%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN470-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:39:14 AM UTC 2025
% Result : Unsatisfiable 0.97s 1.15s
% Output : Proof 1.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN470-1 : TPTP v9.0.0. Released v2.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:40:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.97/1.15 % SZS status Unsatisfiable
% 0.97/1.15 % SZS output start Proof
% 0.97/1.15 tff(c2_1_type, type, (
% 0.97/1.15 c2_1: $i > $o)).
% 0.97/1.15 tff(a496_type, type, (
% 0.97/1.15 a496: $i)).
% 0.97/1.15 tff(hskp2_type, type, (
% 0.97/1.15 hskp2: $o)).
% 0.97/1.15 tff(a509_type, type, (
% 0.97/1.15 a509: $i)).
% 0.97/1.15 tff(hskp10_type, type, (
% 0.97/1.15 hskp10: $o)).
% 0.97/1.15 tff(a528_type, type, (
% 0.97/1.15 a528: $i)).
% 0.97/1.15 tff(a510_type, type, (
% 0.97/1.15 a510: $i)).
% 0.97/1.15 tff(hskp11_type, type, (
% 0.97/1.15 hskp11: $o)).
% 0.97/1.15 tff(c0_1_type, type, (
% 0.97/1.15 c0_1: $i > $o)).
% 0.97/1.15 tff(c3_1_type, type, (
% 0.97/1.15 c3_1: $i > $o)).
% 0.97/1.15 tff(ndr1_0_type, type, (
% 0.97/1.15 ndr1_0: $o)).
% 0.97/1.15 tff(a559_type, type, (
% 0.97/1.15 a559: $i)).
% 0.97/1.15 tff(hskp26_type, type, (
% 0.97/1.15 hskp26: $o)).
% 0.97/1.15 tff(c1_1_type, type, (
% 0.97/1.15 c1_1: $i > $o)).
% 0.97/1.15 tff(a494_type, type, (
% 0.97/1.15 a494: $i)).
% 0.97/1.15 tff(hskp0_type, type, (
% 0.97/1.15 hskp0: $o)).
% 0.97/1.15 tff(a520_type, type, (
% 0.97/1.15 a520: $i)).
% 0.97/1.15 tff(hskp22_type, type, (
% 0.97/1.15 hskp22: $o)).
% 0.97/1.15 tff(hskp15_type, type, (
% 0.97/1.15 hskp15: $o)).
% 0.97/1.15 tff(a532_type, type, (
% 0.97/1.15 a532: $i)).
% 0.97/1.15 tff(hskp17_type, type, (
% 0.97/1.15 hskp17: $o)).
% 0.97/1.15 tff(a540_type, type, (
% 0.97/1.15 a540: $i)).
% 0.97/1.15 tff(hskp27_type, type, (
% 0.97/1.15 hskp27: $o)).
% 0.97/1.15 tff(a568_type, type, (
% 0.97/1.15 a568: $i)).
% 0.97/1.15 tff(hskp7_type, type, (
% 0.97/1.15 hskp7: $o)).
% 0.97/1.15 tff(a502_type, type, (
% 0.97/1.15 a502: $i)).
% 0.97/1.15 tff(a500_type, type, (
% 0.97/1.15 a500: $i)).
% 0.97/1.15 tff(hskp28_type, type, (
% 0.97/1.15 hskp28: $o)).
% 0.97/1.15 tff(a498_type, type, (
% 0.97/1.15 a498: $i)).
% 0.97/1.15 tff(a504_type, type, (
% 0.97/1.15 a504: $i)).
% 0.97/1.15 tff(hskp29_type, type, (
% 0.97/1.15 hskp29: $o)).
% 0.97/1.15 tff(hskp4_type, type, (
% 0.97/1.15 hskp4: $o)).
% 0.97/1.15 tff(hskp13_type, type, (
% 0.97/1.15 hskp13: $o)).
% 0.97/1.15 tff(a507_type, type, (
% 0.97/1.15 a507: $i)).
% 0.97/1.15 tff(a495_type, type, (
% 0.97/1.15 a495: $i)).
% 0.97/1.15 tff(hskp1_type, type, (
% 0.97/1.15 hskp1: $o)).
% 0.97/1.15 tff(a536_type, type, (
% 0.97/1.15 a536: $i)).
% 0.97/1.15 tff(hskp20_type, type, (
% 0.97/1.15 hskp20: $o)).
% 0.97/1.15 tff(a514_type, type, (
% 0.97/1.15 a514: $i)).
% 0.97/1.15 tff(hskp12_type, type, (
% 0.97/1.15 hskp12: $o)).
% 0.97/1.15 tff(a527_type, type, (
% 0.97/1.15 a527: $i)).
% 0.97/1.15 tff(hskp14_type, type, (
% 0.97/1.15 hskp14: $o)).
% 0.97/1.15 tff(hskp6_type, type, (
% 0.97/1.15 hskp6: $o)).
% 0.97/1.15 tff(a501_type, type, (
% 0.97/1.15 a501: $i)).
% 0.97/1.15 tff(a522_type, type, (
% 0.97/1.15 a522: $i)).
% 0.97/1.15 tff(hskp31_type, type, (
% 0.97/1.15 hskp31: $o)).
% 0.97/1.15 tff(hskp9_type, type, (
% 0.97/1.15 hskp9: $o)).
% 0.97/1.15 tff(a505_type, type, (
% 0.97/1.15 a505: $i)).
% 0.97/1.15 tff(hskp8_type, type, (
% 0.97/1.15 hskp8: $o)).
% 0.97/1.15 tff(a499_type, type, (
% 0.97/1.15 a499: $i)).
% 0.97/1.15 tff(hskp5_type, type, (
% 0.97/1.15 hskp5: $o)).
% 0.97/1.15 tff(a554_type, type, (
% 0.97/1.15 a554: $i)).
% 0.97/1.15 tff(hskp24_type, type, (
% 0.97/1.15 hskp24: $o)).
% 0.97/1.15 tff(a541_type, type, (
% 0.97/1.15 a541: $i)).
% 0.97/1.15 tff(hskp23_type, type, (
% 0.97/1.15 hskp23: $o)).
% 0.97/1.15 tff(a538_type, type, (
% 0.97/1.15 a538: $i)).
% 0.97/1.15 tff(hskp21_type, type, (
% 0.97/1.15 hskp21: $o)).
% 0.97/1.15 tff(a497_type, type, (
% 0.97/1.15 a497: $i)).
% 0.97/1.15 tff(hskp3_type, type, (
% 0.97/1.15 hskp3: $o)).
% 0.97/1.15 tff(a534_type, type, (
% 0.97/1.15 a534: $i)).
% 0.97/1.15 tff(hskp19_type, type, (
% 0.97/1.15 hskp19: $o)).
% 0.97/1.15 tff(a533_type, type, (
% 0.97/1.15 a533: $i)).
% 0.97/1.15 tff(hskp18_type, type, (
% 0.97/1.15 hskp18: $o)).
% 0.97/1.15 tff(a558_type, type, (
% 0.97/1.15 a558: $i)).
% 0.97/1.15 tff(hskp25_type, type, (
% 0.97/1.15 hskp25: $o)).
% 0.97/1.15 tff(1,plain,
% 0.97/1.15 (^[U: $i] : refl((hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(2,plain,
% 0.97/1.15 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[1])).
% 0.97/1.15 tff(3,plain,
% 0.97/1.15 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4,plain,
% 0.97/1.15 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp11) <=> ((hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp11))), rewrite(((hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp11) <=> (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp11) <=> (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(5,plain,
% 0.97/1.15 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp11) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[4])).
% 0.97/1.15 tff(6,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 0.97/1.15 tff(7,plain,
% 0.97/1.15 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.97/1.15 tff(8,plain,
% 0.97/1.15 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.97/1.15 tff(9,plain,(
% 0.97/1.15 ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.97/1.15 inference(skolemize,[status(sab)],[8])).
% 0.97/1.15 tff(10,plain,
% 0.97/1.15 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.97/1.15 tff(11,assumption,(~hskp10), introduced(assumption)).
% 0.97/1.15 tff(12,plain,
% 0.97/1.15 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W)))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(13,plain,
% 0.97/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[12])).
% 0.97/1.15 tff(14,plain,
% 0.97/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(15,plain,
% 0.97/1.15 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(16,plain,
% 0.97/1.15 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[15])).
% 0.97/1.15 tff(17,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 0.97/1.15 tff(18,plain,
% 0.97/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.97/1.15 tff(19,plain,
% 0.97/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.97/1.15 tff(20,plain,(
% 0.97/1.15 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 0.97/1.15 inference(skolemize,[status(sab)],[19])).
% 0.97/1.15 tff(21,plain,
% 0.97/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.97/1.15 tff(22,plain,
% 0.97/1.15 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(23,plain,
% 0.97/1.15 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[22])).
% 0.97/1.15 tff(24,plain,
% 0.97/1.15 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(25,plain,
% 0.97/1.15 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | 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)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | 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)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(26,plain,
% 0.97/1.15 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[25])).
% 0.97/1.15 tff(27,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 0.97/1.15 tff(28,plain,
% 0.97/1.15 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.97/1.15 tff(29,plain,
% 0.97/1.15 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.97/1.15 tff(30,plain,(
% 0.97/1.15 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.97/1.15 inference(skolemize,[status(sab)],[29])).
% 0.97/1.15 tff(31,plain,
% 0.97/1.15 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.97/1.15 tff(32,assumption,(~hskp26), introduced(assumption)).
% 0.97/1.15 tff(33,plain,
% 0.97/1.15 (^[U: $i] : refl((hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(34,plain,
% 0.97/1.15 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[33])).
% 0.97/1.15 tff(35,plain,
% 0.97/1.15 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(36,plain,
% 0.97/1.15 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp10) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp10) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(37,plain,
% 0.97/1.15 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp10) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[36])).
% 0.97/1.15 tff(38,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.97/1.15 tff(39,plain,
% 0.97/1.15 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.97/1.15 tff(40,plain,
% 0.97/1.15 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.97/1.15 tff(41,plain,(
% 0.97/1.15 ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.97/1.15 inference(skolemize,[status(sab)],[40])).
% 0.97/1.15 tff(42,plain,
% 0.97/1.15 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.97/1.15 tff(43,assumption,(~hskp15), introduced(assumption)).
% 0.97/1.15 tff(44,plain,
% 0.97/1.15 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(45,plain,
% 0.97/1.15 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[44])).
% 0.97/1.15 tff(46,plain,
% 0.97/1.15 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(47,plain,
% 0.97/1.15 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 0.97/1.15 inference(bind,[status(th)],[])).
% 0.97/1.15 tff(48,plain,
% 0.97/1.15 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.97/1.15 inference(quant_intro,[status(thm)],[47])).
% 0.97/1.15 tff(49,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 0.97/1.16 tff(50,plain,
% 0.97/1.16 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.97/1.16 tff(51,plain,
% 0.97/1.16 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.97/1.16 tff(52,plain,(
% 0.97/1.16 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.97/1.16 inference(skolemize,[status(sab)],[51])).
% 0.97/1.16 tff(53,plain,
% 0.97/1.16 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.97/1.16 tff(54,assumption,(hskp11), introduced(assumption)).
% 0.97/1.16 tff(55,plain,
% 0.97/1.16 (((~hskp11) | (~c2_1(a510))) <=> ((~hskp11) | (~c2_1(a510)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(56,plain,
% 0.97/1.16 (((~c2_1(a510)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a510)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(57,axiom,((~c2_1(a510)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.97/1.16 tff(58,plain,
% 0.97/1.16 ((~hskp11) | (~c2_1(a510))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.97/1.16 tff(59,plain,
% 0.97/1.16 ((~hskp11) | (~c2_1(a510))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.97/1.16 tff(60,plain,
% 0.97/1.16 (~c2_1(a510)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[59, 54])).
% 0.97/1.16 tff(61,plain,
% 0.97/1.16 (((~hskp11) | (~c1_1(a510))) <=> ((~hskp11) | (~c1_1(a510)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(62,plain,
% 0.97/1.16 (((~c1_1(a510)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a510)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(63,axiom,((~c1_1(a510)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.97/1.16 tff(64,plain,
% 0.97/1.16 ((~hskp11) | (~c1_1(a510))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.97/1.16 tff(65,plain,
% 0.97/1.16 ((~hskp11) | (~c1_1(a510))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[64, 61])).
% 0.97/1.16 tff(66,plain,
% 0.97/1.16 (~c1_1(a510)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[65, 54])).
% 0.97/1.16 tff(67,plain,
% 0.97/1.16 (((~hskp11) | c0_1(a510)) <=> ((~hskp11) | c0_1(a510))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(68,axiom,((~hskp11) | c0_1(a510)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.97/1.16 tff(69,plain,
% 0.97/1.16 ((~hskp11) | c0_1(a510)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.97/1.16 tff(70,plain,
% 0.97/1.16 ((~hskp11) | c0_1(a510)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[69, 67])).
% 0.97/1.16 tff(71,plain,
% 0.97/1.16 ((~hskp11) | c0_1(a510)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[70, 67])).
% 0.97/1.16 tff(72,plain,
% 0.97/1.16 ((~hskp11) | c0_1(a510)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.97/1.16 tff(73,plain,
% 0.97/1.16 ((~hskp11) | c0_1(a510)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[72, 67])).
% 0.97/1.16 tff(74,plain,
% 0.97/1.16 (c0_1(a510)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[73, 54])).
% 0.97/1.16 tff(75,assumption,(~ndr1_0), introduced(assumption)).
% 0.97/1.16 tff(76,plain,
% 0.97/1.16 ((ndr1_0 | (~hskp10)) <=> (ndr1_0 | (~hskp10))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(77,plain,
% 0.97/1.16 (((~hskp10) | ndr1_0) <=> (ndr1_0 | (~hskp10))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(78,axiom,((~hskp10) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause22')).
% 0.97/1.16 tff(79,plain,
% 0.97/1.16 (ndr1_0 | (~hskp10)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.97/1.16 tff(80,plain,
% 0.97/1.16 (ndr1_0 | (~hskp10)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.97/1.16 tff(81,plain,
% 0.97/1.16 (~hskp10),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[80, 75])).
% 0.97/1.16 tff(82,plain,
% 0.97/1.16 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(83,plain,
% 0.97/1.16 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(84,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause5')).
% 0.97/1.16 tff(85,plain,
% 0.97/1.16 (ndr1_0 | (~hskp27)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.97/1.16 tff(86,plain,
% 0.97/1.16 (ndr1_0 | (~hskp27)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[85, 82])).
% 0.97/1.16 tff(87,plain,
% 0.97/1.16 (~hskp27),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[86, 75])).
% 0.97/1.16 tff(88,plain,
% 0.97/1.16 ((ndr1_0 | (~hskp26)) <=> (ndr1_0 | (~hskp26))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(89,plain,
% 0.97/1.16 (((~hskp26) | ndr1_0) <=> (ndr1_0 | (~hskp26))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(90,axiom,((~hskp26) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause6')).
% 0.97/1.16 tff(91,plain,
% 0.97/1.16 (ndr1_0 | (~hskp26)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.97/1.16 tff(92,plain,
% 0.97/1.16 (ndr1_0 | (~hskp26)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[91, 88])).
% 0.97/1.16 tff(93,plain,
% 0.97/1.16 (~hskp26),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[92, 75])).
% 0.97/1.16 tff(94,plain,
% 0.97/1.16 ((hskp27 | hskp26 | hskp10) <=> (hskp27 | hskp26 | hskp10)),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(95,plain,
% 0.97/1.16 (((hskp27 | hskp10) | hskp26) <=> (hskp27 | hskp26 | hskp10)),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(96,plain,
% 0.97/1.16 ((hskp27 | hskp10) <=> (hskp27 | hskp10)),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(97,plain,
% 0.97/1.16 (((hskp27 | hskp10) | hskp26) <=> ((hskp27 | hskp10) | hskp26)),
% 0.97/1.16 inference(monotonicity,[status(thm)],[96])).
% 0.97/1.16 tff(98,plain,
% 0.97/1.16 (((hskp27 | hskp10) | hskp26) <=> (hskp27 | hskp26 | hskp10)),
% 0.97/1.16 inference(transitivity,[status(thm)],[97, 95])).
% 0.97/1.16 tff(99,axiom,((hskp27 | hskp10) | hskp26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 0.97/1.16 tff(100,plain,
% 0.97/1.16 (hskp27 | hskp26 | hskp10),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.97/1.16 tff(101,plain,
% 0.97/1.16 (hskp27 | hskp26 | hskp10),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[100, 94])).
% 0.97/1.16 tff(102,plain,
% 0.97/1.16 (hskp27 | hskp26 | hskp10),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.97/1.16 tff(103,plain,
% 0.97/1.16 (hskp27 | hskp26 | hskp10),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[102, 94])).
% 0.97/1.16 tff(104,plain,
% 0.97/1.16 (hskp27 | hskp26 | hskp10),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[103, 94])).
% 0.97/1.16 tff(105,plain,
% 0.97/1.16 ($false),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[104, 93, 87, 81])).
% 0.97/1.16 tff(106,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.97/1.16 tff(107,plain,
% 0.97/1.16 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | c2_1(a510) | (~ndr1_0) | (~c3_1(a510)) | (~c0_1(a510)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a510) | (~ndr1_0) | (~c3_1(a510)) | (~c0_1(a510)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(108,plain,
% 0.97/1.16 ((hskp15 | hskp10 | (~ndr1_0) | c2_1(a510) | (~c3_1(a510)) | (~c0_1(a510))) <=> (hskp15 | hskp10 | c2_1(a510) | (~ndr1_0) | (~c3_1(a510)) | (~c0_1(a510)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(109,plain,
% 0.97/1.16 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a510) | (~c3_1(a510)) | (~c0_1(a510)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | c2_1(a510) | (~ndr1_0) | (~c3_1(a510)) | (~c0_1(a510))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[108])).
% 0.97/1.16 tff(110,plain,
% 0.97/1.16 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a510) | (~c3_1(a510)) | (~c0_1(a510)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a510) | (~ndr1_0) | (~c3_1(a510)) | (~c0_1(a510)))),
% 0.97/1.16 inference(transitivity,[status(thm)],[109, 107])).
% 0.97/1.16 tff(111,plain,
% 0.97/1.16 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a510) | (~c3_1(a510)) | (~c0_1(a510)))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(112,plain,
% 0.97/1.16 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a510) | (~ndr1_0) | (~c3_1(a510)) | (~c0_1(a510))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.97/1.16 tff(113,plain,
% 0.97/1.16 (~c3_1(a510)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[112, 106, 43, 11, 74, 60, 42])).
% 0.97/1.16 tff(114,plain,
% 0.97/1.16 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | c3_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | c3_1(a510) | (~c0_1(a510)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(115,plain,
% 0.97/1.16 ((hskp22 | (~ndr1_0) | c3_1(a510) | c2_1(a510) | (~c0_1(a510)) | c1_1(a510) | c3_1(a510) | (~c0_1(a510))) <=> (hskp22 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | c3_1(a510) | (~c0_1(a510)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(116,plain,
% 0.97/1.16 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a510) | c2_1(a510) | (~c0_1(a510)) | c1_1(a510) | c3_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | c3_1(a510) | (~c0_1(a510))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[115])).
% 0.97/1.16 tff(117,plain,
% 0.97/1.16 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a510) | c2_1(a510) | (~c0_1(a510)) | c1_1(a510) | c3_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | c3_1(a510) | (~c0_1(a510)))),
% 0.97/1.16 inference(transitivity,[status(thm)],[116, 114])).
