612, 608, 606, 383])).
% 0.70/0.86 tff(703,plain,
% 0.70/0.86 (hskp13),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[702, 687, 695])).
% 0.70/0.86 tff(704,assumption,(~c0_1(a846)), introduced(assumption)).
% 0.70/0.86 tff(705,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a846) | c2_1(a846) | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | c1_1(a846))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a846) | c2_1(a846) | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | c1_1(a846))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(706,plain,
% 0.70/0.86 ((hskp0 | (~ndr1_0) | c2_1(a835) | c0_1(a835) | c3_1(a835) | c2_1(a846) | c1_1(a846) | c0_1(a846)) <=> (hskp0 | c0_1(a846) | c2_1(a846) | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | c1_1(a846))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(707,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a835) | c0_1(a835) | c3_1(a835) | c2_1(a846) | c1_1(a846) | c0_1(a846))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a846) | c2_1(a846) | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | c1_1(a846)))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[706])).
% 0.70/0.86 tff(708,plain,
% 0.70/0.86 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a835) | c0_1(a835) | c3_1(a835) | c2_1(a846) | c1_1(a846) | c0_1(a846))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a846) | c2_1(a846) | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | c1_1(a846))),
% 0.70/0.86 inference(transitivity,[status(thm)],[707, 705])).
% 0.70/0.86 tff(709,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a835) | c0_1(a835) | c3_1(a835) | c2_1(a846) | c1_1(a846) | c0_1(a846))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(710,plain,
% 0.70/0.86 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a846) | c2_1(a846) | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | c1_1(a846)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[709, 708])).
% 0.70/0.86 tff(711,plain,
% 0.70/0.86 (hskp0 | c0_1(a846) | c1_1(a846)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[710, 114, 666, 665, 664, 663, 679])).
% 0.70/0.86 tff(712,plain,
% 0.70/0.86 (c1_1(a846)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[711, 669, 704])).
% 0.70/0.86 tff(713,plain,
% 0.70/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 0.70/0.86 inference(bind,[status(th)],[])).
% 0.70/0.86 tff(714,plain,
% 0.70/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.70/0.86 inference(quant_intro,[status(thm)],[713])).
% 0.70/0.86 tff(715,plain,
% 0.70/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(716,plain,
% 0.70/0.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(717,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[716])).
% 0.70/0.87 tff(718,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 0.70/0.87 tff(719,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[718, 717])).
% 0.70/0.87 tff(720,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[719, 715])).
% 0.70/0.87 tff(721,plain,(
% 0.70/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[720])).
% 0.70/0.87 tff(722,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[721, 714])).
% 0.70/0.87 tff(723,plain,
% 0.70/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a846) | c2_1(a846) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c1_1(a846)) | (~c3_1(a846)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a846) | c2_1(a846) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c1_1(a846)) | (~c3_1(a846)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(724,plain,
% 0.70/0.87 (((~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a832) | c3_1(a832) | (~c0_1(a832)) | c0_1(a846) | (~c3_1(a846)) | (~c1_1(a846))) <=> (c0_1(a846) | c2_1(a846) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c1_1(a846)) | (~c3_1(a846)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(725,plain,
% 0.70/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a832) | c3_1(a832) | (~c0_1(a832)) | c0_1(a846) | (~c3_1(a846)) | (~c1_1(a846)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a846) | c2_1(a846) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c1_1(a846)) | (~c3_1(a846))))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[724])).
% 0.70/0.87 tff(726,plain,
% 0.70/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a832) | c3_1(a832) | (~c0_1(a832)) | c0_1(a846) | (~c3_1(a846)) | (~c1_1(a846)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a846) | c2_1(a846) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c1_1(a846)) | (~c3_1(a846)))),
% 0.70/0.87 inference(transitivity,[status(thm)],[725, 723])).
% 0.70/0.87 tff(727,plain,
% 0.70/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a832) | c3_1(a832) | (~c0_1(a832)) | c0_1(a846) | (~c3_1(a846)) | (~c1_1(a846)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(728,plain,
% 0.70/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a846) | c2_1(a846) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c1_1(a846)) | (~c3_1(a846))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[727, 726])).
% 0.70/0.87 tff(729,plain,
% 0.70/0.87 ((~c0_1(a832)) | (~c1_1(a846)) | (~c3_1(a846))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[728, 114, 704, 666, 607, 606, 722])).
% 0.70/0.87 tff(730,plain,
% 0.70/0.87 (~c3_1(a846)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[729, 687, 712])).
% 0.70/0.87 tff(731,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[479, 730, 703])).
% 0.70/0.87 tff(732,plain,(hskp0 | c0_1(a846) | c2_1(a846) | c2_1(a832) | c3_1(a832) | c1_1(a832) | hskp31 | c0_1(a835) | c2_1(a835) | c3_1(a835)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(733,plain,
% 0.70/0.87 (hskp0),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[732, 668, 666, 607, 606, 608, 285, 665, 664, 663])).
% 0.70/0.87 tff(734,plain,
% 0.70/0.87 (((~hskp0) | (~c0_1(a828))) <=> ((~hskp0) | (~c0_1(a828)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(735,plain,
% 0.70/0.87 (((~c0_1(a828)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a828)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(736,axiom,((~c0_1(a828)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.70/0.87 tff(737,plain,
% 0.70/0.87 ((~hskp0) | (~c0_1(a828))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.70/0.87 tff(738,plain,
% 0.70/0.87 ((~hskp0) | (~c0_1(a828))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[737, 734])).
% 0.70/0.87 tff(739,plain,
% 0.70/0.87 (~c0_1(a828)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[738, 733])).
% 0.70/0.87 tff(740,plain,
% 0.70/0.87 (((~hskp0) | c2_1(a828)) <=> ((~hskp0) | c2_1(a828))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(741,axiom,((~hskp0) | c2_1(a828)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.70/0.87 tff(742,plain,
% 0.70/0.87 ((~hskp0) | c2_1(a828)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[741, 740])).
% 0.70/0.87 tff(743,plain,
% 0.70/0.87 ((~hskp0) | c2_1(a828)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[742, 740])).
% 0.70/0.87 tff(744,plain,
% 0.70/0.87 ((~hskp0) | c2_1(a828)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[743, 740])).
% 0.70/0.87 tff(745,plain,
% 0.70/0.87 ((~hskp0) | c2_1(a828)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[744, 740])).
% 0.70/0.87 tff(746,plain,
% 0.70/0.87 ((~hskp0) | c2_1(a828)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[745, 740])).
% 0.70/0.87 tff(747,plain,
% 0.70/0.87 (c2_1(a828)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[746, 733])).
% 0.70/0.87 tff(748,plain,
% 0.70/0.87 (((~hskp0) | c1_1(a828)) <=> ((~hskp0) | c1_1(a828))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(749,axiom,((~hskp0) | c1_1(a828)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.70/0.87 tff(750,plain,
% 0.70/0.87 ((~hskp0) | c1_1(a828)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[749, 748])).
% 0.70/0.87 tff(751,plain,
% 0.70/0.87 ((~hskp0) | c1_1(a828)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[750, 748])).
% 0.70/0.87 tff(752,plain,
% 0.70/0.87 ((~hskp0) | c1_1(a828)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[751, 748])).
% 0.70/0.87 tff(753,plain,
% 0.70/0.87 ((~hskp0) | c1_1(a828)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[752, 748])).
% 0.70/0.87 tff(754,plain,
% 0.70/0.87 ((~hskp0) | c1_1(a828)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[753, 748])).
% 0.70/0.87 tff(755,plain,
% 0.70/0.87 (c1_1(a828)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[754, 733])).
% 0.70/0.87 tff(756,plain,
% 0.70/0.87 (c3_1(a846)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[479, 667])).
% 0.70/0.87 tff(757,plain,
% 0.70/0.87 (^[U: $i] : refl((hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(758,plain,
% 0.70/0.87 (![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[757])).
% 0.70/0.87 tff(759,plain,
% 0.70/0.87 (![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(760,plain,
% 0.70/0.87 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp30))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp16) <=> ((hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp16))), rewrite(((hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp16) <=> (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp16) <=> (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(761,plain,
% 0.70/0.87 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp16) <=> ![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[760])).
% 0.70/0.87 tff(762,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.70/0.87 tff(763,plain,
% 0.70/0.87 (![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[762, 761])).
% 0.70/0.87 tff(764,plain,
% 0.70/0.87 (![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[763, 759])).
% 0.70/0.87 tff(765,plain,(
% 0.70/0.87 ![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[764])).
% 0.70/0.87 tff(766,plain,
% 0.70/0.87 (![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[765, 758])).
% 0.70/0.87 tff(767,plain,
% 0.70/0.87 (((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c3_1(a846)))) <=> ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp16 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c3_1(a846)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(768,plain,
% 0.70/0.87 ((hskp30 | hskp16 | (~ndr1_0) | c2_1(a846) | c0_1(a846) | (~c3_1(a846))) <=> (hskp30 | hskp16 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c3_1(a846)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(769,plain,
% 0.70/0.87 (((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | (~ndr1_0) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c3_1(a846))))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[768])).
% 0.70/0.87 tff(770,plain,
% 0.70/0.87 (((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | (~ndr1_0) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp16 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c3_1(a846)))),
% 0.70/0.87 inference(transitivity,[status(thm)],[769, 767])).
% 0.70/0.87 tff(771,plain,
% 0.70/0.87 ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | (~ndr1_0) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(772,plain,
% 0.70/0.87 ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp16 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c3_1(a846))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[771, 770])).
% 0.70/0.87 tff(773,plain,
% 0.70/0.87 (hskp30 | c0_1(a846) | (~c3_1(a846))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[772, 114, 35, 666, 766])).
% 0.70/0.87 tff(774,plain,
% 0.70/0.87 (hskp30),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[773, 756, 668])).
% 0.70/0.87 tff(775,plain,
% 0.70/0.87 (((~hskp30) | c3_1(a857)) <=> ((~hskp30) | c3_1(a857))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(776,axiom,((~hskp30) | c3_1(a857)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.70/0.87 tff(777,plain,
% 0.70/0.87 ((~hskp30) | c3_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[776, 775])).
% 0.70/0.87 tff(778,plain,
% 0.70/0.87 ((~hskp30) | c3_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[777, 775])).
% 0.70/0.87 tff(779,plain,
% 0.70/0.87 ((~hskp30) | c3_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[778, 775])).
% 0.70/0.87 tff(780,plain,
% 0.70/0.87 ((~hskp30) | c3_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[779, 775])).
% 0.70/0.87 tff(781,plain,
% 0.70/0.87 ((~hskp30) | c3_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[780, 775])).
% 0.70/0.87 tff(782,plain,
% 0.70/0.87 (c3_1(a857)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[781, 774])).
% 0.70/0.87 tff(783,plain,
% 0.70/0.87 (((~hskp30) | c2_1(a857)) <=> ((~hskp30) | c2_1(a857))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(784,axiom,((~hskp30) | c2_1(a857)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.70/0.87 tff(785,plain,
% 0.70/0.87 ((~hskp30) | c2_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[784, 783])).
% 0.70/0.87 tff(786,plain,
% 0.70/0.87 ((~hskp30) | c2_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[785, 783])).
% 0.70/0.87 tff(787,plain,
% 0.70/0.87 ((~hskp30) | c2_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[786, 783])).
% 0.70/0.87 tff(788,plain,
% 0.70/0.87 ((~hskp30) | c2_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[787, 783])).
% 0.70/0.87 tff(789,plain,
% 0.70/0.87 ((~hskp30) | c2_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[788, 783])).
% 0.70/0.87 tff(790,plain,
% 0.70/0.87 (c2_1(a857)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[789, 774])).
% 0.70/0.87 tff(791,plain,
% 0.70/0.87 (((~hskp30) | c1_1(a857)) <=> ((~hskp30) | c1_1(a857))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(792,axiom,((~hskp30) | c1_1(a857)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.70/0.87 tff(793,plain,
% 0.70/0.87 ((~hskp30) | c1_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[792, 791])).
% 0.70/0.87 tff(794,plain,
% 0.70/0.87 ((~hskp30) | c1_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[793, 791])).
% 0.70/0.87 tff(795,plain,
% 0.70/0.87 ((~hskp30) | c1_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[794, 791])).
% 0.70/0.87 tff(796,plain,
% 0.70/0.87 ((~hskp30) | c1_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[795, 791])).
% 0.70/0.87 tff(797,plain,
% 0.70/0.87 ((~hskp30) | c1_1(a857)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[796, 791])).
% 0.70/0.87 tff(798,plain,
% 0.70/0.87 (c1_1(a857)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[797, 774])).
% 0.70/0.87 tff(799,plain,
% 0.70/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a859) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | c2_1(a859) | (~c0_1(a859)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a859) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | c2_1(a859) | (~c0_1(a859)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(800,plain,
% 0.70/0.87 (((~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828))) <=> (c3_1(a859) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | c2_1(a859) | (~c0_1(a859)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(801,plain,
% 0.70/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a859) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | c2_1(a859) | (~c0_1(a859))))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[800])).
% 0.70/0.87 tff(802,plain,
% 0.70/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a859) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | c2_1(a859) | (~c0_1(a859)))),
% 0.70/0.87 inference(transitivity,[status(thm)],[801, 799])).
% 0.70/0.87 tff(803,plain,
% 0.70/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(804,plain,
% 0.70/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a859) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | c2_1(a859) | (~c0_1(a859))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[803, 802])).
% 0.70/0.87 tff(805,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[804, 114, 798, 790, 782, 645, 755, 747, 643, 739, 662, 652])).
% 0.70/0.87 tff(806,plain,(c1_1(a863) | c2_1(a846) | c2_1(a832) | c3_1(a832) | c1_1(a832) | hskp31 | c0_1(a835) | c2_1(a835) | c3_1(a835) | hskp16 | c3_1(a833) | c1_1(a831)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(807,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[806, 605, 604, 510, 534, 603, 285, 549, 543, 542, 35, 538, 526])).
% 0.70/0.87 tff(808,plain,((~hskp17) | hskp31 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(809,plain,
% 0.70/0.87 (~hskp17),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[808, 285, 35])).
% 0.70/0.87 tff(810,plain,
% 0.70/0.87 (hskp2),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[47, 809, 35])).
% 0.70/0.87 tff(811,plain,
% 0.70/0.87 (~c1_1(a830)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[59, 810])).
% 0.70/0.87 tff(812,plain,
% 0.70/0.87 (~c2_1(a830)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[53, 810])).
% 0.70/0.87 tff(813,assumption,(~c2_1(a830)), introduced(assumption)).
% 0.70/0.87 tff(814,assumption,(~c1_1(a830)), introduced(assumption)).
% 0.70/0.87 tff(815,plain,
% 0.70/0.87 (^[U: $i] : refl((hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(816,plain,
% 0.70/0.87 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[815])).
% 0.70/0.87 tff(817,plain,
% 0.70/0.87 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(818,plain,
% 0.70/0.87 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp17) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp17) | hskp4) <=> ((hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp4))), rewrite(((hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp4) <=> (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp17) | hskp4) <=> (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(819,plain,
% 0.70/0.87 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp17) | hskp4) <=> ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[818])).
% 0.70/0.87 tff(820,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp17) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.70/0.87 tff(821,plain,
% 0.70/0.87 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[820, 819])).
% 0.70/0.87 tff(822,plain,
% 0.70/0.87 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[821, 817])).
% 0.70/0.87 tff(823,plain,(
% 0.70/0.87 ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[822])).
% 0.70/0.87 tff(824,plain,
% 0.70/0.87 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[823, 816])).
% 0.70/0.87 tff(825,assumption,(c1_1(a838)), introduced(assumption)).
% 0.70/0.87 tff(826,plain,
% 0.70/0.87 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | c3_1(a838) | (~ndr1_0) | c0_1(a838) | (~c1_1(a838)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp4 | c3_1(a838) | (~ndr1_0) | c0_1(a838) | (~c1_1(a838)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(827,plain,
% 0.70/0.87 ((hskp17 | hskp4 | (~ndr1_0) | c0_1(a838) | c3_1(a838) | (~c1_1(a838))) <=> (hskp17 | hskp4 | c3_1(a838) | (~ndr1_0) | c0_1(a838) | (~c1_1(a838)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(828,plain,
% 0.70/0.87 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c0_1(a838) | c3_1(a838) | (~c1_1(a838)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | c3_1(a838) | (~ndr1_0) | c0_1(a838) | (~c1_1(a838))))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[827])).
% 0.70/0.87 tff(829,plain,
% 0.70/0.87 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c0_1(a838) | c3_1(a838) | (~c1_1(a838)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp4 | c3_1(a838) | (~ndr1_0) | c0_1(a838) | (~c1_1(a838)))),
% 0.70/0.87 inference(transitivity,[status(thm)],[828, 826])).
% 0.70/0.87 tff(830,plain,
% 0.70/0.87 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c0_1(a838) | c3_1(a838) | (~c1_1(a838)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(831,plain,
% 0.70/0.87 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp4 | c3_1(a838) | (~ndr1_0) | c0_1(a838) | (~c1_1(a838))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[830, 829])).
% 0.70/0.87 tff(832,plain,
% 0.70/0.87 (hskp17 | hskp4 | c0_1(a838)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[831, 114, 825, 423, 824])).
% 0.70/0.87 tff(833,plain,
% 0.70/0.87 (c0_1(a838)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[832, 36, 11])).
% 0.70/0.87 tff(834,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c3_1(a838) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a838)) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c3_1(a838) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(835,plain,
% 0.70/0.87 ((hskp17 | (~ndr1_0) | c3_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830))) <=> (hskp17 | c3_1(a838) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(836,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c3_1(a838) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a838)) | (~c1_1(a838))))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[835])).
% 0.70/0.87 tff(837,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c3_1(a838) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 0.70/0.87 inference(transitivity,[status(thm)],[836, 834])).
% 0.70/0.87 tff(838,plain,
% 0.70/0.87 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(839,plain,
% 0.70/0.87 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c3_1(a838) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a838)) | (~c1_1(a838))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[838, 837])).
% 0.70/0.87 tff(840,plain,
% 0.70/0.87 (hskp17 | c1_1(a830) | (~c0_1(a830)) | (~c0_1(a838))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[839, 114, 825, 423, 813, 10])).
% 0.70/0.87 tff(841,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[840, 75, 833, 814, 36])).
% 0.70/0.87 tff(842,plain,(hskp17 | c1_1(a830) | (~c1_1(a838)) | c3_1(a838) | c2_1(a830) | hskp4 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(843,plain,
% 0.70/0.87 (hskp17),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[842, 11, 329, 315, 813, 814, 35])).
% 0.70/0.87 tff(844,plain,
% 0.70/0.87 (~c3_1(a859)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[301, 843])).
% 0.70/0.87 tff(845,plain,
% 0.70/0.87 (~c1_1(a859)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[307, 843])).
% 0.70/0.87 tff(846,plain,
% 0.70/0.87 (c0_1(a859)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[336, 843])).
% 0.70/0.87 tff(847,plain,
% 0.70/0.87 (~c0_1(a838)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[343, 285, 114, 846, 329, 845, 844, 321, 295])).
% 0.70/0.87 tff(848,plain,
% 0.70/0.87 (hskp11 | hskp4 | c0_1(a838)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[430, 114, 321, 315, 422])).
% 0.70/0.87 tff(849,plain,
% 0.70/0.87 (hskp11),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[848, 847, 11])).
% 0.70/0.87 tff(850,plain,
% 0.70/0.87 (~c2_1(a844)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[437, 849])).
% 0.70/0.87 tff(851,plain,
% 0.70/0.87 (~c1_1(a844)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[443, 849])).
% 0.70/0.87 tff(852,plain,
% 0.70/0.87 (c3_1(a844)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[451, 849])).
% 0.70/0.87 tff(853,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp24 | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a859)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(854,plain,
% 0.70/0.87 ((hskp24 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a844) | c1_1(a844) | (~c3_1(a844))) <=> (hskp24 | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a859)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(855,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a844) | c1_1(a844) | (~c3_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a859))))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[854])).
% 0.70/0.88 tff(856,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a844) | c1_1(a844) | (~c3_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp24 | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a859)))),
% 0.70/0.88 inference(transitivity,[status(thm)],[855, 853])).
% 0.70/0.88 tff(857,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a844) | c1_1(a844) | (~c3_1(a844)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(858,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp24 | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a859))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[857, 856])).
% 0.70/0.88 tff(859,plain,
% 0.70/0.88 (hskp24),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[858, 114, 846, 852, 845, 844, 851, 850, 559])).
% 0.70/0.88 tff(860,plain,
% 0.70/0.88 (~c2_1(a884)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[571, 859])).
% 0.70/0.88 tff(861,plain,
% 0.70/0.88 (c1_1(a884)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[579, 859])).
% 0.70/0.88 tff(862,plain,
% 0.70/0.88 (~c0_1(a884)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[586, 285, 114, 861, 846, 860, 845, 844, 295])).
% 0.70/0.88 tff(863,plain,
% 0.70/0.88 (hskp13),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[459, 114, 846, 852, 845, 844, 851, 850, 383])).
% 0.70/0.88 tff(864,plain,
% 0.70/0.88 (~c2_1(a846)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[465, 863])).
% 0.70/0.88 tff(865,plain,
% 0.70/0.88 (~c0_1(a846)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[471, 863])).
% 0.70/0.88 tff(866,plain,
% 0.70/0.88 (c3_1(a846)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[479, 863])).
% 0.70/0.88 tff(867,plain,
% 0.70/0.88 (~c2_1(a859)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[486, 114, 11, 846, 866, 844, 865, 864, 373])).
% 0.70/0.88 tff(868,plain,
% 0.70/0.88 (c3_1(a884)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[594, 859])).
% 0.70/0.88 tff(869,plain,
% 0.70/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a884) | c3_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a884)) | (~c3_1(a884)) | c0_1(a884))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a884) | c3_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a884)) | (~c3_1(a884)) | c0_1(a884))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(870,plain,
% 0.70/0.88 (((~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a884) | (~c3_1(a884)) | (~c1_1(a884))) <=> (c2_1(a884) | c3_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a884)) | (~c3_1(a884)) | c0_1(a884))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(871,plain,
% 0.70/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a884) | (~c3_1(a884)) | (~c1_1(a884)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a884) | c3_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a884)) | (~c3_1(a884)) | c0_1(a884)))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[870])).
% 0.70/0.88 tff(872,plain,
% 0.70/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a884) | (~c3_1(a884)) | (~c1_1(a884)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a884) | c3_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a884)) | (~c3_1(a884)) | c0_1(a884))),
% 0.70/0.88 inference(transitivity,[status(thm)],[871, 869])).
% 0.70/0.88 tff(873,plain,
% 0.70/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a884) | (~c3_1(a884)) | (~c1_1(a884)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(874,plain,
% 0.70/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a884) | c3_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a884)) | (~c3_1(a884)) | c0_1(a884)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.70/0.88 tff(875,plain,
% 0.70/0.88 ($false),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[874, 114, 861, 868, 846, 860, 844, 722, 867, 862])).
% 0.70/0.88 tff(876,plain,(hskp4 | hskp31 | c2_1(a830) | c1_1(a830) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.70/0.88 tff(877,plain,
% 0.70/0.88 (hskp4),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[876, 814, 813, 285, 35])).
% 0.70/0.88 tff(878,plain,
% 0.70/0.88 (~c2_1(a832)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[396, 877])).
% 0.70/0.88 tff(879,plain,
% 0.70/0.88 (~c1_1(a832)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[402, 877])).
% 0.70/0.88 tff(880,plain,
% 0.70/0.88 (~c3_1(a832)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[390, 877])).
% 0.70/0.88 tff(881,assumption,(c1_1(a863)), introduced(assumption)).
% 0.70/0.88 tff(882,plain,
% 0.70/0.88 (~c0_1(a832)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[694, 881])).
% 0.70/0.88 tff(883,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c2_1(a863) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | c0_1(a832) | (~c1_1(a863)) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a863) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | c0_1(a832) | (~c1_1(a863)) | (~c3_1(a863)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(884,plain,
% 0.70/0.88 ((hskp2 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a832) | c1_1(a832) | c0_1(a832)) <=> (hskp2 | c2_1(a863) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | c0_1(a832) | (~c1_1(a863)) | (~c3_1(a863)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(885,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c2_1(a863) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | c0_1(a832) | (~c1_1(a863)) | (~c3_1(a863))))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[884])).
% 0.70/0.88 tff(886,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a863) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | c0_1(a832) | (~c1_1(a863)) | (~c3_1(a863)))),
% 0.70/0.88 inference(transitivity,[status(thm)],[885, 883])).
% 0.70/0.88 tff(887,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a832) | c1_1(a832) | c0_1(a832))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(888,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a863) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | c0_1(a832) | (~c1_1(a863)) | (~c3_1(a863))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[887, 886])).
% 0.70/0.88 tff(889,plain,
% 0.70/0.88 (hskp2 | c0_1(a832) | (~c1_1(a863))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[888, 114, 613, 612, 608, 607, 34])).
% 0.70/0.88 tff(890,plain,
% 0.70/0.88 (hskp2),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[889, 881, 882])).
% 0.70/0.88 tff(891,plain,
% 0.70/0.88 (c0_1(a830)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[74, 890])).
% 0.70/0.88 tff(892,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c2_1(a863) | c1_1(a830) | (~ndr1_0) | c3_1(a830) | (~c0_1(a830)) | (~c1_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c2_1(a863) | c1_1(a830) | (~ndr1_0) | c3_1(a830) | (~c0_1(a830)) | (~c1_1(a863)) | (~c0_1(a863)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(893,plain,
% 0.70/0.88 ((hskp31 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c0_1(a863)) | c1_1(a830) | c3_1(a830) | (~c0_1(a830))) <=> (hskp31 | c2_1(a863) | c1_1(a830) | (~ndr1_0) | c3_1(a830) | (~c0_1(a830)) | (~c1_1(a863)) | (~c0_1(a863)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(894,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c0_1(a863)) | c1_1(a830) | c3_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | c2_1(a863) | c1_1(a830) | (~ndr1_0) | c3_1(a830) | (~c0_1(a830)) | (~c1_1(a863)) | (~c0_1(a863))))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[893])).
% 0.70/0.88 tff(895,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c0_1(a863)) | c1_1(a830) | c3_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c2_1(a863) | c1_1(a830) | (~ndr1_0) | c3_1(a830) | (~c0_1(a830)) | (~c1_1(a863)) | (~c0_1(a863)))),
% 0.70/0.88 inference(transitivity,[status(thm)],[894, 892])).
% 0.70/0.88 tff(896,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c0_1(a863)) | c1_1(a830) | c3_1(a830) | (~c0_1(a830)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(897,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp31 | c2_1(a863) | c1_1(a830) | (~ndr1_0) | c3_1(a830) | (~c0_1(a830)) | (~c1_1(a863)) | (~c0_1(a863))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[896, 895])).
% 0.70/0.88 tff(898,plain,
% 0.70/0.88 (c3_1(a830) | (~c0_1(a830)) | (~c1_1(a863))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[897, 285, 114, 614, 612, 814, 295])).
% 0.70/0.88 tff(899,plain,
% 0.70/0.88 (c3_1(a830)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[898, 891, 881])).
% 0.70/0.88 tff(900,plain,
% 0.70/0.88 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(901,plain,
% 0.70/0.88 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[900])).
% 0.70/0.88 tff(902,plain,
% 0.70/0.88 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(903,plain,
% 0.70/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(904,plain,
% 0.70/0.88 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[903])).
% 0.70/0.88 tff(905,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.70/0.88 tff(906,plain,
% 0.70/0.88 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[905, 904])).
% 0.70/0.88 tff(907,plain,
% 0.70/0.88 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[906, 902])).
% 0.70/0.88 tff(908,plain,(
% 0.70/0.88 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.88 inference(skolemize,[status(sab)],[907])).
% 0.70/0.88 tff(909,plain,
% 0.70/0.88 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[908, 901])).
% 0.70/0.88 tff(910,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | c2_1(a863) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c1_1(a863)) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a863) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c1_1(a863)) | (~c3_1(a863)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(911,plain,
% 0.70/0.88 ((hskp17 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a830) | c1_1(a830) | (~c3_1(a830))) <=> (hskp17 | c2_1(a863) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c1_1(a863)) | (~c3_1(a863)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(912,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a830) | c1_1(a830) | (~c3_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | c2_1(a863) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c1_1(a863)) | (~c3_1(a863))))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[911])).
% 0.70/0.88 tff(913,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a830) | c1_1(a830) | (~c3_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a863) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c1_1(a863)) | (~c3_1(a863)))),
% 0.70/0.88 inference(transitivity,[status(thm)],[912, 910])).
% 0.70/0.88 tff(914,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a830) | c1_1(a830) | (~c3_1(a830)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(915,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a863) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c1_1(a863)) | (~c3_1(a863))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[914, 913])).
% 0.70/0.88 tff(916,plain,
% 0.70/0.88 (hskp17 | (~c3_1(a830)) | (~c1_1(a863))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[915, 114, 613, 612, 814, 813, 909])).
% 0.70/0.88 tff(917,plain,
% 0.70/0.88 (hskp17),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[916, 899, 881])).
% 0.70/0.88 tff(918,plain,
% 0.70/0.88 (~c3_1(a859)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[301, 917])).
% 0.70/0.88 tff(919,plain,
% 0.70/0.88 (~c1_1(a859)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[307, 917])).
% 0.70/0.88 tff(920,plain,
% 0.70/0.88 (c0_1(a859)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[336, 917])).
% 0.72/0.88 tff(921,plain,
% 0.72/0.88 ($false),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[509, 285, 114, 614, 920, 612, 919, 918, 295, 881])).
% 0.72/0.88 tff(922,plain,((~c1_1(a863)) | hskp31 | c1_1(a830) | c2_1(a830) | c1_1(a832) | c2_1(a832) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.88 tff(923,plain,
% 0.72/0.88 (~c1_1(a863)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[922, 880, 814, 813, 879, 878, 285])).
% 0.72/0.88 tff(924,plain,
% 0.72/0.88 (hskp19),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[409, 285, 114, 879, 878, 880, 355])).
% 0.72/0.88 tff(925,plain,
% 0.72/0.88 (~c2_1(a863)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[494, 924])).
% 0.72/0.88 tff(926,plain,
% 0.72/0.88 (c3_1(a863)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[517, 924])).
% 0.72/0.88 tff(927,plain,
% 0.72/0.88 (c0_1(a863)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[502, 924])).
% 0.72/0.88 tff(928,plain,
% 0.72/0.88 (~c1_1(a863)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[922, 608, 814, 813, 285, 607, 606])).
% 0.72/0.88 tff(929,plain,
% 0.72/0.88 (hskp3),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[615, 928])).
% 0.72/0.88 tff(930,plain,
% 0.72/0.88 (c3_1(a831)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[247, 929])).
% 0.72/0.88 tff(931,plain,
% 0.72/0.88 (c2_1(a831)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[255, 929])).
% 0.72/0.88 tff(932,plain,
% 0.72/0.88 (hskp5),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[620, 931, 930])).
% 0.72/0.88 tff(933,plain,
% 0.72/0.88 (~c3_1(a833)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[66, 932])).
% 0.72/0.88 tff(934,plain,
% 0.72/0.88 (c2_1(a833)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[138, 932])).
% 0.72/0.88 tff(935,plain,
% 0.72/0.88 (c0_1(a833)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[82, 932])).
% 0.72/0.88 tff(936,plain,
% 0.72/0.88 (hskp14),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[630, 114, 614, 935, 934, 612, 933, 185, 928])).
% 0.72/0.88 tff(937,plain,
% 0.72/0.88 (~c3_1(a851)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[197, 936])).
% 0.72/0.88 tff(938,plain,
% 0.72/0.88 (c2_1(a851)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[205, 936])).
% 0.72/0.88 tff(939,plain,
% 0.72/0.88 (c1_1(a851)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[213, 936])).
% 0.72/0.88 tff(940,plain,
% 0.72/0.88 (hskp17),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[641, 114, 939, 938, 329, 937, 321, 315, 175])).
% 0.72/0.88 tff(941,plain,
% 0.72/0.88 (~c3_1(a859)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[301, 940])).
% 0.72/0.88 tff(942,plain,
% 0.72/0.88 (~c1_1(a859)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[307, 940])).
% 0.72/0.88 tff(943,plain,
% 0.72/0.88 (c0_1(a859)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[336, 940])).
% 0.72/0.88 tff(944,plain,
% 0.72/0.88 (hskp6),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[145, 114, 35, 935, 934, 933, 131])).
% 0.72/0.88 tff(945,plain,
% 0.72/0.88 (~c3_1(a835)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[151, 944])).
% 0.72/0.88 tff(946,plain,
% 0.72/0.88 (~c2_1(a835)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[157, 944])).
% 0.72/0.88 tff(947,plain,
% 0.72/0.88 (~c0_1(a835)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[548, 944])).
% 0.72/0.88 tff(948,plain,
% 0.72/0.88 (c2_1(a846)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[806, 947, 607, 606, 608, 285, 928, 946, 945, 35, 933, 619])).
% 0.72/0.88 tff(949,plain,
% 0.72/0.88 (~hskp13),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[465, 948])).