% 0.97/1.16 tff(118,plain,
% 0.97/1.16 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a510) | c2_1(a510) | (~c0_1(a510)) | c1_1(a510) | c3_1(a510) | (~c0_1(a510)))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(119,plain,
% 0.97/1.16 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | c3_1(a510) | (~c0_1(a510))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.97/1.16 tff(120,plain,
% 0.97/1.16 (hskp22),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[119, 106, 74, 66, 60, 31, 113])).
% 0.97/1.16 tff(121,plain,
% 0.97/1.16 (((~hskp22) | (~c0_1(a540))) <=> ((~hskp22) | (~c0_1(a540)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(122,plain,
% 0.97/1.16 (((~c0_1(a540)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a540)))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(123,axiom,((~c0_1(a540)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 0.97/1.16 tff(124,plain,
% 0.97/1.16 ((~hskp22) | (~c0_1(a540))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.97/1.16 tff(125,plain,
% 0.97/1.16 ((~hskp22) | (~c0_1(a540))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[124, 121])).
% 0.97/1.16 tff(126,plain,
% 0.97/1.16 (~c0_1(a540)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[125, 120])).
% 0.97/1.16 tff(127,plain,
% 0.97/1.16 (((~hskp22) | c3_1(a540)) <=> ((~hskp22) | c3_1(a540))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(128,axiom,((~hskp22) | c3_1(a540)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.97/1.16 tff(129,plain,
% 0.97/1.16 ((~hskp22) | c3_1(a540)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.97/1.16 tff(130,plain,
% 0.97/1.16 ((~hskp22) | c3_1(a540)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[129, 127])).
% 0.97/1.16 tff(131,plain,
% 0.97/1.16 ((~hskp22) | c3_1(a540)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[130, 127])).
% 0.97/1.16 tff(132,plain,
% 0.97/1.16 ((~hskp22) | c3_1(a540)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.97/1.16 tff(133,plain,
% 0.97/1.16 ((~hskp22) | c3_1(a540)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[132, 127])).
% 0.97/1.16 tff(134,plain,
% 0.97/1.16 (c3_1(a540)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[133, 120])).
% 0.97/1.16 tff(135,plain,
% 0.97/1.16 (((~hskp22) | c1_1(a540)) <=> ((~hskp22) | c1_1(a540))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(136,axiom,((~hskp22) | c1_1(a540)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.97/1.16 tff(137,plain,
% 0.97/1.16 ((~hskp22) | c1_1(a540)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.97/1.16 tff(138,plain,
% 0.97/1.16 ((~hskp22) | c1_1(a540)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[137, 135])).
% 1.00/1.16 tff(139,plain,
% 1.00/1.16 ((~hskp22) | c1_1(a540)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[138, 135])).
% 1.00/1.16 tff(140,plain,
% 1.00/1.16 ((~hskp22) | c1_1(a540)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[139, 135])).
% 1.00/1.16 tff(141,plain,
% 1.00/1.16 ((~hskp22) | c1_1(a540)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[140, 135])).
% 1.00/1.16 tff(142,plain,
% 1.00/1.16 (c1_1(a540)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[141, 120])).
% 1.00/1.16 tff(143,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a540) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a540) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(144,plain,
% 1.00/1.16 ((hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540))) <=> (hskp10 | c0_1(a540) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(145,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a540) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c3_1(a540)) | (~c1_1(a540))))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[144])).
% 1.00/1.16 tff(146,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a540) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.00/1.16 inference(transitivity,[status(thm)],[145, 143])).
% 1.00/1.16 tff(147,plain,
% 1.00/1.16 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(148,plain,
% 1.00/1.16 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a540) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c3_1(a540)) | (~c1_1(a540))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.00/1.16 tff(149,plain,
% 1.00/1.16 ($false),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[148, 106, 11, 142, 134, 74, 126, 66, 60, 53])).
% 1.00/1.16 tff(150,plain,((~hskp11) | hskp10 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.00/1.16 tff(151,plain,
% 1.00/1.16 (~hskp11),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[150, 43, 11])).
% 1.00/1.16 tff(152,plain,
% 1.00/1.16 ((hskp26 | hskp17 | hskp11) <=> (hskp26 | hskp17 | hskp11)),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(153,plain,
% 1.00/1.16 (((hskp11 | hskp17) | hskp26) <=> (hskp26 | hskp17 | hskp11)),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(154,axiom,((hskp11 | hskp17) | hskp26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.00/1.16 tff(155,plain,
% 1.00/1.16 (hskp26 | hskp17 | hskp11),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[154, 153])).
% 1.00/1.16 tff(156,plain,
% 1.00/1.16 (hskp26 | hskp17 | hskp11),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[155, 152])).
% 1.00/1.16 tff(157,plain,
% 1.00/1.16 (hskp26 | hskp17 | hskp11),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[156, 152])).
% 1.00/1.16 tff(158,plain,
% 1.00/1.16 (hskp26 | hskp17 | hskp11),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[157, 152])).
% 1.00/1.16 tff(159,plain,
% 1.00/1.16 (hskp26 | hskp17 | hskp11),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[158, 152])).
% 1.00/1.16 tff(160,plain,
% 1.00/1.16 (hskp17),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[159, 151, 32])).
% 1.00/1.16 tff(161,plain,
% 1.00/1.16 (((~hskp17) | (~c2_1(a532))) <=> ((~hskp17) | (~c2_1(a532)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(162,plain,
% 1.00/1.16 (((~c2_1(a532)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a532)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(163,axiom,((~c2_1(a532)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.00/1.16 tff(164,plain,
% 1.00/1.16 ((~hskp17) | (~c2_1(a532))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.00/1.16 tff(165,plain,
% 1.00/1.16 ((~hskp17) | (~c2_1(a532))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[164, 161])).
% 1.00/1.16 tff(166,plain,
% 1.00/1.16 (~c2_1(a532)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[165, 160])).
% 1.00/1.16 tff(167,plain,
% 1.00/1.16 (((~hskp17) | c3_1(a532)) <=> ((~hskp17) | c3_1(a532))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(168,axiom,((~hskp17) | c3_1(a532)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.00/1.16 tff(169,plain,
% 1.00/1.16 ((~hskp17) | c3_1(a532)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[168, 167])).
% 1.00/1.16 tff(170,plain,
% 1.00/1.16 ((~hskp17) | c3_1(a532)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[169, 167])).
% 1.00/1.16 tff(171,plain,
% 1.00/1.16 ((~hskp17) | c3_1(a532)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[170, 167])).
% 1.00/1.16 tff(172,plain,
% 1.00/1.16 ((~hskp17) | c3_1(a532)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[171, 167])).
% 1.00/1.16 tff(173,plain,
% 1.00/1.16 ((~hskp17) | c3_1(a532)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[172, 167])).
% 1.00/1.16 tff(174,plain,
% 1.00/1.16 (c3_1(a532)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[173, 160])).
% 1.00/1.16 tff(175,plain,
% 1.00/1.16 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | c2_1(a532) | (~ndr1_0) | (~c3_1(a532)) | (~c0_1(a532)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a532) | (~ndr1_0) | (~c3_1(a532)) | (~c0_1(a532)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(176,plain,
% 1.00/1.16 ((hskp15 | hskp10 | (~ndr1_0) | c2_1(a532) | (~c3_1(a532)) | (~c0_1(a532))) <=> (hskp15 | hskp10 | c2_1(a532) | (~ndr1_0) | (~c3_1(a532)) | (~c0_1(a532)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(177,plain,
% 1.00/1.16 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a532) | (~c3_1(a532)) | (~c0_1(a532)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | c2_1(a532) | (~ndr1_0) | (~c3_1(a532)) | (~c0_1(a532))))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[176])).
% 1.00/1.16 tff(178,plain,
% 1.00/1.16 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a532) | (~c3_1(a532)) | (~c0_1(a532)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a532) | (~ndr1_0) | (~c3_1(a532)) | (~c0_1(a532)))),
% 1.00/1.16 inference(transitivity,[status(thm)],[177, 175])).
% 1.00/1.16 tff(179,plain,
% 1.00/1.16 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a532) | (~c3_1(a532)) | (~c0_1(a532)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(180,plain,
% 1.00/1.16 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a532) | (~ndr1_0) | (~c3_1(a532)) | (~c0_1(a532))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.00/1.16 tff(181,plain,
% 1.00/1.16 (~c0_1(a532)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[180, 106, 43, 11, 174, 166, 42])).
% 1.00/1.16 tff(182,plain,
% 1.00/1.16 (hskp27),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[104, 11, 32])).
% 1.00/1.16 tff(183,plain,
% 1.00/1.16 (((~hskp27) | c3_1(a568)) <=> ((~hskp27) | c3_1(a568))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(184,axiom,((~hskp27) | c3_1(a568)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.00/1.16 tff(185,plain,
% 1.00/1.16 ((~hskp27) | c3_1(a568)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.00/1.16 tff(186,plain,
% 1.00/1.16 ((~hskp27) | c3_1(a568)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[185, 183])).
% 1.00/1.16 tff(187,plain,
% 1.00/1.16 ((~hskp27) | c3_1(a568)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[186, 183])).
% 1.00/1.16 tff(188,plain,
% 1.00/1.16 ((~hskp27) | c3_1(a568)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[187, 183])).
% 1.00/1.16 tff(189,plain,
% 1.00/1.16 ((~hskp27) | c3_1(a568)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[188, 183])).
% 1.00/1.16 tff(190,plain,
% 1.00/1.16 (c3_1(a568)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[189, 182])).
% 1.00/1.16 tff(191,plain,
% 1.00/1.16 (((~hskp27) | c0_1(a568)) <=> ((~hskp27) | c0_1(a568))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(192,axiom,((~hskp27) | c0_1(a568)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 1.00/1.16 tff(193,plain,
% 1.00/1.16 ((~hskp27) | c0_1(a568)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[192, 191])).
% 1.00/1.16 tff(194,plain,
% 1.00/1.16 ((~hskp27) | c0_1(a568)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[193, 191])).
% 1.00/1.16 tff(195,plain,
% 1.00/1.16 ((~hskp27) | c0_1(a568)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[194, 191])).
% 1.00/1.16 tff(196,plain,
% 1.00/1.16 ((~hskp27) | c0_1(a568)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[195, 191])).
% 1.00/1.16 tff(197,plain,
% 1.00/1.16 ((~hskp27) | c0_1(a568)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[196, 191])).
% 1.00/1.16 tff(198,plain,
% 1.00/1.16 (c0_1(a568)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[197, 182])).
% 1.00/1.16 tff(199,plain,
% 1.00/1.16 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(200,plain,
% 1.00/1.16 ((hskp15 | hskp10 | (~ndr1_0) | c2_1(a568) | (~c3_1(a568)) | (~c0_1(a568))) <=> (hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(201,plain,
% 1.00/1.16 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a568) | (~c3_1(a568)) | (~c0_1(a568)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568)))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[200])).
% 1.00/1.16 tff(202,plain,
% 1.00/1.16 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a568) | (~c3_1(a568)) | (~c0_1(a568)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))),
% 1.00/1.16 inference(transitivity,[status(thm)],[201, 199])).
% 1.00/1.16 tff(203,plain,
% 1.00/1.16 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a568) | (~c3_1(a568)) | (~c0_1(a568)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(204,plain,
% 1.00/1.16 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[203, 202])).
% 1.00/1.16 tff(205,plain,
% 1.00/1.16 (hskp15 | c2_1(a568)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[204, 106, 11, 198, 190, 42])).
% 1.00/1.16 tff(206,plain,
% 1.00/1.16 (c2_1(a568)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[205, 43])).
% 1.00/1.16 tff(207,plain,
% 1.00/1.16 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(208,plain,
% 1.00/1.16 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[207])).
% 1.00/1.16 tff(209,plain,
% 1.00/1.16 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(210,plain,
% 1.00/1.16 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_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))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_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))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(211,plain,
% 1.00/1.16 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[210])).
% 1.00/1.16 tff(212,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.00/1.16 tff(213,plain,
% 1.00/1.16 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[212, 211])).
% 1.00/1.16 tff(214,plain,
% 1.00/1.16 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[213, 209])).
% 1.00/1.16 tff(215,plain,(
% 1.00/1.16 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.16 inference(skolemize,[status(sab)],[214])).
% 1.00/1.16 tff(216,plain,
% 1.00/1.16 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[215, 208])).
% 1.00/1.16 tff(217,plain,
% 1.00/1.16 (((~hskp17) | (~c1_1(a532))) <=> ((~hskp17) | (~c1_1(a532)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(218,plain,
% 1.00/1.16 (((~c1_1(a532)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a532)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(219,axiom,((~c1_1(a532)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.00/1.16 tff(220,plain,
% 1.00/1.16 ((~hskp17) | (~c1_1(a532))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[219, 218])).
% 1.00/1.16 tff(221,plain,
% 1.00/1.16 ((~hskp17) | (~c1_1(a532))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[220, 217])).
% 1.00/1.16 tff(222,plain,
% 1.00/1.16 (~c1_1(a532)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[221, 160])).
% 1.00/1.16 tff(223,plain,
% 1.00/1.16 (((~hskp27) | (~c1_1(a568))) <=> ((~hskp27) | (~c1_1(a568)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(224,plain,
% 1.00/1.16 (((~c1_1(a568)) | (~hskp27)) <=> ((~hskp27) | (~c1_1(a568)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(225,axiom,((~c1_1(a568)) | (~hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.00/1.16 tff(226,plain,
% 1.00/1.16 ((~hskp27) | (~c1_1(a568))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[225, 224])).
% 1.00/1.16 tff(227,plain,
% 1.00/1.16 ((~hskp27) | (~c1_1(a568))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[226, 223])).
% 1.00/1.16 tff(228,plain,
% 1.00/1.16 (~c1_1(a568)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[227, 182])).
% 1.00/1.16 tff(229,plain,
% 1.00/1.16 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(230,plain,
% 1.00/1.16 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[229])).
% 1.00/1.16 tff(231,plain,
% 1.00/1.16 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(232,plain,
% 1.00/1.16 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~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))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(233,plain,
% 1.00/1.17 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[232])).
% 1.00/1.17 tff(234,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 1.00/1.17 tff(235,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.00/1.17 tff(236,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[235, 231])).
% 1.00/1.17 tff(237,plain,(
% 1.00/1.17 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.17 inference(skolemize,[status(sab)],[236])).
% 1.00/1.17 tff(238,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[237, 230])).
% 1.00/1.17 tff(239,assumption,(~c0_1(a502)), introduced(assumption)).
% 1.00/1.17 tff(240,plain,
% 1.00/1.17 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(241,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[240])).
% 1.00/1.17 tff(242,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(243,plain,
% 1.00/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp29) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp29))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(244,plain,
% 1.00/1.17 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[243])).
% 1.00/1.17 tff(245,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 1.00/1.17 tff(246,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[245, 244])).
% 1.00/1.17 tff(247,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[246, 242])).
% 1.00/1.17 tff(248,plain,(
% 1.00/1.17 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.00/1.17 inference(skolemize,[status(sab)],[247])).
% 1.00/1.17 tff(249,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[248, 241])).
% 1.00/1.17 tff(250,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp29 | c1_1(a568) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp29 | c1_1(a568) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(251,plain,
% 1.00/1.17 ((hskp29 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568))) <=> (hskp29 | c1_1(a568) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(252,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp29 | c1_1(a568) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | (~c2_1(a568))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[251])).
% 1.00/1.17 tff(253,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp29 | c1_1(a568) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[252, 250])).
% 1.00/1.17 tff(254,plain,
% 1.00/1.17 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(255,plain,
% 1.00/1.17 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp29 | c1_1(a568) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | (~c2_1(a568))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[254, 253])).
% 1.00/1.17 tff(256,plain,
% 1.00/1.17 (hskp29 | (~c2_1(a568))),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[255, 106, 198, 190, 228, 249])).
% 1.00/1.17 tff(257,plain,
% 1.00/1.17 (hskp29),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[256, 206])).
% 1.00/1.17 tff(258,plain,
% 1.00/1.17 (((~hskp29) | c3_1(a504)) <=> ((~hskp29) | c3_1(a504))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(259,axiom,((~hskp29) | c3_1(a504)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.00/1.17 tff(260,plain,
% 1.00/1.17 ((~hskp29) | c3_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[259, 258])).
% 1.00/1.17 tff(261,plain,
% 1.00/1.17 ((~hskp29) | c3_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[260, 258])).
% 1.00/1.17 tff(262,plain,
% 1.00/1.17 ((~hskp29) | c3_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[261, 258])).
% 1.00/1.17 tff(263,plain,
% 1.00/1.17 ((~hskp29) | c3_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[262, 258])).
% 1.00/1.17 tff(264,plain,
% 1.00/1.17 ((~hskp29) | c3_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[263, 258])).
% 1.00/1.17 tff(265,plain,
% 1.00/1.17 (c3_1(a504)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[264, 257])).
% 1.00/1.17 tff(266,plain,
% 1.00/1.17 (((~hskp29) | c0_1(a504)) <=> ((~hskp29) | c0_1(a504))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(267,axiom,((~hskp29) | c0_1(a504)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.00/1.17 tff(268,plain,
% 1.00/1.17 ((~hskp29) | c0_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[267, 266])).
% 1.00/1.17 tff(269,plain,
% 1.00/1.17 ((~hskp29) | c0_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[268, 266])).
% 1.00/1.17 tff(270,plain,
% 1.00/1.17 ((~hskp29) | c0_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[269, 266])).
% 1.00/1.17 tff(271,plain,
% 1.00/1.17 ((~hskp29) | c0_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[270, 266])).
% 1.00/1.17 tff(272,plain,
% 1.00/1.17 ((~hskp29) | c0_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[271, 266])).
% 1.00/1.17 tff(273,plain,
% 1.00/1.17 (c0_1(a504)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[272, 257])).
% 1.00/1.17 tff(274,plain,
% 1.00/1.17 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c0_1(a504)) | (~c3_1(a504)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c0_1(a504)) | (~c3_1(a504)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(275,plain,
% 1.00/1.17 ((hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c3_1(a504)) | (~c0_1(a504))) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c0_1(a504)) | (~c3_1(a504)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(276,plain,
% 1.00/1.17 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c3_1(a504)) | (~c0_1(a504)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c0_1(a504)) | (~c3_1(a504))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[275])).
% 1.00/1.17 tff(277,plain,
% 1.00/1.17 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c3_1(a504)) | (~c0_1(a504)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c0_1(a504)) | (~c3_1(a504)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[276, 274])).
% 1.00/1.17 tff(278,plain,
% 1.00/1.17 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c3_1(a504)) | (~c0_1(a504)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(279,plain,
% 1.00/1.17 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c0_1(a504)) | (~c3_1(a504))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[278, 277])).
% 1.00/1.17 tff(280,plain,
% 1.00/1.17 (c2_1(a504)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[279, 106, 43, 11, 273, 265, 42])).
% 1.00/1.17 tff(281,plain,
% 1.00/1.17 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(282,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[281])).
% 1.00/1.17 tff(283,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(284,plain,
% 1.00/1.17 (^[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)) | 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))) | (~c2_1(U))) | (~ndr1_0)) | 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))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(285,plain,
% 1.00/1.17 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[284])).
% 1.00/1.17 tff(286,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 1.00/1.17 tff(287,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[286, 285])).
% 1.00/1.17 tff(288,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[287, 283])).
% 1.00/1.17 tff(289,plain,(
% 1.00/1.17 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.17 inference(skolemize,[status(sab)],[288])).
% 1.00/1.17 tff(290,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[289, 282])).
% 1.00/1.17 tff(291,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a568) | c1_1(a532) | (~ndr1_0) | (~c3_1(a532)) | c0_1(a532) | (~c0_1(a568)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a568) | c1_1(a532) | (~ndr1_0) | (~c3_1(a532)) | c0_1(a532) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(292,plain,
% 1.00/1.17 ((hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a532) | c0_1(a532) | (~c3_1(a532))) <=> (hskp7 | c1_1(a568) | c1_1(a532) | (~ndr1_0) | (~c3_1(a532)) | c0_1(a532) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(293,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a532) | c0_1(a532) | (~c3_1(a532)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a568) | c1_1(a532) | (~ndr1_0) | (~c3_1(a532)) | c0_1(a532) | (~c0_1(a568)) | (~c2_1(a568))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[292])).
% 1.00/1.17 tff(294,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a532) | c0_1(a532) | (~c3_1(a532)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a568) | c1_1(a532) | (~ndr1_0) | (~c3_1(a532)) | c0_1(a532) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[293, 291])).
% 1.00/1.17 tff(295,plain,
% 1.00/1.17 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a532) | c0_1(a532) | (~c3_1(a532)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(296,plain,
% 1.00/1.17 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a568) | c1_1(a532) | (~ndr1_0) | (~c3_1(a532)) | c0_1(a532) | (~c0_1(a568)) | (~c2_1(a568))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[295, 294])).
% 1.00/1.17 tff(297,plain,
% 1.00/1.17 (hskp7),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[296, 106, 198, 174, 228, 222, 216, 206, 181])).
% 1.00/1.17 tff(298,plain,
% 1.00/1.17 (((~hskp7) | (~c3_1(a502))) <=> ((~hskp7) | (~c3_1(a502)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(299,plain,
% 1.00/1.17 (((~c3_1(a502)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a502)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(300,axiom,((~c3_1(a502)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.00/1.17 tff(301,plain,
% 1.00/1.17 ((~hskp7) | (~c3_1(a502))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[300, 299])).
% 1.00/1.17 tff(302,plain,
% 1.00/1.17 ((~hskp7) | (~c3_1(a502))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[301, 298])).
% 1.00/1.17 tff(303,plain,
% 1.00/1.17 (~c3_1(a502)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[302, 297])).
% 1.00/1.17 tff(304,plain,
% 1.00/1.17 (((~hskp7) | (~c1_1(a502))) <=> ((~hskp7) | (~c1_1(a502)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(305,plain,
% 1.00/1.17 (((~c1_1(a502)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a502)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(306,axiom,((~c1_1(a502)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.00/1.17 tff(307,plain,
% 1.00/1.17 ((~hskp7) | (~c1_1(a502))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[306, 305])).
% 1.00/1.17 tff(308,plain,
% 1.00/1.17 ((~hskp7) | (~c1_1(a502))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[307, 304])).
% 1.00/1.17 tff(309,plain,
% 1.00/1.17 (~c1_1(a502)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[308, 297])).
% 1.00/1.17 tff(310,plain,
% 1.00/1.17 (((~hskp29) | c1_1(a504)) <=> ((~hskp29) | c1_1(a504))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(311,axiom,((~hskp29) | c1_1(a504)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.00/1.17 tff(312,plain,
% 1.00/1.17 ((~hskp29) | c1_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[311, 310])).
% 1.00/1.17 tff(313,plain,
% 1.00/1.17 ((~hskp29) | c1_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[312, 310])).
% 1.00/1.17 tff(314,plain,
% 1.00/1.17 ((~hskp29) | c1_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[313, 310])).
% 1.00/1.17 tff(315,plain,
% 1.00/1.17 ((~hskp29) | c1_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[314, 310])).
% 1.00/1.17 tff(316,plain,
% 1.00/1.17 ((~hskp29) | c1_1(a504)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[315, 310])).
% 1.00/1.17 tff(317,plain,
% 1.00/1.17 (c1_1(a504)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[316, 257])).
% 1.00/1.17 tff(318,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(319,plain,
% 1.00/1.17 ((hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(320,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[319])).
% 1.00/1.17 tff(321,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[320, 318])).
% 1.00/1.17 tff(322,plain,
% 1.00/1.17 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(323,plain,
% 1.00/1.17 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[322, 321])).
% 1.00/1.17 tff(324,plain,
% 1.00/1.17 (hskp2),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[323, 106, 273, 317, 239, 309, 303, 290, 280])).
% 1.00/1.17 tff(325,plain,
% 1.00/1.17 (((~hskp2) | (~c3_1(a496))) <=> ((~hskp2) | (~c3_1(a496)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(326,plain,
% 1.00/1.17 (((~c3_1(a496)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a496)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(327,axiom,((~c3_1(a496)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.00/1.17 tff(328,plain,
% 1.00/1.17 ((~hskp2) | (~c3_1(a496))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[327, 326])).
% 1.00/1.17 tff(329,plain,
% 1.00/1.17 ((~hskp2) | (~c3_1(a496))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[328, 325])).
% 1.00/1.17 tff(330,plain,
% 1.00/1.17 (~c3_1(a496)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[329, 324])).
% 1.00/1.17 tff(331,plain,
% 1.00/1.17 (((~hskp2) | (~c2_1(a496))) <=> ((~hskp2) | (~c2_1(a496)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(332,plain,
% 1.00/1.17 (((~c2_1(a496)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a496)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(333,axiom,((~c2_1(a496)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.00/1.17 tff(334,plain,
% 1.00/1.17 ((~hskp2) | (~c2_1(a496))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[333, 332])).
% 1.00/1.17 tff(335,plain,
% 1.00/1.17 ((~hskp2) | (~c2_1(a496))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[334, 331])).
% 1.00/1.17 tff(336,plain,
% 1.00/1.17 (~c2_1(a496)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[335, 324])).
% 1.00/1.17 tff(337,plain,
% 1.00/1.17 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(338,plain,
% 1.00/1.17 ((hskp11 | hskp10 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c0_1(a496)) <=> (hskp11 | hskp10 | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(339,plain,
% 1.00/1.17 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c0_1(a496))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496)))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[338])).
% 1.00/1.17 tff(340,plain,
% 1.00/1.17 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c0_1(a496))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496))),
% 1.00/1.17 inference(transitivity,[status(thm)],[339, 337])).
% 1.00/1.17 tff(341,plain,
% 1.00/1.17 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c0_1(a496))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(342,plain,
% 1.00/1.17 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[341, 340])).
% 1.00/1.17 tff(343,plain,
% 1.00/1.17 (c0_1(a496)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[342, 106, 151, 11, 336, 330, 10])).
% 1.00/1.17 tff(344,plain,
% 1.00/1.17 (((~hskp2) | (~c1_1(a496))) <=> ((~hskp2) | (~c1_1(a496)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(345,plain,
% 1.00/1.17 (((~c1_1(a496)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a496)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(346,axiom,((~c1_1(a496)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.00/1.17 tff(347,plain,
% 1.00/1.17 ((~hskp2) | (~c1_1(a496))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[346, 345])).
% 1.00/1.17 tff(348,plain,
% 1.00/1.17 ((~hskp2) | (~c1_1(a496))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[347, 344])).
% 1.00/1.17 tff(349,plain,
% 1.00/1.17 (~c1_1(a496)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[348, 324])).
% 1.00/1.17 tff(350,plain,
% 1.00/1.17 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(351,plain,
% 1.00/1.18 ((hskp11 | hskp10 | (~ndr1_0) | c3_1(a502) | c2_1(a502) | c0_1(a502)) <=> (hskp11 | hskp10 | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(352,plain,
% 1.00/1.18 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a502) | c2_1(a502) | c0_1(a502))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502)))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[351])).
% 1.00/1.18 tff(353,plain,
% 1.00/1.18 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a502) | c2_1(a502) | c0_1(a502))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502))),
% 1.00/1.18 inference(transitivity,[status(thm)],[352, 350])).
% 1.00/1.18 tff(354,plain,
% 1.00/1.18 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a502) | c2_1(a502) | c0_1(a502))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(355,plain,
% 1.00/1.18 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[354, 353])).
% 1.00/1.18 tff(356,plain,
% 1.00/1.18 (hskp11 | c3_1(a502) | c2_1(a502)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[355, 106, 11, 239, 10])).
% 1.00/1.18 tff(357,plain,
% 1.00/1.18 (c2_1(a502)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[356, 303, 151])).
% 1.00/1.18 tff(358,plain,
% 1.00/1.18 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(359,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[358])).
% 1.00/1.18 tff(360,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(361,plain,
% 1.00/1.18 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_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) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(362,plain,
% 1.00/1.18 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[361])).
% 1.00/1.18 tff(363,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.00/1.18 tff(364,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[363, 362])).
% 1.00/1.18 tff(365,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[364, 360])).
% 1.00/1.18 tff(366,plain,(
% 1.00/1.18 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.00/1.18 inference(skolemize,[status(sab)],[365])).
% 1.00/1.18 tff(367,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[366, 359])).
% 1.00/1.18 tff(368,assumption,(c0_1(a568)), introduced(assumption)).
% 1.00/1.18 tff(369,assumption,(~c1_1(a568)), introduced(assumption)).
% 1.00/1.18 tff(370,assumption,(c3_1(a568)), introduced(assumption)).
% 1.00/1.18 tff(371,assumption,(~hskp13), introduced(assumption)).
% 1.00/1.18 tff(372,plain,
% 1.00/1.18 ((hskp28 | hskp13 | hskp10) <=> (hskp28 | hskp13 | hskp10)),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(373,plain,
% 1.00/1.18 (((hskp28 | hskp13) | hskp10) <=> (hskp28 | hskp13 | hskp10)),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(374,plain,
% 1.00/1.18 ((hskp28 | hskp13) <=> (hskp28 | hskp13)),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(375,plain,
% 1.00/1.18 (((hskp28 | hskp13) | hskp10) <=> ((hskp28 | hskp13) | hskp10)),
% 1.00/1.18 inference(monotonicity,[status(thm)],[374])).
% 1.00/1.18 tff(376,plain,
% 1.00/1.18 (((hskp28 | hskp13) | hskp10) <=> (hskp28 | hskp13 | hskp10)),
% 1.00/1.18 inference(transitivity,[status(thm)],[375, 373])).
% 1.00/1.18 tff(377,axiom,((hskp28 | hskp13) | hskp10), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 1.00/1.18 tff(378,plain,
% 1.00/1.18 (hskp28 | hskp13 | hskp10),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[377, 376])).
% 1.00/1.18 tff(379,plain,
% 1.00/1.18 (hskp28 | hskp13 | hskp10),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[378, 372])).
% 1.00/1.18 tff(380,plain,
% 1.00/1.18 (hskp28 | hskp13 | hskp10),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[379, 372])).
% 1.00/1.18 tff(381,plain,
% 1.00/1.18 (hskp28 | hskp13 | hskp10),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[380, 372])).
% 1.00/1.18 tff(382,plain,
% 1.00/1.18 (hskp28 | hskp13 | hskp10),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[381, 372])).
% 1.00/1.18 tff(383,plain,
% 1.00/1.18 (hskp28),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[382, 371, 11])).
% 1.00/1.18 tff(384,plain,
% 1.00/1.18 (((~hskp28) | c3_1(a500)) <=> ((~hskp28) | c3_1(a500))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(385,axiom,((~hskp28) | c3_1(a500)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.00/1.18 tff(386,plain,
% 1.00/1.18 ((~hskp28) | c3_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[385, 384])).
% 1.00/1.18 tff(387,plain,
% 1.00/1.18 ((~hskp28) | c3_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[386, 384])).
% 1.00/1.18 tff(388,plain,
% 1.00/1.18 ((~hskp28) | c3_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[387, 384])).
% 1.00/1.18 tff(389,plain,
% 1.00/1.18 ((~hskp28) | c3_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[388, 384])).
% 1.00/1.18 tff(390,plain,
% 1.00/1.18 ((~hskp28) | c3_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[389, 384])).
% 1.00/1.18 tff(391,plain,
% 1.00/1.18 (c3_1(a500)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[390, 383])).
% 1.00/1.18 tff(392,plain,
% 1.00/1.18 (((~hskp28) | c2_1(a500)) <=> ((~hskp28) | c2_1(a500))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(393,axiom,((~hskp28) | c2_1(a500)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 1.00/1.18 tff(394,plain,
% 1.00/1.18 ((~hskp28) | c2_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[393, 392])).
% 1.00/1.18 tff(395,plain,
% 1.00/1.18 ((~hskp28) | c2_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[394, 392])).
% 1.00/1.18 tff(396,plain,
% 1.00/1.18 ((~hskp28) | c2_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[395, 392])).
% 1.00/1.18 tff(397,plain,
% 1.00/1.18 ((~hskp28) | c2_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[396, 392])).
% 1.00/1.18 tff(398,plain,
% 1.00/1.18 ((~hskp28) | c2_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[397, 392])).
% 1.00/1.18 tff(399,plain,
% 1.00/1.18 (c2_1(a500)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[398, 383])).
% 1.00/1.18 tff(400,plain,
% 1.00/1.18 (((~hskp28) | c0_1(a500)) <=> ((~hskp28) | c0_1(a500))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(401,axiom,((~hskp28) | c0_1(a500)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.00/1.18 tff(402,plain,
% 1.00/1.18 ((~hskp28) | c0_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[401, 400])).
% 1.00/1.18 tff(403,plain,
% 1.00/1.18 ((~hskp28) | c0_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[402, 400])).
% 1.00/1.18 tff(404,plain,
% 1.00/1.18 ((~hskp28) | c0_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[403, 400])).
% 1.00/1.18 tff(405,plain,
% 1.00/1.18 ((~hskp28) | c0_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[404, 400])).
% 1.00/1.18 tff(406,plain,
% 1.00/1.18 ((~hskp28) | c0_1(a500)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[405, 400])).
% 1.00/1.18 tff(407,plain,
% 1.00/1.18 (c0_1(a500)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[406, 383])).
% 1.00/1.18 tff(408,assumption,(~hskp2), introduced(assumption)).
% 1.00/1.18 tff(409,plain,
% 1.00/1.18 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(410,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[409])).
% 1.00/1.18 tff(411,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(412,plain,
% 1.00/1.18 (^[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)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp2))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(413,plain,
% 1.00/1.18 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[412])).
% 1.00/1.18 tff(414,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)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 1.00/1.18 tff(415,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[414, 413])).
% 1.00/1.18 tff(416,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[415, 411])).
% 1.00/1.18 tff(417,plain,(
% 1.00/1.18 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.18 inference(skolemize,[status(sab)],[416])).
% 1.00/1.18 tff(418,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[417, 410])).
% 1.00/1.18 tff(419,assumption,(hskp15), introduced(assumption)).
% 1.00/1.18 tff(420,plain,
% 1.00/1.18 (((~hskp15) | (~c3_1(a528))) <=> ((~hskp15) | (~c3_1(a528)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(421,plain,
% 1.00/1.18 (((~c3_1(a528)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a528)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(422,axiom,((~c3_1(a528)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.00/1.18 tff(423,plain,
% 1.00/1.18 ((~hskp15) | (~c3_1(a528))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[422, 421])).
% 1.00/1.18 tff(424,plain,
% 1.00/1.18 ((~hskp15) | (~c3_1(a528))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[423, 420])).
% 1.00/1.18 tff(425,plain,
% 1.00/1.18 (~c3_1(a528)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[424, 419])).
% 1.00/1.18 tff(426,plain,
% 1.00/1.18 (((~hskp15) | c1_1(a528)) <=> ((~hskp15) | c1_1(a528))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(427,axiom,((~hskp15) | c1_1(a528)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.00/1.18 tff(428,plain,
% 1.00/1.18 ((~hskp15) | c1_1(a528)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[427, 426])).
% 1.00/1.18 tff(429,plain,
% 1.00/1.18 ((~hskp15) | c1_1(a528)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[428, 426])).
% 1.00/1.18 tff(430,plain,
% 1.00/1.18 ((~hskp15) | c1_1(a528)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[429, 426])).
% 1.00/1.18 tff(431,plain,
% 1.00/1.18 ((~hskp15) | c1_1(a528)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[430, 426])).
% 1.00/1.18 tff(432,plain,
% 1.00/1.18 ((~hskp15) | c1_1(a528)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[431, 426])).
% 1.00/1.18 tff(433,plain,
% 1.00/1.18 (c1_1(a528)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[432, 419])).
% 1.00/1.18 tff(434,plain,
% 1.00/1.18 (((~hskp15) | c0_1(a528)) <=> ((~hskp15) | c0_1(a528))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(435,axiom,((~hskp15) | c0_1(a528)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.00/1.18 tff(436,plain,
% 1.00/1.18 ((~hskp15) | c0_1(a528)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[435, 434])).
% 1.00/1.18 tff(437,plain,
% 1.00/1.18 ((~hskp15) | c0_1(a528)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[436, 434])).
% 1.00/1.18 tff(438,plain,
% 1.00/1.18 ((~hskp15) | c0_1(a528)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[437, 434])).
% 1.00/1.18 tff(439,plain,
% 1.00/1.18 ((~hskp15) | c0_1(a528)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[438, 434])).
% 1.00/1.18 tff(440,plain,
% 1.00/1.18 ((~hskp15) | c0_1(a528)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[439, 434])).
% 1.00/1.18 tff(441,plain,
% 1.00/1.18 (c0_1(a528)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[440, 419])).
% 1.00/1.18 tff(442,assumption,(c3_1(a500)), introduced(assumption)).
% 1.00/1.18 tff(443,assumption,(c2_1(a500)), introduced(assumption)).
% 1.00/1.18 tff(444,assumption,(c0_1(a500)), introduced(assumption)).
% 1.00/1.18 tff(445,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c3_1(a528) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a528) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(446,plain,
% 1.00/1.18 ((hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528))) <=> (hskp2 | c3_1(a528) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(447,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c3_1(a528) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[446])).
% 1.00/1.18 tff(448,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a528) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[447, 445])).
% 1.00/1.18 tff(449,plain,
% 1.00/1.18 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(450,plain,
% 1.00/1.18 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a528) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[449, 448])).
% 1.00/1.18 tff(451,plain,
% 1.00/1.18 ($false),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[450, 106, 408, 444, 443, 442, 441, 433, 425, 418])).
% 1.00/1.18 tff(452,plain,((~hskp15) | hskp2 | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500))), inference(lemma,lemma(discharge,[]))).
% 1.00/1.18 tff(453,plain,
% 1.00/1.18 (~hskp15),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[452, 408, 407, 399, 391])).
% 1.00/1.18 tff(454,plain,
% 1.00/1.18 (hskp15 | c2_1(a568)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[204, 106, 11, 368, 370, 42])).
% 1.00/1.18 tff(455,plain,
% 1.00/1.18 (c2_1(a568)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[454, 453])).
% 1.00/1.18 tff(456,plain,
% 1.00/1.18 (hskp29 | (~c2_1(a568))),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[255, 106, 368, 370, 369, 249])).
% 1.00/1.18 tff(457,plain,
% 1.00/1.18 (hskp29),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[456, 455])).
% 1.00/1.18 tff(458,plain,
% 1.00/1.18 (c3_1(a504)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[264, 457])).
% 1.00/1.18 tff(459,plain,
% 1.00/1.18 (c0_1(a504)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[272, 457])).
% 1.00/1.18 tff(460,plain,
% 1.00/1.18 (c2_1(a504)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[279, 106, 453, 11, 459, 458, 42])).