% 0.72/0.88 tff(950,plain,
% 0.72/0.88 ($false),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[524, 114, 949, 613, 943, 612, 942, 941, 383, 928])).
% 0.72/0.88 tff(951,plain,(c1_1(a832) | c2_1(a832) | c3_1(a832) | hskp31 | hskp16 | c1_1(a831) | c1_1(a830) | c2_1(a830)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.88 tff(952,plain,
% 0.72/0.88 (c1_1(a831)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[951, 878, 880, 285, 35, 879, 814, 813])).
% 0.72/0.88 tff(953,plain,
% 0.72/0.88 (~hskp3),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[239, 952])).
% 0.72/0.88 tff(954,plain,
% 0.72/0.88 ($false),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[532, 114, 953, 927, 926, 925, 276, 923])).
% 0.72/0.88 tff(955,plain,(c1_1(a830) | hskp31 | c2_1(a830) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.72/0.88 tff(956,plain,
% 0.72/0.88 ($false),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[955, 812, 811, 285, 35])).
% 0.72/0.88 tff(957,plain,(hskp31 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.72/0.88 tff(958,plain,
% 0.72/0.88 (hskp31),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[957, 35])).
% 0.72/0.88 tff(959,plain,
% 0.72/0.88 (((~hskp31) | c3_1(a875)) <=> ((~hskp31) | c3_1(a875))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(960,axiom,((~hskp31) | c3_1(a875)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.72/0.88 tff(961,plain,
% 0.72/0.88 ((~hskp31) | c3_1(a875)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[960, 959])).
% 0.72/0.88 tff(962,plain,
% 0.72/0.88 ((~hskp31) | c3_1(a875)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[961, 959])).
% 0.72/0.88 tff(963,plain,
% 0.72/0.88 ((~hskp31) | c3_1(a875)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[962, 959])).
% 0.72/0.88 tff(964,plain,
% 0.72/0.88 ((~hskp31) | c3_1(a875)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[963, 959])).
% 0.72/0.88 tff(965,plain,
% 0.72/0.88 ((~hskp31) | c3_1(a875)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[964, 959])).
% 0.72/0.88 tff(966,plain,
% 0.72/0.88 (c3_1(a875)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[965, 958])).
% 0.72/0.88 tff(967,plain,
% 0.72/0.88 (((~hskp31) | c2_1(a875)) <=> ((~hskp31) | c2_1(a875))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(968,axiom,((~hskp31) | c2_1(a875)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.72/0.88 tff(969,plain,
% 0.72/0.88 ((~hskp31) | c2_1(a875)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[968, 967])).
% 0.72/0.88 tff(970,plain,
% 0.72/0.88 ((~hskp31) | c2_1(a875)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[969, 967])).
% 0.72/0.88 tff(971,plain,
% 0.72/0.88 ((~hskp31) | c2_1(a875)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[970, 967])).
% 0.72/0.88 tff(972,plain,
% 0.72/0.88 ((~hskp31) | c2_1(a875)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[971, 967])).
% 0.72/0.88 tff(973,plain,
% 0.72/0.88 ((~hskp31) | c2_1(a875)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[972, 967])).
% 0.72/0.88 tff(974,plain,
% 0.72/0.88 (c2_1(a875)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[973, 958])).
% 0.72/0.88 tff(975,plain,
% 0.72/0.88 (((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | c1_1(a875) | (~c3_1(a875)) | (~c2_1(a875)))) <=> ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp16 | hskp5 | (~ndr1_0) | c1_1(a875) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(976,plain,
% 0.72/0.88 ((hskp16 | hskp5 | (~ndr1_0) | c1_1(a875) | (~c2_1(a875)) | (~c3_1(a875))) <=> (hskp16 | hskp5 | (~ndr1_0) | c1_1(a875) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(977,plain,
% 0.72/0.88 (((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | c1_1(a875) | (~c2_1(a875)) | (~c3_1(a875)))) <=> ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | c1_1(a875) | (~c3_1(a875)) | (~c2_1(a875))))),
% 0.72/0.88 inference(monotonicity,[status(thm)],[976])).
% 0.72/0.88 tff(978,plain,
% 0.72/0.88 (((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | c1_1(a875) | (~c2_1(a875)) | (~c3_1(a875)))) <=> ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp16 | hskp5 | (~ndr1_0) | c1_1(a875) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.72/0.88 inference(transitivity,[status(thm)],[977, 975])).
% 0.72/0.88 tff(979,plain,
% 0.72/0.88 ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | c1_1(a875) | (~c2_1(a875)) | (~c3_1(a875)))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(980,plain,
% 0.72/0.88 ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp16 | hskp5 | (~ndr1_0) | c1_1(a875) | (~c3_1(a875)) | (~c2_1(a875))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.72/0.88 tff(981,plain,
% 0.72/0.88 (hskp5 | c1_1(a875)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[980, 114, 35, 974, 966, 233])).
% 0.72/0.88 tff(982,plain,
% 0.72/0.88 (c1_1(a875)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[981, 223])).
% 0.72/0.88 tff(983,plain,
% 0.72/0.88 (^[U: $i] : refl((hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(984,plain,
% 0.72/0.88 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[983])).
% 0.72/0.88 tff(985,plain,
% 0.72/0.88 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(986,plain,
% 0.72/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp0) | hskp3) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp3))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp3) <=> (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp0) | hskp3) <=> (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(987,plain,
% 0.72/0.88 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp0) | hskp3) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[986])).
% 0.72/0.88 tff(988,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp0) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 0.72/0.88 tff(989,plain,
% 0.72/0.88 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[988, 987])).
% 0.72/0.88 tff(990,plain,
% 0.72/0.88 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[989, 985])).
% 0.72/0.88 tff(991,plain,(
% 0.72/0.88 ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.88 inference(skolemize,[status(sab)],[990])).
% 0.72/0.88 tff(992,plain,
% 0.72/0.88 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[991, 984])).
% 0.72/0.88 tff(993,plain,
% 0.72/0.88 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp3 | hskp0 | c2_1(a830) | (~ndr1_0) | c3_1(a830) | (~c0_1(a830)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp3 | hskp0 | c2_1(a830) | (~ndr1_0) | c3_1(a830) | (~c0_1(a830)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(994,plain,
% 0.72/0.88 ((hskp3 | hskp0 | (~ndr1_0) | c2_1(a830) | c3_1(a830) | (~c0_1(a830))) <=> (hskp3 | hskp0 | c2_1(a830) | (~ndr1_0) | c3_1(a830) | (~c0_1(a830)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(995,plain,
% 0.72/0.88 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c2_1(a830) | c3_1(a830) | (~c0_1(a830)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp3 | hskp0 | c2_1(a830) | (~ndr1_0) | c3_1(a830) | (~c0_1(a830))))),
% 0.72/0.88 inference(monotonicity,[status(thm)],[994])).
% 0.72/0.88 tff(996,plain,
% 0.72/0.88 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c2_1(a830) | c3_1(a830) | (~c0_1(a830)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp3 | hskp0 | c2_1(a830) | (~ndr1_0) | c3_1(a830) | (~c0_1(a830)))),
% 0.72/0.88 inference(transitivity,[status(thm)],[995, 993])).
% 0.72/0.88 tff(997,plain,
% 0.72/0.88 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c2_1(a830) | c3_1(a830) | (~c0_1(a830)))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(998,plain,
% 0.72/0.88 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp3 | hskp0 | c2_1(a830) | (~ndr1_0) | c3_1(a830) | (~c0_1(a830))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[997, 996])).
% 0.72/0.88 tff(999,plain,
% 0.72/0.88 (hskp3 | hskp0 | c3_1(a830)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[998, 114, 75, 54, 992])).
% 0.72/0.88 tff(1000,plain,
% 0.72/0.88 (hskp0),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[999, 284, 266])).
% 0.72/0.88 tff(1001,plain,
% 0.72/0.88 (~c0_1(a828)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[738, 1000])).
% 0.72/0.88 tff(1002,plain,
% 0.72/0.88 (c2_1(a828)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[746, 1000])).
% 0.72/0.88 tff(1003,plain,
% 0.72/0.88 (c1_1(a828)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[754, 1000])).
% 0.72/0.88 tff(1004,plain,
% 0.72/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a830) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c1_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c3_1(a830) | (~c0_1(a830)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a830) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c1_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c3_1(a830) | (~c0_1(a830)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1005,plain,
% 0.72/0.89 (((~ndr1_0) | (~c2_1(a875)) | (~c1_1(a875)) | (~c3_1(a875)) | c2_1(a830) | c3_1(a830) | (~c0_1(a830)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828))) <=> (c2_1(a830) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c1_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c3_1(a830) | (~c0_1(a830)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1006,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a875)) | (~c1_1(a875)) | (~c3_1(a875)) | c2_1(a830) | c3_1(a830) | (~c0_1(a830)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a830) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c1_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c3_1(a830) | (~c0_1(a830))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[1005])).
% 0.72/0.89 tff(1007,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a875)) | (~c1_1(a875)) | (~c3_1(a875)) | c2_1(a830) | c3_1(a830) | (~c0_1(a830)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a830) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c1_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c3_1(a830) | (~c0_1(a830)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[1006, 1004])).
% 0.72/0.89 tff(1008,plain,
% 0.72/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a875)) | (~c1_1(a875)) | (~c3_1(a875)) | c2_1(a830) | c3_1(a830) | (~c0_1(a830)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(1009,plain,
% 0.72/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a830) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c1_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c3_1(a830) | (~c0_1(a830))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 0.72/0.89 tff(1010,plain,
% 0.72/0.89 ($false),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1009, 114, 974, 966, 75, 1003, 1002, 54, 1001, 662, 982, 284])).
% 0.72/0.89 tff(1011,plain,(hskp17 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.72/0.89 tff(1012,plain,
% 0.72/0.89 (hskp17),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1011, 35])).
% 0.72/0.89 tff(1013,plain,
% 0.72/0.89 (~c1_1(a859)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[307, 1012])).
% 0.72/0.89 tff(1014,assumption,(~hskp2), introduced(assumption)).
% 0.72/0.89 tff(1015,plain,
% 0.72/0.89 (~c3_1(a859)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[301, 1012])).
% 0.72/0.89 tff(1016,plain,
% 0.72/0.89 (c0_1(a859)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[336, 1012])).
% 0.72/0.89 tff(1017,assumption,(hskp11), introduced(assumption)).
% 0.72/0.89 tff(1018,plain,
% 0.72/0.89 (~c2_1(a844)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[437, 1017])).
% 0.72/0.89 tff(1019,plain,
% 0.72/0.89 (~c1_1(a844)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[443, 1017])).
% 0.72/0.89 tff(1020,plain,
% 0.72/0.89 (c3_1(a844)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[451, 1017])).
% 0.72/0.89 tff(1021,assumption,(~hskp13), introduced(assumption)).
% 0.72/0.89 tff(1022,plain,
% 0.72/0.89 ($false),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[459, 114, 1021, 453, 1020, 23, 12, 1019, 1018, 383])).
% 0.72/0.89 tff(1023,plain,((~hskp11) | hskp13 | (~c0_1(a859)) | c1_1(a859) | c3_1(a859)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.89 tff(1024,plain,
% 0.72/0.89 (hskp13),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1023, 1017, 1016, 1013, 1015])).
% 0.72/0.89 tff(1025,plain,
% 0.72/0.89 (~c2_1(a846)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[465, 1024])).
% 0.72/0.89 tff(1026,plain,
% 0.72/0.89 (c3_1(a846)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[479, 1024])).
% 0.72/0.89 tff(1027,plain,
% 0.72/0.89 (~c0_1(a846)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[471, 1024])).
% 0.72/0.89 tff(1028,assumption,(c3_1(a846)), introduced(assumption)).
% 0.72/0.89 tff(1029,plain,
% 0.72/0.89 (hskp4 | (~c2_1(a859))),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[486, 114, 1016, 1028, 1015, 704, 666, 373])).
% 0.72/0.89 tff(1030,plain,
% 0.72/0.89 (~c2_1(a859)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1029, 11])).
% 0.72/0.89 tff(1031,plain,
% 0.72/0.89 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(1032,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[1031])).
% 0.72/0.89 tff(1033,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1034,plain,
% 0.72/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp4))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(1035,plain,
% 0.72/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[1034])).
% 0.72/0.89 tff(1036,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 0.72/0.89 tff(1037,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 0.72/0.89 tff(1038,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1037, 1033])).
% 0.72/0.89 tff(1039,plain,(
% 0.72/0.89 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.89 inference(skolemize,[status(sab)],[1038])).
% 0.72/0.89 tff(1040,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1039, 1032])).
% 0.72/0.89 tff(1041,assumption,(~c2_1(a844)), introduced(assumption)).
% 0.72/0.89 tff(1042,assumption,(~c1_1(a844)), introduced(assumption)).
% 0.72/0.89 tff(1043,plain,
% 0.72/0.89 (((~hskp31) | c0_1(a875)) <=> ((~hskp31) | c0_1(a875))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1044,axiom,((~hskp31) | c0_1(a875)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.72/0.89 tff(1045,plain,
% 0.72/0.89 ((~hskp31) | c0_1(a875)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 0.72/0.89 tff(1046,plain,
% 0.72/0.89 ((~hskp31) | c0_1(a875)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1045, 1043])).
% 0.72/0.89 tff(1047,plain,
% 0.72/0.89 ((~hskp31) | c0_1(a875)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1046, 1043])).
% 0.72/0.89 tff(1048,plain,
% 0.72/0.89 ((~hskp31) | c0_1(a875)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1047, 1043])).
% 0.72/0.89 tff(1049,plain,
% 0.72/0.89 ((~hskp31) | c0_1(a875)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1048, 1043])).
% 0.72/0.89 tff(1050,plain,
% 0.72/0.89 (c0_1(a875)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1049, 958])).
% 0.72/0.89 tff(1051,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c0_1(a844))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c0_1(a844))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1052,plain,
% 0.72/0.89 ((hskp4 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a844) | c1_1(a844) | c0_1(a844)) <=> (hskp4 | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c0_1(a844))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1053,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a844) | c1_1(a844) | c0_1(a844))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c0_1(a844)))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[1052])).
% 0.72/0.89 tff(1054,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a844) | c1_1(a844) | c0_1(a844))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c0_1(a844))),
% 0.72/0.89 inference(transitivity,[status(thm)],[1053, 1051])).
% 0.72/0.89 tff(1055,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a844) | c1_1(a844) | c0_1(a844))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(1056,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c0_1(a844)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1055, 1054])).
% 0.72/0.89 tff(1057,plain,
% 0.72/0.89 (hskp4 | c0_1(a844)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1056, 114, 1050, 974, 966, 1042, 1041, 1040])).
% 0.72/0.89 tff(1058,plain,
% 0.72/0.89 (c0_1(a844)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1057, 11])).
% 0.72/0.89 tff(1059,assumption,(c3_1(a844)), introduced(assumption)).
% 0.72/0.89 tff(1060,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a844)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1061,plain,
% 0.72/0.89 ((hskp3 | (~ndr1_0) | c2_1(a844) | (~c3_1(a844)) | (~c0_1(a844)) | c2_1(a844) | c1_1(a844) | (~c0_1(a844))) <=> (hskp3 | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a844)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1062,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a844) | (~c3_1(a844)) | (~c0_1(a844)) | c2_1(a844) | c1_1(a844) | (~c0_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a844))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[1061])).
% 0.72/0.89 tff(1063,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a844) | (~c3_1(a844)) | (~c0_1(a844)) | c2_1(a844) | c1_1(a844) | (~c0_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a844)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[1062, 1060])).
% 0.72/0.89 tff(1064,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a844) | (~c3_1(a844)) | (~c0_1(a844)) | c2_1(a844) | c1_1(a844) | (~c0_1(a844)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(1065,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | (~c0_1(a844))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 0.72/0.89 tff(1066,plain,
% 0.72/0.89 (hskp3 | (~c0_1(a844))),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1065, 114, 1059, 1042, 1041, 276])).
% 0.72/0.89 tff(1067,plain,
% 0.72/0.89 (hskp3),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1066, 1058])).
% 0.72/0.89 tff(1068,plain,
% 0.72/0.89 (hskp5),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[265, 1067, 35])).
% 0.72/0.89 tff(1069,plain,
% 0.72/0.89 (~c3_1(a833)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[66, 1068])).
% 0.72/0.89 tff(1070,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c1_1(a846))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c1_1(a846))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1071,plain,
% 0.72/0.89 ((hskp4 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a846) | c1_1(a846) | c0_1(a846)) <=> (hskp4 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c1_1(a846))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1072,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a846) | c1_1(a846) | c0_1(a846))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c1_1(a846)))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[1071])).
% 0.72/0.89 tff(1073,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a846) | c1_1(a846) | c0_1(a846))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c1_1(a846))),
% 0.72/0.89 inference(transitivity,[status(thm)],[1072, 1070])).
% 0.72/0.89 tff(1074,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a846) | c1_1(a846) | c0_1(a846))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(1075,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c1_1(a846)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1074, 1073])).
% 0.72/0.89 tff(1076,plain,
% 0.72/0.89 (hskp4 | c1_1(a846)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1075, 114, 1050, 974, 966, 704, 666, 1040])).
% 0.72/0.89 tff(1077,plain,
% 0.72/0.89 (c1_1(a846)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1076, 11])).
% 0.72/0.89 tff(1078,plain,
% 0.72/0.89 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(1079,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[1078])).
% 0.72/0.89 tff(1080,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1081,plain,
% 0.72/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp18) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp18))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(1082,plain,
% 0.72/0.89 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[1081])).
% 0.72/0.89 tff(1083,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 0.72/0.89 tff(1084,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 0.72/0.89 tff(1085,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1084, 1080])).
% 0.72/0.89 tff(1086,plain,(
% 0.72/0.89 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[1085])).
% 0.72/0.89 tff(1087,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1086, 1079])).
% 0.72/0.89 tff(1088,plain,
% 0.72/0.89 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(1089,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[1088])).
% 0.72/0.89 tff(1090,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1091,plain,
% 0.72/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp25) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp25))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(1092,plain,
% 0.72/0.89 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[1091])).
% 0.72/0.89 tff(1093,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.72/0.89 tff(1094,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1093, 1092])).
% 0.72/0.89 tff(1095,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1094, 1090])).
% 0.72/0.89 tff(1096,plain,(
% 0.72/0.89 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[1095])).
% 0.72/0.89 tff(1097,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1096, 1089])).
% 0.72/0.89 tff(1098,plain,
% 0.72/0.89 (hskp30),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[772, 114, 35, 1028, 704, 666, 766])).
% 0.72/0.89 tff(1099,plain,
% 0.72/0.89 (c3_1(a857)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[781, 1098])).
% 0.72/0.89 tff(1100,plain,
% 0.72/0.89 (c2_1(a857)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[789, 1098])).
% 0.72/0.89 tff(1101,plain,
% 0.72/0.89 (c1_1(a857)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[797, 1098])).
% 0.72/0.89 tff(1102,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp25 | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | (~c0_1(a859)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1103,plain,
% 0.72/0.89 ((hskp25 | (~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859))) <=> (hskp25 | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | (~c0_1(a859)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1104,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | (~c0_1(a859))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[1103])).
% 0.72/0.89 tff(1105,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp25 | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | (~c0_1(a859)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[1104, 1102])).
% 0.72/0.89 tff(1106,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(1107,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp25 | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | (~c0_1(a859))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 0.72/0.89 tff(1108,plain,
% 0.72/0.89 (hskp25),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1107, 114, 1101, 1100, 1099, 1016, 1013, 1015, 1097])).
% 0.72/0.89 tff(1109,plain,
% 0.72/0.89 (((~hskp25) | (~c3_1(a890))) <=> ((~hskp25) | (~c3_1(a890)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1110,plain,
% 0.72/0.89 (((~c3_1(a890)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a890)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1111,axiom,((~c3_1(a890)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.72/0.89 tff(1112,plain,
% 0.72/0.89 ((~hskp25) | (~c3_1(a890))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 0.72/0.89 tff(1113,plain,
% 0.72/0.89 ((~hskp25) | (~c3_1(a890))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1112, 1109])).
% 0.72/0.89 tff(1114,plain,
% 0.72/0.89 (~c3_1(a890)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1113, 1108])).
% 0.72/0.89 tff(1115,plain,
% 0.72/0.89 (((~hskp25) | (~c0_1(a890))) <=> ((~hskp25) | (~c0_1(a890)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1116,plain,
% 0.72/0.89 (((~c0_1(a890)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a890)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1117,axiom,((~c0_1(a890)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.72/0.89 tff(1118,plain,
% 0.72/0.89 ((~hskp25) | (~c0_1(a890))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 0.72/0.89 tff(1119,plain,
% 0.72/0.89 ((~hskp25) | (~c0_1(a890))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1118, 1115])).
% 0.72/0.89 tff(1120,plain,
% 0.72/0.89 (~c0_1(a890)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1119, 1108])).
% 0.72/0.89 tff(1121,plain,
% 0.72/0.89 (((~hskp25) | c2_1(a890)) <=> ((~hskp25) | c2_1(a890))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1122,axiom,((~hskp25) | c2_1(a890)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.72/0.89 tff(1123,plain,
% 0.72/0.89 ((~hskp25) | c2_1(a890)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.72/0.89 tff(1124,plain,
% 0.72/0.90 ((~hskp25) | c2_1(a890)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1123, 1121])).
% 0.72/0.90 tff(1125,plain,
% 0.72/0.90 ((~hskp25) | c2_1(a890)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1124, 1121])).
% 0.72/0.90 tff(1126,plain,
% 0.72/0.90 ((~hskp25) | c2_1(a890)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1125, 1121])).
% 0.72/0.90 tff(1127,plain,
% 0.72/0.90 ((~hskp25) | c2_1(a890)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1126, 1121])).
% 0.72/0.90 tff(1128,plain,
% 0.72/0.90 (c2_1(a890)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1127, 1108])).
% 0.72/0.90 tff(1129,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp18 | c0_1(a890) | c3_1(a890) | c0_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | (~c2_1(a890)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp18 | c0_1(a890) | c3_1(a890) | c0_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | (~c2_1(a890)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1130,plain,
% 0.72/0.90 ((hskp18 | (~ndr1_0) | c0_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c0_1(a890) | c3_1(a890) | (~c2_1(a890))) <=> (hskp18 | c0_1(a890) | c3_1(a890) | c0_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | (~c2_1(a890)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1131,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c0_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c0_1(a890) | c3_1(a890) | (~c2_1(a890)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp18 | c0_1(a890) | c3_1(a890) | c0_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | (~c2_1(a890))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[1130])).
% 0.72/0.90 tff(1132,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c0_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c0_1(a890) | c3_1(a890) | (~c2_1(a890)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp18 | c0_1(a890) | c3_1(a890) | c0_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | (~c2_1(a890)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[1131, 1129])).
% 0.72/0.90 tff(1133,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c0_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c0_1(a890) | c3_1(a890) | (~c2_1(a890)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(1134,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp18 | c0_1(a890) | c3_1(a890) | c0_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | (~c2_1(a890))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 0.72/0.90 tff(1135,plain,
% 0.72/0.90 (hskp18 | (~c1_1(a846))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1134, 114, 1128, 1028, 1120, 1114, 704, 1087])).
% 0.72/0.90 tff(1136,plain,
% 0.72/0.90 (hskp18),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1135, 1077])).
% 0.72/0.90 tff(1137,plain,
% 0.72/0.90 (((~hskp18) | (~c1_1(a861))) <=> ((~hskp18) | (~c1_1(a861)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1138,plain,
% 0.72/0.90 (((~c1_1(a861)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a861)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1139,axiom,((~c1_1(a861)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.72/0.90 tff(1140,plain,
% 0.72/0.90 ((~hskp18) | (~c1_1(a861))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 0.72/0.90 tff(1141,plain,
% 0.72/0.90 ((~hskp18) | (~c1_1(a861))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1140, 1137])).
% 0.72/0.90 tff(1142,plain,
% 0.72/0.90 (~c1_1(a861)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1141, 1136])).
% 0.72/0.90 tff(1143,plain,
% 0.72/0.90 (c2_1(a833)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[138, 1068])).
% 0.72/0.90 tff(1144,plain,
% 0.72/0.90 (c0_1(a833)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[82, 1068])).
% 0.72/0.90 tff(1145,plain,
% 0.72/0.90 (((~hskp18) | c2_1(a861)) <=> ((~hskp18) | c2_1(a861))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1146,axiom,((~hskp18) | c2_1(a861)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.72/0.90 tff(1147,plain,
% 0.72/0.90 ((~hskp18) | c2_1(a861)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 0.72/0.90 tff(1148,plain,
% 0.72/0.90 ((~hskp18) | c2_1(a861)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1147, 1145])).
% 0.72/0.90 tff(1149,plain,
% 0.72/0.90 ((~hskp18) | c2_1(a861)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1148, 1145])).
% 0.72/0.90 tff(1150,plain,
% 0.72/0.90 ((~hskp18) | c2_1(a861)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1149, 1145])).
% 0.72/0.90 tff(1151,plain,
% 0.72/0.90 ((~hskp18) | c2_1(a861)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1150, 1145])).
% 0.72/0.90 tff(1152,plain,
% 0.72/0.90 (c2_1(a861)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1151, 1136])).
% 0.72/0.90 tff(1153,plain,
% 0.72/0.90 (((~hskp18) | c0_1(a861)) <=> ((~hskp18) | c0_1(a861))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1154,axiom,((~hskp18) | c0_1(a861)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.72/0.90 tff(1155,plain,
% 0.72/0.90 ((~hskp18) | c0_1(a861)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 0.72/0.90 tff(1156,plain,
% 0.72/0.90 ((~hskp18) | c0_1(a861)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1155, 1153])).
% 0.72/0.90 tff(1157,plain,
% 0.72/0.90 ((~hskp18) | c0_1(a861)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1156, 1153])).
% 0.72/0.90 tff(1158,plain,
% 0.72/0.90 ((~hskp18) | c0_1(a861)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1157, 1153])).
% 0.72/0.90 tff(1159,plain,
% 0.72/0.90 ((~hskp18) | c0_1(a861)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1158, 1153])).
% 0.72/0.90 tff(1160,plain,
% 0.72/0.90 (c0_1(a861)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1159, 1136])).
% 0.72/0.90 tff(1161,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a861) | c1_1(a859) | c3_1(a859) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a859) | (~c2_1(a861)) | (~c0_1(a861)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a861) | c1_1(a859) | c3_1(a859) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a859) | (~c2_1(a861)) | (~c0_1(a861)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1162,plain,
% 0.72/0.90 (((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a861) | (~c2_1(a861)) | (~c0_1(a861)) | c3_1(a859) | c2_1(a859) | c1_1(a859)) <=> (c1_1(a861) | c1_1(a859) | c3_1(a859) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a859) | (~c2_1(a861)) | (~c0_1(a861)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1163,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a861) | (~c2_1(a861)) | (~c0_1(a861)) | c3_1(a859) | c2_1(a859) | c1_1(a859))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a861) | c1_1(a859) | c3_1(a859) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a859) | (~c2_1(a861)) | (~c0_1(a861))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[1162])).
% 0.72/0.90 tff(1164,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a861) | (~c2_1(a861)) | (~c0_1(a861)) | c3_1(a859) | c2_1(a859) | c1_1(a859))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a861) | c1_1(a859) | c3_1(a859) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a859) | (~c2_1(a861)) | (~c0_1(a861)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[1163, 1161])).
% 0.72/0.90 tff(1165,plain,
% 0.72/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a861) | (~c2_1(a861)) | (~c0_1(a861)) | c3_1(a859) | c2_1(a859) | c1_1(a859))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(1166,plain,
% 0.72/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a861) | c1_1(a859) | c3_1(a859) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a859) | (~c2_1(a861)) | (~c0_1(a861))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 0.72/0.90 tff(1167,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1166, 114, 1160, 1152, 1144, 1143, 1142, 1013, 1015, 1069, 22, 1030])).
% 0.72/0.90 tff(1168,plain,(hskp4 | hskp16 | (~c3_1(a844)) | c1_1(a844) | c2_1(a844) | (~c3_1(a846)) | c0_1(a846) | c2_1(a846)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.90 tff(1169,plain,
% 0.72/0.90 (hskp4),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1168, 1027, 35, 1026, 1018, 1019, 1020, 1025])).
% 0.72/0.90 tff(1170,plain,
% 0.72/0.90 (~c3_1(a832)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[390, 1169])).
% 0.72/0.90 tff(1171,plain,
% 0.72/0.90 (~c2_1(a832)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[396, 1169])).
% 0.72/0.90 tff(1172,plain,
% 0.72/0.90 (~c1_1(a832)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[402, 1169])).
% 0.72/0.90 tff(1173,plain,
% 0.72/0.90 (~c2_1(a859)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[651, 114, 1016, 1013, 1015, 1172, 1171, 1170, 22])).
% 0.72/0.90 tff(1174,plain,
% 0.72/0.90 (hskp24),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[858, 114, 1016, 1020, 1013, 1015, 1019, 1018, 559])).
% 0.72/0.90 tff(1175,plain,
% 0.72/0.90 (~c2_1(a884)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[571, 1174])).
% 0.72/0.90 tff(1176,plain,
% 0.72/0.90 (c3_1(a884)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[594, 1174])).
% 0.72/0.90 tff(1177,plain,
% 0.72/0.90 (c1_1(a884)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[579, 1174])).
% 0.72/0.90 tff(1178,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a884) | c3_1(a859) | c0_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a884)) | (~c3_1(a884)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a884) | c3_1(a859) | c0_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1179,plain,
% 0.72/0.90 (((~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a846) | (~c3_1(a846)) | (~c1_1(a846))) <=> (c2_1(a884) | c3_1(a859) | c0_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1180,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a846) | (~c3_1(a846)) | (~c1_1(a846)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a884) | c3_1(a859) | c0_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a884)) | (~c3_1(a884))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[1179])).
% 0.72/0.90 tff(1181,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a846) | (~c3_1(a846)) | (~c1_1(a846)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a884) | c3_1(a859) | c0_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[1180, 1178])).
% 0.72/0.90 tff(1182,plain,
% 0.72/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a846) | (~c3_1(a846)) | (~c1_1(a846)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(1183,plain,
% 0.72/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a884) | c3_1(a859) | c0_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a884)) | (~c3_1(a884))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 0.72/0.90 tff(1184,plain,
% 0.72/0.90 (~c1_1(a846)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1183, 114, 1177, 1176, 1016, 1026, 1175, 1015, 1027, 722, 1173])).
% 0.72/0.90 tff(1185,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c2_1(a884) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c1_1(a884)) | (~c3_1(a884)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a884) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1186,plain,
% 0.72/0.90 ((hskp2 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a846) | c1_1(a846) | c0_1(a846)) <=> (hskp2 | c2_1(a884) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1187,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a846) | c1_1(a846) | c0_1(a846))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c2_1(a884) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c1_1(a884)) | (~c3_1(a884))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[1186])).
% 0.72/0.90 tff(1188,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a846) | c1_1(a846) | c0_1(a846))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a884) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[1187, 1185])).
% 0.72/0.90 tff(1189,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a846) | c1_1(a846) | c0_1(a846))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(1190,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a884) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c1_1(a884)) | (~c3_1(a884))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 0.72/0.90 tff(1191,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1190, 114, 1014, 1177, 1176, 1175, 1027, 1025, 34, 1184])).
% 0.72/0.90 tff(1192,plain,((~hskp11) | hskp2 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.72/0.90 tff(1193,plain,
% 0.72/0.90 (~hskp11),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1192, 1014, 35])).
% 0.72/0.90 tff(1194,assumption,(~hskp11), introduced(assumption)).
% 0.72/0.90 tff(1195,plain,
% 0.72/0.90 (^[U: $i] : refl((hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(1196,plain,
% 0.72/0.90 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[1195])).
% 0.72/0.90 tff(1197,plain,
% 0.72/0.90 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1198,plain,
% 0.72/0.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp11) <=> ((hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp11))), rewrite(((hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp11) <=> (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp11) <=> (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(1199,plain,
% 0.72/0.90 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp11) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[1198])).
% 0.72/0.90 tff(1200,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.72/0.90 tff(1201,plain,
% 0.72/0.90 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 0.72/0.90 tff(1202,plain,
% 0.72/0.90 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1201, 1197])).
% 0.72/0.90 tff(1203,plain,(
% 0.72/0.90 ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.90 inference(skolemize,[status(sab)],[1202])).
% 0.72/0.90 tff(1204,plain,
% 0.72/0.90 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1203, 1196])).
% 0.72/0.90 tff(1205,plain,
% 0.72/0.90 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | c1_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp11 | c1_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1206,plain,
% 0.72/0.90 ((hskp19 | hskp11 | (~ndr1_0) | c2_1(a859) | c1_1(a859) | (~c0_1(a859))) <=> (hskp19 | hskp11 | c1_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1207,plain,
% 0.72/0.90 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c2_1(a859) | c1_1(a859) | (~c0_1(a859)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | c1_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[1206])).
% 0.72/0.90 tff(1208,plain,
% 0.72/0.90 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c2_1(a859) | c1_1(a859) | (~c0_1(a859)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp11 | c1_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[1207, 1205])).