% 1.00/1.18 tff(461,plain,
% 1.00/1.18 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(462,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[461])).
% 1.00/1.18 tff(463,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(464,plain,
% 1.00/1.18 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(465,plain,
% 1.00/1.18 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[464])).
% 1.00/1.18 tff(466,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.00/1.18 tff(467,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[466, 465])).
% 1.00/1.18 tff(468,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[467, 463])).
% 1.00/1.18 tff(469,plain,(
% 1.00/1.18 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.00/1.18 inference(skolemize,[status(sab)],[468])).
% 1.00/1.18 tff(470,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[469, 462])).
% 1.00/1.18 tff(471,plain,
% 1.00/1.18 ((hskp15 | hskp13 | hskp12) <=> (hskp15 | hskp13 | hskp12)),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(472,plain,
% 1.00/1.18 (((hskp15 | hskp13) | hskp12) <=> (hskp15 | hskp13 | hskp12)),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(473,plain,
% 1.00/1.18 ((hskp15 | hskp13) <=> (hskp15 | hskp13)),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(474,plain,
% 1.00/1.18 (((hskp15 | hskp13) | hskp12) <=> ((hskp15 | hskp13) | hskp12)),
% 1.00/1.18 inference(monotonicity,[status(thm)],[473])).
% 1.00/1.18 tff(475,plain,
% 1.00/1.18 (((hskp15 | hskp13) | hskp12) <=> (hskp15 | hskp13 | hskp12)),
% 1.00/1.18 inference(transitivity,[status(thm)],[474, 472])).
% 1.00/1.18 tff(476,axiom,((hskp15 | hskp13) | hskp12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 1.00/1.18 tff(477,plain,
% 1.00/1.18 (hskp15 | hskp13 | hskp12),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[476, 475])).
% 1.00/1.18 tff(478,plain,
% 1.00/1.18 (hskp15 | hskp13 | hskp12),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[477, 471])).
% 1.00/1.18 tff(479,plain,
% 1.00/1.18 (hskp15 | hskp13 | hskp12),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[478, 471])).
% 1.00/1.18 tff(480,plain,
% 1.00/1.18 (hskp15 | hskp13 | hskp12),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[479, 471])).
% 1.00/1.18 tff(481,plain,
% 1.00/1.18 (hskp15 | hskp13 | hskp12),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[480, 471])).
% 1.00/1.18 tff(482,plain,
% 1.00/1.18 (hskp12),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[481, 453, 371])).
% 1.00/1.18 tff(483,plain,
% 1.00/1.18 (((~hskp12) | (~c2_1(a514))) <=> ((~hskp12) | (~c2_1(a514)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(484,plain,
% 1.00/1.18 (((~c2_1(a514)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a514)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(485,axiom,((~c2_1(a514)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.00/1.18 tff(486,plain,
% 1.00/1.18 ((~hskp12) | (~c2_1(a514))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.00/1.18 tff(487,plain,
% 1.00/1.18 ((~hskp12) | (~c2_1(a514))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[486, 483])).
% 1.00/1.18 tff(488,plain,
% 1.00/1.18 (~c2_1(a514)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[487, 482])).
% 1.00/1.18 tff(489,plain,
% 1.00/1.18 (((~hskp12) | c3_1(a514)) <=> ((~hskp12) | c3_1(a514))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(490,axiom,((~hskp12) | c3_1(a514)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.00/1.18 tff(491,plain,
% 1.00/1.18 ((~hskp12) | c3_1(a514)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[490, 489])).
% 1.00/1.18 tff(492,plain,
% 1.00/1.18 ((~hskp12) | c3_1(a514)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[491, 489])).
% 1.00/1.18 tff(493,plain,
% 1.00/1.18 ((~hskp12) | c3_1(a514)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[492, 489])).
% 1.00/1.18 tff(494,plain,
% 1.00/1.18 ((~hskp12) | c3_1(a514)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[493, 489])).
% 1.00/1.18 tff(495,plain,
% 1.00/1.18 ((~hskp12) | c3_1(a514)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[494, 489])).
% 1.00/1.18 tff(496,plain,
% 1.00/1.18 (c3_1(a514)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[495, 482])).
% 1.00/1.18 tff(497,plain,
% 1.00/1.18 (((~hskp12) | c1_1(a514)) <=> ((~hskp12) | c1_1(a514))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(498,axiom,((~hskp12) | c1_1(a514)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.00/1.18 tff(499,plain,
% 1.00/1.18 ((~hskp12) | c1_1(a514)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[498, 497])).
% 1.00/1.18 tff(500,plain,
% 1.00/1.18 ((~hskp12) | c1_1(a514)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[499, 497])).
% 1.00/1.18 tff(501,plain,
% 1.00/1.18 ((~hskp12) | c1_1(a514)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[500, 497])).
% 1.00/1.18 tff(502,plain,
% 1.00/1.18 ((~hskp12) | c1_1(a514)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[501, 497])).
% 1.00/1.18 tff(503,plain,
% 1.00/1.18 ((~hskp12) | c1_1(a514)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[502, 497])).
% 1.00/1.18 tff(504,plain,
% 1.00/1.18 (c1_1(a514)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[503, 482])).
% 1.00/1.18 tff(505,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a568) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c3_1(a568)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a568) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(506,plain,
% 1.00/1.18 ((hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568))) <=> (hskp20 | c1_1(a568) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(507,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a568) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c3_1(a568)) | (~c2_1(a568))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[506])).
% 1.00/1.18 tff(508,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a568) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[507, 505])).
% 1.00/1.18 tff(509,plain,
% 1.00/1.18 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(510,plain,
% 1.00/1.18 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a568) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c3_1(a568)) | (~c2_1(a568))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[509, 508])).
% 1.00/1.18 tff(511,plain,
% 1.00/1.18 (hskp20),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[510, 106, 370, 504, 496, 369, 488, 470, 455])).
% 1.00/1.18 tff(512,plain,
% 1.00/1.18 (((~hskp20) | (~c1_1(a536))) <=> ((~hskp20) | (~c1_1(a536)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(513,plain,
% 1.00/1.18 (((~c1_1(a536)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a536)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(514,axiom,((~c1_1(a536)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.00/1.18 tff(515,plain,
% 1.00/1.18 ((~hskp20) | (~c1_1(a536))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[514, 513])).
% 1.00/1.18 tff(516,plain,
% 1.00/1.18 ((~hskp20) | (~c1_1(a536))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[515, 512])).
% 1.00/1.18 tff(517,plain,
% 1.00/1.18 (~c1_1(a536)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[516, 511])).
% 1.00/1.18 tff(518,plain,
% 1.00/1.18 (((~hskp20) | (~c0_1(a536))) <=> ((~hskp20) | (~c0_1(a536)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(519,plain,
% 1.00/1.18 (((~c0_1(a536)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a536)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(520,axiom,((~c0_1(a536)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 1.00/1.18 tff(521,plain,
% 1.00/1.18 ((~hskp20) | (~c0_1(a536))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[520, 519])).
% 1.00/1.18 tff(522,plain,
% 1.00/1.18 ((~hskp20) | (~c0_1(a536))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[521, 518])).
% 1.00/1.18 tff(523,plain,
% 1.00/1.18 (~c0_1(a536)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[522, 511])).
% 1.00/1.18 tff(524,plain,
% 1.00/1.18 (c1_1(a504)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[316, 457])).
% 1.00/1.18 tff(525,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c3_1(a536))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c3_1(a536))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(526,plain,
% 1.00/1.18 ((hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a536) | c0_1(a536) | c3_1(a536)) <=> (hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c3_1(a536))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(527,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a536) | c0_1(a536) | c3_1(a536))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c3_1(a536)))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[526])).
% 1.00/1.18 tff(528,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a536) | c0_1(a536) | c3_1(a536))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c3_1(a536))),
% 1.00/1.18 inference(transitivity,[status(thm)],[527, 525])).
% 1.00/1.18 tff(529,plain,
% 1.00/1.18 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a536) | c0_1(a536) | c3_1(a536))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(530,plain,
% 1.00/1.18 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c3_1(a536)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[529, 528])).
% 1.00/1.18 tff(531,plain,
% 1.00/1.18 (c3_1(a536)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[530, 106, 408, 459, 524, 523, 517, 290, 460])).
% 1.00/1.18 tff(532,plain,
% 1.00/1.18 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(533,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[532])).
% 1.00/1.19 tff(534,plain,
% 1.00/1.19 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(535,plain,
% 1.00/1.19 (^[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))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~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))) | (~c1_1(V))) | c2_1(U)) <=> ((~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))) | (~c1_1(V))) | c2_1(U)) | 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))) | (~c1_1(V))) | c2_1(U)) | 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))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp2) <=> (hskp2 | (~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))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(536,plain,
% 1.00/1.19 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[535])).
% 1.00/1.19 tff(537,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.00/1.19 tff(538,plain,
% 1.00/1.19 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[537, 536])).
% 1.00/1.19 tff(539,plain,
% 1.00/1.19 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[538, 534])).
% 1.00/1.19 tff(540,plain,(
% 1.00/1.19 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.19 inference(skolemize,[status(sab)],[539])).
% 1.00/1.19 tff(541,plain,
% 1.00/1.19 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[540, 533])).
% 1.00/1.19 tff(542,plain,
% 1.00/1.19 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c0_1(a514)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(543,plain,
% 1.00/1.19 ((hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514))) <=> (hskp2 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(544,plain,
% 1.00/1.19 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c0_1(a514))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[543])).
% 1.00/1.19 tff(545,plain,
% 1.00/1.19 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.00/1.19 inference(transitivity,[status(thm)],[544, 542])).
% 1.00/1.19 tff(546,plain,
% 1.00/1.19 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(547,plain,
% 1.00/1.19 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c0_1(a514))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[546, 545])).
% 1.00/1.19 tff(548,plain,
% 1.00/1.19 (~c0_1(a514)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[547, 106, 408, 504, 496, 488, 541])).
% 1.00/1.19 tff(549,plain,
% 1.00/1.19 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(550,plain,
% 1.00/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_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)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[549])).
% 1.00/1.19 tff(551,plain,
% 1.00/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_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)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(552,plain,
% 1.00/1.19 (^[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) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(553,plain,
% 1.00/1.19 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[552])).
% 1.00/1.19 tff(554,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 1.00/1.19 tff(555,plain,
% 1.00/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[554, 553])).
% 1.00/1.19 tff(556,plain,
% 1.00/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[555, 551])).
% 1.00/1.19 tff(557,plain,(
% 1.00/1.19 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.00/1.19 inference(skolemize,[status(sab)],[556])).
% 1.00/1.19 tff(558,plain,
% 1.00/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[557, 550])).
% 1.00/1.19 tff(559,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a536) | c1_1(a536) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | (~c3_1(a536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a536) | c1_1(a536) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | (~c3_1(a536)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(560,plain,
% 1.00/1.19 (((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536))) <=> (c0_1(a536) | c1_1(a536) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | (~c3_1(a536)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(561,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a536) | c1_1(a536) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | (~c3_1(a536))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[560])).
% 1.00/1.19 tff(562,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a536) | c1_1(a536) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | (~c3_1(a536)))),
% 1.00/1.19 inference(transitivity,[status(thm)],[561, 559])).
% 1.00/1.19 tff(563,plain,
% 1.00/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(564,plain,
% 1.00/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a536) | c1_1(a536) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | (~c3_1(a536))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[563, 562])).
% 1.00/1.19 tff(565,plain,
% 1.00/1.19 ($false),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[564, 106, 504, 496, 523, 517, 488, 558, 548, 531])).
% 1.00/1.19 tff(566,plain,(hskp2 | hskp10 | (~c3_1(a568)) | c1_1(a568) | (~c0_1(a568)) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.00/1.19 tff(567,plain,
% 1.00/1.19 (hskp2),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[566, 371, 370, 369, 368, 11])).
% 1.00/1.19 tff(568,plain,
% 1.00/1.19 (~c2_1(a496)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[335, 567])).
% 1.00/1.19 tff(569,plain,
% 1.00/1.19 (~c1_1(a496)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[348, 567])).
% 1.00/1.19 tff(570,plain,
% 1.00/1.19 (~c3_1(a496)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[329, 567])).
% 1.00/1.19 tff(571,assumption,(~hskp1), introduced(assumption)).
% 1.00/1.19 tff(572,assumption,(~c1_1(a496)), introduced(assumption)).
% 1.00/1.19 tff(573,assumption,(~c3_1(a496)), introduced(assumption)).
% 1.00/1.19 tff(574,assumption,(~c2_1(a496)), introduced(assumption)).
% 1.00/1.19 tff(575,assumption,(~c0_1(a496)), introduced(assumption)).
% 1.00/1.19 tff(576,plain,
% 1.00/1.19 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(577,plain,
% 1.00/1.19 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[576])).
% 1.00/1.19 tff(578,plain,
% 1.00/1.19 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(579,plain,
% 1.00/1.19 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_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)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(580,plain,
% 1.00/1.19 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[579])).
% 1.00/1.19 tff(581,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 1.00/1.19 tff(582,plain,
% 1.00/1.19 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[581, 580])).
% 1.00/1.19 tff(583,plain,
% 1.00/1.19 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[582, 578])).
% 1.00/1.19 tff(584,plain,(
% 1.00/1.19 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.19 inference(skolemize,[status(sab)],[583])).
% 1.00/1.19 tff(585,plain,
% 1.00/1.19 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[584, 577])).
% 1.00/1.19 tff(586,assumption,(hskp6), introduced(assumption)).
% 1.00/1.19 tff(587,plain,
% 1.00/1.19 (((~hskp6) | (~c3_1(a501))) <=> ((~hskp6) | (~c3_1(a501)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(588,plain,
% 1.00/1.19 (((~c3_1(a501)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a501)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(589,axiom,((~c3_1(a501)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.00/1.19 tff(590,plain,
% 1.00/1.19 ((~hskp6) | (~c3_1(a501))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.00/1.19 tff(591,plain,
% 1.00/1.19 ((~hskp6) | (~c3_1(a501))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[590, 587])).
% 1.00/1.19 tff(592,plain,
% 1.00/1.19 (~c3_1(a501)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[591, 586])).
% 1.00/1.19 tff(593,plain,
% 1.00/1.19 (((~hskp6) | c2_1(a501)) <=> ((~hskp6) | c2_1(a501))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(594,axiom,((~hskp6) | c2_1(a501)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.00/1.19 tff(595,plain,
% 1.00/1.19 ((~hskp6) | c2_1(a501)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[594, 593])).
% 1.00/1.19 tff(596,plain,
% 1.00/1.19 ((~hskp6) | c2_1(a501)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[595, 593])).
% 1.00/1.19 tff(597,plain,
% 1.00/1.19 ((~hskp6) | c2_1(a501)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[596, 593])).
% 1.00/1.19 tff(598,plain,
% 1.00/1.19 ((~hskp6) | c2_1(a501)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[597, 593])).
% 1.00/1.19 tff(599,plain,
% 1.00/1.19 ((~hskp6) | c2_1(a501)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[598, 593])).
% 1.00/1.19 tff(600,plain,
% 1.00/1.19 (c2_1(a501)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[599, 586])).
% 1.00/1.19 tff(601,plain,
% 1.00/1.19 (((~hskp6) | c1_1(a501)) <=> ((~hskp6) | c1_1(a501))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(602,axiom,((~hskp6) | c1_1(a501)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.00/1.19 tff(603,plain,
% 1.00/1.19 ((~hskp6) | c1_1(a501)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[602, 601])).
% 1.00/1.19 tff(604,plain,
% 1.00/1.19 ((~hskp6) | c1_1(a501)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[603, 601])).
% 1.00/1.19 tff(605,plain,
% 1.00/1.19 ((~hskp6) | c1_1(a501)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[604, 601])).
% 1.00/1.19 tff(606,plain,
% 1.00/1.19 ((~hskp6) | c1_1(a501)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[605, 601])).
% 1.00/1.19 tff(607,plain,
% 1.00/1.19 ((~hskp6) | c1_1(a501)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[606, 601])).
% 1.00/1.19 tff(608,plain,
% 1.00/1.19 (c1_1(a501)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[607, 586])).
% 1.00/1.19 tff(609,assumption,(~c3_1(a501)), introduced(assumption)).
% 1.00/1.19 tff(610,assumption,(c1_1(a501)), introduced(assumption)).
% 1.00/1.19 tff(611,plain,
% 1.00/1.19 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c3_1(a501) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a501)) | (~c0_1(a501)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a501) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a501)) | (~c0_1(a501)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(612,plain,
% 1.00/1.19 ((hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a501) | (~c1_1(a501)) | (~c0_1(a501))) <=> (hskp2 | c3_1(a501) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a501)) | (~c0_1(a501)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(613,plain,
% 1.00/1.19 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a501) | (~c1_1(a501)) | (~c0_1(a501)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c3_1(a501) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a501)) | (~c0_1(a501))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[612])).
% 1.00/1.19 tff(614,plain,
% 1.00/1.19 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a501) | (~c1_1(a501)) | (~c0_1(a501)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a501) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a501)) | (~c0_1(a501)))),
% 1.00/1.19 inference(transitivity,[status(thm)],[613, 611])).
% 1.00/1.19 tff(615,plain,
% 1.00/1.19 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a501) | (~c1_1(a501)) | (~c0_1(a501)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(616,plain,
% 1.00/1.19 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a501) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a501)) | (~c0_1(a501))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[615, 614])).
% 1.00/1.19 tff(617,plain,
% 1.00/1.19 (hskp2 | (~c0_1(a501))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[616, 106, 444, 443, 442, 610, 609, 418])).
% 1.00/1.19 tff(618,plain,
% 1.00/1.19 (~c0_1(a501)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[617, 408])).
% 1.00/1.19 tff(619,plain,
% 1.00/1.19 (^[U: $i] : refl((hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(620,plain,
% 1.00/1.19 (![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[619])).
% 1.00/1.19 tff(621,plain,
% 1.00/1.19 (![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(622,plain,
% 1.00/1.19 (^[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) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp7) <=> ((hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp7))), rewrite(((hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp7) <=> (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp7) <=> (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(623,plain,
% 1.00/1.19 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp7) <=> ![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[622])).
% 1.00/1.19 tff(624,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 1.00/1.19 tff(625,plain,
% 1.00/1.19 (![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[624, 623])).
% 1.00/1.19 tff(626,plain,
% 1.00/1.19 (![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[625, 621])).
% 1.00/1.19 tff(627,plain,(
% 1.00/1.19 ![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.00/1.19 inference(skolemize,[status(sab)],[626])).
% 1.00/1.19 tff(628,plain,
% 1.00/1.19 (![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[627, 620])).
% 1.00/1.19 tff(629,plain,
% 1.00/1.19 (((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp7 | hskp1 | c3_1(a501) | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501))) <=> ((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp7 | hskp1 | c3_1(a501) | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(630,plain,
% 1.00/1.19 ((hskp7 | hskp1 | (~ndr1_0) | c3_1(a501) | c0_1(a501) | (~c1_1(a501))) <=> (hskp7 | hskp1 | c3_1(a501) | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(631,plain,
% 1.00/1.19 (((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp7 | hskp1 | (~ndr1_0) | c3_1(a501) | c0_1(a501) | (~c1_1(a501)))) <=> ((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp7 | hskp1 | c3_1(a501) | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501)))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[630])).