% 0.72/0.90 tff(1209,plain,
% 0.72/0.90 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c2_1(a859) | c1_1(a859) | (~c0_1(a859)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(1210,plain,
% 0.72/0.90 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp11 | c1_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 0.72/0.90 tff(1211,plain,
% 0.72/0.90 (hskp19 | hskp11 | c2_1(a859)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1210, 114, 1016, 1013, 1204])).
% 0.72/0.90 tff(1212,plain,
% 0.72/0.90 (c2_1(a859)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1211, 1194, 345])).
% 0.72/0.90 tff(1213,plain,
% 0.72/0.90 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(1214,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[1213])).
% 0.72/0.90 tff(1215,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1216,plain,
% 0.72/0.90 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp11))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(1217,plain,
% 0.72/0.90 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[1216])).
% 0.72/0.90 tff(1218,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 0.72/0.90 tff(1219,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 0.72/0.90 tff(1220,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1219, 1215])).
% 0.72/0.90 tff(1221,plain,(
% 0.72/0.90 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.72/0.90 inference(skolemize,[status(sab)],[1220])).
% 0.72/0.90 tff(1222,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1221, 1214])).
% 0.72/0.90 tff(1223,plain,
% 0.72/0.90 (((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | c3_1(a859) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)))) <=> ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp6 | c3_1(a859) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1224,plain,
% 0.72/0.90 ((hskp16 | hskp6 | (~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859))) <=> (hskp16 | hskp6 | c3_1(a859) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1225,plain,
% 0.72/0.90 (((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)))) <=> ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | c3_1(a859) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[1224])).
% 0.72/0.90 tff(1226,plain,
% 0.72/0.90 (((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)))) <=> ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp6 | c3_1(a859) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[1225, 1223])).
% 0.72/0.90 tff(1227,plain,
% 0.72/0.90 ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(1228,plain,
% 0.72/0.90 ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp6 | c3_1(a859) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 0.72/0.90 tff(1229,plain,
% 0.72/0.90 (hskp6 | (~c2_1(a859))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1228, 114, 35, 1016, 1015, 131])).
% 0.72/0.90 tff(1230,plain,
% 0.72/0.90 (hskp6),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1229, 1212])).
% 0.72/0.90 tff(1231,plain,
% 0.72/0.90 (~c3_1(a835)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[151, 1230])).
% 0.72/0.90 tff(1232,plain,
% 0.72/0.90 (~c2_1(a835)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[157, 1230])).
% 0.72/0.90 tff(1233,plain,
% 0.72/0.90 (~c0_1(a835)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[548, 1230])).
% 0.72/0.90 tff(1234,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp11 | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a875)) | (~c0_1(a875)) | (~c2_1(a875)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp11 | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a875)) | (~c0_1(a875)) | (~c2_1(a875)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1235,plain,
% 0.72/0.91 ((hskp11 | (~ndr1_0) | (~c2_1(a875)) | (~c1_1(a875)) | (~c0_1(a875)) | c2_1(a835) | c0_1(a835) | c3_1(a835)) <=> (hskp11 | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a875)) | (~c0_1(a875)) | (~c2_1(a875)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1236,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a875)) | (~c1_1(a875)) | (~c0_1(a875)) | c2_1(a835) | c0_1(a835) | c3_1(a835))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp11 | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a875)) | (~c0_1(a875)) | (~c2_1(a875))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1235])).
% 0.72/0.91 tff(1237,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a875)) | (~c1_1(a875)) | (~c0_1(a875)) | c2_1(a835) | c0_1(a835) | c3_1(a835))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp11 | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a875)) | (~c0_1(a875)) | (~c2_1(a875)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1236, 1234])).
% 0.72/0.91 tff(1238,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a875)) | (~c1_1(a875)) | (~c0_1(a875)) | c2_1(a835) | c0_1(a835) | c3_1(a835))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1239,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp11 | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a875)) | (~c0_1(a875)) | (~c2_1(a875))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 0.72/0.91 tff(1240,plain,
% 0.72/0.91 (~c1_1(a875)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1239, 114, 1194, 1050, 974, 1233, 1232, 1231, 1222])).
% 0.72/0.91 tff(1241,plain,
% 0.72/0.91 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp11 | hskp4 | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1242,plain,
% 0.72/0.91 ((hskp11 | hskp4 | (~ndr1_0) | c2_1(a835) | c0_1(a835) | c3_1(a835)) <=> (hskp11 | hskp4 | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1243,plain,
% 0.72/0.91 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | (~ndr1_0) | c2_1(a835) | c0_1(a835) | c3_1(a835))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0)))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1242])).
% 0.72/0.91 tff(1244,plain,
% 0.72/0.91 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | (~ndr1_0) | c2_1(a835) | c0_1(a835) | c3_1(a835))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp11 | hskp4 | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1243, 1241])).
% 0.72/0.91 tff(1245,plain,
% 0.72/0.91 ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | (~ndr1_0) | c2_1(a835) | c0_1(a835) | c3_1(a835))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1246,plain,
% 0.72/0.91 ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp11 | hskp4 | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 0.72/0.91 tff(1247,plain,
% 0.72/0.91 (hskp4),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1246, 114, 1194, 1233, 1232, 1231, 422])).
% 0.72/0.91 tff(1248,plain,
% 0.72/0.91 (~c3_1(a832)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[390, 1247])).
% 0.72/0.91 tff(1249,plain,
% 0.72/0.91 (~c2_1(a832)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[396, 1247])).
% 0.72/0.91 tff(1250,plain,
% 0.72/0.91 (~c1_1(a832)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[402, 1247])).
% 0.72/0.91 tff(1251,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c1_1(a875) | (~c0_1(a875)) | (~c2_1(a875)) | (~c2_1(a859)) | (~c0_1(a859)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c1_1(a875) | (~c0_1(a875)) | (~c2_1(a875)) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1252,plain,
% 0.72/0.91 (((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a875) | (~c2_1(a875)) | (~c0_1(a875)) | c3_1(a832) | c2_1(a832) | c1_1(a832)) <=> (c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c1_1(a875) | (~c0_1(a875)) | (~c2_1(a875)) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1253,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a875) | (~c2_1(a875)) | (~c0_1(a875)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c1_1(a875) | (~c0_1(a875)) | (~c2_1(a875)) | (~c2_1(a859)) | (~c0_1(a859))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1252])).
% 0.72/0.91 tff(1254,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a875) | (~c2_1(a875)) | (~c0_1(a875)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c1_1(a875) | (~c0_1(a875)) | (~c2_1(a875)) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1253, 1251])).
% 0.72/0.91 tff(1255,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a875) | (~c2_1(a875)) | (~c0_1(a875)) | c3_1(a832) | c2_1(a832) | c1_1(a832))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1256,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c1_1(a875) | (~c0_1(a875)) | (~c2_1(a875)) | (~c2_1(a859)) | (~c0_1(a859))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 0.72/0.91 tff(1257,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1256, 114, 1050, 974, 1016, 1015, 1250, 1249, 1248, 22, 1240, 1212])).
% 0.72/0.91 tff(1258,plain,(hskp11 | hskp16 | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(1259,plain,
% 0.72/0.91 (hskp19),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1258, 1193, 35])).
% 0.72/0.91 tff(1260,plain,
% 0.72/0.91 (~c2_1(a863)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[494, 1259])).
% 0.72/0.91 tff(1261,plain,
% 0.72/0.91 (c0_1(a863)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[502, 1259])).
% 0.72/0.91 tff(1262,plain,
% 0.72/0.91 (c3_1(a863)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[517, 1259])).
% 0.72/0.91 tff(1263,assumption,(~c2_1(a863)), introduced(assumption)).
% 0.72/0.91 tff(1264,assumption,(c3_1(a863)), introduced(assumption)).
% 0.72/0.91 tff(1265,plain,
% 0.72/0.91 (hskp13 | c1_1(a863)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[524, 114, 1264, 453, 1263, 23, 12, 383])).
% 0.72/0.91 tff(1266,plain,
% 0.72/0.91 (c1_1(a863)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1265, 1021])).
% 0.72/0.91 tff(1267,plain,
% 0.72/0.91 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(1268,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[1267])).
% 0.72/0.91 tff(1269,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1270,plain,
% 0.72/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(1271,plain,
% 0.72/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[1270])).
% 0.72/0.91 tff(1272,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.72/0.91 tff(1273,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 0.72/0.91 tff(1274,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1273, 1269])).
% 0.72/0.91 tff(1275,plain,(
% 0.72/0.91 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.91 inference(skolemize,[status(sab)],[1274])).
% 0.72/0.91 tff(1276,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1275, 1268])).
% 0.72/0.91 tff(1277,plain,
% 0.72/0.91 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(1278,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[1277])).
% 0.72/0.91 tff(1279,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1280,plain,
% 0.72/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp25) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp25))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(1281,plain,
% 0.72/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[1280])).
% 0.72/0.91 tff(1282,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 0.72/0.91 tff(1283,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1282, 1281])).
% 0.72/0.91 tff(1284,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1283, 1279])).
% 0.72/0.91 tff(1285,plain,(
% 0.72/0.91 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(skolemize,[status(sab)],[1284])).
% 0.72/0.91 tff(1286,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1285, 1278])).
% 0.72/0.91 tff(1287,assumption,(c0_1(a863)), introduced(assumption)).
% 0.72/0.91 tff(1288,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp25 | c2_1(a863) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp25 | c2_1(a863) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1289,plain,
% 0.72/0.91 ((hskp25 | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863))) <=> (hskp25 | c2_1(a863) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1290,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp25 | c2_1(a863) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1289])).
% 0.72/0.91 tff(1291,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp25 | c2_1(a863) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1290, 1288])).
% 0.72/0.91 tff(1292,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1293,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp25 | c2_1(a863) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 0.72/0.91 tff(1294,plain,
% 0.72/0.91 (hskp25),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1293, 114, 1287, 1264, 1263, 1286, 1266])).
% 0.72/0.91 tff(1295,plain,
% 0.72/0.91 (~c3_1(a890)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1113, 1294])).
% 0.72/0.91 tff(1296,plain,
% 0.72/0.91 (~c0_1(a890)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1119, 1294])).
% 0.72/0.91 tff(1297,plain,
% 0.72/0.91 (c2_1(a890)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1127, 1294])).
% 0.72/0.91 tff(1298,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp11 | c0_1(a890) | c3_1(a890) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | (~c2_1(a890)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp11 | c0_1(a890) | c3_1(a890) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | (~c2_1(a890)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1299,plain,
% 0.72/0.91 ((hskp11 | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | c0_1(a890) | c3_1(a890) | (~c2_1(a890))) <=> (hskp11 | c0_1(a890) | c3_1(a890) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | (~c2_1(a890)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1300,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | c0_1(a890) | c3_1(a890) | (~c2_1(a890)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp11 | c0_1(a890) | c3_1(a890) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | (~c2_1(a890))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1299])).
% 0.72/0.91 tff(1301,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | c0_1(a890) | c3_1(a890) | (~c2_1(a890)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp11 | c0_1(a890) | c3_1(a890) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | (~c2_1(a890)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1300, 1298])).
% 0.72/0.91 tff(1302,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | c0_1(a890) | c3_1(a890) | (~c2_1(a890)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1303,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp11 | c0_1(a890) | c3_1(a890) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)) | (~c0_1(a863)) | (~c2_1(a890))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 0.72/0.91 tff(1304,plain,
% 0.72/0.91 (hskp11),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1303, 114, 1297, 1287, 1264, 1296, 1295, 1276, 1266])).
% 0.72/0.91 tff(1305,plain,
% 0.72/0.91 (~c2_1(a844)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[437, 1304])).
% 0.72/0.91 tff(1306,plain,
% 0.72/0.91 (~c1_1(a844)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[443, 1304])).
% 0.72/0.91 tff(1307,plain,
% 0.72/0.91 (c3_1(a844)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[451, 1304])).
% 0.72/0.91 tff(1308,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[459, 114, 1021, 453, 1307, 23, 12, 1306, 1305, 383])).
% 0.72/0.91 tff(1309,plain,(hskp13 | (~c0_1(a859)) | c1_1(a859) | c3_1(a859) | (~c0_1(a863)) | (~c3_1(a863)) | c2_1(a863)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(1310,plain,
% 0.72/0.91 (hskp13),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1309, 1262, 1013, 1015, 1016, 1261, 1260])).
% 0.72/0.91 tff(1311,plain,
% 0.72/0.91 (~c2_1(a846)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[465, 1310])).
% 0.72/0.91 tff(1312,plain,
% 0.72/0.91 (~c0_1(a846)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[471, 1310])).
% 0.72/0.91 tff(1313,plain,
% 0.72/0.91 (c3_1(a846)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[479, 1310])).
% 0.72/0.91 tff(1314,plain,
% 0.72/0.91 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(1315,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[1314])).
% 0.72/0.91 tff(1316,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1317,plain,
% 0.72/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp18) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(1318,plain,
% 0.72/0.91 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[1317])).
% 0.72/0.91 tff(1319,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 0.72/0.91 tff(1320,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 0.72/0.91 tff(1321,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1320, 1316])).
% 0.72/0.91 tff(1322,plain,(
% 0.72/0.91 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(skolemize,[status(sab)],[1321])).
% 0.72/0.91 tff(1323,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1322, 1315])).
% 0.72/0.91 tff(1324,plain,
% 0.72/0.91 (hskp30),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[772, 114, 35, 1313, 1312, 1311, 766])).
% 0.72/0.91 tff(1325,plain,
% 0.72/0.91 (c3_1(a857)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[781, 1324])).
% 0.72/0.91 tff(1326,plain,
% 0.72/0.91 (c2_1(a857)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[789, 1324])).
% 0.72/0.91 tff(1327,plain,
% 0.72/0.91 (c1_1(a857)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[797, 1324])).
% 0.72/0.91 tff(1328,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c2_1(a863) | (~ndr1_0) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | (~c3_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a863) | (~ndr1_0) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1329,plain,
% 0.72/0.91 ((hskp18 | (~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863))) <=> (hskp18 | c2_1(a863) | (~ndr1_0) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1330,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c2_1(a863) | (~ndr1_0) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | (~c3_1(a863)) | (~c0_1(a863))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1329])).
% 0.72/0.91 tff(1331,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a863) | (~ndr1_0) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1330, 1328])).
% 0.72/0.91 tff(1332,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1333,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a863) | (~ndr1_0) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)) | (~c3_1(a863)) | (~c0_1(a863))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 0.72/0.91 tff(1334,plain,
% 0.72/0.91 (hskp18),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1333, 114, 1327, 1326, 1325, 1261, 1262, 1260, 1323])).
% 0.72/0.91 tff(1335,plain,
% 0.72/0.91 (~c1_1(a861)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1141, 1334])).
% 0.72/0.91 tff(1336,plain,
% 0.72/0.91 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(1337,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[1336])).
% 0.72/0.92 tff(1338,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1339,plain,
% 0.72/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp2))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(1340,plain,
% 0.72/0.92 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[1339])).
% 0.72/0.92 tff(1341,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 0.72/0.92 tff(1342,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 0.76/0.92 tff(1343,plain,
% 0.76/0.92 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1342, 1338])).
% 0.76/0.92 tff(1344,plain,(
% 0.76/0.92 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.76/0.92 inference(skolemize,[status(sab)],[1343])).
% 0.76/0.92 tff(1345,plain,
% 0.76/0.92 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1344, 1337])).
% 0.76/0.92 tff(1346,plain,
% 0.76/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c1_1(a875)) | (~c0_1(a875)) | (~c2_1(a875)) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c1_1(a875)) | (~c0_1(a875)) | (~c2_1(a875)) | (~c3_1(a846)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1347,plain,
% 0.76/0.92 ((hskp2 | (~ndr1_0) | (~c2_1(a875)) | (~c1_1(a875)) | (~c0_1(a875)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846))) <=> (hskp2 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c1_1(a875)) | (~c0_1(a875)) | (~c2_1(a875)) | (~c3_1(a846)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1348,plain,
% 0.76/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a875)) | (~c1_1(a875)) | (~c0_1(a875)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c1_1(a875)) | (~c0_1(a875)) | (~c2_1(a875)) | (~c3_1(a846))))),
% 0.76/0.92 inference(monotonicity,[status(thm)],[1347])).
% 0.76/0.92 tff(1349,plain,
% 0.76/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a875)) | (~c1_1(a875)) | (~c0_1(a875)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c1_1(a875)) | (~c0_1(a875)) | (~c2_1(a875)) | (~c3_1(a846)))),
% 0.76/0.92 inference(transitivity,[status(thm)],[1348, 1346])).
% 0.76/0.92 tff(1350,plain,
% 0.76/0.92 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a875)) | (~c1_1(a875)) | (~c0_1(a875)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))),
% 0.76/0.92 inference(quant_inst,[status(thm)],[])).
% 0.76/0.92 tff(1351,plain,
% 0.76/0.92 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c1_1(a875)) | (~c0_1(a875)) | (~c2_1(a875)) | (~c3_1(a846))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 0.76/0.92 tff(1352,plain,
% 0.76/0.92 (~c1_1(a875)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1351, 114, 1014, 1050, 974, 1313, 1312, 1311, 1345])).
% 0.76/0.92 tff(1353,plain,
% 0.76/0.92 (hskp5),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[981, 1352])).
% 0.76/0.92 tff(1354,plain,
% 0.76/0.92 (c0_1(a861)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1159, 1334])).
% 0.76/0.92 tff(1355,plain,
% 0.76/0.92 (c2_1(a861)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1151, 1334])).
% 0.76/0.92 tff(1356,assumption,(~c1_1(a861)), introduced(assumption)).
% 0.76/0.92 tff(1357,assumption,(c2_1(a861)), introduced(assumption)).
% 0.76/0.92 tff(1358,assumption,(c0_1(a861)), introduced(assumption)).
% 0.76/0.92 tff(1359,plain,
% 0.76/0.92 (c2_1(a859)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1166, 114, 1358, 1357, 83, 139, 1356, 23, 12, 67, 22])).
% 0.76/0.92 tff(1360,plain,
% 0.76/0.92 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a846) | c2_1(a846) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a846) | c2_1(a846) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a846)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1361,plain,
% 0.76/0.92 ((hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846))) <=> (hskp4 | c0_1(a846) | c2_1(a846) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a846)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1362,plain,
% 0.76/0.92 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a846) | c2_1(a846) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a846))))),
% 0.76/0.92 inference(monotonicity,[status(thm)],[1361])).
% 0.76/0.92 tff(1363,plain,
% 0.76/0.92 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a846) | c2_1(a846) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a846)))),
% 0.76/0.92 inference(transitivity,[status(thm)],[1362, 1360])).
% 0.76/0.92 tff(1364,plain,
% 0.76/0.92 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))),
% 0.76/0.92 inference(quant_inst,[status(thm)],[])).
% 0.76/0.92 tff(1365,plain,
% 0.76/0.92 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a846) | c2_1(a846) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a846))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 0.76/0.92 tff(1366,plain,
% 0.76/0.92 (hskp4),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1365, 114, 1028, 83, 139, 704, 666, 67, 373])).
% 0.76/0.92 tff(1367,plain,
% 0.76/0.92 (~c3_1(a832)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[390, 1366])).
% 0.76/0.92 tff(1368,plain,
% 0.76/0.92 (~c2_1(a832)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[396, 1366])).
% 0.76/0.92 tff(1369,plain,
% 0.76/0.92 (~c1_1(a832)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[402, 1366])).
% 0.76/0.92 tff(1370,plain,
% 0.76/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a861) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)) | (~c2_1(a861)) | (~c0_1(a861)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a861) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)) | (~c2_1(a861)) | (~c0_1(a861)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1371,plain,
% 0.76/0.92 (((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a861) | (~c2_1(a861)) | (~c0_1(a861)) | c3_1(a832) | c2_1(a832) | c1_1(a832)) <=> (c1_1(a861) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)) | (~c2_1(a861)) | (~c0_1(a861)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1372,plain,
% 0.76/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a861) | (~c2_1(a861)) | (~c0_1(a861)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a861) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)) | (~c2_1(a861)) | (~c0_1(a861))))),
% 0.76/0.92 inference(monotonicity,[status(thm)],[1371])).
% 0.76/0.92 tff(1373,plain,
% 0.76/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a861) | (~c2_1(a861)) | (~c0_1(a861)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a861) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)) | (~c2_1(a861)) | (~c0_1(a861)))),
% 0.76/0.92 inference(transitivity,[status(thm)],[1372, 1370])).
% 0.76/0.92 tff(1374,plain,
% 0.76/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a861) | (~c2_1(a861)) | (~c0_1(a861)) | c3_1(a832) | c2_1(a832) | c1_1(a832))),
% 0.76/0.92 inference(quant_inst,[status(thm)],[])).
% 0.76/0.92 tff(1375,plain,
% 0.76/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a861) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a859)) | (~c0_1(a859)) | (~c2_1(a861)) | (~c0_1(a861))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 0.76/0.92 tff(1376,plain,
% 0.76/0.92 ($false),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1375, 114, 1358, 1357, 453, 1356, 12, 1369, 1368, 1367, 22, 1359])).
% 0.76/0.92 tff(1377,plain,((~hskp5) | (~c0_1(a861)) | (~c2_1(a861)) | (~c0_1(a859)) | c1_1(a861) | c3_1(a859) | (~c3_1(a846)) | c0_1(a846) | c2_1(a846) | c1_1(a859)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.92 tff(1378,plain,
% 0.76/0.92 ($false),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1377, 1355, 1354, 1353, 1016, 1335, 1015, 1313, 1312, 1311, 1013])).
% 0.76/0.92 tff(1379,plain,(hskp2 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.76/0.92 tff(1380,plain,
% 0.76/0.92 (hskp2),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1379, 35])).
% 0.76/0.92 tff(1381,plain,
% 0.76/0.92 (~c1_1(a830)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[59, 1380])).
% 0.76/0.92 tff(1382,plain,
% 0.76/0.92 (~c2_1(a830)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[53, 1380])).
% 0.76/0.92 tff(1383,assumption,(hskp13), introduced(assumption)).
% 0.76/0.92 tff(1384,plain,
% 0.76/0.92 (~c2_1(a846)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[465, 1383])).
% 0.76/0.92 tff(1385,plain,
% 0.76/0.92 (~c0_1(a846)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[471, 1383])).
% 0.76/0.92 tff(1386,plain,
% 0.76/0.92 (c3_1(a846)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[479, 1383])).
% 0.76/0.92 tff(1387,plain,
% 0.76/0.92 (^[U: $i] : refl((hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.76/0.92 inference(bind,[status(th)],[])).
% 0.76/0.92 tff(1388,plain,
% 0.76/0.92 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.76/0.92 inference(quant_intro,[status(thm)],[1387])).
% 0.76/0.92 tff(1389,plain,
% 0.76/0.92 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1390,plain,
% 0.76/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp19))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> ((hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp20))), rewrite(((hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.76/0.92 inference(bind,[status(th)],[])).
% 0.76/0.92 tff(1391,plain,
% 0.76/0.92 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.76/0.92 inference(quant_intro,[status(thm)],[1390])).
% 0.76/0.92 tff(1392,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.76/0.92 tff(1393,plain,
% 0.76/0.92 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 0.76/0.92 tff(1394,plain,
% 0.76/0.92 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1393, 1389])).
% 0.76/0.92 tff(1395,plain,(
% 0.76/0.92 ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.76/0.92 inference(skolemize,[status(sab)],[1394])).
% 0.76/0.92 tff(1396,plain,
% 0.76/0.92 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1395, 1388])).
% 0.76/0.92 tff(1397,plain,
% 0.76/0.92 (hskp30),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[772, 114, 35, 1386, 1385, 1384, 766])).
% 0.76/0.92 tff(1398,plain,
% 0.76/0.92 (c3_1(a857)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[781, 1397])).
% 0.76/0.92 tff(1399,plain,
% 0.76/0.92 (c2_1(a857)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[789, 1397])).
% 0.76/0.92 tff(1400,plain,
% 0.76/0.92 (c1_1(a857)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[797, 1397])).
% 0.76/0.92 tff(1401,plain,
% 0.76/0.92 (hskp25),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1107, 114, 1400, 1399, 1398, 1016, 1013, 1015, 1097])).
% 0.76/0.92 tff(1402,plain,
% 0.76/0.92 (~c3_1(a890)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1113, 1401])).
% 0.76/0.92 tff(1403,plain,
% 0.76/0.92 (~c0_1(a890)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1119, 1401])).
% 0.76/0.92 tff(1404,plain,
% 0.76/0.92 (c2_1(a890)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1127, 1401])).
% 0.76/0.92 tff(1405,plain,
% 0.76/0.92 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | c0_1(a890) | c3_1(a890) | (~ndr1_0) | (~c2_1(a890)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp20 | hskp19 | c0_1(a890) | c3_1(a890) | (~ndr1_0) | (~c2_1(a890)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1406,plain,
% 0.76/0.92 ((hskp20 | hskp19 | (~ndr1_0) | c0_1(a890) | c3_1(a890) | (~c2_1(a890))) <=> (hskp20 | hskp19 | c0_1(a890) | c3_1(a890) | (~ndr1_0) | (~c2_1(a890)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1407,plain,
% 0.76/0.92 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c0_1(a890) | c3_1(a890) | (~c2_1(a890)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | c0_1(a890) | c3_1(a890) | (~ndr1_0) | (~c2_1(a890))))),
% 0.76/0.92 inference(monotonicity,[status(thm)],[1406])).
% 0.76/0.92 tff(1408,plain,
% 0.76/0.92 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c0_1(a890) | c3_1(a890) | (~c2_1(a890)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp20 | hskp19 | c0_1(a890) | c3_1(a890) | (~ndr1_0) | (~c2_1(a890)))),
% 0.76/0.92 inference(transitivity,[status(thm)],[1407, 1405])).
% 0.76/0.92 tff(1409,plain,
% 0.76/0.92 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c0_1(a890) | c3_1(a890) | (~c2_1(a890)))),
% 0.76/0.92 inference(quant_inst,[status(thm)],[])).
% 0.76/0.92 tff(1410,plain,
% 0.76/0.92 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp20 | hskp19 | c0_1(a890) | c3_1(a890) | (~ndr1_0) | (~c2_1(a890))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1409, 1408])).
% 0.76/0.92 tff(1411,plain,
% 0.76/0.92 (hskp20),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1410, 114, 345, 1404, 1403, 1402, 1396])).
% 0.76/0.92 tff(1412,plain,
% 0.76/0.92 (((~hskp20) | c1_1(a864)) <=> ((~hskp20) | c1_1(a864))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1413,axiom,((~hskp20) | c1_1(a864)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.76/0.92 tff(1414,plain,
% 0.76/0.92 ((~hskp20) | c1_1(a864)),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 0.76/0.92 tff(1415,plain,
% 0.76/0.92 ((~hskp20) | c1_1(a864)),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1414, 1412])).
% 0.76/0.92 tff(1416,plain,
% 0.76/0.92 ((~hskp20) | c1_1(a864)),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1415, 1412])).
% 0.76/0.92 tff(1417,plain,
% 0.76/0.92 ((~hskp20) | c1_1(a864)),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1416, 1412])).
% 0.76/0.92 tff(1418,plain,
% 0.76/0.92 ((~hskp20) | c1_1(a864)),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1417, 1412])).
% 0.76/0.92 tff(1419,plain,
% 0.76/0.92 (c1_1(a864)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1418, 1411])).
% 0.76/0.92 tff(1420,plain,
% 0.76/0.92 (((~hskp20) | (~c2_1(a864))) <=> ((~hskp20) | (~c2_1(a864)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1421,plain,
% 0.76/0.92 (((~c2_1(a864)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a864)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1422,axiom,((~c2_1(a864)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.76/0.92 tff(1423,plain,
% 0.76/0.92 ((~hskp20) | (~c2_1(a864))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1422, 1421])).
% 0.76/0.92 tff(1424,plain,
% 0.76/0.92 ((~hskp20) | (~c2_1(a864))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1423, 1420])).
% 0.76/0.92 tff(1425,plain,
% 0.76/0.92 (~c2_1(a864)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1424, 1411])).
% 0.76/0.92 tff(1426,plain,
% 0.76/0.92 (((~hskp20) | (~c0_1(a864))) <=> ((~hskp20) | (~c0_1(a864)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1427,plain,
% 0.76/0.92 (((~c0_1(a864)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a864)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1428,axiom,((~c0_1(a864)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.76/0.92 tff(1429,plain,
% 0.76/0.92 ((~hskp20) | (~c0_1(a864))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 0.76/0.92 tff(1430,plain,
% 0.76/0.92 ((~hskp20) | (~c0_1(a864))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1429, 1426])).
% 0.76/0.92 tff(1431,plain,
% 0.76/0.92 (~c0_1(a864)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1430, 1411])).
% 0.76/0.92 tff(1432,assumption,(~c0_1(a830)), introduced(assumption)).
% 0.76/0.92 tff(1433,plain,
% 0.76/0.92 (~hskp2),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[74, 1432])).
% 0.76/0.92 tff(1434,assumption,(~c2_1(a864)), introduced(assumption)).
% 0.76/0.92 tff(1435,assumption,(c1_1(a864)), introduced(assumption)).
% 0.76/0.92 tff(1436,plain,
% 0.76/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a830) | c2_1(a864) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a864)) | (~c3_1(a864)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a830) | c2_1(a864) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a864)) | (~c3_1(a864)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1437,plain,
% 0.76/0.92 ((hskp2 | (~ndr1_0) | c2_1(a864) | (~c1_1(a864)) | (~c3_1(a864)) | c2_1(a830) | c1_1(a830) | c0_1(a830)) <=> (hskp2 | c0_1(a830) | c2_1(a864) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a864)) | (~c3_1(a864)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1438,plain,
% 0.76/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a864) | (~c1_1(a864)) | (~c3_1(a864)) | c2_1(a830) | c1_1(a830) | c0_1(a830))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a830) | c2_1(a864) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a864)) | (~c3_1(a864))))),
% 0.76/0.92 inference(monotonicity,[status(thm)],[1437])).
% 0.76/0.92 tff(1439,plain,
% 0.76/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a864) | (~c1_1(a864)) | (~c3_1(a864)) | c2_1(a830) | c1_1(a830) | c0_1(a830))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a830) | c2_1(a864) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a864)) | (~c3_1(a864)))),
% 0.76/0.92 inference(transitivity,[status(thm)],[1438, 1436])).
% 0.76/0.92 tff(1440,plain,
% 0.76/0.92 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a864) | (~c1_1(a864)) | (~c3_1(a864)) | c2_1(a830) | c1_1(a830) | c0_1(a830))),
% 0.76/0.92 inference(quant_inst,[status(thm)],[])).
% 0.76/0.92 tff(1441,plain,
% 0.76/0.92 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a830) | c2_1(a864) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a864)) | (~c3_1(a864))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 0.76/0.92 tff(1442,plain,
% 0.76/0.92 (hskp2 | c0_1(a830) | (~c3_1(a864))),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1441, 114, 1435, 1434, 814, 813, 34])).
% 0.76/0.92 tff(1443,plain,
% 0.76/0.92 (~c3_1(a864)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1442, 1433, 1432])).
% 0.76/0.92 tff(1444,plain,
% 0.76/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a830) | c2_1(a846) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a830) | c2_1(a846) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1445,plain,
% 0.76/0.92 ((hskp2 | (~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a830) | c1_1(a830) | c0_1(a830)) <=> (hskp2 | c0_1(a830) | c2_1(a846) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)))),
% 0.76/0.92 inference(rewrite,[status(thm)],[])).
% 0.76/0.92 tff(1446,plain,
% 0.76/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a830) | c1_1(a830) | c0_1(a830))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a830) | c2_1(a846) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846))))),
% 0.76/0.92 inference(monotonicity,[status(thm)],[1445])).
% 0.76/0.92 tff(1447,plain,
% 0.76/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a830) | c1_1(a830) | c0_1(a830))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a830) | c2_1(a846) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)))),
% 0.76/0.92 inference(transitivity,[status(thm)],[1446, 1444])).
% 0.76/0.92 tff(1448,plain,
% 0.76/0.92 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a830) | c1_1(a830) | c0_1(a830))),
% 0.76/0.92 inference(quant_inst,[status(thm)],[])).
% 0.76/0.92 tff(1449,plain,
% 0.76/0.92 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a830) | c2_1(a846) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846))),
% 0.76/0.92 inference(modus_ponens,[status(thm)],[1448, 1447])).
% 0.76/0.92 tff(1450,plain,
% 0.76/0.92 (hskp2 | c0_1(a830) | (~c1_1(a846))),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1449, 114, 1028, 666, 814, 813, 34])).
% 0.76/0.92 tff(1451,plain,
% 0.76/0.92 (~c1_1(a846)),
% 0.76/0.92 inference(unit_resolution,[status(thm)],[1450, 1433, 1432])).
% 0.76/0.92 tff(1452,assumption,(~c0_1(a864)), introduced(assumption)).
% 0.76/0.92 tff(1453,plain,
% 0.76/0.92 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a864) | c2_1(a864) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | c3_1(a864))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a864) | c2_1(a864) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | c3_1(a864))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(1454,plain,
% 0.76/0.93 ((hskp0 | (~ndr1_0) | c2_1(a864) | c0_1(a864) | c3_1(a864) | c2_1(a846) | c1_1(a846) | c0_1(a846)) <=> (hskp0 | c0_1(a864) | c2_1(a864) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | c3_1(a864))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(1455,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a864) | c0_1(a864) | c3_1(a864) | c2_1(a846) | c1_1(a846) | c0_1(a846))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a864) | c2_1(a864) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | c3_1(a864)))),
% 0.76/0.93 inference(monotonicity,[status(thm)],[1454])).
% 0.76/0.93 tff(1456,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a864) | c0_1(a864) | c3_1(a864) | c2_1(a846) | c1_1(a846) | c0_1(a846))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a864) | c2_1(a864) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | c3_1(a864))),
% 0.76/0.93 inference(transitivity,[status(thm)],[1455, 1453])).
% 0.76/0.93 tff(1457,plain,
% 0.76/0.93 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a864) | c0_1(a864) | c3_1(a864) | c2_1(a846) | c1_1(a846) | c0_1(a846))),
% 0.76/0.93 inference(quant_inst,[status(thm)],[])).
% 0.76/0.93 tff(1458,plain,
% 0.76/0.93 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a864) | c2_1(a864) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | c3_1(a864)),
% 0.76/0.93 inference(modus_ponens,[status(thm)],[1457, 1456])).
% 0.76/0.93 tff(1459,plain,
% 0.76/0.93 (hskp0 | c1_1(a846) | c3_1(a864)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[1458, 114, 1452, 1434, 704, 666, 679])).
% 0.76/0.93 tff(1460,plain,
% 0.76/0.93 (hskp0),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[1459, 1451, 1443])).
% 0.76/0.93 tff(1461,plain,
% 0.76/0.93 (~c0_1(a828)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[738, 1460])).
% 0.76/0.93 tff(1462,assumption,(c3_1(a875)), introduced(assumption)).
% 0.76/0.93 tff(1463,assumption,(c2_1(a875)), introduced(assumption)).
% 0.76/0.93 tff(1464,assumption,(c0_1(a875)), introduced(assumption)).
% 0.76/0.93 tff(1465,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a830) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a830) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(1466,plain,
% 0.76/0.93 ((hskp4 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a830) | c1_1(a830) | c0_1(a830)) <=> (hskp4 | c0_1(a830) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(1467,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a830) | c1_1(a830) | c0_1(a830))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a830) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875))))),
% 0.76/0.93 inference(monotonicity,[status(thm)],[1466])).
% 0.76/0.93 tff(1468,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a830) | c1_1(a830) | c0_1(a830))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a830) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.76/0.93 inference(transitivity,[status(thm)],[1467, 1465])).
% 0.76/0.93 tff(1469,plain,
% 0.76/0.93 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a830) | c1_1(a830) | c0_1(a830))),
% 0.76/0.93 inference(quant_inst,[status(thm)],[])).
% 0.76/0.93 tff(1470,plain,
% 0.76/0.93 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a830) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875))),
% 0.76/0.93 inference(modus_ponens,[status(thm)],[1469, 1468])).
% 0.76/0.93 tff(1471,plain,
% 0.76/0.93 (hskp4 | c0_1(a830) | c1_1(a830)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[1470, 114, 1464, 1463, 1462, 813, 1040])).
% 0.76/0.93 tff(1472,plain,
% 0.76/0.93 (hskp4),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[1471, 1432, 814])).
% 0.76/0.93 tff(1473,plain,
% 0.76/0.93 (~c3_1(a832)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[390, 1472])).
% 0.76/0.93 tff(1474,plain,
% 0.76/0.93 (~c2_1(a832)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[396, 1472])).
% 0.76/0.93 tff(1475,plain,
% 0.76/0.93 (c2_1(a828)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[746, 1460])).
% 0.76/0.93 tff(1476,plain,
% 0.76/0.93 (c1_1(a828)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[754, 1460])).
% 0.76/0.93 tff(1477,assumption,(c3_1(a857)), introduced(assumption)).
% 0.76/0.93 tff(1478,assumption,(c2_1(a857)), introduced(assumption)).
% 0.76/0.93 tff(1479,assumption,(c1_1(a857)), introduced(assumption)).
% 0.76/0.93 tff(1480,plain,
% 0.76/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a832) | c3_1(a832) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a832)) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a832) | c3_1(a832) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a832)) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(1481,plain,
% 0.76/0.93 (((~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c2_1(a832) | c3_1(a832) | (~c0_1(a832)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828))) <=> (c2_1(a832) | c3_1(a832) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a832)) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(1482,plain,
% 0.76/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c2_1(a832) | c3_1(a832) | (~c0_1(a832)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a832) | c3_1(a832) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a832)) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857))))),
% 0.76/0.93 inference(monotonicity,[status(thm)],[1481])).
% 0.76/0.93 tff(1483,plain,
% 0.76/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c2_1(a832) | c3_1(a832) | (~c0_1(a832)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a832) | c3_1(a832) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a832)) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857)))),
% 0.76/0.93 inference(transitivity,[status(thm)],[1482, 1480])).
% 0.76/0.93 tff(1484,plain,
% 0.76/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a857)) | (~c1_1(a857)) | (~c3_1(a857)) | c2_1(a832) | c3_1(a832) | (~c0_1(a832)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828)))),
% 0.76/0.93 inference(quant_inst,[status(thm)],[])).
% 0.76/0.93 tff(1485,plain,
% 0.76/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a832) | c3_1(a832) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a832)) | (~c1_1(a857)) | (~c3_1(a857)) | (~c2_1(a857))),
% 0.76/0.93 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 0.76/0.93 tff(1486,plain,
% 0.76/0.93 (~c0_1(a832)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[1485, 114, 1479, 1478, 1477, 1476, 1475, 1474, 1473, 1461, 662])).
% 0.76/0.93 tff(1487,plain,
% 0.76/0.93 (~c1_1(a832)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[402, 1472])).
% 0.76/0.93 tff(1488,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | c1_1(a859) | c3_1(a859) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c3_1(a846)) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp24 | c1_1(a859) | c3_1(a859) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c3_1(a846)) | (~c0_1(a859)))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(1489,plain,
% 0.76/0.93 ((hskp24 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a846) | c1_1(a846) | (~c3_1(a846))) <=> (hskp24 | c1_1(a859) | c3_1(a859) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c3_1(a846)) | (~c0_1(a859)))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(1490,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a846) | c1_1(a846) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | c1_1(a859) | c3_1(a859) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c3_1(a846)) | (~c0_1(a859))))),
% 0.76/0.93 inference(monotonicity,[status(thm)],[1489])).
% 0.76/0.93 tff(1491,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a846) | c1_1(a846) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp24 | c1_1(a859) | c3_1(a859) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c3_1(a846)) | (~c0_1(a859)))),
% 0.76/0.93 inference(transitivity,[status(thm)],[1490, 1488])).
% 0.76/0.93 tff(1492,plain,
% 0.76/0.93 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a846) | c1_1(a846) | (~c3_1(a846)))),
% 0.76/0.93 inference(quant_inst,[status(thm)],[])).
% 0.76/0.93 tff(1493,plain,
% 0.76/0.93 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp24 | c1_1(a859) | c3_1(a859) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c3_1(a846)) | (~c0_1(a859))),
% 0.76/0.93 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 0.76/0.93 tff(1494,plain,
% 0.76/0.93 (hskp24 | c1_1(a846)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[1493, 114, 453, 1028, 23, 12, 666, 559])).
% 0.76/0.93 tff(1495,plain,
% 0.76/0.93 (hskp24),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[1494, 1451])).
% 0.76/0.93 tff(1496,plain,
% 0.76/0.93 (~c2_1(a884)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[571, 1495])).
% 0.76/0.93 tff(1497,plain,
% 0.76/0.93 (c3_1(a884)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[594, 1495])).
% 0.76/0.93 tff(1498,plain,
% 0.76/0.93 (c1_1(a884)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[579, 1495])).
% 0.76/0.93 tff(1499,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c2_1(a884) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | c0_1(a832) | (~c1_1(a884)) | (~c3_1(a884)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a884) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | c0_1(a832) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(1500,plain,
% 0.76/0.93 ((hskp2 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a832) | c1_1(a832) | c0_1(a832)) <=> (hskp2 | c2_1(a884) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | c0_1(a832) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(1501,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c2_1(a884) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | c0_1(a832) | (~c1_1(a884)) | (~c3_1(a884))))),
% 0.76/0.93 inference(monotonicity,[status(thm)],[1500])).
% 0.76/0.93 tff(1502,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a884) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | c0_1(a832) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.76/0.93 inference(transitivity,[status(thm)],[1501, 1499])).
% 0.76/0.93 tff(1503,plain,
% 0.76/0.93 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a832) | c1_1(a832) | c0_1(a832))),
% 0.76/0.93 inference(quant_inst,[status(thm)],[])).
% 0.76/0.93 tff(1504,plain,
% 0.76/0.93 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a884) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | c0_1(a832) | (~c1_1(a884)) | (~c3_1(a884))),
% 0.76/0.93 inference(modus_ponens,[status(thm)],[1503, 1502])).
% 0.76/0.93 tff(1505,plain,
% 0.76/0.93 ($false),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[1504, 114, 1433, 1498, 1497, 1496, 1487, 1474, 34, 1486])).
% 0.76/0.93 tff(1506,plain,(c0_1(a830) | (~c1_1(a857)) | (~c2_1(a857)) | (~c3_1(a857)) | c0_1(a864) | c2_1(a864) | c0_1(a846) | c2_1(a846) | (~c0_1(a859)) | (~c3_1(a846)) | c1_1(a859) | c3_1(a859) | (~c1_1(a864)) | c1_1(a830) | c2_1(a830) | (~c0_1(a875)) | (~c2_1(a875)) | (~c3_1(a875))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.93 tff(1507,plain,
% 0.76/0.93 (c0_1(a830)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[1506, 1400, 1399, 1398, 1431, 1425, 1385, 1384, 1016, 1386, 1013, 1015, 1419, 814, 813, 1050, 974, 966])).
% 0.76/0.93 tff(1508,plain,
% 0.76/0.93 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp11 | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(1509,plain,
% 0.76/0.93 ((hskp19 | hskp11 | (~ndr1_0) | c2_1(a830) | c1_1(a830) | (~c0_1(a830))) <=> (hskp19 | hskp11 | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(1510,plain,
% 0.76/0.93 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830))))),
% 0.76/0.93 inference(monotonicity,[status(thm)],[1509])).
% 0.76/0.93 tff(1511,plain,
% 0.76/0.93 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp11 | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[1510, 1508])).
% 0.77/0.93 tff(1512,plain,
% 0.77/0.93 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1513,plain,
% 0.77/0.93 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp11 | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 0.77/0.93 tff(1514,plain,
% 0.77/0.93 (hskp19 | hskp11 | c1_1(a830) | (~c0_1(a830))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1513, 114, 813, 1204])).
% 0.77/0.93 tff(1515,plain,
% 0.77/0.93 (hskp11),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1514, 1507, 345, 814])).
% 0.77/0.93 tff(1516,plain,
% 0.77/0.93 (~c2_1(a844)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[437, 1515])).
% 0.77/0.93 tff(1517,plain,
% 0.77/0.93 (~c1_1(a844)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[443, 1515])).
% 0.77/0.93 tff(1518,plain,
% 0.77/0.93 (c3_1(a844)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[451, 1515])).
% 0.77/0.93 tff(1519,plain,
% 0.77/0.93 (hskp4),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1168, 1518, 35, 1517, 1516, 1386, 1385, 1384])).
% 0.77/0.93 tff(1520,plain,
% 0.77/0.93 (~c3_1(a832)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[390, 1519])).
% 0.77/0.93 tff(1521,plain,
% 0.77/0.93 (~c2_1(a832)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[396, 1519])).
% 0.77/0.93 tff(1522,plain,
% 0.77/0.93 (~c1_1(a832)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[402, 1519])).
% 0.77/0.93 tff(1523,plain,
% 0.77/0.93 (~c2_1(a859)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[651, 114, 1016, 1013, 1015, 1522, 1521, 1520, 22])).
% 0.77/0.93 tff(1524,plain,
% 0.77/0.93 (hskp24),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[858, 114, 1016, 1518, 1013, 1015, 1517, 1516, 559])).
% 0.77/0.93 tff(1525,plain,
% 0.77/0.93 (~c2_1(a884)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[571, 1524])).
% 0.77/0.93 tff(1526,plain,
% 0.77/0.93 (c3_1(a884)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[594, 1524])).
% 0.77/0.93 tff(1527,plain,
% 0.77/0.93 (c1_1(a884)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[579, 1524])).
% 0.77/0.93 tff(1528,plain,
% 0.77/0.93 (~c1_1(a846)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1183, 114, 1527, 1526, 1016, 1386, 1525, 1015, 1385, 722, 1523])).
% 0.77/0.93 tff(1529,plain,
% 0.77/0.93 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(1530,plain,
% 0.77/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[1529])).
% 0.77/0.93 tff(1531,plain,
% 0.77/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1532,plain,
% 0.77/0.93 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(1533,plain,
% 0.77/0.93 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[1532])).
% 0.77/0.93 tff(1534,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause205')).
% 0.77/0.93 tff(1535,plain,
% 0.77/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 0.77/0.93 tff(1536,plain,
% 0.77/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1535, 1531])).
% 0.77/0.93 tff(1537,plain,(
% 0.77/0.93 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.93 inference(skolemize,[status(sab)],[1536])).
% 0.77/0.93 tff(1538,plain,
% 0.77/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1537, 1530])).
% 0.77/0.93 tff(1539,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a884) | c0_1(a864) | c3_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a864)) | (~c3_1(a864)) | (~c1_1(a884)) | (~c3_1(a884)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a884) | c0_1(a864) | c3_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a864)) | (~c3_1(a864)) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1540,plain,
% 0.77/0.93 (((~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a864) | (~c3_1(a864)) | (~c1_1(a864))) <=> (c2_1(a884) | c0_1(a864) | c3_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a864)) | (~c3_1(a864)) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1541,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a864) | (~c3_1(a864)) | (~c1_1(a864)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a884) | c0_1(a864) | c3_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a864)) | (~c3_1(a864)) | (~c1_1(a884)) | (~c3_1(a884))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[1540])).
% 0.77/0.93 tff(1542,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a864) | (~c3_1(a864)) | (~c1_1(a864)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a884) | c0_1(a864) | c3_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a864)) | (~c3_1(a864)) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[1541, 1539])).
% 0.77/0.93 tff(1543,plain,
% 0.77/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a864) | (~c3_1(a864)) | (~c1_1(a864)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1544,plain,
% 0.77/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a884) | c0_1(a864) | c3_1(a859) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)) | (~c1_1(a864)) | (~c3_1(a864)) | (~c1_1(a884)) | (~c3_1(a884))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 0.77/0.93 tff(1545,plain,
% 0.77/0.93 (~c3_1(a864)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1544, 114, 1527, 1526, 1419, 1016, 1525, 1431, 1015, 722, 1523])).
% 0.77/0.93 tff(1546,plain,
% 0.77/0.93 (hskp0 | c1_1(a846) | c3_1(a864)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1458, 114, 1431, 1425, 1385, 1384, 679])).
% 0.77/0.93 tff(1547,plain,
% 0.77/0.93 (hskp0),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1546, 1528, 1545])).
% 0.77/0.93 tff(1548,plain,
% 0.77/0.93 (~c0_1(a828)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[738, 1547])).
% 0.77/0.93 tff(1549,plain,
% 0.77/0.93 (c2_1(a828)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[746, 1547])).
% 0.77/0.93 tff(1550,plain,
% 0.77/0.93 (c1_1(a828)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[754, 1547])).
% 0.77/0.93 tff(1551,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a846) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c1_1(a846) | (~c3_1(a846)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a846) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c1_1(a846) | (~c3_1(a846)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1552,plain,
% 0.77/0.93 (((~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a846) | c0_1(a846) | (~c3_1(a846))) <=> (c0_1(a846) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c1_1(a846) | (~c3_1(a846)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1553,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a846) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c1_1(a846) | (~c3_1(a846))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1552])).
% 0.77/0.94 tff(1554,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a846) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c1_1(a846) | (~c3_1(a846)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1553, 1551])).
% 0.77/0.94 tff(1555,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a846) | c0_1(a846) | (~c3_1(a846)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1556,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a846) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c1_1(a846) | (~c3_1(a846))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1555, 1554])).
% 0.77/0.94 tff(1557,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1556, 114, 1050, 974, 966, 1386, 1550, 1549, 1385, 1548, 1538, 1528])).
% 0.77/0.94 tff(1558,plain,((~hskp13) | hskp16 | hskp19 | c1_1(a830) | c2_1(a830)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(1559,plain,
% 0.77/0.94 (~hskp13),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1558, 345, 35, 814, 813])).
% 0.77/0.94 tff(1560,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | c1_1(a859) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a859) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c0_1(a859)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1561,plain,
% 0.77/0.94 ((hskp13 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a830) | c1_1(a830) | (~c3_1(a830))) <=> (hskp13 | c1_1(a859) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c0_1(a859)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1562,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a830) | c1_1(a830) | (~c3_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | c1_1(a859) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c0_1(a859))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1561])).
% 0.77/0.94 tff(1563,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a830) | c1_1(a830) | (~c3_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a859) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c0_1(a859)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1562, 1560])).
% 0.77/0.94 tff(1564,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a859) | c3_1(a859) | (~c0_1(a859)) | c2_1(a830) | c1_1(a830) | (~c3_1(a830)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1565,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a859) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c3_1(a830)) | (~c0_1(a859))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 0.77/0.94 tff(1566,plain,
% 0.77/0.94 (hskp13 | c1_1(a830) | (~c3_1(a830))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1565, 114, 1016, 1013, 1015, 813, 383])).
% 0.77/0.94 tff(1567,plain,
% 0.77/0.94 (~c3_1(a830)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1566, 1559, 814])).
% 0.77/0.94 tff(1568,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a859) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | c3_1(a830) | (~c2_1(a859)) | (~c0_1(a859)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a859) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | c3_1(a830) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1569,plain,
% 0.77/0.94 (((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c3_1(a830) | c2_1(a830) | c1_1(a830)) <=> (c1_1(a859) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | c3_1(a830) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1570,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c3_1(a830) | c2_1(a830) | c1_1(a830))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a859) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | c3_1(a830) | (~c2_1(a859)) | (~c0_1(a859))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1569])).
% 0.77/0.94 tff(1571,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c3_1(a830) | c2_1(a830) | c1_1(a830))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a859) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | c3_1(a830) | (~c2_1(a859)) | (~c0_1(a859)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1570, 1568])).
% 0.77/0.94 tff(1572,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c1_1(a859) | (~c2_1(a859)) | (~c0_1(a859)) | c3_1(a830) | c2_1(a830) | c1_1(a830))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1573,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a859) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | c3_1(a830) | (~c2_1(a859)) | (~c0_1(a859))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 0.77/0.94 tff(1574,plain,
% 0.77/0.94 (~c2_1(a859)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1573, 114, 1016, 1013, 1015, 814, 813, 22, 1567])).
% 0.77/0.94 tff(1575,plain,
% 0.77/0.94 (hskp11),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1211, 1574, 345])).
% 0.77/0.94 tff(1576,plain,
% 0.77/0.94 (~c2_1(a844)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[437, 1575])).
% 0.77/0.94 tff(1577,plain,
% 0.77/0.94 (~c1_1(a844)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[443, 1575])).
% 0.77/0.94 tff(1578,plain,
% 0.77/0.94 (c3_1(a844)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[451, 1575])).
% 0.77/0.94 tff(1579,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[459, 114, 1559, 1016, 1578, 1013, 1015, 1577, 1576, 383])).
% 0.77/0.94 tff(1580,plain,(hskp19 | c1_1(a830) | c2_1(a830) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(1581,plain,
% 0.77/0.94 (hskp19),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1580, 814, 813, 35])).
% 0.77/0.94 tff(1582,plain,
% 0.77/0.94 (~c2_1(a863)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[494, 1581])).
% 0.77/0.94 tff(1583,plain,
% 0.77/0.94 (c3_1(a863)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[517, 1581])).
% 0.77/0.94 tff(1584,plain,
% 0.77/0.94 (c0_1(a863)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[502, 1581])).
% 0.77/0.94 tff(1585,plain,
% 0.77/0.94 (hskp13),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1309, 1584, 1013, 1015, 1016, 1583, 1582])).
% 0.77/0.94 tff(1586,plain,
% 0.77/0.94 (~c2_1(a846)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[465, 1585])).
% 0.77/0.94 tff(1587,plain,
% 0.77/0.94 (~c0_1(a846)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[471, 1585])).
% 0.77/0.94 tff(1588,plain,
% 0.77/0.94 (c3_1(a846)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[479, 1585])).
% 0.77/0.94 tff(1589,plain,
% 0.77/0.94 (hskp30),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[772, 114, 35, 1588, 1587, 1586, 766])).
% 0.77/0.94 tff(1590,plain,
% 0.77/0.94 (c3_1(a857)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[781, 1589])).
% 0.77/0.94 tff(1591,plain,
% 0.77/0.94 (c2_1(a857)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[789, 1589])).
% 0.77/0.94 tff(1592,plain,
% 0.77/0.94 (c1_1(a857)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[797, 1589])).
% 0.77/0.94 tff(1593,plain,
% 0.77/0.94 (hskp18),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1333, 114, 1592, 1591, 1590, 1584, 1583, 1582, 1323])).
% 0.77/0.94 tff(1594,plain,
% 0.77/0.94 (~c1_1(a861)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1141, 1593])).
% 0.77/0.94 tff(1595,plain,
% 0.77/0.94 (c2_1(a861)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1151, 1593])).
% 0.77/0.94 tff(1596,plain,
% 0.77/0.94 (c0_1(a861)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1159, 1593])).
% 0.77/0.94 tff(1597,plain,
% 0.77/0.94 (~hskp5),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1377, 1596, 1595, 1016, 1594, 1015, 1588, 1587, 1586, 1013])).
% 0.77/0.94 tff(1598,plain,
% 0.77/0.94 (~hskp3),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[265, 1597, 35])).
% 0.77/0.94 tff(1599,plain,
% 0.77/0.94 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(1600,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[1599])).
% 0.77/0.94 tff(1601,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1602,plain,
% 0.77/0.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(1603,plain,
% 0.77/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[1602])).
% 0.77/0.94 tff(1604,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 0.77/0.94 tff(1605,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 0.77/0.94 tff(1606,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1605, 1601])).
% 0.77/0.94 tff(1607,plain,(
% 0.77/0.94 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(skolemize,[status(sab)],[1606])).
% 0.77/0.94 tff(1608,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1607, 1600])).
% 0.77/0.94 tff(1609,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c0_1(a830) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c0_1(a830) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1610,plain,
% 0.77/0.94 ((hskp3 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a830) | c1_1(a830) | c0_1(a830)) <=> (hskp3 | c0_1(a830) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1611,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a830) | c1_1(a830) | c0_1(a830))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c0_1(a830) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1610])).
% 0.77/0.94 tff(1612,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a830) | c1_1(a830) | c0_1(a830))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c0_1(a830) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1611, 1609])).
% 0.77/0.94 tff(1613,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a830) | c1_1(a830) | c0_1(a830))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1614,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c0_1(a830) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1613, 1612])).
% 0.77/0.94 tff(1615,plain,
% 0.77/0.94 (hskp3 | c0_1(a830) | c1_1(a830)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1614, 114, 1050, 974, 966, 813, 1608])).
% 0.77/0.94 tff(1616,plain,
% 0.77/0.94 (c0_1(a830)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1615, 1598, 814])).
% 0.77/0.94 tff(1617,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a863) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c3_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a863) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1618,plain,
% 0.77/0.94 ((hskp3 | (~ndr1_0) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830))) <=> (hskp3 | c2_1(a863) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1619,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a863) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c3_1(a863)) | (~c0_1(a863))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1618])).
% 0.77/0.94 tff(1620,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a863) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1619, 1617])).
% 0.77/0.94 tff(1621,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1622,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a863) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c3_1(a863)) | (~c0_1(a863))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 0.77/0.94 tff(1623,plain,
% 0.77/0.94 (hskp3 | (~c0_1(a830))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1622, 114, 1584, 1583, 1582, 814, 813, 276])).
% 0.77/0.94 tff(1624,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1623, 1616, 1598])).
% 0.77/0.94 tff(1625,plain,(c1_1(a830) | c2_1(a830) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(1626,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1625, 1382, 1381, 35])).
% 0.77/0.94 tff(1627,plain,(hskp16), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(1628,plain,
% 0.77/0.94 (((~hskp16) | (~c2_1(a858))) <=> ((~hskp16) | (~c2_1(a858)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1629,plain,
% 0.77/0.94 (((~c2_1(a858)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a858)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1630,axiom,((~c2_1(a858)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.77/0.94 tff(1631,plain,
% 0.77/0.94 ((~hskp16) | (~c2_1(a858))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 0.77/0.94 tff(1632,plain,
% 0.77/0.94 ((~hskp16) | (~c2_1(a858))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1631, 1628])).
% 0.77/0.94 tff(1633,plain,
% 0.77/0.94 (~c2_1(a858)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1632, 1627])).
% 0.77/0.94 tff(1634,plain,
% 0.77/0.94 (((~hskp16) | (~c1_1(a858))) <=> ((~hskp16) | (~c1_1(a858)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1635,plain,
% 0.77/0.94 (((~c1_1(a858)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a858)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1636,axiom,((~c1_1(a858)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.77/0.94 tff(1637,plain,
% 0.77/0.94 ((~hskp16) | (~c1_1(a858))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1636, 1635])).
% 0.77/0.94 tff(1638,plain,
% 0.77/0.94 ((~hskp16) | (~c1_1(a858))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1637, 1634])).
% 0.77/0.94 tff(1639,plain,
% 0.77/0.94 (~c1_1(a858)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1638, 1627])).
% 0.77/0.94 tff(1640,plain,
% 0.77/0.94 (((~hskp16) | (~c0_1(a858))) <=> ((~hskp16) | (~c0_1(a858)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1641,plain,
% 0.77/0.94 (((~c0_1(a858)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a858)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1642,axiom,((~c0_1(a858)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.77/0.94 tff(1643,plain,
% 0.77/0.94 ((~hskp16) | (~c0_1(a858))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 0.77/0.94 tff(1644,plain,
% 0.77/0.94 ((~hskp16) | (~c0_1(a858))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1643, 1640])).
% 0.77/0.94 tff(1645,plain,
% 0.77/0.94 (~c0_1(a858)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1644, 1627])).
% 0.77/0.94 tff(1646,plain,
% 0.77/0.94 (~hskp17),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[336, 24])).
% 0.77/0.94 tff(1647,plain,
% 0.77/0.94 (^[U: $i] : refl((hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(1648,plain,
% 0.77/0.94 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[1647])).
% 0.77/0.94 tff(1649,plain,
% 0.77/0.94 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1650,plain,
% 0.77/0.94 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp4) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp4))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp4) <=> (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp4) <=> (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(1651,plain,
% 0.77/0.94 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp4) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[1650])).
% 0.77/0.94 tff(1652,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.77/0.94 tff(1653,plain,
% 0.77/0.94 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 0.77/0.94 tff(1654,plain,
% 0.77/0.94 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1653, 1649])).
% 0.77/0.94 tff(1655,plain,(
% 0.77/0.94 ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(skolemize,[status(sab)],[1654])).
% 0.77/0.94 tff(1656,plain,
% 0.77/0.94 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1655, 1648])).
% 0.77/0.94 tff(1657,plain,
% 0.77/0.94 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1658,plain,
% 0.77/0.94 ((hskp5 | hskp4 | (~ndr1_0) | c2_1(a858) | c1_1(a858) | c0_1(a858)) <=> (hskp5 | hskp4 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1659,plain,
% 0.77/0.94 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c2_1(a858) | c1_1(a858) | c0_1(a858))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0)))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1658])).
% 0.77/0.94 tff(1660,plain,
% 0.77/0.94 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c2_1(a858) | c1_1(a858) | c0_1(a858))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1659, 1657])).
% 0.77/0.94 tff(1661,plain,
% 0.77/0.94 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c2_1(a858) | c1_1(a858) | c0_1(a858))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1662,plain,
% 0.77/0.94 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp5 | hskp4 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 0.77/0.94 tff(1663,plain,
% 0.77/0.94 (hskp5 | hskp4),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1662, 114, 1645, 1639, 1633, 1656])).
% 0.77/0.94 tff(1664,plain,
% 0.77/0.94 (hskp5),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1663, 11])).
% 0.77/0.94 tff(1665,plain,
% 0.77/0.94 (~c3_1(a833)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[66, 1664])).
% 0.77/0.94 tff(1666,plain,
% 0.77/0.94 (c2_1(a833)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[138, 1664])).
% 0.77/0.94 tff(1667,plain,
% 0.77/0.94 (c0_1(a833)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[82, 1664])).
% 0.77/0.94 tff(1668,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a858) | c2_1(a858) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a858)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a858) | c2_1(a858) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a858)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1669,plain,
% 0.77/0.94 ((hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a858) | c0_1(a858) | (~c3_1(a858))) <=> (hskp4 | c0_1(a858) | c2_1(a858) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a858)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1670,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a858) | c0_1(a858) | (~c3_1(a858)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a858) | c2_1(a858) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a858))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1669])).
% 0.77/0.94 tff(1671,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a858) | c0_1(a858) | (~c3_1(a858)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a858) | c2_1(a858) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a858)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1670, 1668])).
% 0.77/0.94 tff(1672,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a858) | c0_1(a858) | (~c3_1(a858)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1673,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a858) | c2_1(a858) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a858))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1672, 1671])).
% 0.77/0.94 tff(1674,plain,
% 0.77/0.94 (~c3_1(a858)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1673, 114, 11, 1667, 1666, 1645, 1633, 1665, 373])).
% 0.77/0.94 tff(1675,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1676,plain,
% 0.77/0.94 ((hskp0 | (~ndr1_0) | c2_1(a858) | c0_1(a858) | c3_1(a858) | c2_1(a858) | c1_1(a858) | c0_1(a858)) <=> (hskp0 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1677,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a858) | c0_1(a858) | c3_1(a858) | c2_1(a858) | c1_1(a858) | c0_1(a858))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858)))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1676])).
% 0.77/0.95 tff(1678,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a858) | c0_1(a858) | c3_1(a858) | c2_1(a858) | c1_1(a858) | c0_1(a858))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1677, 1675])).
% 0.77/0.95 tff(1679,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a858) | c0_1(a858) | c3_1(a858) | c2_1(a858) | c1_1(a858) | c0_1(a858))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1680,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 0.77/0.95 tff(1681,plain,
% 0.77/0.95 (hskp0 | c3_1(a858)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1680, 114, 1645, 1639, 1633, 679])).
% 0.77/0.95 tff(1682,plain,
% 0.77/0.95 (hskp0),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1681, 1674])).
% 0.77/0.95 tff(1683,plain,
% 0.77/0.95 (~c0_1(a828)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[738, 1682])).
% 0.77/0.95 tff(1684,plain,
% 0.77/0.95 (c1_1(a828)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[754, 1682])).
% 0.77/0.95 tff(1685,plain,
% 0.77/0.95 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | c3_1(a828))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp4 | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | c3_1(a828))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1686,plain,
% 0.77/0.95 ((hskp17 | hskp4 | (~ndr1_0) | c0_1(a828) | c3_1(a828) | (~c1_1(a828))) <=> (hskp17 | hskp4 | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | c3_1(a828))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1687,plain,
% 0.77/0.95 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c0_1(a828) | c3_1(a828) | (~c1_1(a828)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | c3_1(a828)))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1686])).
% 0.77/0.95 tff(1688,plain,
% 0.77/0.95 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c0_1(a828) | c3_1(a828) | (~c1_1(a828)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp4 | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | c3_1(a828))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1687, 1685])).
% 0.77/0.95 tff(1689,plain,
% 0.77/0.95 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c0_1(a828) | c3_1(a828) | (~c1_1(a828)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1690,plain,
% 0.77/0.95 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp4 | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | c3_1(a828)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 0.77/0.95 tff(1691,plain,
% 0.77/0.95 (c3_1(a828)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1690, 114, 36, 11, 1684, 1683, 824])).
% 0.77/0.95 tff(1692,plain,
% 0.77/0.95 (^[U: $i] : refl((hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(1693,plain,
% 0.77/0.95 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[1692])).
% 0.77/0.95 tff(1694,plain,
% 0.77/0.95 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1695,plain,
% 0.77/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | 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))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | 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) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp2) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp2))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp2) <=> (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp2) <=> (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(1696,plain,
% 0.77/0.95 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp2) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[1695])).
% 0.77/0.95 tff(1697,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.77/0.95 tff(1698,plain,
% 0.77/0.95 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1697, 1696])).
% 0.77/0.95 tff(1699,plain,
% 0.77/0.95 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1698, 1694])).
% 0.77/0.95 tff(1700,plain,(
% 0.77/0.95 ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.77/0.95 inference(skolemize,[status(sab)],[1699])).
% 0.77/0.95 tff(1701,plain,
% 0.77/0.95 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1700, 1693])).
% 0.77/0.95 tff(1702,plain,
% 0.77/0.95 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp9 | hskp2 | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp9 | hskp2 | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1703,plain,
% 0.77/0.95 ((hskp9 | hskp2 | (~ndr1_0) | c2_1(a858) | c1_1(a858) | c3_1(a858)) <=> (hskp9 | hskp2 | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1704,plain,
% 0.77/0.95 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a858) | c1_1(a858) | c3_1(a858))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp9 | hskp2 | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858)))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1703])).