% 1.00/1.19 tff(632,plain,
% 1.00/1.19 (((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp7 | hskp1 | (~ndr1_0) | c3_1(a501) | c0_1(a501) | (~c1_1(a501)))) <=> ((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp7 | hskp1 | c3_1(a501) | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501))),
% 1.00/1.19 inference(transitivity,[status(thm)],[631, 629])).
% 1.00/1.19 tff(633,plain,
% 1.00/1.19 ((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp7 | hskp1 | (~ndr1_0) | c3_1(a501) | c0_1(a501) | (~c1_1(a501)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(634,plain,
% 1.00/1.19 ((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp7 | hskp1 | c3_1(a501) | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[633, 632])).
% 1.00/1.19 tff(635,plain,
% 1.00/1.19 (hskp7 | c0_1(a501)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[634, 106, 571, 610, 609, 628])).
% 1.00/1.19 tff(636,plain,
% 1.00/1.19 (hskp7),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[635, 618])).
% 1.00/1.19 tff(637,plain,
% 1.00/1.19 (~c3_1(a502)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[302, 636])).
% 1.00/1.19 tff(638,plain,
% 1.00/1.19 (~c1_1(a502)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[308, 636])).
% 1.00/1.19 tff(639,plain,
% 1.00/1.19 (((~hskp7) | (~c0_1(a502))) <=> ((~hskp7) | (~c0_1(a502)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(640,plain,
% 1.00/1.19 (((~c0_1(a502)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a502)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(641,axiom,((~c0_1(a502)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.00/1.20 tff(642,plain,
% 1.00/1.20 ((~hskp7) | (~c0_1(a502))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[641, 640])).
% 1.00/1.20 tff(643,plain,
% 1.00/1.20 ((~hskp7) | (~c0_1(a502))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[642, 639])).
% 1.00/1.20 tff(644,plain,
% 1.00/1.20 (~c0_1(a502)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[643, 636])).
% 1.00/1.20 tff(645,plain,
% 1.00/1.20 (^[U: $i] : refl((hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.00/1.20 inference(bind,[status(th)],[])).
% 1.00/1.20 tff(646,plain,
% 1.00/1.20 (![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.00/1.20 inference(quant_intro,[status(thm)],[645])).
% 1.00/1.20 tff(647,plain,
% 1.00/1.20 (![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(648,plain,
% 1.00/1.20 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp31) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp31))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp31) <=> (hskp31 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp31) <=> (hskp31 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp31) | hskp1) <=> ((hskp31 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp1))), rewrite(((hskp31 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp1) <=> (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp31) | hskp1) <=> (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.00/1.20 inference(bind,[status(th)],[])).
% 1.00/1.20 tff(649,plain,
% 1.00/1.20 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp31) | hskp1) <=> ![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.00/1.20 inference(quant_intro,[status(thm)],[648])).
% 1.00/1.20 tff(650,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp31) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 1.00/1.20 tff(651,plain,
% 1.00/1.20 (![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[650, 649])).
% 1.00/1.20 tff(652,plain,
% 1.00/1.20 (![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[651, 647])).
% 1.00/1.20 tff(653,plain,(
% 1.00/1.20 ![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.00/1.20 inference(skolemize,[status(sab)],[652])).
% 1.00/1.20 tff(654,plain,
% 1.00/1.20 (![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[653, 646])).
% 1.00/1.20 tff(655,assumption,(c2_1(a501)), introduced(assumption)).
% 1.00/1.20 tff(656,plain,
% 1.00/1.20 (((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp31 | hskp1 | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501) | (~c2_1(a501)))) <=> ((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp31 | hskp1 | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501) | (~c2_1(a501)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(657,plain,
% 1.00/1.20 ((hskp31 | hskp1 | (~ndr1_0) | c0_1(a501) | (~c2_1(a501)) | (~c1_1(a501))) <=> (hskp31 | hskp1 | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501) | (~c2_1(a501)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(658,plain,
% 1.00/1.20 (((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp31 | hskp1 | (~ndr1_0) | c0_1(a501) | (~c2_1(a501)) | (~c1_1(a501)))) <=> ((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp31 | hskp1 | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501) | (~c2_1(a501))))),
% 1.00/1.20 inference(monotonicity,[status(thm)],[657])).
% 1.00/1.20 tff(659,plain,
% 1.00/1.20 (((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp31 | hskp1 | (~ndr1_0) | c0_1(a501) | (~c2_1(a501)) | (~c1_1(a501)))) <=> ((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp31 | hskp1 | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501) | (~c2_1(a501)))),
% 1.00/1.20 inference(transitivity,[status(thm)],[658, 656])).
% 1.00/1.20 tff(660,plain,
% 1.00/1.20 ((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp31 | hskp1 | (~ndr1_0) | c0_1(a501) | (~c2_1(a501)) | (~c1_1(a501)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(661,plain,
% 1.00/1.20 ((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp31 | hskp1 | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501) | (~c2_1(a501))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[660, 659])).
% 1.00/1.20 tff(662,plain,
% 1.00/1.20 (hskp31 | c0_1(a501)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[661, 106, 571, 610, 655, 654])).
% 1.00/1.20 tff(663,plain,
% 1.00/1.20 (hskp31),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[662, 618])).
% 1.00/1.20 tff(664,plain,
% 1.00/1.20 (((~hskp31) | c2_1(a522)) <=> ((~hskp31) | c2_1(a522))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(665,axiom,((~hskp31) | c2_1(a522)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.00/1.20 tff(666,plain,
% 1.00/1.20 ((~hskp31) | c2_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[665, 664])).
% 1.00/1.20 tff(667,plain,
% 1.00/1.20 ((~hskp31) | c2_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[666, 664])).
% 1.00/1.20 tff(668,plain,
% 1.00/1.20 ((~hskp31) | c2_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[667, 664])).
% 1.00/1.20 tff(669,plain,
% 1.00/1.20 ((~hskp31) | c2_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[668, 664])).
% 1.00/1.20 tff(670,plain,
% 1.00/1.20 ((~hskp31) | c2_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[669, 664])).
% 1.00/1.20 tff(671,plain,
% 1.00/1.20 (c2_1(a522)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[670, 663])).
% 1.00/1.20 tff(672,plain,
% 1.00/1.20 (((~hskp31) | c1_1(a522)) <=> ((~hskp31) | c1_1(a522))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(673,axiom,((~hskp31) | c1_1(a522)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.00/1.20 tff(674,plain,
% 1.00/1.20 ((~hskp31) | c1_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[673, 672])).
% 1.00/1.20 tff(675,plain,
% 1.00/1.20 ((~hskp31) | c1_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[674, 672])).
% 1.00/1.20 tff(676,plain,
% 1.00/1.20 ((~hskp31) | c1_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[675, 672])).
% 1.00/1.20 tff(677,plain,
% 1.00/1.20 ((~hskp31) | c1_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[676, 672])).
% 1.00/1.20 tff(678,plain,
% 1.00/1.20 ((~hskp31) | c1_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[677, 672])).
% 1.00/1.20 tff(679,plain,
% 1.00/1.20 (c1_1(a522)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[678, 663])).
% 1.00/1.20 tff(680,plain,
% 1.00/1.20 (((~hskp31) | c0_1(a522)) <=> ((~hskp31) | c0_1(a522))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(681,axiom,((~hskp31) | c0_1(a522)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.00/1.20 tff(682,plain,
% 1.00/1.20 ((~hskp31) | c0_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[681, 680])).
% 1.00/1.20 tff(683,plain,
% 1.00/1.20 ((~hskp31) | c0_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[682, 680])).
% 1.00/1.20 tff(684,plain,
% 1.00/1.20 ((~hskp31) | c0_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[683, 680])).
% 1.00/1.20 tff(685,plain,
% 1.00/1.20 ((~hskp31) | c0_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[684, 680])).
% 1.00/1.20 tff(686,plain,
% 1.00/1.20 ((~hskp31) | c0_1(a522)),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[685, 680])).
% 1.00/1.20 tff(687,plain,
% 1.00/1.20 (c0_1(a522)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[686, 663])).
% 1.00/1.20 tff(688,plain,
% 1.00/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(689,plain,
% 1.00/1.20 ((hskp2 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(690,plain,
% 1.00/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522))))),
% 1.00/1.20 inference(monotonicity,[status(thm)],[689])).
% 1.00/1.20 tff(691,plain,
% 1.00/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))),
% 1.00/1.20 inference(transitivity,[status(thm)],[690, 688])).
% 1.00/1.20 tff(692,plain,
% 1.00/1.20 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(693,plain,
% 1.00/1.20 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[692, 691])).
% 1.00/1.20 tff(694,plain,
% 1.00/1.20 ($false),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[693, 106, 408, 687, 679, 671, 644, 638, 637, 290])).
% 1.00/1.20 tff(695,plain,(hskp2 | hskp1 | (~c1_1(a501)) | c3_1(a501) | (~c2_1(a501)) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500))), inference(lemma,lemma(discharge,[]))).
% 1.00/1.20 tff(696,plain,
% 1.00/1.20 (hskp2),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[695, 608, 571, 592, 600, 444, 443, 442])).
% 1.00/1.20 tff(697,plain,
% 1.00/1.20 (~c1_1(a496)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[348, 696])).
% 1.00/1.20 tff(698,plain,
% 1.00/1.20 (~c2_1(a496)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[335, 696])).
% 1.00/1.20 tff(699,plain,
% 1.00/1.20 (~c3_1(a496)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[329, 696])).
% 1.00/1.20 tff(700,plain,
% 1.00/1.20 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.00/1.20 inference(bind,[status(th)],[])).
% 1.00/1.20 tff(701,plain,
% 1.00/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.00/1.20 inference(quant_intro,[status(thm)],[700])).
% 1.00/1.20 tff(702,plain,
% 1.00/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(703,plain,
% 1.00/1.20 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.00/1.20 inference(bind,[status(th)],[])).
% 1.00/1.20 tff(704,plain,
% 1.00/1.20 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.00/1.20 inference(quant_intro,[status(thm)],[703])).
% 1.00/1.20 tff(705,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 1.00/1.20 tff(706,plain,
% 1.00/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[705, 704])).
% 1.00/1.20 tff(707,plain,
% 1.00/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[706, 702])).
% 1.00/1.20 tff(708,plain,(
% 1.00/1.20 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.00/1.20 inference(skolemize,[status(sab)],[707])).
% 1.00/1.20 tff(709,plain,
% 1.00/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[708, 701])).
% 1.00/1.20 tff(710,plain,
% 1.00/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a501) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a501) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(711,plain,
% 1.00/1.20 (((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496)) <=> (c3_1(a501) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(712,plain,
% 1.00/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a501) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501))))),
% 1.00/1.20 inference(monotonicity,[status(thm)],[711])).
% 1.00/1.20 tff(713,plain,
% 1.00/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a501) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 1.00/1.20 inference(transitivity,[status(thm)],[712, 710])).
% 1.00/1.20 tff(714,plain,
% 1.00/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(715,plain,
% 1.00/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a501) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[714, 713])).
% 1.00/1.20 tff(716,plain,
% 1.00/1.20 (c0_1(a496)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[715, 106, 610, 655, 609, 572, 574, 573, 709])).
% 1.00/1.20 tff(717,plain,
% 1.00/1.20 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(718,plain,
% 1.00/1.20 ((hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496))) <=> (hskp22 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(719,plain,
% 1.00/1.20 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496))))),
% 1.00/1.20 inference(monotonicity,[status(thm)],[718])).
% 1.00/1.20 tff(720,plain,
% 1.00/1.20 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.00/1.20 inference(transitivity,[status(thm)],[719, 717])).
% 1.00/1.20 tff(721,plain,
% 1.00/1.20 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(722,plain,
% 1.00/1.20 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[721, 720])).
% 1.00/1.20 tff(723,plain,
% 1.00/1.20 (hskp22),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[722, 106, 572, 574, 573, 31, 716])).
% 1.00/1.20 tff(724,plain,
% 1.00/1.20 (~c0_1(a540)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[125, 723])).
% 1.00/1.20 tff(725,plain,
% 1.00/1.20 (c3_1(a540)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[133, 723])).
% 1.00/1.20 tff(726,plain,
% 1.00/1.20 (c1_1(a540)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[141, 723])).
% 1.00/1.20 tff(727,plain,
% 1.00/1.20 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(728,plain,
% 1.00/1.20 ((hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540))) <=> (hskp10 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(729,plain,
% 1.00/1.20 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540))))),
% 1.00/1.20 inference(monotonicity,[status(thm)],[728])).
% 1.00/1.20 tff(730,plain,
% 1.00/1.20 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.00/1.20 inference(transitivity,[status(thm)],[729, 727])).
% 1.00/1.20 tff(731,plain,
% 1.00/1.20 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(732,plain,
% 1.00/1.20 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[731, 730])).
% 1.00/1.20 tff(733,plain,
% 1.00/1.20 ($false),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[732, 106, 11, 726, 725, 724, 572, 574, 53, 716])).
% 1.00/1.20 tff(734,plain,(c3_1(a496) | hskp10 | c1_1(a496) | c2_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c3_1(a501)), inference(lemma,lemma(discharge,[]))).
% 1.00/1.20 tff(735,plain,
% 1.00/1.20 ($false),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[734, 699, 698, 697, 11, 608, 600, 592])).
% 1.00/1.20 tff(736,plain,((~hskp6) | hskp10 | hskp1 | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500))), inference(lemma,lemma(discharge,[]))).
% 1.00/1.20 tff(737,plain,
% 1.00/1.20 (~hskp6),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[736, 571, 11, 407, 399, 391])).
% 1.00/1.20 tff(738,plain,
% 1.00/1.20 ((hskp14 | hskp13 | hskp6) <=> (hskp14 | hskp13 | hskp6)),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(739,plain,
% 1.00/1.20 (((hskp13 | hskp6) | hskp14) <=> (hskp14 | hskp13 | hskp6)),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(740,axiom,((hskp13 | hskp6) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 1.00/1.20 tff(741,plain,
% 1.00/1.20 (hskp14 | hskp13 | hskp6),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[740, 739])).
% 1.00/1.20 tff(742,plain,
% 1.00/1.20 (hskp14 | hskp13 | hskp6),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[741, 738])).
% 1.00/1.20 tff(743,plain,
% 1.00/1.20 (hskp14 | hskp13 | hskp6),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[742, 738])).
% 1.00/1.20 tff(744,plain,
% 1.00/1.20 (hskp14 | hskp13 | hskp6),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[743, 738])).
% 1.00/1.20 tff(745,plain,
% 1.00/1.20 (hskp14 | hskp13 | hskp6),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[744, 738])).
% 1.00/1.20 tff(746,plain,
% 1.00/1.20 (hskp14),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[745, 737, 371])).
% 1.00/1.20 tff(747,plain,
% 1.00/1.20 (((~hskp14) | (~c3_1(a527))) <=> ((~hskp14) | (~c3_1(a527)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(748,plain,
% 1.00/1.20 (((~c3_1(a527)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a527)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(749,axiom,((~c3_1(a527)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.00/1.20 tff(750,plain,
% 1.00/1.20 ((~hskp14) | (~c3_1(a527))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[749, 748])).
% 1.00/1.20 tff(751,plain,
% 1.00/1.20 ((~hskp14) | (~c3_1(a527))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[750, 747])).
% 1.00/1.20 tff(752,plain,
% 1.00/1.20 (~c3_1(a527)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[751, 746])).
% 1.00/1.20 tff(753,plain,
% 1.00/1.20 (((~hskp14) | (~c1_1(a527))) <=> ((~hskp14) | (~c1_1(a527)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(754,plain,
% 1.00/1.20 (((~c1_1(a527)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a527)))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(755,axiom,((~c1_1(a527)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 1.00/1.20 tff(756,plain,
% 1.00/1.20 ((~hskp14) | (~c1_1(a527))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[755, 754])).
% 1.00/1.20 tff(757,plain,
% 1.00/1.20 ((~hskp14) | (~c1_1(a527))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[756, 753])).
% 1.00/1.20 tff(758,plain,
% 1.00/1.20 (~c1_1(a527)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[757, 746])).
% 1.00/1.20 tff(759,plain,
% 1.00/1.20 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c0_1(a527)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c0_1(a527)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(760,plain,
% 1.00/1.21 ((hskp1 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c0_1(a527)) | c1_1(a496) | c0_1(a496) | c3_1(a496)) <=> (hskp1 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c0_1(a527)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(761,plain,
% 1.00/1.21 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c0_1(a527)) | c1_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c0_1(a527))))),
% 1.00/1.21 inference(monotonicity,[status(thm)],[760])).
% 1.00/1.21 tff(762,plain,
% 1.00/1.21 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c0_1(a527)) | c1_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c0_1(a527)))),
% 1.00/1.21 inference(transitivity,[status(thm)],[761, 759])).
% 1.00/1.21 tff(763,plain,
% 1.00/1.21 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c0_1(a527)) | c1_1(a496) | c0_1(a496) | c3_1(a496))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(764,plain,
% 1.00/1.21 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c0_1(a527))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[763, 762])).
% 1.00/1.21 tff(765,plain,
% 1.00/1.21 (c3_1(a496) | c0_1(a496) | (~c0_1(a527))),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[764, 106, 571, 758, 752, 572, 585])).
% 1.00/1.21 tff(766,plain,
% 1.00/1.21 (~c0_1(a527)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[765, 575, 573])).
% 1.00/1.21 tff(767,plain,
% 1.00/1.21 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.00/1.21 inference(bind,[status(th)],[])).
% 1.00/1.21 tff(768,plain,
% 1.00/1.21 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.00/1.21 inference(quant_intro,[status(thm)],[767])).
% 1.00/1.21 tff(769,plain,
% 1.00/1.21 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(770,plain,
% 1.00/1.21 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.00/1.21 inference(bind,[status(th)],[])).
% 1.00/1.21 tff(771,plain,
% 1.00/1.21 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.00/1.21 inference(quant_intro,[status(thm)],[770])).
% 1.00/1.21 tff(772,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 1.00/1.21 tff(773,plain,
% 1.00/1.21 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[772, 771])).
% 1.00/1.21 tff(774,plain,
% 1.00/1.21 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[773, 769])).
% 1.00/1.21 tff(775,plain,(
% 1.00/1.21 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.00/1.21 inference(skolemize,[status(sab)],[774])).
% 1.00/1.21 tff(776,plain,
% 1.00/1.21 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[775, 768])).
% 1.00/1.21 tff(777,plain,
% 1.00/1.21 (((~hskp14) | c2_1(a527)) <=> ((~hskp14) | c2_1(a527))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(778,axiom,((~hskp14) | c2_1(a527)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.00/1.21 tff(779,plain,
% 1.00/1.21 ((~hskp14) | c2_1(a527)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[778, 777])).
% 1.00/1.21 tff(780,plain,
% 1.00/1.21 ((~hskp14) | c2_1(a527)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[779, 777])).
% 1.00/1.21 tff(781,plain,
% 1.00/1.21 ((~hskp14) | c2_1(a527)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[780, 777])).
% 1.00/1.21 tff(782,plain,
% 1.00/1.21 ((~hskp14) | c2_1(a527)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[781, 777])).
% 1.00/1.21 tff(783,plain,
% 1.00/1.21 ((~hskp14) | c2_1(a527)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[782, 777])).
% 1.00/1.21 tff(784,plain,
% 1.00/1.21 (c2_1(a527)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[783, 746])).
% 1.00/1.21 tff(785,plain,
% 1.00/1.21 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c2_1(a527)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c2_1(a527)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(786,plain,
% 1.00/1.21 ((hskp0 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)) | c2_1(a496) | c1_1(a496) | c0_1(a496)) <=> (hskp0 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c2_1(a527)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(787,plain,
% 1.00/1.21 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)) | c2_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c2_1(a527))))),
% 1.00/1.21 inference(monotonicity,[status(thm)],[786])).