% 0.77/0.95 tff(1705,plain,
% 0.77/0.95 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a858) | c1_1(a858) | c3_1(a858))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp9 | hskp2 | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1704, 1702])).
% 0.77/0.95 tff(1706,plain,
% 0.77/0.95 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a858) | c1_1(a858) | c3_1(a858))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1707,plain,
% 0.77/0.95 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp9 | hskp2 | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 0.77/0.95 tff(1708,plain,
% 0.77/0.95 (hskp9 | hskp2 | c3_1(a858)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1707, 114, 1639, 1633, 1701])).
% 0.77/0.95 tff(1709,plain,
% 0.77/0.95 (hskp9),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1708, 1674, 1014])).
% 0.77/0.95 tff(1710,plain,
% 0.77/0.95 (((~hskp9) | (~c2_1(a841))) <=> ((~hskp9) | (~c2_1(a841)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1711,plain,
% 0.77/0.95 (((~c2_1(a841)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a841)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1712,axiom,((~c2_1(a841)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.77/0.95 tff(1713,plain,
% 0.77/0.95 ((~hskp9) | (~c2_1(a841))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 0.77/0.95 tff(1714,plain,
% 0.77/0.95 ((~hskp9) | (~c2_1(a841))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1713, 1710])).
% 0.77/0.95 tff(1715,plain,
% 0.77/0.95 (~c2_1(a841)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1714, 1709])).
% 0.77/0.95 tff(1716,plain,
% 0.77/0.95 (c2_1(a828)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[746, 1682])).
% 0.77/0.95 tff(1717,plain,
% 0.77/0.95 (((~hskp9) | c0_1(a841)) <=> ((~hskp9) | c0_1(a841))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1718,axiom,((~hskp9) | c0_1(a841)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.77/0.95 tff(1719,plain,
% 0.77/0.95 ((~hskp9) | c0_1(a841)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1718, 1717])).
% 0.77/0.95 tff(1720,plain,
% 0.77/0.95 ((~hskp9) | c0_1(a841)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1719, 1717])).
% 0.77/0.95 tff(1721,plain,
% 0.77/0.95 ((~hskp9) | c0_1(a841)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1720, 1717])).
% 0.77/0.95 tff(1722,plain,
% 0.77/0.95 ((~hskp9) | c0_1(a841)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1721, 1717])).
% 0.77/0.95 tff(1723,plain,
% 0.77/0.95 ((~hskp9) | c0_1(a841)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1722, 1717])).
% 0.77/0.95 tff(1724,plain,
% 0.77/0.95 (c0_1(a841)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1723, 1709])).
% 0.77/0.95 tff(1725,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a841) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c3_1(a828)) | (~c2_1(a828)) | c3_1(a841) | (~c0_1(a841)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a841) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c3_1(a828)) | (~c2_1(a828)) | c3_1(a841) | (~c0_1(a841)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1726,plain,
% 0.77/0.95 (((~ndr1_0) | (~c2_1(a828)) | (~c1_1(a828)) | (~c3_1(a828)) | c2_1(a841) | c3_1(a841) | (~c0_1(a841)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828))) <=> (c2_1(a841) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c3_1(a828)) | (~c2_1(a828)) | c3_1(a841) | (~c0_1(a841)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1727,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a828)) | (~c1_1(a828)) | (~c3_1(a828)) | c2_1(a841) | c3_1(a841) | (~c0_1(a841)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a841) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c3_1(a828)) | (~c2_1(a828)) | c3_1(a841) | (~c0_1(a841))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1726])).
% 0.77/0.95 tff(1728,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a828)) | (~c1_1(a828)) | (~c3_1(a828)) | c2_1(a841) | c3_1(a841) | (~c0_1(a841)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a841) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c3_1(a828)) | (~c2_1(a828)) | c3_1(a841) | (~c0_1(a841)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1727, 1725])).
% 0.77/0.95 tff(1729,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a828)) | (~c1_1(a828)) | (~c3_1(a828)) | c2_1(a841) | c3_1(a841) | (~c0_1(a841)) | c0_1(a828) | (~c1_1(a828)) | (~c2_1(a828)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1730,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a841) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c3_1(a828)) | (~c2_1(a828)) | c3_1(a841) | (~c0_1(a841))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1729, 1728])).
% 0.77/0.95 tff(1731,plain,
% 0.77/0.95 (c3_1(a841)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1730, 114, 1724, 1684, 1716, 1715, 1683, 662, 1691])).
% 0.77/0.95 tff(1732,plain,
% 0.77/0.95 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | c0_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp11 | hskp4 | c0_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1733,plain,
% 0.77/0.95 ((hskp11 | hskp4 | (~ndr1_0) | c2_1(a858) | c0_1(a858) | c3_1(a858)) <=> (hskp11 | hskp4 | c0_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1734,plain,
% 0.77/0.95 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | (~ndr1_0) | c2_1(a858) | c0_1(a858) | c3_1(a858))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | c0_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858)))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1733])).
% 0.77/0.95 tff(1735,plain,
% 0.77/0.95 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | (~ndr1_0) | c2_1(a858) | c0_1(a858) | c3_1(a858))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp11 | hskp4 | c0_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1734, 1732])).
% 0.77/0.95 tff(1736,plain,
% 0.77/0.95 ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp11 | hskp4 | (~ndr1_0) | c2_1(a858) | c0_1(a858) | c3_1(a858))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1737,plain,
% 0.77/0.95 ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp11 | hskp4 | c0_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 0.77/0.95 tff(1738,plain,
% 0.77/0.95 (hskp11 | hskp4 | c3_1(a858)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1737, 114, 1645, 1633, 422])).
% 0.77/0.95 tff(1739,plain,
% 0.77/0.95 (hskp11),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1738, 1674, 11])).
% 0.77/0.95 tff(1740,plain,
% 0.77/0.95 (~c2_1(a844)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[437, 1739])).
% 0.77/0.95 tff(1741,plain,
% 0.77/0.95 (~c1_1(a844)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[443, 1739])).
% 0.77/0.95 tff(1742,plain,
% 0.77/0.95 (((~hskp9) | c1_1(a841)) <=> ((~hskp9) | c1_1(a841))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1743,axiom,((~hskp9) | c1_1(a841)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.77/0.95 tff(1744,plain,
% 0.77/0.95 ((~hskp9) | c1_1(a841)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 0.77/0.95 tff(1745,plain,
% 0.77/0.95 ((~hskp9) | c1_1(a841)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1744, 1742])).
% 0.77/0.95 tff(1746,plain,
% 0.77/0.95 ((~hskp9) | c1_1(a841)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1745, 1742])).
% 0.77/0.95 tff(1747,plain,
% 0.77/0.95 ((~hskp9) | c1_1(a841)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1746, 1742])).
% 0.77/0.95 tff(1748,plain,
% 0.77/0.95 ((~hskp9) | c1_1(a841)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1747, 1742])).
% 0.77/0.95 tff(1749,plain,
% 0.77/0.95 (c1_1(a841)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1748, 1709])).
% 0.77/0.95 tff(1750,plain,
% 0.77/0.95 (c3_1(a844)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[451, 1739])).
% 0.77/0.95 tff(1751,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | c1_1(a844) | c2_1(a844) | c2_1(a841) | (~ndr1_0) | (~c1_1(a841)) | (~c3_1(a841)) | (~c3_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c1_1(a844) | c2_1(a844) | c2_1(a841) | (~ndr1_0) | (~c1_1(a841)) | (~c3_1(a841)) | (~c3_1(a844)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1752,plain,
% 0.77/0.95 ((hskp17 | (~ndr1_0) | c2_1(a841) | (~c1_1(a841)) | (~c3_1(a841)) | c2_1(a844) | c1_1(a844) | (~c3_1(a844))) <=> (hskp17 | c1_1(a844) | c2_1(a844) | c2_1(a841) | (~ndr1_0) | (~c1_1(a841)) | (~c3_1(a841)) | (~c3_1(a844)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1753,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a841) | (~c1_1(a841)) | (~c3_1(a841)) | c2_1(a844) | c1_1(a844) | (~c3_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | c1_1(a844) | c2_1(a844) | c2_1(a841) | (~ndr1_0) | (~c1_1(a841)) | (~c3_1(a841)) | (~c3_1(a844))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1752])).
% 0.77/0.95 tff(1754,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a841) | (~c1_1(a841)) | (~c3_1(a841)) | c2_1(a844) | c1_1(a844) | (~c3_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c1_1(a844) | c2_1(a844) | c2_1(a841) | (~ndr1_0) | (~c1_1(a841)) | (~c3_1(a841)) | (~c3_1(a844)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1753, 1751])).
% 0.77/0.95 tff(1755,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a841) | (~c1_1(a841)) | (~c3_1(a841)) | c2_1(a844) | c1_1(a844) | (~c3_1(a844)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1756,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c1_1(a844) | c2_1(a844) | c2_1(a841) | (~ndr1_0) | (~c1_1(a841)) | (~c3_1(a841)) | (~c3_1(a844))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1755, 1754])).
% 0.77/0.95 tff(1757,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1756, 114, 36, 1750, 1749, 1741, 1740, 1715, 909, 1731])).
% 0.77/0.95 tff(1758,plain,(hskp4 | hskp17 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(1759,plain,
% 0.77/0.95 (hskp4),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1758, 1014, 1646])).
% 0.77/0.95 tff(1760,plain,
% 0.77/0.95 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(1761,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[1760])).
% 0.77/0.95 tff(1762,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1763,plain,
% 0.77/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(1764,plain,
% 0.77/0.95 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[1763])).
% 0.77/0.95 tff(1765,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 0.77/0.95 tff(1766,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1765, 1764])).
% 0.77/0.95 tff(1767,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1766, 1762])).
% 0.77/0.95 tff(1768,plain,(
% 0.77/0.95 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(skolemize,[status(sab)],[1767])).
% 0.77/0.95 tff(1769,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1768, 1761])).
% 0.77/0.95 tff(1770,plain,
% 0.77/0.95 (hskp31),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[411, 385, 345])).
% 0.77/0.95 tff(1771,plain,
% 0.77/0.95 (c3_1(a875)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[965, 1770])).
% 0.77/0.95 tff(1772,plain,
% 0.77/0.95 (c2_1(a875)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[973, 1770])).
% 0.77/0.95 tff(1773,plain,
% 0.77/0.95 (c0_1(a875)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1049, 1770])).
% 0.77/0.95 tff(1774,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a859) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a859) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1775,plain,
% 0.77/0.95 ((hskp5 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a859) | c0_1(a859) | c3_1(a859)) <=> (hskp5 | c0_1(a859) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1776,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a859) | c0_1(a859) | c3_1(a859))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a859) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1775])).
% 0.77/0.95 tff(1777,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a859) | c0_1(a859) | c3_1(a859))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a859) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1776, 1774])).
% 0.77/0.95 tff(1778,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a859) | c0_1(a859) | c3_1(a859))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1779,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a859) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 0.77/0.95 tff(1780,plain,
% 0.77/0.95 (hskp5),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1779, 114, 1773, 1772, 1771, 24, 23, 12, 1769])).
% 0.77/0.95 tff(1781,plain,
% 0.77/0.95 (~c3_1(a833)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[66, 1780])).
% 0.77/0.95 tff(1782,plain,
% 0.77/0.95 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(1783,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[1782])).
% 0.77/0.95 tff(1784,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1785,plain,
% 0.77/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(1786,plain,
% 0.77/0.96 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[1785])).
% 0.77/0.96 tff(1787,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.77/0.96 tff(1788,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1787, 1786])).
% 0.77/0.96 tff(1789,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1788, 1784])).
% 0.77/0.96 tff(1790,plain,(
% 0.77/0.96 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.96 inference(skolemize,[status(sab)],[1789])).
% 0.77/0.96 tff(1791,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1790, 1783])).
% 0.77/0.96 tff(1792,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a859) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a859) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1793,plain,
% 0.77/0.96 ((hskp8 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a859) | c0_1(a859) | c3_1(a859)) <=> (hskp8 | c0_1(a859) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1794,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a859) | c0_1(a859) | c3_1(a859))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a859) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[1793])).
% 0.77/0.96 tff(1795,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a859) | c0_1(a859) | c3_1(a859))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a859) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[1794, 1792])).
% 0.77/0.96 tff(1796,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a859) | c0_1(a859) | c3_1(a859))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1797,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a859) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1796, 1795])).
% 0.77/0.96 tff(1798,plain,
% 0.77/0.96 (hskp8),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1797, 114, 1773, 1772, 1771, 24, 23, 12, 1791])).
% 0.77/0.96 tff(1799,plain,
% 0.77/0.96 (~c3_1(a838)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[314, 1798])).
% 0.77/0.96 tff(1800,plain,
% 0.77/0.96 (~c2_1(a838)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[320, 1798])).
% 0.77/0.96 tff(1801,plain,
% 0.77/0.96 (c2_1(a833)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[138, 1780])).
% 0.77/0.96 tff(1802,plain,
% 0.77/0.96 (c1_1(a838)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[328, 1798])).
% 0.77/0.96 tff(1803,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a838) | c3_1(a838) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a838) | c3_1(a838) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c1_1(a838)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1804,plain,
% 0.77/0.96 ((hskp17 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a838) | c3_1(a838) | (~c1_1(a838))) <=> (hskp17 | c2_1(a838) | c3_1(a838) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c1_1(a838)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1805,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a838) | c3_1(a838) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a838) | c3_1(a838) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c1_1(a838))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[1804])).
% 0.77/0.96 tff(1806,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a838) | c3_1(a838) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a838) | c3_1(a838) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c1_1(a838)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[1805, 1803])).
% 0.77/0.96 tff(1807,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a838) | c3_1(a838) | (~c1_1(a838)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1808,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a838) | c3_1(a838) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c1_1(a838))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 0.77/0.96 tff(1809,plain,
% 0.77/0.96 (~c1_1(a833)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1808, 114, 1646, 1802, 1801, 1800, 1799, 1781, 175])).
% 0.77/0.96 tff(1810,plain,
% 0.77/0.96 (c0_1(a833)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[82, 1780])).
% 0.77/0.96 tff(1811,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1812,plain,
% 0.77/0.96 (((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c3_1(a832) | c2_1(a832) | c1_1(a832)) <=> (c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1813,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833)))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[1812])).
% 0.77/0.96 tff(1814,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833))),
% 0.77/0.96 inference(transitivity,[status(thm)],[1813, 1811])).
% 0.77/0.96 tff(1815,plain,
% 0.77/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c3_1(a832) | c2_1(a832) | c1_1(a832))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1816,plain,
% 0.77/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1815, 1814])).
% 0.77/0.96 tff(1817,plain,
% 0.77/0.96 ($false),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1816, 114, 1810, 1801, 1781, 403, 397, 391, 22, 1809])).
% 0.77/0.96 tff(1818,plain,((~hskp4) | c0_1(a859) | c1_1(a859) | c3_1(a859) | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.77/0.96 tff(1819,plain,
% 0.77/0.96 (hskp19),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1818, 1759, 23, 12, 24])).
% 0.77/0.96 tff(1820,plain,
% 0.77/0.96 (~c2_1(a863)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[494, 1819])).
% 0.77/0.96 tff(1821,plain,
% 0.77/0.96 (c3_1(a863)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[517, 1819])).
% 0.77/0.96 tff(1822,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c2_1(a863) | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a863) | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1823,plain,
% 0.77/0.96 ((hskp2 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a858) | c1_1(a858) | c0_1(a858)) <=> (hskp2 | c2_1(a863) | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1824,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a858) | c1_1(a858) | c0_1(a858))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c2_1(a863) | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[1823])).
% 0.77/0.96 tff(1825,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a858) | c1_1(a858) | c0_1(a858))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a863) | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[1824, 1822])).
% 0.77/0.96 tff(1826,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a858) | c1_1(a858) | c0_1(a858))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1827,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a863) | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c1_1(a863)) | (~c3_1(a863))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 0.77/0.96 tff(1828,plain,
% 0.77/0.96 (~c1_1(a863)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1827, 114, 1014, 1821, 1820, 1645, 1639, 1633, 34])).
% 0.77/0.96 tff(1829,plain,
% 0.77/0.96 (~c3_1(a832)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[390, 1759])).
% 0.77/0.96 tff(1830,plain,
% 0.77/0.96 (~c2_1(a832)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[396, 1759])).
% 0.77/0.96 tff(1831,plain,
% 0.77/0.96 (~c1_1(a832)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[402, 1759])).
% 0.77/0.96 tff(1832,plain,
% 0.77/0.96 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp9 | hskp2 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp9 | hskp2 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1833,plain,
% 0.77/0.96 ((hskp9 | hskp2 | (~ndr1_0) | c2_1(a832) | c1_1(a832) | c3_1(a832)) <=> (hskp9 | hskp2 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1834,plain,
% 0.77/0.96 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a832) | c1_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp9 | hskp2 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0)))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[1833])).
% 0.77/0.96 tff(1835,plain,
% 0.77/0.96 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a832) | c1_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp9 | hskp2 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0))),
% 0.77/0.96 inference(transitivity,[status(thm)],[1834, 1832])).
% 0.77/0.96 tff(1836,plain,
% 0.77/0.96 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a832) | c1_1(a832) | c3_1(a832))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1837,plain,
% 0.77/0.96 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp9 | hskp2 | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1836, 1835])).
% 0.77/0.96 tff(1838,plain,
% 0.77/0.96 (hskp9),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1837, 114, 1014, 1831, 1830, 1829, 1701])).
% 0.77/0.96 tff(1839,plain,
% 0.77/0.96 (~c2_1(a841)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1714, 1838])).
% 0.77/0.96 tff(1840,plain,
% 0.77/0.96 (c1_1(a841)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1748, 1838])).
% 0.77/0.96 tff(1841,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | c2_1(a863) | c2_1(a841) | (~ndr1_0) | (~c1_1(a841)) | (~c3_1(a841)) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a863) | c2_1(a841) | (~ndr1_0) | (~c1_1(a841)) | (~c3_1(a841)) | c1_1(a863) | (~c3_1(a863)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1842,plain,
% 0.77/0.96 ((hskp17 | (~ndr1_0) | c2_1(a841) | (~c1_1(a841)) | (~c3_1(a841)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863))) <=> (hskp17 | c2_1(a863) | c2_1(a841) | (~ndr1_0) | (~c1_1(a841)) | (~c3_1(a841)) | c1_1(a863) | (~c3_1(a863)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1843,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a841) | (~c1_1(a841)) | (~c3_1(a841)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | c2_1(a863) | c2_1(a841) | (~ndr1_0) | (~c1_1(a841)) | (~c3_1(a841)) | c1_1(a863) | (~c3_1(a863))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[1842])).
% 0.77/0.96 tff(1844,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a841) | (~c1_1(a841)) | (~c3_1(a841)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a863) | c2_1(a841) | (~ndr1_0) | (~c1_1(a841)) | (~c3_1(a841)) | c1_1(a863) | (~c3_1(a863)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[1843, 1841])).
% 0.77/0.96 tff(1845,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a841) | (~c1_1(a841)) | (~c3_1(a841)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1846,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a863) | c2_1(a841) | (~ndr1_0) | (~c1_1(a841)) | (~c3_1(a841)) | c1_1(a863) | (~c3_1(a863))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 0.77/0.96 tff(1847,plain,
% 0.77/0.96 (~c3_1(a841)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1846, 114, 1646, 1821, 1840, 1820, 1839, 909, 1828])).
% 0.77/0.96 tff(1848,plain,
% 0.77/0.96 (c0_1(a841)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1723, 1838])).
% 0.77/0.96 tff(1849,plain,
% 0.77/0.96 (c0_1(a863)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[502, 1819])).
% 0.77/0.96 tff(1850,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a863) | (~ndr1_0) | (~c1_1(a841)) | c3_1(a841) | (~c0_1(a841)) | c1_1(a863) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a863) | (~ndr1_0) | (~c1_1(a841)) | c3_1(a841) | (~c0_1(a841)) | c1_1(a863) | (~c0_1(a863)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1851,plain,
% 0.77/0.96 ((hskp17 | (~ndr1_0) | c3_1(a841) | (~c1_1(a841)) | (~c0_1(a841)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863))) <=> (hskp17 | c2_1(a863) | (~ndr1_0) | (~c1_1(a841)) | c3_1(a841) | (~c0_1(a841)) | c1_1(a863) | (~c0_1(a863)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1852,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a841) | (~c1_1(a841)) | (~c0_1(a841)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a863) | (~ndr1_0) | (~c1_1(a841)) | c3_1(a841) | (~c0_1(a841)) | c1_1(a863) | (~c0_1(a863))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[1851])).
% 0.77/0.96 tff(1853,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a841) | (~c1_1(a841)) | (~c0_1(a841)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a863) | (~ndr1_0) | (~c1_1(a841)) | c3_1(a841) | (~c0_1(a841)) | c1_1(a863) | (~c0_1(a863)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[1852, 1850])).
% 0.77/0.96 tff(1854,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a841) | (~c1_1(a841)) | (~c0_1(a841)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1855,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a863) | (~ndr1_0) | (~c1_1(a841)) | c3_1(a841) | (~c0_1(a841)) | c1_1(a863) | (~c0_1(a863))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 0.77/0.96 tff(1856,plain,
% 0.77/0.96 ($false),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1855, 114, 1646, 1849, 1848, 1840, 1820, 10, 1828, 1847])).
% 0.77/0.96 tff(1857,plain,(hskp2 | c1_1(a859) | c3_1(a859) | c0_1(a859)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.96 tff(1858,plain,
% 0.77/0.96 (hskp2),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1857, 24, 12, 23])).
% 0.77/0.96 tff(1859,plain,
% 0.77/0.96 (~c1_1(a830)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[59, 1858])).
% 0.77/0.96 tff(1860,plain,
% 0.77/0.96 (~c2_1(a830)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[53, 1858])).
% 0.77/0.96 tff(1861,plain,
% 0.77/0.96 (~hskp4),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1818, 345, 23, 12, 24])).
% 0.77/0.96 tff(1862,plain,
% 0.77/0.96 (hskp5),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1663, 1861])).
% 0.77/0.96 tff(1863,plain,
% 0.77/0.96 (~c3_1(a833)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[66, 1862])).
% 0.77/0.96 tff(1864,plain,
% 0.77/0.96 (c2_1(a833)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[138, 1862])).
% 0.77/0.96 tff(1865,plain,
% 0.77/0.96 (c0_1(a833)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[82, 1862])).
% 0.77/0.96 tff(1866,plain,
% 0.77/0.96 (~c3_1(a858)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1673, 114, 1861, 1865, 1864, 1645, 1633, 1863, 373])).
% 0.77/0.96 tff(1867,plain,
% 0.77/0.96 (hskp0),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1681, 1866])).
% 0.77/0.96 tff(1868,plain,
% 0.77/0.96 (~c0_1(a828)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[738, 1867])).
% 0.77/0.96 tff(1869,plain,
% 0.77/0.96 (^[U: $i] : refl((hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(1870,plain,
% 0.77/0.96 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[1869])).
% 0.77/0.96 tff(1871,plain,
% 0.77/0.96 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1872,plain,
% 0.77/0.96 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp12) | hskp13) <=> ((hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp13))), rewrite(((hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp12) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(1873,plain,
% 0.77/0.96 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp12) | hskp13) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[1872])).
% 0.77/0.96 tff(1874,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp12) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.77/0.96 tff(1875,plain,
% 0.77/0.96 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1874, 1873])).
% 0.77/0.96 tff(1876,plain,
% 0.77/0.96 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1875, 1871])).
% 0.77/0.96 tff(1877,plain,(
% 0.77/0.96 ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.77/0.96 inference(skolemize,[status(sab)],[1876])).
% 0.77/0.96 tff(1878,plain,
% 0.77/0.96 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1877, 1870])).
% 0.77/0.96 tff(1879,plain,
% 0.77/0.96 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp13 | hskp12 | c0_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp13 | hskp12 | c0_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1880,plain,
% 0.77/0.96 ((hskp13 | hskp12 | (~ndr1_0) | c2_1(a858) | c0_1(a858) | c3_1(a858)) <=> (hskp13 | hskp12 | c0_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1881,plain,
% 0.77/0.96 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp13 | hskp12 | (~ndr1_0) | c2_1(a858) | c0_1(a858) | c3_1(a858))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp13 | hskp12 | c0_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858)))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[1880])).
% 0.77/0.96 tff(1882,plain,
% 0.77/0.96 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp13 | hskp12 | (~ndr1_0) | c2_1(a858) | c0_1(a858) | c3_1(a858))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp13 | hskp12 | c0_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.96 inference(transitivity,[status(thm)],[1881, 1879])).
% 0.77/0.96 tff(1883,plain,
% 0.77/0.96 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp13 | hskp12 | (~ndr1_0) | c2_1(a858) | c0_1(a858) | c3_1(a858))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1884,plain,
% 0.77/0.96 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp13 | hskp12 | c0_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1883, 1882])).
% 0.77/0.96 tff(1885,plain,
% 0.77/0.96 (hskp13 | hskp12 | c3_1(a858)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1884, 114, 1645, 1633, 1878])).
% 0.77/0.96 tff(1886,plain,
% 0.77/0.96 (hskp12),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1885, 1866, 1021])).
% 0.77/0.96 tff(1887,plain,
% 0.77/0.96 (((~hskp12) | (~c1_1(a845))) <=> ((~hskp12) | (~c1_1(a845)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1888,plain,
% 0.77/0.96 (((~c1_1(a845)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a845)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1889,axiom,((~c1_1(a845)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.77/0.97 tff(1890,plain,
% 0.77/0.97 ((~hskp12) | (~c1_1(a845))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1889, 1888])).
% 0.77/0.97 tff(1891,plain,
% 0.77/0.97 ((~hskp12) | (~c1_1(a845))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1890, 1887])).
% 0.77/0.97 tff(1892,plain,
% 0.77/0.97 (~c1_1(a845)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1891, 1886])).
% 0.77/0.97 tff(1893,plain,
% 0.77/0.97 (((~hskp12) | (~c0_1(a845))) <=> ((~hskp12) | (~c0_1(a845)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1894,plain,
% 0.77/0.97 (((~c0_1(a845)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a845)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1895,axiom,((~c0_1(a845)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.77/0.97 tff(1896,plain,
% 0.77/0.97 ((~hskp12) | (~c0_1(a845))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 0.77/0.97 tff(1897,plain,
% 0.77/0.97 ((~hskp12) | (~c0_1(a845))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1896, 1893])).
% 0.77/0.97 tff(1898,plain,
% 0.77/0.97 (~c0_1(a845)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1897, 1886])).
% 0.77/0.97 tff(1899,plain,
% 0.77/0.97 (c2_1(a828)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[746, 1867])).
% 0.77/0.97 tff(1900,plain,
% 0.77/0.97 (c1_1(a828)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[754, 1867])).
% 0.77/0.97 tff(1901,plain,
% 0.77/0.97 (((~hskp12) | c3_1(a845)) <=> ((~hskp12) | c3_1(a845))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1902,axiom,((~hskp12) | c3_1(a845)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.77/0.97 tff(1903,plain,
% 0.77/0.97 ((~hskp12) | c3_1(a845)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1902, 1901])).
% 0.77/0.97 tff(1904,plain,
% 0.77/0.97 ((~hskp12) | c3_1(a845)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1903, 1901])).
% 0.77/0.97 tff(1905,plain,
% 0.77/0.97 ((~hskp12) | c3_1(a845)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1904, 1901])).
% 0.77/0.97 tff(1906,plain,
% 0.77/0.97 ((~hskp12) | c3_1(a845)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1905, 1901])).
% 0.77/0.97 tff(1907,plain,
% 0.77/0.97 ((~hskp12) | c3_1(a845)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1906, 1901])).
% 0.77/0.97 tff(1908,plain,
% 0.77/0.97 (c3_1(a845)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1907, 1886])).
% 0.77/0.97 tff(1909,plain,
% 0.77/0.97 (((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))) <=> ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp31 | hskp19 | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1910,plain,
% 0.77/0.97 ((hskp31 | hskp19 | (~ndr1_0) | c2_1(a858) | c1_1(a858) | c3_1(a858)) <=> (hskp31 | hskp19 | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1911,plain,
% 0.77/0.97 (((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | (~ndr1_0) | c2_1(a858) | c1_1(a858) | c3_1(a858))) <=> ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858)))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1910])).
% 0.77/0.97 tff(1912,plain,
% 0.77/0.97 (((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | (~ndr1_0) | c2_1(a858) | c1_1(a858) | c3_1(a858))) <=> ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp31 | hskp19 | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1911, 1909])).
% 0.77/0.97 tff(1913,plain,
% 0.77/0.97 ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp31 | hskp19 | (~ndr1_0) | c2_1(a858) | c1_1(a858) | c3_1(a858))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1914,plain,
% 0.77/0.97 ((~![U: $i] : (hskp31 | hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp31 | hskp19 | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c3_1(a858)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 0.77/0.97 tff(1915,plain,
% 0.77/0.97 (hskp31 | hskp19 | c3_1(a858)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1914, 114, 1639, 1633, 355])).
% 0.77/0.97 tff(1916,plain,
% 0.77/0.97 (hskp31),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1915, 1866, 345])).
% 0.77/0.97 tff(1917,plain,
% 0.77/0.97 (c3_1(a875)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[965, 1916])).
% 0.77/0.97 tff(1918,plain,
% 0.77/0.97 (c2_1(a875)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[973, 1916])).
% 0.77/0.97 tff(1919,plain,
% 0.77/0.97 (c0_1(a875)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1049, 1916])).
% 0.77/0.97 tff(1920,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a845) | c1_1(a845) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | (~c3_1(a845)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a845) | c1_1(a845) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | (~c3_1(a845)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1921,plain,
% 0.77/0.97 (((~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a845) | c0_1(a845) | (~c3_1(a845))) <=> (c0_1(a845) | c1_1(a845) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | (~c3_1(a845)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1922,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a845) | c0_1(a845) | (~c3_1(a845)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a845) | c1_1(a845) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | (~c3_1(a845))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1921])).
% 0.77/0.97 tff(1923,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a845) | c0_1(a845) | (~c3_1(a845)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a845) | c1_1(a845) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | (~c3_1(a845)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1922, 1920])).
% 0.77/0.97 tff(1924,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a845) | c0_1(a845) | (~c3_1(a845)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1925,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a845) | c1_1(a845) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | (~c3_1(a845))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1924, 1923])).
% 0.77/0.97 tff(1926,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1925, 114, 1919, 1918, 1917, 1908, 1900, 1899, 1898, 1892, 1868, 1538])).
% 0.77/0.97 tff(1927,plain,(hskp19 | hskp13 | c1_1(a859) | c3_1(a859) | c0_1(a859)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(1928,plain,
% 0.77/0.97 (hskp19),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1927, 1021, 23, 12, 24])).
% 0.77/0.97 tff(1929,plain,
% 0.77/0.97 (c3_1(a863)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[517, 1928])).
% 0.77/0.97 tff(1930,plain,
% 0.77/0.97 (~c2_1(a863)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[494, 1928])).
% 0.77/0.97 tff(1931,plain,
% 0.77/0.97 (c0_1(a863)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[502, 1928])).
% 0.77/0.97 tff(1932,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a844) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a844)) | c0_1(a844))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a844) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a844)) | c0_1(a844))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1933,plain,
% 0.77/0.97 ((hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a844) | c0_1(a844) | (~c3_1(a844))) <=> (hskp4 | c2_1(a844) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a844)) | c0_1(a844))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1934,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a844) | c0_1(a844) | (~c3_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a844) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a844)) | c0_1(a844)))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1933])).
% 0.77/0.97 tff(1935,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a844) | c0_1(a844) | (~c3_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a844) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a844)) | c0_1(a844))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1934, 1932])).
% 0.77/0.97 tff(1936,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c2_1(a844) | c0_1(a844) | (~c3_1(a844)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1937,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a844) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c3_1(a844)) | c0_1(a844)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 0.77/0.97 tff(1938,plain,
% 0.77/0.97 (c0_1(a844)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1937, 114, 11, 1750, 1667, 1666, 1740, 1665, 373])).
% 0.77/0.97 tff(1939,plain,
% 0.77/0.97 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(1940,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[1939])).
% 0.77/0.97 tff(1941,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1942,plain,
% 0.77/0.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(1943,plain,
% 0.77/0.97 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[1942])).
% 0.77/0.97 tff(1944,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.77/0.97 tff(1945,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1944, 1943])).
% 0.77/0.97 tff(1946,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1945, 1941])).
% 0.77/0.97 tff(1947,plain,(
% 0.77/0.97 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.97 inference(skolemize,[status(sab)],[1946])).
% 0.77/0.97 tff(1948,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1947, 1940])).
% 0.77/0.97 tff(1949,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a859) | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a859) | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a844)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1950,plain,
% 0.77/0.97 ((hskp6 | (~ndr1_0) | c2_1(a844) | c1_1(a844) | (~c0_1(a844)) | c1_1(a859) | c0_1(a859) | c3_1(a859)) <=> (hskp6 | c0_1(a859) | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a844)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1951,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a844) | c1_1(a844) | (~c0_1(a844)) | c1_1(a859) | c0_1(a859) | c3_1(a859))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a859) | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a844))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1950])).