% 1.00/1.21 tff(788,plain,
% 1.00/1.21 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)) | c2_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c2_1(a527)))),
% 1.00/1.21 inference(transitivity,[status(thm)],[787, 785])).
% 1.00/1.21 tff(789,plain,
% 1.00/1.21 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)) | c2_1(a496) | c1_1(a496) | c0_1(a496))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(790,plain,
% 1.00/1.21 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c2_1(a527))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[789, 788])).
% 1.00/1.21 tff(791,plain,
% 1.00/1.21 (hskp0 | c0_1(a496)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[790, 106, 784, 758, 752, 572, 574, 776])).
% 1.00/1.21 tff(792,plain,
% 1.00/1.21 (hskp0),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[791, 575])).
% 1.00/1.21 tff(793,plain,
% 1.00/1.21 (((~hskp0) | (~c0_1(a494))) <=> ((~hskp0) | (~c0_1(a494)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(794,plain,
% 1.00/1.21 (((~c0_1(a494)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a494)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(795,axiom,((~c0_1(a494)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.00/1.21 tff(796,plain,
% 1.00/1.21 ((~hskp0) | (~c0_1(a494))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[795, 794])).
% 1.00/1.21 tff(797,plain,
% 1.00/1.21 ((~hskp0) | (~c0_1(a494))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[796, 793])).
% 1.00/1.21 tff(798,plain,
% 1.00/1.21 (~c0_1(a494)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[797, 792])).
% 1.00/1.21 tff(799,plain,
% 1.00/1.21 (hskp11 | c2_1(a496) | c0_1(a496)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[342, 106, 11, 573, 10])).
% 1.00/1.21 tff(800,plain,
% 1.00/1.21 (hskp11),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[799, 575, 574])).
% 1.00/1.21 tff(801,plain,
% 1.00/1.21 (~c2_1(a510)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[59, 800])).
% 1.00/1.21 tff(802,plain,
% 1.00/1.21 (~c1_1(a510)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[65, 800])).
% 1.00/1.21 tff(803,plain,
% 1.00/1.21 (((~hskp0) | c3_1(a494)) <=> ((~hskp0) | c3_1(a494))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(804,axiom,((~hskp0) | c3_1(a494)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.00/1.21 tff(805,plain,
% 1.00/1.21 ((~hskp0) | c3_1(a494)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[804, 803])).
% 1.00/1.21 tff(806,plain,
% 1.00/1.21 ((~hskp0) | c3_1(a494)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[805, 803])).
% 1.00/1.21 tff(807,plain,
% 1.00/1.21 ((~hskp0) | c3_1(a494)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[806, 803])).
% 1.00/1.21 tff(808,plain,
% 1.00/1.21 ((~hskp0) | c3_1(a494)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[807, 803])).
% 1.00/1.21 tff(809,plain,
% 1.00/1.21 ((~hskp0) | c3_1(a494)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[808, 803])).
% 1.00/1.21 tff(810,plain,
% 1.00/1.21 (c3_1(a494)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[809, 792])).
% 1.00/1.21 tff(811,plain,
% 1.00/1.21 (c0_1(a510)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[73, 800])).
% 1.00/1.21 tff(812,plain,
% 1.00/1.21 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a510) | c2_1(a510) | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a494)) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a510) | c2_1(a510) | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a494)) | (~c0_1(a510)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(813,plain,
% 1.00/1.21 ((hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a494) | (~c1_1(a494)) | (~c3_1(a494))) <=> (hskp10 | c1_1(a510) | c2_1(a510) | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a494)) | (~c0_1(a510)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(814,plain,
% 1.00/1.21 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a494) | (~c1_1(a494)) | (~c3_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a510) | c2_1(a510) | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a494)) | (~c0_1(a510))))),
% 1.00/1.21 inference(monotonicity,[status(thm)],[813])).
% 1.00/1.21 tff(815,plain,
% 1.00/1.21 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a494) | (~c1_1(a494)) | (~c3_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a510) | c2_1(a510) | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a494)) | (~c0_1(a510)))),
% 1.00/1.21 inference(transitivity,[status(thm)],[814, 812])).
% 1.00/1.21 tff(816,plain,
% 1.00/1.21 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a494) | (~c1_1(a494)) | (~c3_1(a494)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(817,plain,
% 1.00/1.21 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a510) | c2_1(a510) | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a494)) | (~c0_1(a510))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[816, 815])).
% 1.00/1.21 tff(818,plain,
% 1.00/1.21 (~c1_1(a494)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[817, 106, 11, 811, 810, 802, 801, 798, 53])).
% 1.00/1.21 tff(819,plain,
% 1.00/1.21 (^[U: $i] : refl((hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))))),
% 1.00/1.21 inference(bind,[status(th)],[])).
% 1.00/1.21 tff(820,plain,
% 1.00/1.21 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.00/1.21 inference(quant_intro,[status(thm)],[819])).
% 1.00/1.21 tff(821,plain,
% 1.00/1.21 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(822,plain,
% 1.00/1.21 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp9) <=> ((hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) | hskp9))), rewrite(((hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) | hskp9) <=> (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp9) <=> (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))))),
% 1.00/1.21 inference(bind,[status(th)],[])).
% 1.00/1.21 tff(823,plain,
% 1.00/1.21 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp9) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.00/1.21 inference(quant_intro,[status(thm)],[822])).
% 1.00/1.21 tff(824,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 1.00/1.21 tff(825,plain,
% 1.00/1.21 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[824, 823])).
% 1.00/1.21 tff(826,plain,
% 1.00/1.21 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[825, 821])).
% 1.00/1.21 tff(827,plain,(
% 1.00/1.21 ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.00/1.21 inference(skolemize,[status(sab)],[826])).
% 1.00/1.21 tff(828,plain,
% 1.00/1.21 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[827, 820])).
% 1.00/1.21 tff(829,plain,
% 1.00/1.21 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | c1_1(a494))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp6 | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | c1_1(a494))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(830,plain,
% 1.00/1.21 ((hskp9 | hskp6 | (~ndr1_0) | c0_1(a494) | c1_1(a494) | (~c3_1(a494))) <=> (hskp9 | hskp6 | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | c1_1(a494))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(831,plain,
% 1.00/1.21 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c0_1(a494) | c1_1(a494) | (~c3_1(a494)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | c1_1(a494)))),
% 1.00/1.21 inference(monotonicity,[status(thm)],[830])).
% 1.00/1.21 tff(832,plain,
% 1.00/1.21 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c0_1(a494) | c1_1(a494) | (~c3_1(a494)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp6 | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | c1_1(a494))),
% 1.00/1.21 inference(transitivity,[status(thm)],[831, 829])).
% 1.00/1.21 tff(833,plain,
% 1.00/1.21 ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c0_1(a494) | c1_1(a494) | (~c3_1(a494)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(834,plain,
% 1.00/1.21 ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp6 | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | c1_1(a494)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[833, 832])).
% 1.00/1.21 tff(835,plain,
% 1.00/1.21 (hskp9),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[834, 106, 737, 810, 798, 828, 818])).
% 1.00/1.21 tff(836,plain,
% 1.00/1.21 (((~hskp9) | (~c1_1(a507))) <=> ((~hskp9) | (~c1_1(a507)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(837,plain,
% 1.00/1.21 (((~c1_1(a507)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a507)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(838,axiom,((~c1_1(a507)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.00/1.21 tff(839,plain,
% 1.00/1.21 ((~hskp9) | (~c1_1(a507))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[838, 837])).
% 1.00/1.21 tff(840,plain,
% 1.00/1.21 ((~hskp9) | (~c1_1(a507))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[839, 836])).
% 1.00/1.21 tff(841,plain,
% 1.00/1.21 (~c1_1(a507)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[840, 835])).
% 1.00/1.21 tff(842,plain,
% 1.00/1.21 (((~hskp9) | (~c0_1(a507))) <=> ((~hskp9) | (~c0_1(a507)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(843,plain,
% 1.00/1.21 (((~c0_1(a507)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a507)))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(844,axiom,((~c0_1(a507)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.00/1.21 tff(845,plain,
% 1.00/1.21 ((~hskp9) | (~c0_1(a507))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[844, 843])).
% 1.00/1.21 tff(846,plain,
% 1.00/1.21 ((~hskp9) | (~c0_1(a507))),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[845, 842])).
% 1.00/1.21 tff(847,plain,
% 1.00/1.21 (~c0_1(a507)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[846, 835])).
% 1.00/1.21 tff(848,plain,
% 1.00/1.21 (((~hskp9) | c3_1(a507)) <=> ((~hskp9) | c3_1(a507))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(849,axiom,((~hskp9) | c3_1(a507)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.00/1.21 tff(850,plain,
% 1.00/1.21 ((~hskp9) | c3_1(a507)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[849, 848])).
% 1.00/1.21 tff(851,plain,
% 1.00/1.21 ((~hskp9) | c3_1(a507)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[850, 848])).
% 1.00/1.21 tff(852,plain,
% 1.00/1.21 ((~hskp9) | c3_1(a507)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[851, 848])).
% 1.00/1.21 tff(853,plain,
% 1.00/1.21 ((~hskp9) | c3_1(a507)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[852, 848])).
% 1.00/1.21 tff(854,plain,
% 1.00/1.21 ((~hskp9) | c3_1(a507)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[853, 848])).
% 1.00/1.21 tff(855,plain,
% 1.00/1.21 (c3_1(a507)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[854, 835])).
% 1.00/1.21 tff(856,assumption,(~c1_1(a507)), introduced(assumption)).
% 1.00/1.21 tff(857,assumption,(~c0_1(a507)), introduced(assumption)).
% 1.00/1.21 tff(858,assumption,(hskp12), introduced(assumption)).
% 1.00/1.21 tff(859,plain,
% 1.00/1.21 (~c2_1(a514)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[487, 858])).
% 1.00/1.21 tff(860,assumption,(c3_1(a507)), introduced(assumption)).
% 1.00/1.21 tff(861,plain,
% 1.00/1.21 (c3_1(a514)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[495, 858])).
% 1.00/1.21 tff(862,plain,
% 1.00/1.21 (c1_1(a514)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[503, 858])).
% 1.00/1.21 tff(863,plain,
% 1.00/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a514) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a514) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(864,plain,
% 1.00/1.21 (((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (c2_1(a514) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(865,plain,
% 1.00/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a514) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514)))),
% 1.00/1.21 inference(monotonicity,[status(thm)],[864])).
% 1.00/1.21 tff(866,plain,
% 1.00/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a514) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.00/1.21 inference(transitivity,[status(thm)],[865, 863])).
% 1.00/1.21 tff(867,plain,
% 1.00/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 1.00/1.21 inference(quant_inst,[status(thm)],[])).
% 1.00/1.21 tff(868,plain,
% 1.00/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a514) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514)),
% 1.00/1.21 inference(modus_ponens,[status(thm)],[867, 866])).
% 1.00/1.21 tff(869,plain,
% 1.00/1.21 (c0_1(a514)),
% 1.00/1.21 inference(unit_resolution,[status(thm)],[868, 106, 862, 861, 860, 859, 857, 856, 558])).
% 1.00/1.21 tff(870,plain,
% 1.00/1.21 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.00/1.21 inference(bind,[status(th)],[])).
% 1.00/1.21 tff(871,plain,
% 1.00/1.21 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.21 inference(quant_intro,[status(thm)],[870])).
% 1.00/1.21 tff(872,plain,
% 1.00/1.21 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.21 inference(rewrite,[status(thm)],[])).
% 1.00/1.21 tff(873,plain,
% 1.00/1.21 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | 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))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | 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))) | (~ndr1_0)) | c2_1(U)) | 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))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp6) <=> (hskp6 | (~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))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.00/1.21 inference(bind,[status(th)],[])).
% 1.00/1.22 tff(874,plain,
% 1.00/1.22 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.22 inference(quant_intro,[status(thm)],[873])).
% 1.00/1.22 tff(875,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 1.00/1.22 tff(876,plain,
% 1.00/1.22 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[875, 874])).
% 1.00/1.22 tff(877,plain,
% 1.00/1.22 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[876, 872])).
% 1.00/1.22 tff(878,plain,(
% 1.00/1.22 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.22 inference(skolemize,[status(sab)],[877])).
% 1.00/1.22 tff(879,plain,
% 1.00/1.22 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[878, 871])).
% 1.00/1.22 tff(880,assumption,(~hskp6), introduced(assumption)).
% 1.00/1.22 tff(881,plain,
% 1.00/1.22 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(882,plain,
% 1.00/1.22 ((hskp6 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c2_1(a496) | c0_1(a496) | c3_1(a496)) <=> (hskp6 | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(883,plain,
% 1.00/1.22 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c2_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514))))),
% 1.00/1.22 inference(monotonicity,[status(thm)],[882])).
% 1.00/1.22 tff(884,plain,
% 1.00/1.22 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c2_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.00/1.22 inference(transitivity,[status(thm)],[883, 881])).
% 1.00/1.22 tff(885,plain,
% 1.00/1.22 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c2_1(a496) | c0_1(a496) | c3_1(a496))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(886,plain,
% 1.00/1.22 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[885, 884])).
% 1.00/1.22 tff(887,plain,
% 1.00/1.22 ($false),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[886, 106, 880, 862, 859, 574, 573, 879, 575, 869])).
% 1.00/1.22 tff(888,plain,((~hskp12) | hskp6 | c2_1(a496) | c3_1(a496) | c0_1(a496) | (~c3_1(a507)) | c0_1(a507) | c1_1(a507)), inference(lemma,lemma(discharge,[]))).
% 1.00/1.22 tff(889,plain,
% 1.00/1.22 (~hskp12),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[888, 855, 574, 573, 737, 575, 847, 841])).
% 1.00/1.22 tff(890,plain,
% 1.00/1.22 (hskp15),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[481, 889, 371])).
% 1.00/1.22 tff(891,plain,
% 1.00/1.22 (~c3_1(a528)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[424, 890])).
% 1.00/1.22 tff(892,plain,
% 1.00/1.22 (c1_1(a528)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[432, 890])).
% 1.00/1.22 tff(893,plain,
% 1.00/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a528) | c1_1(a527) | c3_1(a527) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c1_1(a527) | c3_1(a527) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(894,plain,
% 1.00/1.22 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a527) | c1_1(a527) | c0_1(a527)) <=> (c3_1(a528) | c1_1(a527) | c3_1(a527) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(895,plain,
% 1.00/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a527) | c1_1(a527) | c0_1(a527))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a528) | c1_1(a527) | c3_1(a527) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528))))),
% 1.00/1.22 inference(monotonicity,[status(thm)],[894])).
% 1.00/1.22 tff(896,plain,
% 1.00/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a527) | c1_1(a527) | c0_1(a527))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c1_1(a527) | c3_1(a527) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.00/1.22 inference(transitivity,[status(thm)],[895, 893])).
% 1.00/1.22 tff(897,plain,
% 1.00/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a527) | c1_1(a527) | c0_1(a527))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(898,plain,
% 1.00/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c1_1(a527) | c3_1(a527) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[897, 896])).
% 1.00/1.22 tff(899,plain,
% 1.00/1.22 (~c2_1(a528)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[898, 106, 892, 891, 758, 752, 574, 573, 709, 766, 575])).
% 1.00/1.22 tff(900,plain,
% 1.00/1.22 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 1.00/1.22 inference(bind,[status(th)],[])).
% 1.00/1.22 tff(901,plain,
% 1.00/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.00/1.22 inference(quant_intro,[status(thm)],[900])).
% 1.00/1.22 tff(902,plain,
% 1.00/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(903,plain,
% 1.00/1.22 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~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))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~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))) | (~c1_1(V))) | c3_1(U)) <=> ((~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))) | (~c1_1(V))) | c3_1(U)) | 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))) | (~c1_1(V))) | c3_1(U)) | 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))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 1.00/1.22 inference(bind,[status(th)],[])).
% 1.00/1.22 tff(904,plain,
% 1.00/1.22 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.00/1.22 inference(quant_intro,[status(thm)],[903])).
% 1.00/1.22 tff(905,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 1.00/1.22 tff(906,plain,
% 1.00/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[905, 904])).
% 1.00/1.22 tff(907,plain,
% 1.00/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[906, 902])).
% 1.00/1.22 tff(908,plain,(
% 1.00/1.22 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.00/1.22 inference(skolemize,[status(sab)],[907])).
% 1.00/1.22 tff(909,plain,
% 1.00/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[908, 901])).
% 1.00/1.22 tff(910,plain,
% 1.00/1.22 (c0_1(a528)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[440, 890])).
% 1.00/1.22 tff(911,plain,
% 1.00/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(912,plain,
% 1.00/1.22 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(913,plain,
% 1.00/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528)))),
% 1.00/1.22 inference(monotonicity,[status(thm)],[912])).
% 1.00/1.22 tff(914,plain,
% 1.00/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.00/1.22 inference(transitivity,[status(thm)],[913, 911])).
% 1.00/1.22 tff(915,plain,
% 1.00/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(916,plain,
% 1.00/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[915, 914])).
% 1.00/1.22 tff(917,plain,
% 1.00/1.22 ($false),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[916, 106, 910, 892, 891, 574, 573, 909, 575, 899])).
% 1.00/1.22 tff(918,plain,(c0_1(a496) | c2_1(a496) | c3_1(a496) | hskp13 | hskp10 | c1_1(a496) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.00/1.22 tff(919,plain,
% 1.00/1.22 (c0_1(a496)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[918, 574, 573, 371, 11, 572, 571])).
% 1.00/1.22 tff(920,plain,
% 1.00/1.22 (hskp22 | c2_1(a496) | (~c0_1(a496))),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[722, 106, 572, 573, 31])).
% 1.00/1.22 tff(921,plain,
% 1.00/1.22 (hskp22),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[920, 919, 574])).
% 1.00/1.22 tff(922,plain,
% 1.00/1.22 (~c0_1(a540)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[125, 921])).
% 1.00/1.22 tff(923,plain,
% 1.00/1.22 (c3_1(a540)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[133, 921])).
% 1.00/1.22 tff(924,plain,
% 1.00/1.22 (c1_1(a540)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[141, 921])).
% 1.00/1.22 tff(925,plain,
% 1.00/1.22 ($false),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[732, 106, 11, 924, 923, 922, 572, 574, 53, 919])).
% 1.00/1.22 tff(926,plain,(c2_1(a496) | hskp10 | c1_1(a496) | c3_1(a496) | hskp13 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.00/1.22 tff(927,plain,
% 1.00/1.22 (hskp1),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[926, 570, 569, 11, 371, 568])).
% 1.00/1.22 tff(928,plain,
% 1.00/1.22 (((~hskp1) | (~c3_1(a495))) <=> ((~hskp1) | (~c3_1(a495)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(929,plain,
% 1.00/1.22 (((~c3_1(a495)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a495)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(930,axiom,((~c3_1(a495)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.00/1.22 tff(931,plain,
% 1.00/1.22 ((~hskp1) | (~c3_1(a495))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[930, 929])).
% 1.00/1.22 tff(932,plain,
% 1.00/1.22 ((~hskp1) | (~c3_1(a495))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[931, 928])).
% 1.00/1.22 tff(933,plain,
% 1.00/1.22 (~c3_1(a495)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[932, 927])).