% 0.77/0.97 tff(1952,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a844) | c1_1(a844) | (~c0_1(a844)) | c1_1(a859) | c0_1(a859) | c3_1(a859))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a859) | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a844)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1951, 1949])).
% 0.77/0.97 tff(1953,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a844) | c1_1(a844) | (~c0_1(a844)) | c1_1(a859) | c0_1(a859) | c3_1(a859))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1954,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a859) | c1_1(a859) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a844))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1953, 1952])).
% 0.77/0.97 tff(1955,plain,
% 0.77/0.97 (hskp6),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1954, 114, 24, 23, 12, 1741, 1740, 1948, 1938])).
% 0.77/0.97 tff(1956,plain,
% 0.77/0.97 (~c3_1(a835)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[151, 1955])).
% 0.77/0.97 tff(1957,plain,
% 0.77/0.97 (~c2_1(a835)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[157, 1955])).
% 0.77/0.97 tff(1958,plain,
% 0.77/0.97 (c3_1(a828)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1690, 114, 1646, 11, 1684, 1683, 824])).
% 0.77/0.97 tff(1959,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c2_1(a863) | (~ndr1_0) | (~c1_1(a828)) | (~c3_1(a828)) | (~c2_1(a828)) | (~c3_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a863) | (~ndr1_0) | (~c1_1(a828)) | (~c3_1(a828)) | (~c2_1(a828)) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1960,plain,
% 0.77/0.97 ((hskp18 | (~ndr1_0) | (~c2_1(a828)) | (~c1_1(a828)) | (~c3_1(a828)) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863))) <=> (hskp18 | c2_1(a863) | (~ndr1_0) | (~c1_1(a828)) | (~c3_1(a828)) | (~c2_1(a828)) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1961,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a828)) | (~c1_1(a828)) | (~c3_1(a828)) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c2_1(a863) | (~ndr1_0) | (~c1_1(a828)) | (~c3_1(a828)) | (~c2_1(a828)) | (~c3_1(a863)) | (~c0_1(a863))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1960])).
% 0.77/0.97 tff(1962,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a828)) | (~c1_1(a828)) | (~c3_1(a828)) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a863) | (~ndr1_0) | (~c1_1(a828)) | (~c3_1(a828)) | (~c2_1(a828)) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1961, 1959])).
% 0.77/0.97 tff(1963,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a828)) | (~c1_1(a828)) | (~c3_1(a828)) | c2_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1964,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a863) | (~ndr1_0) | (~c1_1(a828)) | (~c3_1(a828)) | (~c2_1(a828)) | (~c3_1(a863)) | (~c0_1(a863))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 0.77/0.97 tff(1965,plain,
% 0.77/0.97 (hskp18),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1964, 114, 1287, 1264, 1684, 1716, 1263, 1323, 1958])).
% 0.77/0.97 tff(1966,plain,
% 0.77/0.97 (~c1_1(a861)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1141, 1965])).
% 0.77/0.97 tff(1967,plain,
% 0.77/0.97 (c2_1(a861)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1151, 1965])).
% 0.77/0.97 tff(1968,plain,
% 0.77/0.97 (c0_1(a861)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1159, 1965])).
% 0.77/0.97 tff(1969,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a861) | c2_1(a835) | c3_1(a835) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a835) | (~c2_1(a861)) | (~c0_1(a861)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a861) | c2_1(a835) | c3_1(a835) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a835) | (~c2_1(a861)) | (~c0_1(a861)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1970,plain,
% 0.77/0.97 (((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a861) | (~c2_1(a861)) | (~c0_1(a861)) | c3_1(a835) | c2_1(a835) | c1_1(a835)) <=> (c1_1(a861) | c2_1(a835) | c3_1(a835) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a835) | (~c2_1(a861)) | (~c0_1(a861)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1971,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a861) | (~c2_1(a861)) | (~c0_1(a861)) | c3_1(a835) | c2_1(a835) | c1_1(a835))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a861) | c2_1(a835) | c3_1(a835) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a835) | (~c2_1(a861)) | (~c0_1(a861))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1970])).
% 0.77/0.97 tff(1972,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a861) | (~c2_1(a861)) | (~c0_1(a861)) | c3_1(a835) | c2_1(a835) | c1_1(a835))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a861) | c2_1(a835) | c3_1(a835) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a835) | (~c2_1(a861)) | (~c0_1(a861)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1971, 1969])).
% 0.77/0.97 tff(1973,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a861) | (~c2_1(a861)) | (~c0_1(a861)) | c3_1(a835) | c2_1(a835) | c1_1(a835))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1974,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a861) | c2_1(a835) | c3_1(a835) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a835) | (~c2_1(a861)) | (~c0_1(a861))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1973, 1972])).
% 0.77/0.97 tff(1975,plain,
% 0.77/0.97 (c1_1(a835)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1974, 114, 1968, 1967, 1667, 1666, 1966, 1957, 1956, 1665, 22])).
% 0.77/0.97 tff(1976,plain,
% 0.77/0.97 (~c0_1(a835)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[548, 1955])).
% 0.77/0.97 tff(1977,plain,
% 0.77/0.97 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | c0_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a835)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp4 | c0_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a835)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1978,plain,
% 0.77/0.97 ((hskp17 | hskp4 | (~ndr1_0) | c0_1(a835) | c3_1(a835) | (~c1_1(a835))) <=> (hskp17 | hskp4 | c0_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a835)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1979,plain,
% 0.77/0.97 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c0_1(a835) | c3_1(a835) | (~c1_1(a835)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | c0_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a835))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1978])).
% 0.77/0.97 tff(1980,plain,
% 0.77/0.97 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c0_1(a835) | c3_1(a835) | (~c1_1(a835)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp4 | c0_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a835)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1979, 1977])).
% 0.77/0.97 tff(1981,plain,
% 0.77/0.97 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c0_1(a835) | c3_1(a835) | (~c1_1(a835)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1982,plain,
% 0.77/0.97 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp4 | c0_1(a835) | c3_1(a835) | (~ndr1_0) | (~c1_1(a835))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 0.77/0.97 tff(1983,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1982, 114, 1646, 11, 1976, 1956, 824, 1975])).
% 0.77/0.97 tff(1984,plain,(hskp4 | c0_1(a859) | c1_1(a859) | c3_1(a859) | (~c0_1(a863)) | (~c3_1(a863)) | c2_1(a863)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(1985,plain,
% 0.77/0.97 (hskp4),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1984, 1931, 23, 12, 24, 1929, 1930])).
% 0.77/0.97 tff(1986,plain,
% 0.77/0.97 (~c3_1(a832)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[390, 1985])).
% 0.77/0.97 tff(1987,plain,
% 0.77/0.97 (~c2_1(a832)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[396, 1985])).
% 0.77/0.97 tff(1988,plain,
% 0.77/0.97 (~c1_1(a832)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[402, 1985])).
% 0.77/0.97 tff(1989,plain,
% 0.77/0.97 ((~c0_1(a832)) | c1_1(a863)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[701, 114, 1021, 1264, 1263, 608, 606, 383])).
% 0.77/0.97 tff(1990,plain,
% 0.77/0.97 (~c0_1(a832)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1989, 609])).
% 0.77/0.97 tff(1991,plain,
% 0.77/0.97 (hskp0 | c0_1(a832)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[685, 114, 608, 607, 606, 679])).
% 0.77/0.97 tff(1992,plain,
% 0.77/0.97 (hskp0),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1991, 1990])).
% 0.77/0.97 tff(1993,plain,
% 0.77/0.97 (~c0_1(a828)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[738, 1992])).
% 0.77/0.97 tff(1994,plain,
% 0.77/0.97 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp13 | hskp12 | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp13 | hskp12 | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1995,plain,
% 0.77/0.97 ((hskp13 | hskp12 | (~ndr1_0) | c2_1(a832) | c0_1(a832) | c3_1(a832)) <=> (hskp13 | hskp12 | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1996,plain,
% 0.77/0.97 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp13 | hskp12 | (~ndr1_0) | c2_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp13 | hskp12 | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832)))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1995])).
% 0.77/0.97 tff(1997,plain,
% 0.77/0.97 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp13 | hskp12 | (~ndr1_0) | c2_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp13 | hskp12 | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 0.77/0.98 inference(transitivity,[status(thm)],[1996, 1994])).
% 0.77/0.98 tff(1998,plain,
% 0.77/0.98 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp13 | hskp12 | (~ndr1_0) | c2_1(a832) | c0_1(a832) | c3_1(a832))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(1999,plain,
% 0.77/0.98 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp13 | hskp12 | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 0.77/0.98 tff(2000,plain,
% 0.77/0.98 (hskp12 | c0_1(a832)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1999, 114, 1021, 607, 606, 1878])).
% 0.77/0.98 tff(2001,plain,
% 0.77/0.98 (hskp12),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2000, 1990])).
% 0.77/0.98 tff(2002,plain,
% 0.77/0.98 (~c1_1(a845)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1891, 2001])).
% 0.77/0.98 tff(2003,plain,
% 0.77/0.98 (~c0_1(a845)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1897, 2001])).
% 0.77/0.98 tff(2004,plain,
% 0.77/0.98 (c2_1(a828)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[746, 1992])).
% 0.77/0.98 tff(2005,plain,
% 0.77/0.98 (c1_1(a828)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[754, 1992])).
% 0.77/0.98 tff(2006,plain,
% 0.77/0.98 (hskp3 | c1_1(a863)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[532, 114, 1287, 1264, 1263, 276])).
% 0.77/0.98 tff(2007,plain,
% 0.77/0.98 (hskp3),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2006, 609])).
% 0.77/0.98 tff(2008,plain,
% 0.77/0.98 (c3_1(a831)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[247, 2007])).
% 0.77/0.98 tff(2009,plain,
% 0.77/0.98 (c2_1(a831)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[255, 2007])).
% 0.77/0.98 tff(2010,plain,
% 0.77/0.98 (c3_1(a845)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1907, 2001])).
% 0.77/0.98 tff(2011,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a845) | c1_1(a845) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)) | (~c3_1(a845)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a845) | c1_1(a845) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)) | (~c3_1(a845)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2012,plain,
% 0.77/0.98 (((~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)) | (~c0_1(a831)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a845) | c0_1(a845) | (~c3_1(a845))) <=> (c0_1(a845) | c1_1(a845) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)) | (~c3_1(a845)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2013,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)) | (~c0_1(a831)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a845) | c0_1(a845) | (~c3_1(a845)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a845) | c1_1(a845) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)) | (~c3_1(a845))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[2012])).
% 0.77/0.98 tff(2014,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)) | (~c0_1(a831)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a845) | c0_1(a845) | (~c3_1(a845)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a845) | c1_1(a845) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)) | (~c3_1(a845)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[2013, 2011])).
% 0.77/0.98 tff(2015,plain,
% 0.77/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)) | (~c0_1(a831)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a845) | c0_1(a845) | (~c3_1(a845)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2016,plain,
% 0.77/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a845) | c1_1(a845) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)) | (~c3_1(a845))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2015, 2014])).
% 0.77/0.98 tff(2017,plain,
% 0.77/0.98 (~c0_1(a831)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2016, 114, 2010, 2009, 2008, 2005, 2004, 2003, 2002, 1993, 1538])).
% 0.77/0.98 tff(2018,plain,
% 0.77/0.98 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.77/0.98 inference(bind,[status(th)],[])).
% 0.77/0.98 tff(2019,plain,
% 0.77/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.77/0.98 inference(quant_intro,[status(thm)],[2018])).
% 0.77/0.98 tff(2020,plain,
% 0.77/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2021,plain,
% 0.77/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.77/0.98 inference(bind,[status(th)],[])).
% 0.77/0.98 tff(2022,plain,
% 0.77/0.98 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.77/0.98 inference(quant_intro,[status(thm)],[2021])).
% 0.77/0.98 tff(2023,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.77/0.98 tff(2024,plain,
% 0.77/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2023, 2022])).
% 0.77/0.98 tff(2025,plain,
% 0.77/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2024, 2020])).
% 0.77/0.98 tff(2026,plain,(
% 0.77/0.98 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.77/0.98 inference(skolemize,[status(sab)],[2025])).
% 0.77/0.98 tff(2027,plain,
% 0.77/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2026, 2019])).
% 0.77/0.98 tff(2028,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a831)) | c0_1(a831) | (~c2_1(a831)) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | (~ndr1_0) | (~c3_1(a831)) | c0_1(a831) | (~c2_1(a831)) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2029,plain,
% 0.77/0.98 ((hskp5 | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863)) | c0_1(a831) | (~c3_1(a831)) | (~c2_1(a831))) <=> (hskp5 | (~ndr1_0) | (~c3_1(a831)) | c0_1(a831) | (~c2_1(a831)) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2030,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863)) | c0_1(a831) | (~c3_1(a831)) | (~c2_1(a831)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a831)) | c0_1(a831) | (~c2_1(a831)) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[2029])).
% 0.77/0.98 tff(2031,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863)) | c0_1(a831) | (~c3_1(a831)) | (~c2_1(a831)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | (~ndr1_0) | (~c3_1(a831)) | c0_1(a831) | (~c2_1(a831)) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[2030, 2028])).
% 0.77/0.98 tff(2032,plain,
% 0.77/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863)) | c0_1(a831) | (~c3_1(a831)) | (~c2_1(a831)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2033,plain,
% 0.77/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | (~ndr1_0) | (~c3_1(a831)) | c0_1(a831) | (~c2_1(a831)) | c1_1(a863) | (~c3_1(a863)) | (~c0_1(a863))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2032, 2031])).
% 0.77/0.98 tff(2034,plain,
% 0.77/0.98 (hskp5),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2033, 114, 1287, 1264, 2009, 2008, 2027, 609, 2017])).
% 0.77/0.98 tff(2035,plain,
% 0.77/0.98 (~c3_1(a833)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[66, 2034])).
% 0.77/0.98 tff(2036,plain,
% 0.77/0.98 (c0_1(a833)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[82, 2034])).
% 0.77/0.98 tff(2037,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a863) | c3_1(a833) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)) | c1_1(a863) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a863) | c3_1(a833) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)) | c1_1(a863) | (~c0_1(a863)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2038,plain,
% 0.77/0.98 ((hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863))) <=> (hskp17 | c2_1(a863) | c3_1(a833) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)) | c1_1(a863) | (~c0_1(a863)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2039,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a863) | c3_1(a833) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)) | c1_1(a863) | (~c0_1(a863))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[2038])).
% 0.77/0.98 tff(2040,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a863) | c3_1(a833) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)) | c1_1(a863) | (~c0_1(a863)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[2039, 2037])).
% 0.77/0.98 tff(2041,plain,
% 0.77/0.98 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2042,plain,
% 0.77/0.98 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a863) | c3_1(a833) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)) | c1_1(a863) | (~c0_1(a863))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2041, 2040])).
% 0.77/0.98 tff(2043,plain,
% 0.77/0.98 (~c1_1(a833)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2042, 114, 36, 1287, 2036, 1263, 2035, 10, 609])).
% 0.77/0.98 tff(2044,plain,
% 0.77/0.98 (c2_1(a833)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[138, 2034])).
% 0.77/0.98 tff(2045,plain,
% 0.77/0.98 ($false),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1816, 114, 2036, 2044, 2035, 608, 607, 606, 22, 2043])).
% 0.77/0.98 tff(2046,plain,(c1_1(a863) | c1_1(a832) | c2_1(a832) | c3_1(a832) | hskp17 | (~c0_1(a863)) | c2_1(a863) | (~c3_1(a863)) | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.77/0.98 tff(2047,plain,
% 0.77/0.98 (c1_1(a863)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2046, 1988, 1987, 1986, 1646, 1931, 1930, 1929, 1021])).
% 0.77/0.98 tff(2048,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | c2_1(a863) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c3_1(a858)) | (~c1_1(a863)) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a863) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c3_1(a858)) | (~c1_1(a863)) | (~c3_1(a863)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2049,plain,
% 0.77/0.98 ((hskp17 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858))) <=> (hskp17 | c2_1(a863) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c3_1(a858)) | (~c1_1(a863)) | (~c3_1(a863)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2050,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | c2_1(a863) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c3_1(a858)) | (~c1_1(a863)) | (~c3_1(a863))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[2049])).
% 0.77/0.98 tff(2051,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a863) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c3_1(a858)) | (~c1_1(a863)) | (~c3_1(a863)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[2050, 2048])).
% 0.77/0.98 tff(2052,plain,
% 0.77/0.98 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a863) | (~c1_1(a863)) | (~c3_1(a863)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2053,plain,
% 0.77/0.98 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a863) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c3_1(a858)) | (~c1_1(a863)) | (~c3_1(a863))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2052, 2051])).
% 0.77/0.98 tff(2054,plain,
% 0.77/0.98 ((~c3_1(a858)) | (~c1_1(a863))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2053, 114, 1646, 1929, 1930, 1639, 1633, 909])).
% 0.77/0.98 tff(2055,plain,
% 0.77/0.98 (~c3_1(a858)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2054, 2047])).
% 0.77/0.98 tff(2056,plain,
% 0.77/0.98 (hskp0),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1681, 2055])).
% 0.77/0.98 tff(2057,plain,
% 0.77/0.98 (~c0_1(a828)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[738, 2056])).
% 0.77/0.98 tff(2058,plain,
% 0.77/0.98 (hskp12),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1885, 2055, 1021])).
% 0.77/0.98 tff(2059,plain,
% 0.77/0.98 (~c1_1(a845)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1891, 2058])).
% 0.77/0.98 tff(2060,plain,
% 0.77/0.98 (~c0_1(a845)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1897, 2058])).
% 0.77/0.98 tff(2061,plain,
% 0.77/0.98 (c2_1(a828)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[746, 2056])).
% 0.77/0.98 tff(2062,plain,
% 0.77/0.98 (c1_1(a828)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[754, 2056])).
% 0.77/0.98 tff(2063,plain,
% 0.77/0.98 (c3_1(a845)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1907, 2058])).
% 0.77/0.98 tff(2064,plain,
% 0.77/0.98 (hskp31),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[922, 2047, 814, 813, 1988, 1987, 1986])).
% 0.77/0.98 tff(2065,plain,
% 0.77/0.98 (c3_1(a875)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[965, 2064])).
% 0.77/0.98 tff(2066,plain,
% 0.77/0.98 (c2_1(a875)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[973, 2064])).
% 0.77/0.98 tff(2067,plain,
% 0.77/0.98 (c0_1(a875)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1049, 2064])).
% 0.77/0.98 tff(2068,plain,
% 0.77/0.98 ($false),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1925, 114, 2067, 2066, 2065, 2063, 2062, 2061, 2060, 2059, 2057, 1538])).
% 0.77/0.98 tff(2069,plain,(hskp13 | c1_1(a830) | c2_1(a830) | c1_1(a859) | c3_1(a859) | c0_1(a859)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.98 tff(2070,plain,
% 0.77/0.98 (hskp13),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2069, 813, 814, 23, 12, 24])).
% 0.77/0.98 tff(2071,plain,
% 0.77/0.98 (~c2_1(a846)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[465, 2070])).
% 0.77/0.98 tff(2072,plain,
% 0.77/0.98 (~c0_1(a846)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[471, 2070])).
% 0.77/0.98 tff(2073,plain,
% 0.77/0.98 (c3_1(a846)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[479, 2070])).
% 0.77/0.98 tff(2074,plain,
% 0.77/0.98 ($false),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1365, 114, 11, 1028, 1667, 1666, 704, 666, 1665, 373])).
% 0.77/0.98 tff(2075,plain,(hskp4 | (~c3_1(a846)) | c0_1(a846) | c2_1(a846)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.98 tff(2076,plain,
% 0.77/0.98 (hskp4),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2075, 2073, 2072, 2071])).
% 0.77/0.98 tff(2077,plain,
% 0.77/0.98 (~c3_1(a832)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[390, 2076])).
% 0.77/0.98 tff(2078,plain,
% 0.77/0.98 (~c2_1(a832)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[396, 2076])).
% 0.77/0.98 tff(2079,plain,
% 0.77/0.98 (~c1_1(a832)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[402, 2076])).
% 0.77/0.98 tff(2080,plain,
% 0.77/0.98 (~c1_1(a863)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[922, 285, 814, 813, 2079, 2078, 2077])).
% 0.77/0.98 tff(2081,plain,
% 0.77/0.98 (hskp19),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1818, 2076, 23, 12, 24])).
% 0.77/0.98 tff(2082,plain,
% 0.77/0.98 (~c2_1(a863)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[494, 2081])).
% 0.77/0.98 tff(2083,plain,
% 0.77/0.98 (c3_1(a863)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[517, 2081])).
% 0.77/0.98 tff(2084,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | c2_1(a863) | c2_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a863) | c2_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c1_1(a863) | (~c3_1(a863)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2085,plain,
% 0.77/0.98 ((hskp17 | (~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863))) <=> (hskp17 | c2_1(a863) | c2_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c1_1(a863) | (~c3_1(a863)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2086,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | c2_1(a863) | c2_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c1_1(a863) | (~c3_1(a863))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[2085])).
% 0.77/0.98 tff(2087,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a863) | c2_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c1_1(a863) | (~c3_1(a863)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[2086, 2084])).
% 0.77/0.98 tff(2088,plain,
% 0.77/0.98 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2089,plain,
% 0.77/0.98 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a863) | c2_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c1_1(a863) | (~c3_1(a863))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2088, 2087])).
% 0.77/0.98 tff(2090,plain,
% 0.77/0.98 ((~c1_1(a846)) | c1_1(a863)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2089, 114, 1646, 2083, 2073, 2082, 2071, 909])).
% 0.77/0.98 tff(2091,plain,
% 0.77/0.98 (~c1_1(a846)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2090, 2080])).
% 0.77/0.98 tff(2092,plain,
% 0.77/0.98 (c0_1(a863)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[502, 2081])).
% 0.77/0.98 tff(2093,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a859) | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | c1_1(a863) | (~c0_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a859) | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | c1_1(a863) | (~c0_1(a863)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2094,plain,
% 0.77/0.98 ((hskp6 | (~ndr1_0) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)) | c1_1(a859) | c0_1(a859) | c3_1(a859)) <=> (hskp6 | c0_1(a859) | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | c1_1(a863) | (~c0_1(a863)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2095,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)) | c1_1(a859) | c0_1(a859) | c3_1(a859))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c0_1(a859) | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | c1_1(a863) | (~c0_1(a863))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[2094])).
% 0.77/0.98 tff(2096,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)) | c1_1(a859) | c0_1(a859) | c3_1(a859))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a859) | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | c1_1(a863) | (~c0_1(a863)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[2095, 2093])).
% 0.77/0.98 tff(2097,plain,
% 0.77/0.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a863) | c1_1(a863) | (~c0_1(a863)) | c1_1(a859) | c0_1(a859) | c3_1(a859))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2098,plain,
% 0.77/0.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c0_1(a859) | c2_1(a863) | c1_1(a859) | c3_1(a859) | (~ndr1_0) | c1_1(a863) | (~c0_1(a863))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2097, 2096])).
% 0.77/0.98 tff(2099,plain,
% 0.77/0.98 (hskp6 | c1_1(a863)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2098, 114, 2092, 24, 2082, 23, 12, 1948])).
% 0.77/0.98 tff(2100,plain,
% 0.77/0.98 (hskp6),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2099, 2080])).
% 0.77/0.98 tff(2101,plain,
% 0.77/0.98 (~c3_1(a835)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[151, 2100])).
% 0.77/0.98 tff(2102,plain,
% 0.77/0.98 (~c2_1(a835)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[157, 2100])).
% 0.77/0.98 tff(2103,plain,
% 0.77/0.98 (~c0_1(a835)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[548, 2100])).
% 0.77/0.98 tff(2104,plain,
% 0.77/0.98 (hskp0),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[732, 2103, 2072, 2078, 2077, 2079, 2071, 285, 2102, 2101])).
% 0.77/0.98 tff(2105,plain,
% 0.77/0.98 (~c0_1(a828)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[738, 2104])).
% 0.77/0.98 tff(2106,plain,
% 0.77/0.98 (c2_1(a828)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[746, 2104])).
% 0.77/0.98 tff(2107,plain,
% 0.77/0.98 (c1_1(a828)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[754, 2104])).
% 0.77/0.98 tff(2108,plain,
% 0.77/0.98 (hskp3 | c1_1(a863)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[532, 114, 2092, 2083, 2082, 276])).
% 0.77/0.98 tff(2109,plain,
% 0.77/0.98 (hskp3),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2108, 2080])).
% 0.77/0.98 tff(2110,plain,
% 0.77/0.98 (c3_1(a831)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[247, 2109])).
% 0.77/0.98 tff(2111,plain,
% 0.77/0.98 (c2_1(a831)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[255, 2109])).
% 0.77/0.98 tff(2112,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a846) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)) | c1_1(a846) | (~c3_1(a846)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a846) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)) | c1_1(a846) | (~c3_1(a846)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2113,plain,
% 0.77/0.98 (((~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)) | (~c0_1(a831)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a846) | c0_1(a846) | (~c3_1(a846))) <=> (c0_1(a846) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)) | c1_1(a846) | (~c3_1(a846)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(2114,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)) | (~c0_1(a831)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a846) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)) | c1_1(a846) | (~c3_1(a846))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[2113])).
% 0.77/0.98 tff(2115,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)) | (~c0_1(a831)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a846) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)) | c1_1(a846) | (~c3_1(a846)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[2114, 2112])).
% 0.77/0.98 tff(2116,plain,
% 0.77/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)) | (~c0_1(a831)) | c0_1(a828) | (~c2_1(a828)) | (~c1_1(a828)) | c1_1(a846) | c0_1(a846) | (~c3_1(a846)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(2117,plain,
% 0.77/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a846) | c0_1(a828) | (~ndr1_0) | (~c1_1(a828)) | (~c2_1(a828)) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)) | c1_1(a846) | (~c3_1(a846))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 0.77/0.98 tff(2118,plain,
% 0.77/0.98 (~c0_1(a831)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2117, 114, 2073, 2111, 2110, 2107, 2106, 2072, 2105, 1538, 2091])).
% 0.77/0.98 tff(2119,plain,
% 0.77/0.98 (hskp5),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2033, 114, 2092, 2083, 2111, 2110, 2027, 2080, 2118])).
% 0.77/0.98 tff(2120,plain,
% 0.77/0.98 (~c3_1(a833)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[66, 2119])).
% 0.77/0.98 tff(2121,plain,
% 0.77/0.98 (c0_1(a833)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[82, 2119])).
% 0.77/0.98 tff(2122,plain,
% 0.77/0.98 (~c1_1(a833)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2042, 114, 1646, 2092, 2121, 2082, 2120, 10, 2080])).
% 0.77/0.98 tff(2123,plain,
% 0.77/0.98 (c2_1(a833)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[138, 2119])).
% 0.77/0.98 tff(2124,plain,
% 0.77/0.98 ($false),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1816, 114, 2121, 2123, 2120, 2079, 2078, 2077, 22, 2122])).
% 0.77/0.98 tff(2125,plain,(hskp31 | c0_1(a859) | c1_1(a859) | c3_1(a859) | c1_1(a830) | c2_1(a830)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.98 tff(2126,plain,
% 0.77/0.98 (hskp31),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[2125, 813, 23, 12, 814, 24])).
% 0.77/0.98 tff(2127,plain,
% 0.77/0.98 (c3_1(a875)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[965, 2126])).
% 0.77/0.98 tff(2128,plain,
% 0.77/0.98 (c2_1(a875)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[973, 2126])).
% 0.77/0.98 tff(2129,plain,
% 0.77/0.98 (c0_1(a875)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1049, 2126])).
% 0.77/0.98 tff(2130,plain,
% 0.77/0.98 (hskp5),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1779, 114, 2129, 2128, 2127, 24, 23, 12, 1769])).
% 0.77/0.98 tff(2131,plain,
% 0.77/0.98 (~c3_1(a833)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[66, 2130])).
% 0.77/0.98 tff(2132,plain,
% 0.77/0.98 (hskp8),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1797, 114, 2129, 2128, 2127, 24, 23, 12, 1791])).
% 0.77/0.98 tff(2133,plain,
% 0.77/0.98 (~c3_1(a838)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[314, 2132])).
% 0.77/0.98 tff(2134,plain,
% 0.77/0.98 (~c2_1(a838)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[320, 2132])).
% 0.77/0.98 tff(2135,plain,
% 0.77/0.98 (c2_1(a833)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[138, 2130])).
% 0.77/0.98 tff(2136,plain,
% 0.77/0.98 (c1_1(a838)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[328, 2132])).
% 0.77/0.98 tff(2137,plain,
% 0.77/0.98 (~c1_1(a833)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1808, 114, 1646, 2136, 2135, 2134, 2133, 2131, 175])).
% 0.77/0.99 tff(2138,plain,
% 0.77/0.99 (c0_1(a833)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[82, 2130])).
% 0.77/0.99 tff(2139,plain,
% 0.77/0.99 ($false),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1816, 114, 2138, 2135, 2131, 2079, 2078, 2077, 22, 2137])).
% 0.77/0.99 tff(2140,plain,(c2_1(a830) | c0_1(a859) | c1_1(a859) | c3_1(a859) | c1_1(a830)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.99 tff(2141,plain,
% 0.77/0.99 ($false),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2140, 1860, 1859, 23, 12, 24])).
% 0.77/0.99 tff(2142,plain,(c0_1(a859) | c1_1(a859) | c3_1(a859)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.99 tff(2143,plain,
% 0.77/0.99 (c0_1(a859)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2142, 23, 12])).
% 0.77/0.99 tff(2144,plain,
% 0.77/0.99 (hskp13),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1023, 1739, 2143, 23, 12])).
% 0.77/0.99 tff(2145,plain,
% 0.77/0.99 (~c2_1(a846)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[465, 2144])).
% 0.77/0.99 tff(2146,plain,
% 0.77/0.99 (c3_1(a846)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[479, 2144])).
% 0.77/0.99 tff(2147,plain,
% 0.77/0.99 (~c0_1(a846)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[471, 2144])).
% 0.77/0.99 tff(2148,plain,
% 0.77/0.99 ($false),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2075, 2147, 2146, 11, 2145])).
% 0.77/0.99 tff(2149,plain,(hskp4 | c1_1(a859) | c3_1(a859)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.99 tff(2150,plain,
% 0.77/0.99 (hskp4),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2149, 23, 12])).
% 0.77/0.99 tff(2151,plain,
% 0.77/0.99 (~c3_1(a832)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[390, 2150])).
% 0.77/0.99 tff(2152,plain,
% 0.77/0.99 (~c2_1(a832)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[396, 2150])).
% 0.77/0.99 tff(2153,plain,
% 0.77/0.99 (~c1_1(a832)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[402, 2150])).
% 0.77/0.99 tff(2154,plain,
% 0.77/0.99 (~c2_1(a859)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[651, 114, 2143, 23, 12, 2153, 2152, 2151, 22])).
% 0.77/0.99 tff(2155,plain,
% 0.77/0.99 (~hskp11),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1023, 1021, 2143, 23, 12])).
% 0.77/0.99 tff(2156,plain,
% 0.77/0.99 (hskp19 | hskp11 | c2_1(a859) | (~c0_1(a859))),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1210, 114, 23, 1204])).
% 0.77/0.99 tff(2157,plain,
% 0.77/0.99 (hskp19),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2156, 2155, 2143, 2154])).
% 0.77/0.99 tff(2158,plain,
% 0.77/0.99 (~c2_1(a863)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[494, 2157])).
% 0.77/0.99 tff(2159,plain,
% 0.77/0.99 (c0_1(a863)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[502, 2157])).
% 0.77/0.99 tff(2160,plain,
% 0.77/0.99 (c3_1(a863)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[517, 2157])).
% 0.77/0.99 tff(2161,plain,
% 0.77/0.99 ($false),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1309, 2160, 2159, 23, 12, 2143, 1021, 2158])).
% 0.77/0.99 tff(2162,plain,(hskp13 | c1_1(a859) | c3_1(a859)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.99 tff(2163,plain,
% 0.77/0.99 (hskp13),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2162, 23, 12])).
% 0.77/0.99 tff(2164,plain,
% 0.77/0.99 (~c2_1(a846)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[465, 2163])).
% 0.77/0.99 tff(2165,plain,
% 0.77/0.99 (~c0_1(a846)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[471, 2163])).
% 0.77/0.99 tff(2166,plain,
% 0.77/0.99 (c3_1(a846)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[479, 2163])).
% 0.77/0.99 tff(2167,plain,
% 0.77/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a859) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | (~c0_1(a859)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a859) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | (~c0_1(a859)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2168,plain,
% 0.77/0.99 (((~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a846) | (~c3_1(a846)) | (~c1_1(a846))) <=> (c3_1(a859) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | (~c0_1(a859)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2169,plain,
% 0.77/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a846) | (~c3_1(a846)) | (~c1_1(a846)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a859) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | (~c0_1(a859))))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[2168])).
% 0.77/0.99 tff(2170,plain,
% 0.77/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a846) | (~c3_1(a846)) | (~c1_1(a846)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a859) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | (~c0_1(a859)))),
% 0.77/0.99 inference(transitivity,[status(thm)],[2169, 2167])).