% 1.00/1.22 tff(934,plain,
% 1.00/1.22 (((~hskp1) | (~c0_1(a495))) <=> ((~hskp1) | (~c0_1(a495)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(935,plain,
% 1.00/1.22 (((~c0_1(a495)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a495)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(936,axiom,((~c0_1(a495)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.00/1.22 tff(937,plain,
% 1.00/1.22 ((~hskp1) | (~c0_1(a495))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[936, 935])).
% 1.00/1.22 tff(938,plain,
% 1.00/1.22 ((~hskp1) | (~c0_1(a495))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[937, 934])).
% 1.00/1.22 tff(939,plain,
% 1.00/1.22 (~c0_1(a495)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[938, 927])).
% 1.00/1.22 tff(940,assumption,(~c3_1(a502)), introduced(assumption)).
% 1.00/1.22 tff(941,plain,
% 1.00/1.22 (((~hskp1) | c1_1(a495)) <=> ((~hskp1) | c1_1(a495))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(942,axiom,((~hskp1) | c1_1(a495)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.00/1.22 tff(943,plain,
% 1.00/1.22 ((~hskp1) | c1_1(a495)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[942, 941])).
% 1.00/1.22 tff(944,plain,
% 1.00/1.22 ((~hskp1) | c1_1(a495)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[943, 941])).
% 1.00/1.22 tff(945,plain,
% 1.00/1.22 ((~hskp1) | c1_1(a495)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[944, 941])).
% 1.00/1.22 tff(946,plain,
% 1.00/1.22 ((~hskp1) | c1_1(a495)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[945, 941])).
% 1.00/1.22 tff(947,plain,
% 1.00/1.22 ((~hskp1) | c1_1(a495)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[946, 941])).
% 1.00/1.22 tff(948,plain,
% 1.00/1.22 (c1_1(a495)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[947, 927])).
% 1.00/1.22 tff(949,assumption,(~c1_1(a502)), introduced(assumption)).
% 1.00/1.22 tff(950,plain,
% 1.00/1.22 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.00/1.22 inference(bind,[status(th)],[])).
% 1.00/1.22 tff(951,plain,
% 1.00/1.22 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.00/1.22 inference(quant_intro,[status(thm)],[950])).
% 1.00/1.22 tff(952,plain,
% 1.00/1.22 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(953,plain,
% 1.00/1.22 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.00/1.22 inference(bind,[status(th)],[])).
% 1.00/1.22 tff(954,plain,
% 1.00/1.22 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.00/1.22 inference(quant_intro,[status(thm)],[953])).
% 1.00/1.22 tff(955,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.00/1.22 tff(956,plain,
% 1.00/1.22 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[955, 954])).
% 1.00/1.22 tff(957,plain,
% 1.00/1.22 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[956, 952])).
% 1.00/1.22 tff(958,plain,(
% 1.00/1.22 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.00/1.22 inference(skolemize,[status(sab)],[957])).
% 1.00/1.22 tff(959,plain,
% 1.00/1.22 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[958, 951])).
% 1.00/1.22 tff(960,plain,
% 1.00/1.22 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a568) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a568) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(961,plain,
% 1.00/1.22 ((hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495))) <=> (hskp8 | c1_1(a568) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(962,plain,
% 1.00/1.22 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a568) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.00/1.22 inference(monotonicity,[status(thm)],[961])).
% 1.00/1.22 tff(963,plain,
% 1.00/1.22 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a568) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.00/1.22 inference(transitivity,[status(thm)],[962, 960])).
% 1.00/1.22 tff(964,plain,
% 1.00/1.22 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)))),
% 1.00/1.22 inference(quant_inst,[status(thm)],[])).
% 1.00/1.22 tff(965,plain,
% 1.00/1.22 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a568) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[964, 963])).
% 1.00/1.22 tff(966,plain,
% 1.00/1.22 (hskp8),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[965, 106, 368, 370, 948, 369, 939, 933, 959])).
% 1.00/1.22 tff(967,plain,
% 1.00/1.22 (((~hskp8) | c2_1(a505)) <=> ((~hskp8) | c2_1(a505))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(968,axiom,((~hskp8) | c2_1(a505)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.00/1.22 tff(969,plain,
% 1.00/1.22 ((~hskp8) | c2_1(a505)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[968, 967])).
% 1.00/1.22 tff(970,plain,
% 1.00/1.22 ((~hskp8) | c2_1(a505)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[969, 967])).
% 1.00/1.22 tff(971,plain,
% 1.00/1.22 ((~hskp8) | c2_1(a505)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[970, 967])).
% 1.00/1.22 tff(972,plain,
% 1.00/1.22 ((~hskp8) | c2_1(a505)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[971, 967])).
% 1.00/1.22 tff(973,plain,
% 1.00/1.22 ((~hskp8) | c2_1(a505)),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[972, 967])).
% 1.00/1.22 tff(974,plain,
% 1.00/1.22 (c2_1(a505)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[973, 966])).
% 1.00/1.22 tff(975,plain,
% 1.00/1.22 (((~hskp8) | (~c0_1(a505))) <=> ((~hskp8) | (~c0_1(a505)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(976,plain,
% 1.00/1.22 (((~c0_1(a505)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a505)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(977,axiom,((~c0_1(a505)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.00/1.22 tff(978,plain,
% 1.00/1.22 ((~hskp8) | (~c0_1(a505))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[977, 976])).
% 1.00/1.22 tff(979,plain,
% 1.00/1.22 ((~hskp8) | (~c0_1(a505))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[978, 975])).
% 1.00/1.22 tff(980,plain,
% 1.00/1.22 (~c0_1(a505)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[979, 966])).
% 1.00/1.22 tff(981,assumption,(~hskp12), introduced(assumption)).
% 1.00/1.22 tff(982,assumption,(~c3_1(a495)), introduced(assumption)).
% 1.00/1.22 tff(983,assumption,(~c0_1(a495)), introduced(assumption)).
% 1.00/1.22 tff(984,assumption,(c1_1(a495)), introduced(assumption)).
% 1.00/1.22 tff(985,plain,
% 1.00/1.22 (hskp15),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[481, 981, 371])).
% 1.00/1.22 tff(986,plain,
% 1.00/1.22 (~c3_1(a528)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[424, 985])).
% 1.00/1.22 tff(987,plain,
% 1.00/1.22 (c1_1(a528)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[432, 985])).
% 1.00/1.22 tff(988,plain,
% 1.00/1.22 (c0_1(a528)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[440, 985])).
% 1.00/1.22 tff(989,assumption,(~c3_1(a528)), introduced(assumption)).
% 1.00/1.22 tff(990,assumption,(hskp20), introduced(assumption)).
% 1.00/1.22 tff(991,plain,
% 1.00/1.22 (((~hskp20) | (~c2_1(a536))) <=> ((~hskp20) | (~c2_1(a536)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(992,plain,
% 1.00/1.22 (((~c2_1(a536)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a536)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(993,axiom,((~c2_1(a536)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.00/1.22 tff(994,plain,
% 1.00/1.22 ((~hskp20) | (~c2_1(a536))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[993, 992])).
% 1.00/1.22 tff(995,plain,
% 1.00/1.22 ((~hskp20) | (~c2_1(a536))),
% 1.00/1.22 inference(modus_ponens,[status(thm)],[994, 991])).
% 1.00/1.22 tff(996,plain,
% 1.00/1.22 (~c2_1(a536)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[995, 990])).
% 1.00/1.22 tff(997,plain,
% 1.00/1.22 (~c0_1(a536)),
% 1.00/1.22 inference(unit_resolution,[status(thm)],[522, 990])).
% 1.00/1.22 tff(998,assumption,(c1_1(a528)), introduced(assumption)).
% 1.00/1.22 tff(999,assumption,(c0_1(a528)), introduced(assumption)).
% 1.00/1.22 tff(1000,plain,
% 1.00/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(1001,plain,
% 1.00/1.22 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536)) <=> (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))),
% 1.00/1.22 inference(rewrite,[status(thm)],[])).
% 1.00/1.22 tff(1002,plain,
% 1.00/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536))))),
% 1.00/1.22 inference(monotonicity,[status(thm)],[1001])).
% 1.00/1.22 tff(1003,plain,
% 1.00/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))),
% 1.00/1.23 inference(transitivity,[status(thm)],[1002, 1000])).
% 1.00/1.23 tff(1004,plain,
% 1.00/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(1005,plain,
% 1.00/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 1.00/1.23 tff(1006,plain,
% 1.00/1.23 (~c3_1(a536)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[1005, 106, 999, 998, 984, 997, 996, 989, 983, 982, 21])).
% 1.00/1.23 tff(1007,plain,
% 1.00/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(1008,plain,
% 1.00/1.23 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a502) | c1_1(a502) | c0_1(a502)) <=> (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(1009,plain,
% 1.00/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536)))),
% 1.00/1.23 inference(monotonicity,[status(thm)],[1008])).
% 1.00/1.23 tff(1010,plain,
% 1.00/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.00/1.23 inference(transitivity,[status(thm)],[1009, 1007])).
% 1.00/1.23 tff(1011,plain,
% 1.00/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a502) | c1_1(a502) | c0_1(a502))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(1012,plain,
% 1.00/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536)),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 1.00/1.23 tff(1013,plain,
% 1.00/1.23 ((~c2_1(a528)) | c3_1(a536)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[1012, 106, 998, 997, 996, 989, 239, 949, 940, 709])).
% 1.00/1.23 tff(1014,plain,
% 1.00/1.23 (~c2_1(a528)),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[1013, 1006])).
% 1.00/1.23 tff(1015,plain,
% 1.00/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c3_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c3_1(a536))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(1016,plain,
% 1.00/1.23 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a536) | c0_1(a536) | c2_1(a536)) <=> (c0_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c3_1(a536))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(1017,plain,
% 1.00/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a536) | c0_1(a536) | c2_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c3_1(a536)))),
% 1.00/1.23 inference(monotonicity,[status(thm)],[1016])).
% 1.00/1.23 tff(1018,plain,
% 1.00/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a536) | c0_1(a536) | c2_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c3_1(a536))),
% 1.00/1.23 inference(transitivity,[status(thm)],[1017, 1015])).
% 1.00/1.23 tff(1019,plain,
% 1.00/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a536) | c0_1(a536) | c2_1(a536))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.00/1.23 tff(1020,plain,
% 1.00/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c3_1(a536)),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 1.00/1.23 tff(1021,plain,
% 1.00/1.23 ($false),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[1020, 106, 999, 998, 997, 996, 989, 909, 1014, 1006])).
% 1.00/1.23 tff(1022,plain,((~hskp20) | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~c1_1(a495)) | c0_1(a495) | c3_1(a495)), inference(lemma,lemma(discharge,[]))).
% 1.00/1.23 tff(1023,plain,
% 1.00/1.23 (~hskp20),
% 1.00/1.23 inference(unit_resolution,[status(thm)],[1022, 988, 987, 986, 239, 949, 940, 984, 983, 982])).
% 1.00/1.23 tff(1024,plain,
% 1.00/1.23 (^[U: $i] : refl((hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 1.00/1.23 inference(bind,[status(th)],[])).
% 1.00/1.23 tff(1025,plain,
% 1.00/1.23 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.00/1.23 inference(quant_intro,[status(thm)],[1024])).
% 1.00/1.23 tff(1026,plain,
% 1.00/1.23 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(1027,plain,
% 1.00/1.23 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp20) <=> ((hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp20))), rewrite(((hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp20) <=> (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp20) <=> (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 1.00/1.23 inference(bind,[status(th)],[])).
% 1.00/1.23 tff(1028,plain,
% 1.00/1.23 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp20) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.00/1.23 inference(quant_intro,[status(thm)],[1027])).
% 1.00/1.23 tff(1029,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.00/1.23 tff(1030,plain,
% 1.00/1.23 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 1.00/1.23 tff(1031,plain,
% 1.00/1.23 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[1030, 1026])).
% 1.00/1.23 tff(1032,plain,(
% 1.00/1.23 ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.00/1.23 inference(skolemize,[status(sab)],[1031])).
% 1.00/1.23 tff(1033,plain,
% 1.00/1.23 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.00/1.23 inference(modus_ponens,[status(thm)],[1032, 1025])).
% 1.00/1.23 tff(1034,plain,
% 1.00/1.23 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a502)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a502)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(1035,plain,
% 1.00/1.23 ((hskp20 | hskp12 | (~ndr1_0) | c3_1(a502) | c1_1(a502) | (~c2_1(a502))) <=> (hskp20 | hskp12 | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a502)))),
% 1.00/1.23 inference(rewrite,[status(thm)],[])).
% 1.00/1.23 tff(1036,plain,
% 1.00/1.23 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a502) | c1_1(a502) | (~c2_1(a502)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a502))))),
% 1.00/1.23 inference(monotonicity,[status(thm)],[1035])).
% 1.00/1.23 tff(1037,plain,
% 1.00/1.23 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a502) | c1_1(a502) | (~c2_1(a502)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a502)))),
% 1.00/1.23 inference(transitivity,[status(thm)],[1036, 1034])).
% 1.00/1.23 tff(1038,plain,
% 1.00/1.23 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a502) | c1_1(a502) | (~c2_1(a502)))),
% 1.00/1.23 inference(quant_inst,[status(thm)],[])).
% 1.08/1.23 tff(1039,plain,
% 1.08/1.23 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a502))),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 1.08/1.23 tff(1040,plain,
% 1.08/1.23 (hskp20 | hskp12 | c3_1(a502) | (~c2_1(a502))),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1039, 106, 949, 1033])).
% 1.08/1.23 tff(1041,plain,
% 1.08/1.23 (~c2_1(a502)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1040, 1023, 940, 981])).
% 1.08/1.23 tff(1042,plain,
% 1.08/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c2_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(1043,plain,
% 1.08/1.23 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a502) | c0_1(a502) | c3_1(a502) | c3_1(a502) | c1_1(a502) | c0_1(a502)) <=> (c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(1044,plain,
% 1.08/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a502) | c0_1(a502) | c3_1(a502) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c2_1(a528))))),
% 1.08/1.23 inference(monotonicity,[status(thm)],[1043])).
% 1.08/1.23 tff(1045,plain,
% 1.08/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a502) | c0_1(a502) | c3_1(a502) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.08/1.23 inference(transitivity,[status(thm)],[1044, 1042])).
% 1.08/1.23 tff(1046,plain,
% 1.08/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a502) | c0_1(a502) | c3_1(a502) | c3_1(a502) | c1_1(a502) | c0_1(a502))),
% 1.08/1.23 inference(quant_inst,[status(thm)],[])).
% 1.08/1.23 tff(1047,plain,
% 1.08/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c2_1(a528))),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 1.08/1.23 tff(1048,plain,
% 1.08/1.23 (~c2_1(a528)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1047, 106, 987, 986, 239, 949, 940, 709, 1041])).
% 1.08/1.23 tff(1049,plain,
% 1.08/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(1050,plain,
% 1.08/1.23 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a502) | c0_1(a502) | c2_1(a502)) <=> (c3_1(a528) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(1051,plain,
% 1.08/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528)))),
% 1.08/1.23 inference(monotonicity,[status(thm)],[1050])).
% 1.08/1.23 tff(1052,plain,
% 1.08/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.08/1.23 inference(transitivity,[status(thm)],[1051, 1049])).
% 1.08/1.23 tff(1053,plain,
% 1.08/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a502) | c0_1(a502) | c2_1(a502))),
% 1.08/1.23 inference(quant_inst,[status(thm)],[])).
% 1.08/1.23 tff(1054,plain,
% 1.08/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528)),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 1.08/1.23 tff(1055,plain,
% 1.08/1.23 ($false),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1054, 106, 988, 987, 986, 239, 940, 909, 1041, 1048])).
% 1.08/1.23 tff(1056,plain,(hskp12 | c0_1(a502) | c3_1(a502) | c1_1(a502) | (~c1_1(a495)) | c0_1(a495) | c3_1(a495) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.08/1.23 tff(1057,plain,
% 1.08/1.23 (hskp12),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1056, 239, 940, 949, 948, 939, 933, 371])).
% 1.08/1.23 tff(1058,plain,
% 1.08/1.23 (~c2_1(a514)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[487, 1057])).
% 1.08/1.23 tff(1059,plain,
% 1.08/1.23 (((~hskp8) | c3_1(a505)) <=> ((~hskp8) | c3_1(a505))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(1060,axiom,((~hskp8) | c3_1(a505)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.08/1.23 tff(1061,plain,
% 1.08/1.23 ((~hskp8) | c3_1(a505)),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 1.08/1.23 tff(1062,plain,
% 1.08/1.23 ((~hskp8) | c3_1(a505)),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[1061, 1059])).
% 1.08/1.23 tff(1063,plain,
% 1.08/1.23 ((~hskp8) | c3_1(a505)),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[1062, 1059])).
% 1.08/1.23 tff(1064,plain,
% 1.08/1.23 ((~hskp8) | c3_1(a505)),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[1063, 1059])).
% 1.08/1.23 tff(1065,plain,
% 1.08/1.23 ((~hskp8) | c3_1(a505)),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[1064, 1059])).
% 1.08/1.23 tff(1066,plain,
% 1.08/1.23 (c3_1(a505)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1065, 966])).
% 1.08/1.23 tff(1067,plain,
% 1.08/1.23 (c3_1(a514)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[495, 1057])).
% 1.08/1.23 tff(1068,plain,
% 1.08/1.23 (c1_1(a514)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[503, 1057])).
% 1.08/1.23 tff(1069,assumption,(~c0_1(a514)), introduced(assumption)).
% 1.08/1.23 tff(1070,plain,
% 1.08/1.23 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 1.08/1.23 inference(bind,[status(th)],[])).
% 1.08/1.23 tff(1071,plain,
% 1.08/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.08/1.23 inference(quant_intro,[status(thm)],[1070])).
% 1.08/1.23 tff(1072,plain,
% 1.08/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(1073,plain,
% 1.08/1.23 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 1.08/1.23 inference(bind,[status(th)],[])).
% 1.08/1.23 tff(1074,plain,
% 1.08/1.23 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.08/1.23 inference(quant_intro,[status(thm)],[1073])).
% 1.08/1.23 tff(1075,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 1.08/1.23 tff(1076,plain,
% 1.08/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 1.08/1.23 tff(1077,plain,
% 1.08/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[1076, 1072])).
% 1.08/1.23 tff(1078,plain,(
% 1.08/1.23 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.08/1.23 inference(skolemize,[status(sab)],[1077])).
% 1.08/1.23 tff(1079,plain,
% 1.08/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[1078, 1071])).
% 1.08/1.23 tff(1080,assumption,(~c0_1(a505)), introduced(assumption)).
% 1.08/1.23 tff(1081,assumption,(~c2_1(a514)), introduced(assumption)).
% 1.08/1.23 tff(1082,assumption,(c2_1(a505)), introduced(assumption)).
% 1.08/1.23 tff(1083,assumption,(c3_1(a514)), introduced(assumption)).
% 1.08/1.23 tff(1084,assumption,(c1_1(a514)), introduced(assumption)).
% 1.08/1.23 tff(1085,plain,
% 1.08/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a514) | c0_1(a505) | (~ndr1_0) | (~c1_1(a505)) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a514) | c0_1(a505) | (~ndr1_0) | (~c1_1(a505)) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(1086,plain,
% 1.08/1.23 (((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514))) <=> (c2_1(a514) | c0_1(a505) | (~ndr1_0) | (~c1_1(a505)) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(1087,plain,
% 1.08/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a514) | c0_1(a505) | (~ndr1_0) | (~c1_1(a505)) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514)))),
% 1.08/1.24 inference(monotonicity,[status(thm)],[1086])).