% 0.77/0.99 tff(2171,plain,
% 0.77/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a846) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | c3_1(a859) | (~c0_1(a859)) | c0_1(a846) | (~c3_1(a846)) | (~c1_1(a846)))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(2172,plain,
% 0.77/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a859) | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c1_1(a846)) | (~c3_1(a846)) | c2_1(a859) | (~c0_1(a859))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2171, 2170])).
% 0.77/0.99 tff(2173,plain,
% 0.77/0.99 (~c1_1(a846)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2172, 114, 2143, 2166, 12, 2165, 2164, 722, 2154])).
% 0.77/0.99 tff(2174,plain,
% 0.77/0.99 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.77/0.99 inference(bind,[status(th)],[])).
% 0.77/0.99 tff(2175,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.99 inference(quant_intro,[status(thm)],[2174])).
% 0.77/0.99 tff(2176,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2177,plain,
% 0.77/0.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.77/0.99 inference(bind,[status(th)],[])).
% 0.77/0.99 tff(2178,plain,
% 0.77/0.99 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.99 inference(quant_intro,[status(thm)],[2177])).
% 0.77/0.99 tff(2179,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.77/0.99 tff(2180,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2179, 2178])).
% 0.77/0.99 tff(2181,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2180, 2176])).
% 0.77/0.99 tff(2182,plain,(
% 0.77/0.99 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.99 inference(skolemize,[status(sab)],[2181])).
% 0.77/0.99 tff(2183,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2182, 2175])).
% 0.77/0.99 tff(2184,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c3_1(a846)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2185,plain,
% 0.77/0.99 ((hskp1 | (~ndr1_0) | c2_1(a846) | c1_1(a846) | (~c3_1(a846)) | c2_1(a846) | c1_1(a846) | c0_1(a846)) <=> (hskp1 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c3_1(a846)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2186,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a846) | c1_1(a846) | (~c3_1(a846)) | c2_1(a846) | c1_1(a846) | c0_1(a846))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c3_1(a846))))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[2185])).
% 0.77/0.99 tff(2187,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a846) | c1_1(a846) | (~c3_1(a846)) | c2_1(a846) | c1_1(a846) | c0_1(a846))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c3_1(a846)))),
% 0.77/0.99 inference(transitivity,[status(thm)],[2186, 2184])).
% 0.77/0.99 tff(2188,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a846) | c1_1(a846) | (~c3_1(a846)) | c2_1(a846) | c1_1(a846) | c0_1(a846))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(2189,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | c1_1(a846) | (~c3_1(a846))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 0.77/0.99 tff(2190,plain,
% 0.77/0.99 (hskp1),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2189, 114, 2166, 2165, 2164, 2183, 2173])).
% 0.77/0.99 tff(2191,plain,
% 0.77/0.99 (((~hskp1) | (~c3_1(a829))) <=> ((~hskp1) | (~c3_1(a829)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2192,plain,
% 0.77/0.99 (((~c3_1(a829)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a829)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2193,axiom,((~c3_1(a829)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 0.77/0.99 tff(2194,plain,
% 0.77/0.99 ((~hskp1) | (~c3_1(a829))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2193, 2192])).
% 0.77/0.99 tff(2195,plain,
% 0.77/0.99 ((~hskp1) | (~c3_1(a829))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2194, 2191])).
% 0.77/0.99 tff(2196,plain,
% 0.77/0.99 (~c3_1(a829)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2195, 2190])).
% 0.77/0.99 tff(2197,plain,
% 0.77/0.99 (((~hskp1) | (~c1_1(a829))) <=> ((~hskp1) | (~c1_1(a829)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2198,plain,
% 0.77/0.99 (((~c1_1(a829)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a829)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2199,axiom,((~c1_1(a829)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.77/0.99 tff(2200,plain,
% 0.77/0.99 ((~hskp1) | (~c1_1(a829))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2199, 2198])).
% 0.77/0.99 tff(2201,plain,
% 0.77/0.99 ((~hskp1) | (~c1_1(a829))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2200, 2197])).
% 0.77/0.99 tff(2202,plain,
% 0.77/0.99 (~c1_1(a829)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2201, 2190])).
% 0.77/0.99 tff(2203,plain,
% 0.77/0.99 (((~hskp1) | (~c0_1(a829))) <=> ((~hskp1) | (~c0_1(a829)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2204,plain,
% 0.77/0.99 (((~c0_1(a829)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a829)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2205,axiom,((~c0_1(a829)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 0.77/0.99 tff(2206,plain,
% 0.77/0.99 ((~hskp1) | (~c0_1(a829))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2205, 2204])).
% 0.77/0.99 tff(2207,plain,
% 0.77/0.99 ((~hskp1) | (~c0_1(a829))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2206, 2203])).
% 0.77/0.99 tff(2208,plain,
% 0.77/0.99 (~c0_1(a829)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2207, 2190])).
% 0.77/0.99 tff(2209,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c1_1(a859) | c0_1(a829) | c1_1(a829) | c3_1(a829) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c1_1(a859) | c0_1(a829) | c1_1(a829) | c3_1(a829) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2210,plain,
% 0.77/0.99 ((hskp6 | (~ndr1_0) | c2_1(a859) | c1_1(a859) | (~c0_1(a859)) | c1_1(a829) | c0_1(a829) | c3_1(a829)) <=> (hskp6 | c1_1(a859) | c0_1(a829) | c1_1(a829) | c3_1(a829) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2211,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a859) | c1_1(a859) | (~c0_1(a859)) | c1_1(a829) | c0_1(a829) | c3_1(a829))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c1_1(a859) | c0_1(a829) | c1_1(a829) | c3_1(a829) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859))))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[2210])).
% 0.77/0.99 tff(2212,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a859) | c1_1(a859) | (~c0_1(a859)) | c1_1(a829) | c0_1(a829) | c3_1(a829))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c1_1(a859) | c0_1(a829) | c1_1(a829) | c3_1(a829) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859)))),
% 0.77/0.99 inference(transitivity,[status(thm)],[2211, 2209])).
% 0.77/0.99 tff(2213,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a859) | c1_1(a859) | (~c0_1(a859)) | c1_1(a829) | c0_1(a829) | c3_1(a829))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(2214,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c1_1(a859) | c0_1(a829) | c1_1(a829) | c3_1(a829) | (~ndr1_0) | c2_1(a859) | (~c0_1(a859))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2213, 2212])).
% 0.77/0.99 tff(2215,plain,
% 0.77/0.99 (hskp6),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2214, 114, 2143, 23, 2208, 2202, 2196, 1948, 2154])).
% 0.77/0.99 tff(2216,plain,
% 0.77/0.99 (~c3_1(a835)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[151, 2215])).
% 0.77/0.99 tff(2217,plain,
% 0.77/0.99 (~c2_1(a835)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[157, 2215])).
% 0.77/0.99 tff(2218,plain,
% 0.77/0.99 (~c0_1(a835)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[548, 2215])).
% 0.77/0.99 tff(2219,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a858) | c1_1(a858) | c2_1(a858) | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a858) | c1_1(a858) | c2_1(a858) | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2220,plain,
% 0.77/0.99 ((hskp0 | (~ndr1_0) | c2_1(a835) | c0_1(a835) | c3_1(a835) | c2_1(a858) | c1_1(a858) | c0_1(a858)) <=> (hskp0 | c0_1(a858) | c1_1(a858) | c2_1(a858) | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2221,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a835) | c0_1(a835) | c3_1(a835) | c2_1(a858) | c1_1(a858) | c0_1(a858))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a858) | c1_1(a858) | c2_1(a858) | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0)))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[2220])).
% 0.77/0.99 tff(2222,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a835) | c0_1(a835) | c3_1(a835) | c2_1(a858) | c1_1(a858) | c0_1(a858))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a858) | c1_1(a858) | c2_1(a858) | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0))),
% 0.77/0.99 inference(transitivity,[status(thm)],[2221, 2219])).
% 0.77/0.99 tff(2223,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a835) | c0_1(a835) | c3_1(a835) | c2_1(a858) | c1_1(a858) | c0_1(a858))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(2224,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a858) | c1_1(a858) | c2_1(a858) | c0_1(a835) | c2_1(a835) | c3_1(a835) | (~ndr1_0)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2223, 2222])).
% 0.77/0.99 tff(2225,plain,
% 0.77/0.99 (hskp0),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2224, 114, 1645, 1639, 1633, 2218, 2217, 2216, 679])).
% 0.77/0.99 tff(2226,plain,
% 0.77/0.99 (~c0_1(a828)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[738, 2225])).
% 0.77/0.99 tff(2227,plain,
% 0.77/0.99 (c2_1(a828)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[746, 2225])).
% 0.77/0.99 tff(2228,plain,
% 0.77/0.99 (c1_1(a828)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[754, 2225])).
% 0.77/0.99 tff(2229,assumption,(~c1_1(a846)), introduced(assumption)).
% 0.77/0.99 tff(2230,assumption,(~c0_1(a828)), introduced(assumption)).
% 0.77/0.99 tff(2231,assumption,(c2_1(a828)), introduced(assumption)).
% 0.77/0.99 tff(2232,assumption,(c1_1(a828)), introduced(assumption)).
% 0.77/0.99 tff(2233,assumption,(hskp31), introduced(assumption)).
% 0.77/0.99 tff(2234,plain,
% 0.77/0.99 (c3_1(a875)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[965, 2233])).
% 0.77/0.99 tff(2235,plain,
% 0.77/0.99 (c2_1(a875)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[973, 2233])).
% 0.77/0.99 tff(2236,plain,
% 0.77/0.99 (c0_1(a875)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1049, 2233])).
% 0.77/0.99 tff(2237,plain,
% 0.77/0.99 ($false),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1556, 114, 2236, 2235, 2234, 1028, 2232, 2231, 704, 2230, 1538, 2229])).
% 0.77/0.99 tff(2238,plain,((~hskp31) | (~c3_1(a846)) | (~c1_1(a828)) | (~c2_1(a828)) | c0_1(a846) | c0_1(a828) | c1_1(a846)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.99 tff(2239,plain,
% 0.77/0.99 (~hskp31),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2238, 2166, 2228, 2227, 2165, 2226, 2173])).
% 0.77/0.99 tff(2240,plain,
% 0.77/0.99 (hskp24),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1493, 114, 2143, 2166, 23, 12, 2164, 559, 2173])).
% 0.77/0.99 tff(2241,plain,
% 0.77/0.99 (~c2_1(a884)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[571, 2240])).
% 0.77/0.99 tff(2242,plain,
% 0.77/0.99 (c1_1(a884)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[579, 2240])).
% 0.77/0.99 tff(2243,plain,
% 0.77/0.99 (hskp31 | (~c0_1(a884))),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[586, 114, 2242, 2143, 2241, 23, 12, 295])).
% 0.77/0.99 tff(2244,plain,
% 0.77/0.99 (~c0_1(a884)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2243, 2239])).
% 0.77/0.99 tff(2245,plain,
% 0.77/0.99 (c3_1(a884)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[594, 2240])).
% 0.77/0.99 tff(2246,plain,
% 0.77/0.99 ($false),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[874, 114, 2242, 2245, 2143, 2241, 12, 722, 2154, 2244])).
% 0.77/0.99 tff(2247,plain,(c1_1(a859) | c3_1(a859)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.99 tff(2248,plain,
% 0.77/0.99 (c1_1(a859)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2247, 12])).
% 0.77/0.99 tff(2249,plain,
% 0.77/0.99 (~hskp17),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[307, 2248])).
% 0.77/0.99 tff(2250,plain,
% 0.77/0.99 (hskp2),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1758, 11, 2249])).
% 0.77/0.99 tff(2251,plain,
% 0.77/0.99 (~c2_1(a830)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[53, 2250])).
% 0.77/0.99 tff(2252,plain,
% 0.77/0.99 (~c1_1(a830)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[59, 2250])).
% 0.77/0.99 tff(2253,plain,
% 0.77/0.99 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | c0_1(a859) | (~c1_1(a859)) | c3_1(a859) | (~ndr1_0))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp4 | c0_1(a859) | (~c1_1(a859)) | c3_1(a859) | (~ndr1_0))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2254,plain,
% 0.77/0.99 ((hskp17 | hskp4 | (~ndr1_0) | c0_1(a859) | c3_1(a859) | (~c1_1(a859))) <=> (hskp17 | hskp4 | c0_1(a859) | (~c1_1(a859)) | c3_1(a859) | (~ndr1_0))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2255,plain,
% 0.77/0.99 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c0_1(a859) | c3_1(a859) | (~c1_1(a859)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | c0_1(a859) | (~c1_1(a859)) | c3_1(a859) | (~ndr1_0)))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[2254])).
% 0.77/0.99 tff(2256,plain,
% 0.77/0.99 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c0_1(a859) | c3_1(a859) | (~c1_1(a859)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp4 | c0_1(a859) | (~c1_1(a859)) | c3_1(a859) | (~ndr1_0))),
% 0.77/0.99 inference(transitivity,[status(thm)],[2255, 2253])).
% 0.77/0.99 tff(2257,plain,
% 0.77/0.99 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c0_1(a859) | c3_1(a859) | (~c1_1(a859)))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(2258,plain,
% 0.77/0.99 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp4 | c0_1(a859) | (~c1_1(a859)) | c3_1(a859) | (~ndr1_0)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 0.77/0.99 tff(2259,plain,
% 0.77/0.99 (hskp17 | hskp4 | c0_1(a859) | (~c1_1(a859))),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2258, 114, 12, 824])).
% 0.77/0.99 tff(2260,plain,
% 0.77/0.99 (hskp4),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2259, 24, 2248, 2249])).
% 0.77/0.99 tff(2261,plain,
% 0.77/0.99 (~c3_1(a832)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[390, 2260])).
% 0.77/0.99 tff(2262,plain,
% 0.77/0.99 (~c2_1(a832)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[396, 2260])).
% 0.77/0.99 tff(2263,plain,
% 0.77/0.99 (~c1_1(a832)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[402, 2260])).
% 0.77/0.99 tff(2264,plain,
% 0.77/0.99 (hskp19),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[411, 285, 385])).
% 0.77/0.99 tff(2265,plain,
% 0.77/0.99 (~c2_1(a863)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[494, 2264])).
% 0.77/0.99 tff(2266,plain,
% 0.77/0.99 (c3_1(a863)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[517, 2264])).
% 0.77/0.99 tff(2267,plain,
% 0.77/0.99 (c0_1(a863)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[502, 2264])).
% 0.77/0.99 tff(2268,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c2_1(a863) | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a863) | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2269,plain,
% 0.77/0.99 ((hskp1 | (~ndr1_0) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)) | c2_1(a858) | c1_1(a858) | c0_1(a858)) <=> (hskp1 | c2_1(a863) | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(2270,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)) | c2_1(a858) | c1_1(a858) | c0_1(a858))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c2_1(a863) | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c1_1(a863) | (~c3_1(a863))))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[2269])).
% 0.77/0.99 tff(2271,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)) | c2_1(a858) | c1_1(a858) | c0_1(a858))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a863) | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c1_1(a863) | (~c3_1(a863)))),
% 0.77/0.99 inference(transitivity,[status(thm)],[2270, 2268])).
% 0.77/0.99 tff(2272,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a863) | c1_1(a863) | (~c3_1(a863)) | c2_1(a858) | c1_1(a858) | c0_1(a858))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(2273,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a863) | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | c1_1(a863) | (~c3_1(a863))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[2272, 2271])).
% 0.77/0.99 tff(2274,plain,
% 0.77/0.99 (hskp1 | c1_1(a863)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2273, 114, 1264, 1263, 1645, 1639, 1633, 2183])).
% 0.77/0.99 tff(2275,plain,
% 0.77/0.99 (hskp1),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2274, 609])).
% 0.77/0.99 tff(2276,plain,
% 0.77/0.99 (~c3_1(a829)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2195, 2275])).
% 0.77/0.99 tff(2277,plain,
% 0.77/0.99 (~c1_1(a829)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2201, 2275])).
% 0.77/0.99 tff(2278,plain,
% 0.77/0.99 (~c0_1(a829)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[2207, 2275])).
% 0.77/0.99 tff(2279,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a829) | c1_1(a829) | c3_1(a829) | (~ndr1_0) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a829) | c1_1(a829) | c3_1(a829) | (~ndr1_0) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2280,plain,
% 0.77/1.00 ((hskp5 | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)) | (~c0_1(a831)) | c1_1(a829) | c0_1(a829) | c3_1(a829)) <=> (hskp5 | c0_1(a829) | c1_1(a829) | c3_1(a829) | (~ndr1_0) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2281,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)) | (~c0_1(a831)) | c1_1(a829) | c0_1(a829) | c3_1(a829))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a829) | c1_1(a829) | c3_1(a829) | (~ndr1_0) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831))))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[2280])).
% 0.77/1.00 tff(2282,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)) | (~c0_1(a831)) | c1_1(a829) | c0_1(a829) | c3_1(a829))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a829) | c1_1(a829) | c3_1(a829) | (~ndr1_0) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831)))),
% 0.77/1.00 inference(transitivity,[status(thm)],[2281, 2279])).
% 0.77/1.00 tff(2283,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)) | (~c0_1(a831)) | c1_1(a829) | c0_1(a829) | c3_1(a829))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(2284,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a829) | c1_1(a829) | c3_1(a829) | (~ndr1_0) | (~c3_1(a831)) | (~c0_1(a831)) | (~c2_1(a831))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[2283, 2282])).
% 0.77/1.00 tff(2285,plain,
% 0.77/1.00 (~c0_1(a831)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2284, 114, 257, 2009, 2008, 2278, 2277, 2276, 1769])).
% 0.77/1.00 tff(2286,plain,
% 0.77/1.00 ($false),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2033, 114, 257, 1287, 1264, 2009, 2008, 2027, 609, 2285])).
% 0.77/1.00 tff(2287,plain,(c1_1(a863) | hskp5 | (~c0_1(a863)) | (~c3_1(a863)) | c2_1(a863)), inference(lemma,lemma(discharge,[]))).
% 0.77/1.00 tff(2288,plain,
% 0.77/1.00 (c1_1(a863)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2287, 2267, 257, 2266, 2265])).
% 0.77/1.00 tff(2289,plain,
% 0.77/1.00 (hskp2 | (~c1_1(a863))),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[1827, 114, 2266, 2265, 1645, 1639, 1633, 34])).
% 0.77/1.00 tff(2290,plain,
% 0.77/1.00 (hskp2),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2289, 2288])).
% 0.77/1.00 tff(2291,plain,
% 0.77/1.00 (~c1_1(a830)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[59, 2290])).
% 0.77/1.00 tff(2292,plain,
% 0.77/1.00 (~c2_1(a830)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[53, 2290])).
% 0.77/1.00 tff(2293,plain,
% 0.77/1.00 ($false),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[922, 2292, 2291, 285, 2288, 403, 397, 391])).
% 0.77/1.00 tff(2294,plain,(hskp31 | hskp5 | (~hskp4)), inference(lemma,lemma(discharge,[]))).
% 0.77/1.00 tff(2295,plain,
% 0.77/1.00 (hskp31),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2294, 257, 385])).
% 0.77/1.00 tff(2296,plain,
% 0.77/1.00 (c3_1(a875)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[965, 2295])).
% 0.77/1.00 tff(2297,plain,
% 0.77/1.00 (c2_1(a875)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[973, 2295])).
% 0.77/1.00 tff(2298,plain,
% 0.77/1.00 (c0_1(a875)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[1049, 2295])).
% 0.77/1.00 tff(2299,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a858) | c1_1(a858) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c3_1(a858))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a858) | c1_1(a858) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c3_1(a858))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2300,plain,
% 0.77/1.00 ((hskp5 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a858) | c0_1(a858) | c3_1(a858)) <=> (hskp5 | c0_1(a858) | c1_1(a858) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c3_1(a858))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2301,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a858) | c0_1(a858) | c3_1(a858))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a858) | c1_1(a858) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c3_1(a858)))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[2300])).
% 0.77/1.00 tff(2302,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a858) | c0_1(a858) | c3_1(a858))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a858) | c1_1(a858) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c3_1(a858))),
% 0.77/1.00 inference(transitivity,[status(thm)],[2301, 2299])).
% 0.77/1.00 tff(2303,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a858) | c0_1(a858) | c3_1(a858))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(2304,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a858) | c1_1(a858) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c3_1(a858)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[2303, 2302])).
% 0.77/1.00 tff(2305,plain,
% 0.77/1.00 (c3_1(a858)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2304, 114, 257, 2298, 2297, 2296, 1645, 1639, 1769])).
% 0.77/1.00 tff(2306,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c0_1(a832))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2307,plain,
% 0.77/1.00 ((hskp5 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a832) | c0_1(a832) | c3_1(a832)) <=> (hskp5 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c0_1(a832))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2308,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c0_1(a832)))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[2307])).
% 0.77/1.00 tff(2309,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c0_1(a832))),
% 0.77/1.00 inference(transitivity,[status(thm)],[2308, 2306])).
% 0.77/1.00 tff(2310,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c1_1(a832) | c0_1(a832) | c3_1(a832))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(2311,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | c0_1(a832)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[2310, 2309])).
% 0.77/1.00 tff(2312,plain,
% 0.77/1.00 (c0_1(a832)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2311, 114, 257, 2298, 2297, 2296, 403, 391, 1769])).
% 0.77/1.00 tff(2313,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | c1_1(a858) | c2_1(a858) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c3_1(a858)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp24 | c1_1(a858) | c2_1(a858) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c3_1(a858)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2314,plain,
% 0.77/1.00 ((hskp24 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858))) <=> (hskp24 | c1_1(a858) | c2_1(a858) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c3_1(a858)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2315,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | c1_1(a858) | c2_1(a858) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c3_1(a858))))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[2314])).
% 0.77/1.00 tff(2316,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp24 | c1_1(a858) | c2_1(a858) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c3_1(a858)))),
% 0.77/1.00 inference(transitivity,[status(thm)],[2315, 2313])).
% 0.77/1.00 tff(2317,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858)))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(2318,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp24 | c1_1(a858) | c2_1(a858) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c3_1(a858))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[2317, 2316])).
% 0.77/1.00 tff(2319,plain,
% 0.77/1.00 (hskp24 | (~c0_1(a832)) | (~c3_1(a858))),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2318, 114, 1639, 1633, 403, 391, 559])).
% 0.77/1.00 tff(2320,plain,
% 0.77/1.00 (hskp24),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2319, 2305, 2312])).
% 0.77/1.00 tff(2321,plain,
% 0.77/1.00 (~c2_1(a884)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[571, 2320])).
% 0.77/1.00 tff(2322,plain,
% 0.77/1.00 (c3_1(a884)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[594, 2320])).
% 0.77/1.00 tff(2323,plain,
% 0.77/1.00 (c1_1(a884)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[579, 2320])).
% 0.77/1.00 tff(2324,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | c2_1(a884) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c3_1(a858)) | (~c1_1(a884)) | (~c3_1(a884)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a884) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c3_1(a858)) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2325,plain,
% 0.77/1.00 ((hskp17 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858))) <=> (hskp17 | c2_1(a884) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c3_1(a858)) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2326,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | c2_1(a884) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c3_1(a858)) | (~c1_1(a884)) | (~c3_1(a884))))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[2325])).
% 0.77/1.00 tff(2327,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a884) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c3_1(a858)) | (~c1_1(a884)) | (~c3_1(a884)))),
% 0.77/1.00 inference(transitivity,[status(thm)],[2326, 2324])).
% 0.77/1.00 tff(2328,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a884) | (~c1_1(a884)) | (~c3_1(a884)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858)))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(2329,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp17 | c2_1(a884) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c3_1(a858)) | (~c1_1(a884)) | (~c3_1(a884))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[2328, 2327])).
% 0.77/1.00 tff(2330,plain,
% 0.77/1.00 ($false),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2329, 114, 36, 2323, 2322, 2321, 1639, 1633, 909, 2305])).
% 0.77/1.00 tff(2331,plain,(hskp5 | hskp17 | (~hskp4)), inference(lemma,lemma(discharge,[]))).
% 0.77/1.00 tff(2332,plain,
% 0.77/1.00 (hskp5),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2331, 2260, 2249])).
% 0.77/1.00 tff(2333,plain,
% 0.77/1.00 (~c3_1(a833)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[66, 2332])).
% 0.77/1.00 tff(2334,plain,
% 0.77/1.00 (c2_1(a833)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[138, 2332])).
% 0.77/1.00 tff(2335,plain,
% 0.77/1.00 (c0_1(a833)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[82, 2332])).
% 0.77/1.00 tff(2336,assumption,(~c1_1(a833)), introduced(assumption)).
% 0.77/1.00 tff(2337,assumption,(c2_1(a833)), introduced(assumption)).
% 0.77/1.00 tff(2338,assumption,(c0_1(a833)), introduced(assumption)).
% 0.77/1.00 tff(2339,plain,
% 0.77/1.00 ($false),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[1816, 114, 2338, 2337, 624, 608, 607, 606, 22, 2336])).
% 0.77/1.00 tff(2340,plain,(c1_1(a833) | (~c0_1(a833)) | (~c2_1(a833)) | c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 0.77/1.00 tff(2341,plain,
% 0.77/1.00 (c1_1(a833)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2340, 2335, 2334, 2333, 2263, 2262, 2261])).
% 0.77/1.00 tff(2342,plain,
% 0.77/1.00 (c1_1(a863)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2046, 2266, 36, 391, 397, 403, 1021, 2265, 2267])).
% 0.77/1.00 tff(2343,plain,
% 0.77/1.00 (hskp2),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[1827, 114, 2266, 2265, 1645, 1639, 1633, 34, 2342])).
% 0.77/1.00 tff(2344,plain,
% 0.77/1.00 (~c1_1(a830)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[59, 2343])).
% 0.77/1.00 tff(2345,plain,
% 0.77/1.00 (~c2_1(a830)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[53, 2343])).
% 0.77/1.00 tff(2346,plain,
% 0.77/1.00 ($false),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[922, 2345, 2344, 285, 2342, 403, 397, 391])).
% 0.77/1.00 tff(2347,plain,(hskp31 | hskp17 | hskp13 | (~hskp4)), inference(lemma,lemma(discharge,[]))).
% 0.77/1.00 tff(2348,plain,
% 0.77/1.00 (hskp31),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2347, 1021, 2249, 2260])).
% 0.77/1.00 tff(2349,plain,
% 0.77/1.00 (c3_1(a875)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[965, 2348])).
% 0.77/1.00 tff(2350,plain,
% 0.77/1.00 (c2_1(a875)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[973, 2348])).
% 0.77/1.00 tff(2351,plain,
% 0.77/1.00 (c0_1(a875)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[1049, 2348])).
% 0.77/1.00 tff(2352,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2353,plain,
% 0.77/1.00 ((hskp3 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a858) | c1_1(a858) | c0_1(a858)) <=> (hskp3 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2354,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a858) | c1_1(a858) | c0_1(a858))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875))))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[2353])).
% 0.77/1.00 tff(2355,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a858) | c1_1(a858) | c0_1(a858))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)))),
% 0.77/1.00 inference(transitivity,[status(thm)],[2354, 2352])).
% 0.77/1.00 tff(2356,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c2_1(a858) | c1_1(a858) | c0_1(a858))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(2357,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c0_1(a858) | c1_1(a858) | c2_1(a858) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 0.77/1.00 tff(2358,plain,
% 0.77/1.00 (hskp3),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2357, 114, 2351, 2350, 2349, 1645, 1639, 1633, 1608])).
% 0.77/1.00 tff(2359,plain,
% 0.77/1.00 (~c1_1(a831)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[239, 2358])).
% 0.77/1.00 tff(2360,plain,
% 0.77/1.00 (c3_1(a858)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2304, 114, 257, 2236, 2235, 2234, 1645, 1639, 1769])).
% 0.77/1.00 tff(2361,plain,
% 0.77/1.00 (c0_1(a832)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2311, 114, 257, 2236, 2235, 2234, 608, 606, 1769])).
% 0.77/1.00 tff(2362,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | c1_1(a858) | c2_1(a858) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c3_1(a858)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a858) | c2_1(a858) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c3_1(a858)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2363,plain,
% 0.77/1.00 ((hskp13 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858))) <=> (hskp13 | c1_1(a858) | c2_1(a858) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c3_1(a858)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2364,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | c1_1(a858) | c2_1(a858) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c3_1(a858))))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[2363])).
% 0.77/1.00 tff(2365,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a858) | c2_1(a858) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c3_1(a858)))),
% 0.77/1.00 inference(transitivity,[status(thm)],[2364, 2362])).
% 0.77/1.00 tff(2366,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a858) | c1_1(a858) | (~c3_1(a858)))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(2367,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a858) | c2_1(a858) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c3_1(a858))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[2366, 2365])).
% 0.77/1.00 tff(2368,plain,
% 0.77/1.00 (hskp13 | (~c0_1(a832)) | (~c3_1(a858))),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2367, 114, 1639, 1633, 608, 606, 383])).
% 0.77/1.00 tff(2369,plain,
% 0.77/1.00 ($false),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2368, 2361, 2360, 1021])).
% 0.77/1.00 tff(2370,plain,((~hskp31) | hskp13 | c1_1(a832) | c3_1(a832) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.77/1.00 tff(2371,plain,
% 0.77/1.00 (hskp5),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2370, 2348, 2263, 2261, 1021])).
% 0.77/1.00 tff(2372,plain,
% 0.77/1.00 (~c3_1(a833)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[66, 2371])).
% 0.77/1.00 tff(2373,plain,
% 0.77/1.00 (c2_1(a831)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[255, 2358])).
% 0.77/1.00 tff(2374,plain,
% 0.77/1.00 (c2_1(a833)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[138, 2371])).
% 0.77/1.00 tff(2375,plain,
% 0.77/1.00 (c0_1(a833)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[82, 2371])).
% 0.77/1.00 tff(2376,plain,
% 0.77/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | c1_1(a831) | (~ndr1_0) | (~c0_1(a831)) | (~c2_1(a831)) | (~c2_1(a833)) | (~c0_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | c1_1(a831) | (~ndr1_0) | (~c0_1(a831)) | (~c2_1(a831)) | (~c2_1(a833)) | (~c0_1(a833)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2377,plain,
% 0.77/1.00 (((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a831) | (~c2_1(a831)) | (~c0_1(a831)) | c3_1(a832) | c2_1(a832) | c1_1(a832)) <=> (c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | c1_1(a831) | (~ndr1_0) | (~c0_1(a831)) | (~c2_1(a831)) | (~c2_1(a833)) | (~c0_1(a833)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2378,plain,
% 0.77/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a831) | (~c2_1(a831)) | (~c0_1(a831)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | c1_1(a831) | (~ndr1_0) | (~c0_1(a831)) | (~c2_1(a831)) | (~c2_1(a833)) | (~c0_1(a833))))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[2377])).
% 0.77/1.00 tff(2379,plain,
% 0.77/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a831) | (~c2_1(a831)) | (~c0_1(a831)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | c1_1(a831) | (~ndr1_0) | (~c0_1(a831)) | (~c2_1(a831)) | (~c2_1(a833)) | (~c0_1(a833)))),
% 0.77/1.00 inference(transitivity,[status(thm)],[2378, 2376])).
% 0.77/1.00 tff(2380,plain,
% 0.77/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a831) | (~c2_1(a831)) | (~c0_1(a831)) | c3_1(a832) | c2_1(a832) | c1_1(a832))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(2381,plain,
% 0.77/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | c1_1(a831) | (~ndr1_0) | (~c0_1(a831)) | (~c2_1(a831)) | (~c2_1(a833)) | (~c0_1(a833))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[2380, 2379])).
% 0.77/1.00 tff(2382,plain,
% 0.77/1.00 (~c0_1(a831)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2381, 114, 2375, 2374, 2373, 2372, 2263, 2262, 2261, 2359, 22])).
% 0.77/1.00 tff(2383,plain,
% 0.77/1.00 (c3_1(a831)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[247, 2358])).
% 0.77/1.00 tff(2384,plain,
% 0.77/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a859) | (~c1_1(a859)) | c1_1(a831) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | (~c3_1(a831)) | c0_1(a831) | (~c2_1(a859)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a859) | (~c1_1(a859)) | c1_1(a831) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | (~c3_1(a831)) | c0_1(a831) | (~c2_1(a859)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2385,plain,
% 0.77/1.00 (((~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c0_1(a859) | (~c2_1(a859)) | (~c1_1(a859)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831))) <=> (c0_1(a859) | (~c1_1(a859)) | c1_1(a831) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | (~c3_1(a831)) | c0_1(a831) | (~c2_1(a859)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2386,plain,
% 0.77/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c0_1(a859) | (~c2_1(a859)) | (~c1_1(a859)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a859) | (~c1_1(a859)) | c1_1(a831) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | (~c3_1(a831)) | c0_1(a831) | (~c2_1(a859))))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[2385])).
% 0.77/1.00 tff(2387,plain,
% 0.77/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c0_1(a859) | (~c2_1(a859)) | (~c1_1(a859)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a859) | (~c1_1(a859)) | c1_1(a831) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | (~c3_1(a831)) | c0_1(a831) | (~c2_1(a859)))),
% 0.77/1.00 inference(transitivity,[status(thm)],[2386, 2384])).
% 0.77/1.00 tff(2388,plain,
% 0.77/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a875)) | (~c3_1(a875)) | (~c0_1(a875)) | c0_1(a859) | (~c2_1(a859)) | (~c1_1(a859)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(2389,plain,
% 0.77/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a859) | (~c1_1(a859)) | c1_1(a831) | (~ndr1_0) | (~c0_1(a875)) | (~c3_1(a875)) | (~c2_1(a875)) | (~c3_1(a831)) | c0_1(a831) | (~c2_1(a859))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[2388, 2387])).
% 0.77/1.00 tff(2390,plain,
% 0.77/1.00 (c0_1(a831) | (~c2_1(a859))),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[2389, 114, 2351, 2350, 2349, 24, 2383, 2248, 2359, 1538])).
% 0.77/1.01 tff(2391,plain,
% 0.77/1.01 (~c2_1(a859)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[2390, 2382])).
% 0.77/1.01 tff(2392,plain,
% 0.77/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a859)) | c3_1(a859) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a859))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a859)) | c3_1(a859) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a859))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(2393,plain,
% 0.77/1.01 ((hskp17 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a859) | c3_1(a859) | (~c1_1(a859))) <=> (hskp17 | (~c1_1(a859)) | c3_1(a859) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a859))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(2394,plain,
% 0.77/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a859) | c3_1(a859) | (~c1_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a859)) | c3_1(a859) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a859)))),
% 0.77/1.01 inference(monotonicity,[status(thm)],[2393])).
% 0.77/1.01 tff(2395,plain,
% 0.77/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a859) | c3_1(a859) | (~c1_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a859)) | c3_1(a859) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a859))),
% 0.77/1.01 inference(transitivity,[status(thm)],[2394, 2392])).
% 0.77/1.01 tff(2396,plain,
% 0.77/1.01 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a859) | c3_1(a859) | (~c1_1(a859)))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(2397,plain,
% 0.77/1.01 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a859)) | c3_1(a859) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | c2_1(a859)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2396, 2395])).
% 0.77/1.01 tff(2398,plain,
% 0.77/1.01 (~c1_1(a833)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[2397, 114, 2249, 2374, 2248, 12, 2372, 175, 2391])).
% 0.77/1.01 tff(2399,plain,
% 0.77/1.01 ($false),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[1816, 114, 2375, 2374, 2372, 2263, 2262, 2261, 22, 2398])).
% 0.77/1.01 tff(2400,plain,(hskp13 | c3_1(a859) | c0_1(a859)), inference(lemma,lemma(discharge,[]))).
% 0.77/1.01 tff(2401,plain,
% 0.77/1.01 (hskp13),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[2400, 24, 12])).
% 0.77/1.01 tff(2402,plain,
% 0.77/1.01 (~c2_1(a846)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[465, 2401])).
% 0.77/1.01 tff(2403,plain,
% 0.77/1.01 (~c0_1(a846)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[471, 2401])).
% 0.77/1.01 tff(2404,plain,
% 0.77/1.01 (c3_1(a846)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[479, 2401])).
% 0.77/1.01 tff(2405,plain,
% 0.77/1.01 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c1_1(a833)) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c1_1(a833)) | (~c3_1(a846)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(2406,plain,
% 0.77/1.01 ((hskp2 | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846))) <=> (hskp2 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c1_1(a833)) | (~c3_1(a846)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(2407,plain,
% 0.77/1.01 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c1_1(a833)) | (~c3_1(a846))))),
% 0.77/1.01 inference(monotonicity,[status(thm)],[2406])).
% 0.77/1.01 tff(2408,plain,
% 0.77/1.01 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c1_1(a833)) | (~c3_1(a846)))),
% 0.77/1.01 inference(transitivity,[status(thm)],[2407, 2405])).
% 0.77/1.01 tff(2409,plain,
% 0.77/1.01 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a846) | c0_1(a846) | (~c3_1(a846)))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(2410,plain,
% 0.77/1.01 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a846) | c2_1(a846) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | (~c1_1(a833)) | (~c3_1(a846))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2409, 2408])).
% 0.77/1.01 tff(2411,plain,
% 0.77/1.01 (hskp2 | (~c1_1(a833))),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[2410, 114, 2404, 2335, 2334, 2403, 2402, 1345])).
% 0.77/1.01 tff(2412,plain,
% 0.77/1.01 (hskp2),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[2411, 2341])).
% 0.77/1.01 tff(2413,plain,
% 0.77/1.01 (~c2_1(a830)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[53, 2412])).
% 0.77/1.01 tff(2414,plain,
% 0.77/1.01 (~c1_1(a830)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[59, 2412])).
% 0.77/1.01 tff(2415,plain,
% 0.77/1.01 (c0_1(a830)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[74, 2412])).
% 0.77/1.01 tff(2416,plain,
% 0.77/1.01 ($false),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[120, 114, 2249, 2335, 2415, 2333, 2414, 2413, 10, 2341])).
% 0.77/1.01 tff(2417,plain,(c0_1(a859) | c3_1(a859)), inference(lemma,lemma(discharge,[]))).
% 0.77/1.01 tff(2418,plain,
% 0.77/1.01 (c0_1(a859)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[2417, 12])).
% 0.77/1.01 tff(2419,plain,
% 0.77/1.01 (^[U: $i] : refl((hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(2420,plain,
% 0.77/1.01 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[2419])).
% 0.77/1.01 tff(2421,plain,
% 0.77/1.01 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(2422,plain,
% 0.77/1.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) | hskp4) <=> ((hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp4))), rewrite(((hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) | hskp4) <=> (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(2423,plain,
% 0.77/1.01 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) | hskp4) <=> ![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[2422])).
% 0.77/1.01 tff(2424,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.77/1.01 tff(2425,plain,
% 0.77/1.01 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2424, 2423])).
% 0.77/1.01 tff(2426,plain,
% 0.77/1.01 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2425, 2421])).
% 0.77/1.01 tff(2427,plain,(
% 0.77/1.01 ![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/1.01 inference(skolemize,[status(sab)],[2426])).
% 0.77/1.01 tff(2428,plain,
% 0.77/1.01 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2427, 2420])).
% 0.77/1.01 tff(2429,plain,
% 0.77/1.01 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp4 | (~c1_1(a859)) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp4 | (~c1_1(a859)) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(2430,plain,
% 0.77/1.01 ((hskp22 | hskp4 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859))) <=> (hskp22 | hskp4 | (~c1_1(a859)) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(2431,plain,
% 0.77/1.01 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp4 | (~c1_1(a859)) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859))))),
% 0.77/1.01 inference(monotonicity,[status(thm)],[2430])).
% 0.77/1.01 tff(2432,plain,
% 0.77/1.01 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp4 | (~c1_1(a859)) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859)))),
% 0.77/1.01 inference(transitivity,[status(thm)],[2431, 2429])).
% 0.77/1.01 tff(2433,plain,
% 0.77/1.01 ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(2434,plain,
% 0.77/1.01 ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp4 | (~c1_1(a859)) | c3_1(a859) | (~ndr1_0) | (~c0_1(a859))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 0.77/1.01 tff(2435,plain,
% 0.77/1.01 (hskp22 | hskp4 | (~c1_1(a859)) | (~c0_1(a859))),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[2434, 114, 12, 2428])).
% 0.77/1.01 tff(2436,plain,
% 0.77/1.01 (hskp22),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[2435, 11, 2248, 2418])).
% 0.77/1.01 tff(2437,plain,
% 0.77/1.01 (((~hskp22) | (~c3_1(a866))) <=> ((~hskp22) | (~c3_1(a866)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(2438,plain,
% 0.77/1.01 (((~c3_1(a866)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a866)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(2439,axiom,((~c3_1(a866)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.77/1.01 tff(2440,plain,
% 0.77/1.01 ((~hskp22) | (~c3_1(a866))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2439, 2438])).
% 0.77/1.01 tff(2441,plain,
% 0.77/1.01 ((~hskp22) | (~c3_1(a866))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2440, 2437])).
% 0.77/1.01 tff(2442,plain,
% 0.77/1.01 (~c3_1(a866)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[2441, 2436])).
% 0.77/1.01 tff(2443,plain,
% 0.77/1.01 (c0_1(a830)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[74, 2250])).
% 0.77/1.01 tff(2444,plain,
% 0.77/1.01 (((~hskp22) | c1_1(a866)) <=> ((~hskp22) | c1_1(a866))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(2445,axiom,((~hskp22) | c1_1(a866)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.77/1.01 tff(2446,plain,
% 0.77/1.01 ((~hskp22) | c1_1(a866)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2445, 2444])).
% 0.77/1.01 tff(2447,plain,
% 0.77/1.01 ((~hskp22) | c1_1(a866)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2446, 2444])).
% 0.77/1.01 tff(2448,plain,
% 0.77/1.01 ((~hskp22) | c1_1(a866)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2447, 2444])).
% 0.77/1.01 tff(2449,plain,
% 0.77/1.01 ((~hskp22) | c1_1(a866)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2448, 2444])).
% 0.77/1.01 tff(2450,plain,
% 0.77/1.01 ((~hskp22) | c1_1(a866)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2449, 2444])).
% 0.77/1.01 tff(2451,plain,
% 0.77/1.01 (c1_1(a866)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[2450, 2436])).
% 0.77/1.01 tff(2452,plain,
% 0.77/1.01 (((~hskp22) | c0_1(a866)) <=> ((~hskp22) | c0_1(a866))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(2453,axiom,((~hskp22) | c0_1(a866)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.77/1.01 tff(2454,plain,
% 0.77/1.01 ((~hskp22) | c0_1(a866)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2453, 2452])).
% 0.77/1.01 tff(2455,plain,
% 0.77/1.01 ((~hskp22) | c0_1(a866)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2454, 2452])).
% 0.77/1.01 tff(2456,plain,
% 0.77/1.01 ((~hskp22) | c0_1(a866)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2455, 2452])).
% 0.77/1.01 tff(2457,plain,
% 0.77/1.01 ((~hskp22) | c0_1(a866)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2456, 2452])).
% 0.77/1.01 tff(2458,plain,
% 0.77/1.01 ((~hskp22) | c0_1(a866)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[2457, 2452])).
% 0.77/1.01 tff(2459,plain,
% 0.77/1.01 (c0_1(a866)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[2458, 2436])).
% 0.77/1.01 tff(2460,plain,
% 0.77/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c3_1(a866) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a866)) | (~c1_1(a866)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c3_1(a866) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a866)) | (~c1_1(a866)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(2461,plain,
% 0.77/1.01 ((hskp17 | (~ndr1_0) | c3_1(a866) | (~c1_1(a866)) | (~c0_1(a866)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830))) <=> (hskp17 | c3_1(a866) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a866)) | (~c1_1(a866)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(2462,plain,
% 0.77/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a866) | (~c1_1(a866)) | (~c0_1(a866)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c3_1(a866) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a866)) | (~c1_1(a866))))),
% 0.77/1.01 inference(monotonicity,[status(thm)],[2461])).
% 0.77/1.01 tff(2463,plain,
% 0.77/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a866) | (~c1_1(a866)) | (~c0_1(a866)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c3_1(a866) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a866)) | (~c1_1(a866)))),
% 0.77/1.01 inference(transitivity,[status(thm)],[2462, 2460])).
% 0.77/1.01 tff(2464,plain,
% 0.77/1.01 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a866) | (~c1_1(a866)) | (~c0_1(a866)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(2465,plain,
% 0.85/1.01 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c3_1(a866) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a866)) | (~c1_1(a866))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2464, 2463])).
% 0.85/1.01 tff(2466,plain,
% 0.85/1.01 ($false),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2465, 114, 2249, 2459, 2451, 2443, 2442, 2252, 2251, 10])).
% 0.85/1.01 tff(2467,plain,(hskp4 | c3_1(a859)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.01 tff(2468,plain,
% 0.85/1.01 (hskp4),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2467, 12])).
% 0.85/1.01 tff(2469,plain,
% 0.85/1.01 (~c2_1(a832)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[396, 2468])).
% 0.85/1.01 tff(2470,plain,
% 0.85/1.01 (~c1_1(a832)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[402, 2468])).
% 0.85/1.01 tff(2471,plain,
% 0.85/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c0_1(a859)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2472,plain,
% 0.85/1.01 ((hskp17 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a832) | c1_1(a832) | (~c0_1(a832))) <=> (hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c0_1(a859)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2473,plain,
% 0.85/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a832) | c1_1(a832) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c0_1(a859))))),
% 0.85/1.01 inference(monotonicity,[status(thm)],[2472])).
% 0.85/1.01 tff(2474,plain,
% 0.85/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a832) | c1_1(a832) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c0_1(a859)))),
% 0.85/1.01 inference(transitivity,[status(thm)],[2473, 2471])).
% 0.85/1.01 tff(2475,plain,
% 0.85/1.01 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a832) | c1_1(a832) | (~c0_1(a832)))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(2476,plain,
% 0.85/1.01 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c0_1(a859))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2475, 2474])).
% 0.85/1.01 tff(2477,plain,
% 0.85/1.01 (~c0_1(a832)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2476, 114, 2249, 2418, 2248, 12, 2470, 2469, 10])).
% 0.85/1.01 tff(2478,plain,
% 0.85/1.01 (hskp5),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2331, 2468, 2249])).
% 0.85/1.01 tff(2479,plain,
% 0.85/1.01 (c0_1(a833)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[82, 2478])).
% 0.85/1.01 tff(2480,plain,
% 0.85/1.01 (~c3_1(a833)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[66, 2478])).
% 0.85/1.01 tff(2481,plain,
% 0.85/1.01 (~c3_1(a832)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[390, 2468])).
% 0.85/1.01 tff(2482,plain,
% 0.85/1.01 (c2_1(a833)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[138, 2478])).
% 0.85/1.01 tff(2483,plain,
% 0.85/1.01 (c1_1(a833)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2340, 2482, 2481, 2480, 2470, 2469, 2479])).
% 0.85/1.01 tff(2484,plain,
% 0.85/1.01 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp11 | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832) | (~c2_1(a833)) | (~c0_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp11 | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832) | (~c2_1(a833)) | (~c0_1(a833)) | (~c1_1(a833)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2485,plain,
% 0.85/1.01 ((hskp11 | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a832) | c0_1(a832) | c3_1(a832)) <=> (hskp11 | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832) | (~c2_1(a833)) | (~c0_1(a833)) | (~c1_1(a833)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2486,plain,
% 0.85/1.01 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp11 | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832) | (~c2_1(a833)) | (~c0_1(a833)) | (~c1_1(a833))))),
% 0.85/1.01 inference(monotonicity,[status(thm)],[2485])).
% 0.85/1.01 tff(2487,plain,
% 0.85/1.01 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp11 | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832) | (~c2_1(a833)) | (~c0_1(a833)) | (~c1_1(a833)))),
% 0.85/1.01 inference(transitivity,[status(thm)],[2486, 2484])).
% 0.85/1.01 tff(2488,plain,
% 0.85/1.01 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a832) | c0_1(a832) | c3_1(a832))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(2489,plain,
% 0.85/1.01 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp11 | c2_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832) | (~c2_1(a833)) | (~c0_1(a833)) | (~c1_1(a833))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2488, 2487])).
% 0.85/1.01 tff(2490,plain,
% 0.85/1.01 (hskp11 | c0_1(a832)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2489, 114, 2479, 2482, 2469, 2481, 1222, 2483])).
% 0.85/1.01 tff(2491,plain,
% 0.85/1.01 (hskp11),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2490, 2477])).
% 0.85/1.01 tff(2492,plain,
% 0.85/1.01 (~c2_1(a844)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[437, 2491])).
% 0.85/1.01 tff(2493,plain,
% 0.85/1.01 (~c1_1(a844)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[443, 2491])).
% 0.85/1.01 tff(2494,plain,
% 0.85/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c0_1(a859)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2495,plain,
% 0.85/1.01 ((hskp17 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a844) | c1_1(a844) | (~c0_1(a844))) <=> (hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c0_1(a859)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2496,plain,
% 0.85/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a844) | c1_1(a844) | (~c0_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c0_1(a859))))),
% 0.85/1.01 inference(monotonicity,[status(thm)],[2495])).
% 0.85/1.01 tff(2497,plain,
% 0.85/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a844) | c1_1(a844) | (~c0_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c0_1(a859)))),
% 0.85/1.01 inference(transitivity,[status(thm)],[2496, 2494])).
% 0.85/1.01 tff(2498,plain,
% 0.85/1.01 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a844) | c1_1(a844) | (~c0_1(a844)))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(2499,plain,
% 0.85/1.01 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a844) | c2_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c0_1(a859))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2498, 2497])).
% 0.85/1.01 tff(2500,plain,
% 0.85/1.01 (~c0_1(a844)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2499, 114, 2249, 2418, 2248, 12, 2493, 2492, 10])).
% 0.85/1.01 tff(2501,plain,
% 0.85/1.01 (c3_1(a844)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[451, 2491])).
% 0.85/1.01 tff(2502,plain,
% 0.85/1.01 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.85/1.01 inference(bind,[status(th)],[])).
% 0.85/1.01 tff(2503,plain,
% 0.85/1.01 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.01 inference(quant_intro,[status(thm)],[2502])).
% 0.85/1.01 tff(2504,plain,
% 0.85/1.01 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2505,plain,
% 0.85/1.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(2506,plain,
% 0.85/1.02 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[2505])).
% 0.85/1.02 tff(2507,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.85/1.02 tff(2508,plain,
% 0.85/1.02 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2507, 2506])).
% 0.85/1.02 tff(2509,plain,
% 0.85/1.02 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2508, 2504])).
% 0.85/1.02 tff(2510,plain,(
% 0.85/1.02 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.02 inference(skolemize,[status(sab)],[2509])).
% 0.85/1.02 tff(2511,plain,
% 0.85/1.02 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2510, 2503])).
% 0.85/1.02 tff(2512,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp29 | (~c1_1(a859)) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp29 | (~c1_1(a859)) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a859)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2513,plain,
% 0.85/1.02 ((hskp29 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a832) | c1_1(a832) | c3_1(a832)) <=> (hskp29 | (~c1_1(a859)) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a859)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2514,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp29 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a832) | c1_1(a832) | c3_1(a832))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp29 | (~c1_1(a859)) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a859))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[2513])).
% 0.85/1.02 tff(2515,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp29 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a832) | c1_1(a832) | c3_1(a832))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp29 | (~c1_1(a859)) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a859)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[2514, 2512])).
% 0.85/1.02 tff(2516,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp29 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a832) | c1_1(a832) | c3_1(a832))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(2517,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp29 | (~c1_1(a859)) | c3_1(a859) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a859))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2516, 2515])).
% 0.85/1.02 tff(2518,plain,
% 0.85/1.02 (hskp29),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2517, 114, 2418, 2248, 12, 2470, 2469, 2481, 2511])).
% 0.85/1.02 tff(2519,plain,
% 0.85/1.02 (((~hskp29) | c2_1(a849)) <=> ((~hskp29) | c2_1(a849))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2520,axiom,((~hskp29) | c2_1(a849)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.85/1.02 tff(2521,plain,
% 0.85/1.02 ((~hskp29) | c2_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2520, 2519])).
% 0.85/1.02 tff(2522,plain,
% 0.85/1.02 ((~hskp29) | c2_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2521, 2519])).
% 0.85/1.02 tff(2523,plain,
% 0.85/1.02 ((~hskp29) | c2_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2522, 2519])).
% 0.85/1.02 tff(2524,plain,
% 0.85/1.02 ((~hskp29) | c2_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2523, 2519])).
% 0.85/1.02 tff(2525,plain,
% 0.85/1.02 ((~hskp29) | c2_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2524, 2519])).
% 0.85/1.02 tff(2526,plain,
% 0.85/1.02 (c2_1(a849)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2525, 2518])).
% 0.85/1.02 tff(2527,plain,
% 0.85/1.02 (((~hskp29) | c1_1(a849)) <=> ((~hskp29) | c1_1(a849))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2528,axiom,((~hskp29) | c1_1(a849)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.85/1.02 tff(2529,plain,
% 0.85/1.02 ((~hskp29) | c1_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2528, 2527])).
% 0.85/1.02 tff(2530,plain,
% 0.85/1.02 ((~hskp29) | c1_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2529, 2527])).
% 0.85/1.02 tff(2531,plain,
% 0.85/1.02 ((~hskp29) | c1_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2530, 2527])).
% 0.85/1.02 tff(2532,plain,
% 0.85/1.02 ((~hskp29) | c1_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2531, 2527])).
% 0.85/1.02 tff(2533,plain,
% 0.85/1.02 ((~hskp29) | c1_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2532, 2527])).
% 0.85/1.02 tff(2534,plain,
% 0.85/1.02 (c1_1(a849)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2533, 2518])).
% 0.85/1.02 tff(2535,plain,
% 0.85/1.02 (((~hskp29) | c0_1(a849)) <=> ((~hskp29) | c0_1(a849))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2536,axiom,((~hskp29) | c0_1(a849)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.85/1.02 tff(2537,plain,
% 0.85/1.02 ((~hskp29) | c0_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 0.85/1.02 tff(2538,plain,
% 0.85/1.02 ((~hskp29) | c0_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2537, 2535])).
% 0.85/1.02 tff(2539,plain,
% 0.85/1.02 ((~hskp29) | c0_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2538, 2535])).
% 0.85/1.02 tff(2540,plain,
% 0.85/1.02 ((~hskp29) | c0_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2539, 2535])).
% 0.85/1.02 tff(2541,plain,
% 0.85/1.02 ((~hskp29) | c0_1(a849)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2540, 2535])).
% 0.85/1.02 tff(2542,plain,
% 0.85/1.02 (c0_1(a849)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2541, 2518])).
% 0.85/1.02 tff(2543,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | c0_1(a844) | (~c1_1(a849)) | (~c0_1(a849)) | (~c2_1(a849)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | c0_1(a844) | (~c1_1(a849)) | (~c0_1(a849)) | (~c2_1(a849)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2544,plain,
% 0.85/1.02 ((hskp2 | (~ndr1_0) | (~c2_1(a849)) | (~c1_1(a849)) | (~c0_1(a849)) | c2_1(a844) | c0_1(a844) | (~c3_1(a844))) <=> (hskp2 | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | c0_1(a844) | (~c1_1(a849)) | (~c0_1(a849)) | (~c2_1(a849)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2545,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a849)) | (~c1_1(a849)) | (~c0_1(a849)) | c2_1(a844) | c0_1(a844) | (~c3_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | c0_1(a844) | (~c1_1(a849)) | (~c0_1(a849)) | (~c2_1(a849))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[2544])).
% 0.85/1.02 tff(2546,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a849)) | (~c1_1(a849)) | (~c0_1(a849)) | c2_1(a844) | c0_1(a844) | (~c3_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | c0_1(a844) | (~c1_1(a849)) | (~c0_1(a849)) | (~c2_1(a849)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[2545, 2543])).
% 0.85/1.02 tff(2547,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a849)) | (~c1_1(a849)) | (~c0_1(a849)) | c2_1(a844) | c0_1(a844) | (~c3_1(a844)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(2548,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a844) | (~ndr1_0) | (~c3_1(a844)) | c0_1(a844) | (~c1_1(a849)) | (~c0_1(a849)) | (~c2_1(a849))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2547, 2546])).
% 0.85/1.02 tff(2549,plain,
% 0.85/1.02 (hskp2 | c0_1(a844)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2548, 114, 2542, 2534, 2526, 2501, 2492, 1345])).
% 0.85/1.02 tff(2550,plain,
% 0.85/1.02 (hskp2),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2549, 2500])).
% 0.85/1.02 tff(2551,plain,
% 0.85/1.02 (~c2_1(a830)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[53, 2550])).
% 0.85/1.02 tff(2552,plain,
% 0.85/1.02 (~c1_1(a830)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[59, 2550])).
% 0.85/1.02 tff(2553,plain,
% 0.85/1.02 (c0_1(a830)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[74, 2550])).
% 0.85/1.02 tff(2554,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a859)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a859)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2555,plain,
% 0.85/1.02 ((hskp17 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830))) <=> (hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a859)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2556,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a859))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[2555])).
% 0.85/1.02 tff(2557,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a859)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[2556, 2554])).
% 0.85/1.02 tff(2558,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a859) | (~c1_1(a859)) | (~c0_1(a859)) | c2_1(a830) | c1_1(a830) | (~c0_1(a830)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(2559,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | (~c1_1(a859)) | c3_1(a859) | c1_1(a830) | c2_1(a830) | (~ndr1_0) | (~c0_1(a830)) | (~c0_1(a859))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2558, 2557])).
% 0.85/1.02 tff(2560,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2559, 114, 2249, 2418, 2553, 2248, 12, 2552, 2551, 10])).
% 0.85/1.02 tff(2561,plain,(c3_1(a859)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(2562,plain,
% 0.85/1.02 (~hskp17),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[301, 2561])).
% 0.85/1.02 tff(2563,plain,
% 0.85/1.02 (hskp4 | hskp2),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1758, 2562])).
% 0.85/1.02 tff(2564,plain,
% 0.85/1.02 (hskp2),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2563, 11])).
% 0.85/1.02 tff(2565,plain,
% 0.85/1.02 (~c2_1(a830)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[53, 2564])).
% 0.85/1.02 tff(2566,plain,
% 0.85/1.02 (~c1_1(a830)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[59, 2564])).
% 0.85/1.02 tff(2567,plain,
% 0.85/1.02 (c0_1(a830)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[74, 2564])).
% 0.85/1.02 tff(2568,plain,
% 0.85/1.02 (~c1_1(a833)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[120, 114, 2562, 1667, 2567, 1665, 2566, 2565, 10])).
% 0.85/1.02 tff(2569,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a858) | c2_1(a858) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | c3_1(a858))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a858) | c2_1(a858) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | c3_1(a858))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2570,plain,
% 0.85/1.02 (((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c3_1(a858) | c2_1(a858) | c1_1(a858)) <=> (c1_1(a858) | c2_1(a858) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | c3_1(a858))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2571,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c3_1(a858) | c2_1(a858) | c1_1(a858))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a858) | c2_1(a858) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | c3_1(a858)))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[2570])).
% 0.85/1.02 tff(2572,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c3_1(a858) | c2_1(a858) | c1_1(a858))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a858) | c2_1(a858) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | c3_1(a858))),
% 0.85/1.02 inference(transitivity,[status(thm)],[2571, 2569])).
% 0.85/1.02 tff(2573,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | (~c2_1(a833)) | (~c0_1(a833)) | c3_1(a858) | c2_1(a858) | c1_1(a858))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(2574,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a858) | c2_1(a858) | c3_1(a833) | (~ndr1_0) | (~c2_1(a833)) | (~c0_1(a833)) | c1_1(a833) | c3_1(a858)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2573, 2572])).
% 0.85/1.02 tff(2575,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2574, 114, 1667, 1666, 1639, 1633, 1665, 22, 1674, 2568])).
% 0.85/1.02 tff(2576,plain,(hskp4), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(2577,plain,
% 0.85/1.02 (hskp5 | (~hskp4)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2331, 2562])).
% 0.85/1.02 tff(2578,plain,
% 0.85/1.02 (hskp5),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2577, 2576])).
% 0.85/1.02 tff(2579,plain,
% 0.85/1.02 (c0_1(a833)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[82, 2578])).
% 0.85/1.02 tff(2580,plain,
% 0.85/1.02 (~c2_1(a832)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[396, 2576])).
% 0.85/1.02 tff(2581,plain,
% 0.85/1.02 (c2_1(a833)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[138, 2578])).
% 0.85/1.02 tff(2582,plain,
% 0.85/1.02 (~c3_1(a832)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[390, 2576])).
% 0.85/1.02 tff(2583,plain,
% 0.85/1.02 (~c1_1(a832)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[402, 2576])).
% 0.85/1.02 tff(2584,plain,
% 0.85/1.02 (~c3_1(a833)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[66, 2578])).
% 0.85/1.02 tff(2585,plain,
% 0.85/1.02 (c1_1(a833)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2340, 2584, 2583, 2582, 2581, 2580, 2579])).
% 0.85/1.02 tff(2586,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c3_1(a833) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c0_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c3_1(a833) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c0_1(a833)) | (~c1_1(a833)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2587,plain,
% 0.85/1.02 ((hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a832) | c1_1(a832) | (~c0_1(a832))) <=> (hskp17 | c3_1(a833) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c0_1(a833)) | (~c1_1(a833)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2588,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a832) | c1_1(a832) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c3_1(a833) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c0_1(a833)) | (~c1_1(a833))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[2587])).
% 0.85/1.02 tff(2589,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a832) | c1_1(a832) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c3_1(a833) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c0_1(a833)) | (~c1_1(a833)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[2588, 2586])).
% 0.85/1.02 tff(2590,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a832) | c1_1(a832) | (~c0_1(a832)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(2591,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c3_1(a833) | c1_1(a832) | c2_1(a832) | (~ndr1_0) | (~c0_1(a832)) | (~c0_1(a833)) | (~c1_1(a833))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2590, 2589])).
% 0.85/1.02 tff(2592,plain,
% 0.85/1.02 (~c0_1(a832)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2591, 114, 2562, 2579, 2584, 2583, 2580, 10, 2585])).
% 0.85/1.02 tff(2593,plain,
% 0.85/1.02 (hskp11 | c0_1(a832)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2489, 114, 2579, 2581, 2580, 2582, 1222, 2585])).
% 0.85/1.02 tff(2594,plain,
% 0.85/1.02 (hskp11),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2593, 2592])).
% 0.85/1.02 tff(2595,plain,
% 0.85/1.02 (~c2_1(a844)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[437, 2594])).
% 0.85/1.02 tff(2596,plain,
% 0.85/1.02 (~c1_1(a844)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[443, 2594])).
% 0.85/1.02 tff(2597,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a844) | c2_1(a844) | c3_1(a833) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)) | (~c0_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a844) | c2_1(a844) | c3_1(a833) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)) | (~c0_1(a844)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2598,plain,
% 0.85/1.02 ((hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a844) | c1_1(a844) | (~c0_1(a844))) <=> (hskp17 | c1_1(a844) | c2_1(a844) | c3_1(a833) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)) | (~c0_1(a844)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2599,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a844) | c1_1(a844) | (~c0_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a844) | c2_1(a844) | c3_1(a833) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)) | (~c0_1(a844))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[2598])).
% 0.85/1.02 tff(2600,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a844) | c1_1(a844) | (~c0_1(a844)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a844) | c2_1(a844) | c3_1(a833) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)) | (~c0_1(a844)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[2599, 2597])).
% 0.85/1.02 tff(2601,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a844) | c1_1(a844) | (~c0_1(a844)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(2602,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a844) | c2_1(a844) | c3_1(a833) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)) | (~c0_1(a844))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2601, 2600])).
% 0.85/1.02 tff(2603,plain,
% 0.85/1.02 (~c0_1(a844)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2602, 114, 2562, 2579, 2596, 2595, 2584, 10, 2585])).
% 0.85/1.02 tff(2604,plain,
% 0.85/1.02 (c3_1(a844)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[451, 2594])).
% 0.85/1.02 tff(2605,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp29 | c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp29 | c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2606,plain,
% 0.85/1.02 ((hskp29 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a832) | c1_1(a832) | c3_1(a832)) <=> (hskp29 | c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(2607,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp29 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a832) | c1_1(a832) | c3_1(a832))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp29 | c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[2606])).
% 0.85/1.02 tff(2608,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp29 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a832) | c1_1(a832) | c3_1(a832))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp29 | c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[2607, 2605])).
% 0.85/1.02 tff(2609,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp29 | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a832) | c1_1(a832) | c3_1(a832))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(2610,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp29 | c3_1(a833) | c1_1(a832) | c2_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a833)) | (~c1_1(a833))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[2609, 2608])).
% 0.85/1.03 tff(2611,plain,
% 0.85/1.03 (hskp29),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2610, 114, 2579, 2584, 2583, 2580, 2582, 2511, 2585])).
% 0.85/1.03 tff(2612,plain,
% 0.85/1.03 (c2_1(a849)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2525, 2611])).
% 0.85/1.03 tff(2613,plain,
% 0.85/1.03 (c1_1(a849)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2533, 2611])).
% 0.85/1.03 tff(2614,plain,
% 0.85/1.03 (c0_1(a849)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2541, 2611])).
% 0.85/1.03 tff(2615,plain,
% 0.85/1.03 (hskp2 | c0_1(a844)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2548, 114, 2614, 2613, 2612, 2604, 2595, 1345])).
% 0.85/1.03 tff(2616,plain,
% 0.85/1.03 (hskp2),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[2615, 2603])).
% 0.85/1.03 tff(2617,plain,
% 0.85/1.03 (~c2_1(a830)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[53, 2616])).
% 0.85/1.03 tff(2618,plain,
% 0.85/1.03 (~c1_1(a830)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[59, 2616])).
% 0.85/1.03 tff(2619,plain,
% 0.85/1.03 (c0_1(a830)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[74, 2616])).
% 0.85/1.03 tff(2620,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[120, 114, 2562, 2579, 2619, 2584, 2618, 2617, 10, 2585])).
% 0.85/1.03 % SZS output end Proof
% 0.85/1.03 % E exiting
%------------------------------------------------------------------------------