% 1.08/1.24 tff(1088,plain,
% 1.08/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a514) | c0_1(a505) | (~ndr1_0) | (~c1_1(a505)) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.08/1.24 inference(transitivity,[status(thm)],[1087, 1085])).
% 1.08/1.24 tff(1089,plain,
% 1.08/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514)))),
% 1.08/1.24 inference(quant_inst,[status(thm)],[])).
% 1.08/1.24 tff(1090,plain,
% 1.08/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a514) | c0_1(a505) | (~ndr1_0) | (~c1_1(a505)) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514)),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[1089, 1088])).
% 1.08/1.24 tff(1091,plain,
% 1.08/1.24 (~c1_1(a505)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1090, 106, 1084, 1083, 1082, 1081, 1080, 1079, 1069])).
% 1.08/1.24 tff(1092,plain,
% 1.08/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a514) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a514) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1093,plain,
% 1.08/1.24 (((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514))) <=> (c2_1(a514) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1094,plain,
% 1.08/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a514) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514)))),
% 1.08/1.24 inference(monotonicity,[status(thm)],[1093])).
% 1.08/1.24 tff(1095,plain,
% 1.08/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a514) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.08/1.24 inference(transitivity,[status(thm)],[1094, 1092])).
% 1.08/1.24 tff(1096,plain,
% 1.08/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514)))),
% 1.08/1.24 inference(quant_inst,[status(thm)],[])).
% 1.08/1.24 tff(1097,plain,
% 1.08/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a514) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514)),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 1.08/1.24 tff(1098,plain,
% 1.08/1.24 (~c2_1(a495)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1097, 106, 1084, 1083, 984, 1081, 983, 1079, 1069])).
% 1.08/1.24 tff(1099,assumption,(c3_1(a505)), introduced(assumption)).
% 1.08/1.24 tff(1100,plain,
% 1.08/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a514) | c0_1(a505) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | c2_1(a495) | (~c3_1(a505)) | c1_1(a505) | (~c3_1(a514)) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a514) | c0_1(a505) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | c2_1(a495) | (~c3_1(a505)) | c1_1(a505) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1101,plain,
% 1.08/1.24 (((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a495) | c0_1(a495) | (~c1_1(a495)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505))) <=> (c2_1(a514) | c0_1(a505) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | c2_1(a495) | (~c3_1(a505)) | c1_1(a505) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1102,plain,
% 1.08/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a495) | c0_1(a495) | (~c1_1(a495)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a514) | c0_1(a505) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | c2_1(a495) | (~c3_1(a505)) | c1_1(a505) | (~c3_1(a514)) | (~c1_1(a514))))),
% 1.08/1.24 inference(monotonicity,[status(thm)],[1101])).
% 1.08/1.24 tff(1103,plain,
% 1.08/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a495) | c0_1(a495) | (~c1_1(a495)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a514) | c0_1(a505) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | c2_1(a495) | (~c3_1(a505)) | c1_1(a505) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.08/1.24 inference(transitivity,[status(thm)],[1102, 1100])).
% 1.08/1.24 tff(1104,plain,
% 1.08/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a495) | c0_1(a495) | (~c1_1(a495)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))),
% 1.08/1.24 inference(quant_inst,[status(thm)],[])).
% 1.08/1.24 tff(1105,plain,
% 1.08/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a514) | c0_1(a505) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | c2_1(a495) | (~c3_1(a505)) | c1_1(a505) | (~c3_1(a514)) | (~c1_1(a514))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 1.08/1.24 tff(1106,plain,
% 1.08/1.24 ($false),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1105, 106, 1084, 1083, 1099, 984, 1081, 1080, 983, 558, 1098, 1091])).
% 1.08/1.24 tff(1107,plain,(c0_1(a514) | (~c1_1(a514)) | (~c3_1(a514)) | (~c3_1(a505)) | (~c1_1(a495)) | c2_1(a514) | c0_1(a505) | c0_1(a495) | (~c2_1(a505))), inference(lemma,lemma(discharge,[]))).
% 1.08/1.24 tff(1108,plain,
% 1.08/1.24 (c0_1(a514)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1107, 1068, 1067, 1066, 948, 1058, 980, 939, 974])).
% 1.08/1.24 tff(1109,plain,
% 1.08/1.24 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1110,plain,
% 1.08/1.24 ((hskp15 | hskp10 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514))) <=> (hskp15 | hskp10 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1111,plain,
% 1.08/1.24 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514))))),
% 1.08/1.24 inference(monotonicity,[status(thm)],[1110])).
% 1.08/1.24 tff(1112,plain,
% 1.08/1.24 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)))),
% 1.08/1.24 inference(transitivity,[status(thm)],[1111, 1109])).
% 1.08/1.24 tff(1113,plain,
% 1.08/1.24 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)))),
% 1.08/1.24 inference(quant_inst,[status(thm)],[])).
% 1.08/1.24 tff(1114,plain,
% 1.08/1.24 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 1.08/1.24 tff(1115,plain,
% 1.08/1.24 (hskp15 | (~c0_1(a514))),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1114, 106, 11, 1067, 1058, 42])).
% 1.08/1.24 tff(1116,plain,
% 1.08/1.24 (hskp15),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1115, 1108])).
% 1.08/1.24 tff(1117,plain,
% 1.08/1.24 (~c3_1(a528)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[424, 1116])).
% 1.08/1.24 tff(1118,plain,
% 1.08/1.24 (c0_1(a528)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[440, 1116])).
% 1.08/1.24 tff(1119,plain,
% 1.08/1.24 (c1_1(a528)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[432, 1116])).
% 1.08/1.24 tff(1120,plain,
% 1.08/1.24 (~hskp20),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1022, 1119, 1118, 1117, 239, 949, 940, 948, 939, 933])).
% 1.08/1.24 tff(1121,plain,
% 1.08/1.24 (hskp20 | (~c2_1(a568))),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[510, 106, 370, 1068, 1067, 369, 1058, 470])).
% 1.08/1.24 tff(1122,plain,
% 1.08/1.24 (~c2_1(a568)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1121, 1120])).
% 1.08/1.24 tff(1123,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c0_1(a568)) | c2_1(a568))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c0_1(a568)) | c2_1(a568))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1124,plain,
% 1.08/1.24 ((hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505))) <=> (hskp10 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c0_1(a568)) | c2_1(a568))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1125,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c0_1(a568)) | c2_1(a568)))),
% 1.08/1.24 inference(monotonicity,[status(thm)],[1124])).
% 1.08/1.24 tff(1126,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c0_1(a568)) | c2_1(a568))),
% 1.08/1.24 inference(transitivity,[status(thm)],[1125, 1123])).
% 1.08/1.24 tff(1127,plain,
% 1.08/1.24 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505)))),
% 1.08/1.24 inference(quant_inst,[status(thm)],[])).
% 1.08/1.24 tff(1128,plain,
% 1.08/1.24 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c0_1(a568)) | c2_1(a568)),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 1.08/1.24 tff(1129,plain,
% 1.08/1.24 (~c1_1(a505)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1128, 106, 11, 368, 1066, 369, 980, 53, 1122])).
% 1.08/1.24 tff(1130,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c2_1(a514) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c2_1(a514) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1131,plain,
% 1.08/1.24 ((hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a505))) <=> (hskp20 | c2_1(a514) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1132,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c2_1(a514) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514))))),
% 1.08/1.24 inference(monotonicity,[status(thm)],[1131])).
% 1.08/1.24 tff(1133,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c2_1(a514) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.08/1.24 inference(transitivity,[status(thm)],[1132, 1130])).
% 1.08/1.24 tff(1134,plain,
% 1.08/1.24 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))),
% 1.08/1.24 inference(quant_inst,[status(thm)],[])).
% 1.08/1.24 tff(1135,plain,
% 1.08/1.24 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c2_1(a514) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 1.08/1.24 tff(1136,plain,
% 1.08/1.24 ($false),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1135, 106, 1120, 1068, 1067, 974, 1066, 1058, 470, 1129])).
% 1.08/1.24 tff(1137,plain,(c0_1(a502) | hskp10 | (~c0_1(a568)) | c1_1(a568) | (~c3_1(a568)) | c1_1(a502) | c3_1(a502) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.08/1.24 tff(1138,plain,
% 1.08/1.24 (c1_1(a502)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1137, 940, 368, 369, 370, 239, 11, 371])).
% 1.08/1.24 tff(1139,plain,
% 1.08/1.24 (~hskp7),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[308, 1138])).
% 1.08/1.24 tff(1140,assumption,(c1_1(a505)), introduced(assumption)).
% 1.08/1.24 tff(1141,plain,
% 1.08/1.24 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 1.08/1.24 inference(bind,[status(th)],[])).
% 1.08/1.24 tff(1142,plain,
% 1.08/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.08/1.24 inference(quant_intro,[status(thm)],[1141])).
% 1.08/1.24 tff(1143,plain,
% 1.08/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1144,plain,
% 1.08/1.24 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 1.08/1.24 inference(bind,[status(th)],[])).
% 1.08/1.24 tff(1145,plain,
% 1.08/1.24 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.08/1.24 inference(quant_intro,[status(thm)],[1144])).
% 1.08/1.24 tff(1146,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 1.08/1.24 tff(1147,plain,
% 1.08/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 1.08/1.24 tff(1148,plain,
% 1.08/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[1147, 1143])).
% 1.08/1.24 tff(1149,plain,(
% 1.08/1.24 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.08/1.24 inference(skolemize,[status(sab)],[1148])).
% 1.08/1.24 tff(1150,plain,
% 1.08/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[1149, 1142])).
% 1.08/1.24 tff(1151,plain,
% 1.08/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a505) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a505)) | (~c1_1(a505)) | (~c2_1(a505)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a505) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a505)) | (~c1_1(a505)) | (~c2_1(a505)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1152,plain,
% 1.08/1.24 (((~ndr1_0) | (~c2_1(a505)) | (~c3_1(a505)) | (~c1_1(a505)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c0_1(a505) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a505)) | (~c1_1(a505)) | (~c2_1(a505)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1153,plain,
% 1.08/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a505)) | (~c3_1(a505)) | (~c1_1(a505)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a505) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a505)) | (~c1_1(a505)) | (~c2_1(a505))))),
% 1.08/1.24 inference(monotonicity,[status(thm)],[1152])).
% 1.08/1.24 tff(1154,plain,
% 1.08/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a505)) | (~c3_1(a505)) | (~c1_1(a505)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a505) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a505)) | (~c1_1(a505)) | (~c2_1(a505)))),
% 1.08/1.24 inference(transitivity,[status(thm)],[1153, 1151])).
% 1.08/1.24 tff(1155,plain,
% 1.08/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a505)) | (~c3_1(a505)) | (~c1_1(a505)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 1.08/1.24 inference(quant_inst,[status(thm)],[])).
% 1.08/1.24 tff(1156,plain,
% 1.08/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a505) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a505)) | (~c1_1(a505)) | (~c2_1(a505))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 1.08/1.24 tff(1157,plain,
% 1.08/1.24 (c0_1(a496) | (~c1_1(a505))),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1156, 106, 1082, 1099, 1080, 574, 573, 1150])).
% 1.08/1.24 tff(1158,plain,
% 1.08/1.24 (c0_1(a496)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1157, 1140])).
% 1.08/1.24 tff(1159,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a505)) | (~c1_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a505)) | (~c1_1(a505)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1160,plain,
% 1.08/1.24 ((hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505))) <=> (hskp10 | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a505)) | (~c1_1(a505)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(1161,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a505)) | (~c1_1(a505))))),
% 1.08/1.24 inference(monotonicity,[status(thm)],[1160])).
% 1.08/1.24 tff(1162,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a505)) | (~c1_1(a505)))),
% 1.08/1.24 inference(transitivity,[status(thm)],[1161, 1159])).
% 1.08/1.24 tff(1163,plain,
% 1.08/1.24 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505)))),
% 1.08/1.24 inference(quant_inst,[status(thm)],[])).
% 1.08/1.24 tff(1164,plain,
% 1.08/1.24 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a505)) | (~c1_1(a505))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 1.08/1.25 tff(1165,plain,
% 1.08/1.25 ((~c0_1(a496)) | (~c1_1(a505))),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[1164, 106, 11, 1099, 1080, 572, 574, 53])).
% 1.08/1.25 tff(1166,plain,
% 1.08/1.25 ($false),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[1165, 1158, 1140])).
% 1.08/1.25 tff(1167,plain,((~c1_1(a505)) | hskp10 | (~c3_1(a505)) | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~c2_1(a505)) | c3_1(a496)), inference(lemma,lemma(discharge,[]))).
% 1.08/1.25 tff(1168,plain,
% 1.08/1.25 (~c1_1(a505)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[1167, 1066, 11, 980, 569, 568, 974, 570])).
% 1.08/1.25 tff(1169,plain,
% 1.08/1.25 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1170,plain,
% 1.08/1.25 ((hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505))) <=> (hskp7 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1171,plain,
% 1.08/1.25 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c2_1(a568))))),
% 1.08/1.25 inference(monotonicity,[status(thm)],[1170])).
% 1.08/1.25 tff(1172,plain,
% 1.08/1.25 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.08/1.25 inference(transitivity,[status(thm)],[1171, 1169])).
% 1.08/1.25 tff(1173,plain,
% 1.08/1.25 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(1174,plain,
% 1.08/1.25 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c2_1(a568))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 1.08/1.25 tff(1175,plain,
% 1.08/1.25 (hskp7 | (~c2_1(a568))),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[1174, 106, 368, 1066, 369, 980, 216, 1168])).
% 1.08/1.25 tff(1176,plain,
% 1.08/1.25 (~c2_1(a568)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[1175, 1139])).
% 1.08/1.25 tff(1177,plain,
% 1.08/1.25 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(1178,plain,
% 1.08/1.25 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[1177])).
% 1.08/1.25 tff(1179,plain,
% 1.08/1.25 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1180,plain,
% 1.08/1.25 (^[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)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp9) <=> (hskp9 | (~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)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(1181,plain,
% 1.08/1.25 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[1180])).
% 1.08/1.25 tff(1182,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)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.08/1.25 tff(1183,plain,
% 1.08/1.25 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 1.08/1.25 tff(1184,plain,
% 1.08/1.25 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[1183, 1179])).
% 1.08/1.25 tff(1185,plain,(
% 1.08/1.25 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.08/1.25 inference(skolemize,[status(sab)],[1184])).
% 1.08/1.25 tff(1186,plain,
% 1.08/1.25 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[1185, 1178])).
% 1.08/1.25 tff(1187,plain,
% 1.08/1.25 (hskp15),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[454, 1176])).
% 1.08/1.25 tff(1188,plain,
% 1.08/1.25 (~c3_1(a528)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[424, 1187])).
% 1.08/1.25 tff(1189,plain,
% 1.08/1.25 (c1_1(a528)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[432, 1187])).
% 1.08/1.25 tff(1190,plain,
% 1.08/1.25 (c0_1(a528)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[440, 1187])).
% 1.08/1.25 tff(1191,plain,
% 1.08/1.25 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a568) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | c2_1(a568))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a568) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | c2_1(a568))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1192,plain,
% 1.08/1.25 ((hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a568) | c1_1(a568) | (~c0_1(a568))) <=> (hskp9 | c1_1(a568) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | c2_1(a568))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1193,plain,
% 1.08/1.25 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a568) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | c2_1(a568)))),
% 1.08/1.25 inference(monotonicity,[status(thm)],[1192])).
% 1.08/1.25 tff(1194,plain,
% 1.08/1.25 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a568) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | c2_1(a568))),
% 1.08/1.25 inference(transitivity,[status(thm)],[1193, 1191])).
% 1.08/1.25 tff(1195,plain,
% 1.08/1.25 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(1196,plain,
% 1.08/1.25 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a568) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | c2_1(a568)),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 1.08/1.25 tff(1197,plain,
% 1.08/1.25 (hskp9),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[1196, 106, 368, 1190, 1189, 369, 1188, 1186, 1176])).
% 1.08/1.25 tff(1198,plain,
% 1.08/1.25 (~c0_1(a507)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[846, 1197])).
% 1.08/1.25 tff(1199,plain,
% 1.08/1.25 (c3_1(a507)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[854, 1197])).
% 1.08/1.25 tff(1200,plain,
% 1.08/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c3_1(a528) | c0_1(a507) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a507) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1201,plain,
% 1.08/1.25 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507)) <=> (c3_1(a528) | c0_1(a507) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1202,plain,
% 1.08/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c3_1(a528) | c0_1(a507) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.08/1.25 inference(monotonicity,[status(thm)],[1201])).
% 1.08/1.25 tff(1203,plain,
% 1.08/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a507) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.08/1.25 inference(transitivity,[status(thm)],[1202, 1200])).
% 1.08/1.25 tff(1204,plain,
% 1.08/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(1205,plain,
% 1.08/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a507) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 1.08/1.25 tff(1206,plain,
% 1.08/1.25 (c2_1(a507)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[1205, 106, 1190, 1189, 1199, 1188, 1198, 239, 1138, 940, 21])).
% 1.08/1.25 tff(1207,plain,
% 1.08/1.25 (~c1_1(a507)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[840, 1197])).
% 1.08/1.25 tff(1208,plain,
% 1.08/1.25 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(1209,plain,
% 1.08/1.25 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[1208])).
% 1.08/1.25 tff(1210,plain,
% 1.08/1.25 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1211,plain,
% 1.08/1.25 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.08/1.25 inference(bind,[status(th)],[])).
% 1.08/1.25 tff(1212,plain,
% 1.08/1.25 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.08/1.25 inference(quant_intro,[status(thm)],[1211])).
% 1.08/1.25 tff(1213,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 1.08/1.25 tff(1214,plain,
% 1.08/1.25 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 1.08/1.25 tff(1215,plain,
% 1.08/1.25 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[1214, 1210])).
% 1.08/1.25 tff(1216,plain,(
% 1.08/1.25 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.08/1.25 inference(skolemize,[status(sab)],[1215])).
% 1.08/1.25 tff(1217,plain,
% 1.08/1.25 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[1216, 1209])).
% 1.08/1.25 tff(1218,plain,
% 1.08/1.25 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c0_1(a568)) | c2_1(a568))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp14 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c0_1(a568)) | c2_1(a568))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1219,plain,
% 1.08/1.25 ((hskp14 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505))) <=> (hskp14 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c0_1(a568)) | c2_1(a568))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1220,plain,
% 1.08/1.25 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c0_1(a568)) | c2_1(a568)))),
% 1.08/1.25 inference(monotonicity,[status(thm)],[1219])).
% 1.08/1.25 tff(1221,plain,
% 1.08/1.25 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp14 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c0_1(a568)) | c2_1(a568))),
% 1.08/1.25 inference(transitivity,[status(thm)],[1220, 1218])).
% 1.08/1.25 tff(1222,plain,
% 1.08/1.25 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(1223,plain,
% 1.08/1.25 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp14 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c0_1(a568)) | c2_1(a568)),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 1.08/1.25 tff(1224,plain,
% 1.08/1.25 (hskp14),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[1223, 106, 368, 974, 1066, 369, 980, 1217, 1176])).
% 1.08/1.25 tff(1225,plain,
% 1.08/1.25 (~c1_1(a527)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[757, 1224])).
% 1.08/1.25 tff(1226,plain,
% 1.08/1.25 (c2_1(a527)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[783, 1224])).
% 1.08/1.25 tff(1227,plain,
% 1.08/1.25 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a527) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a527)) | (~c2_1(a527)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a527) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a527)) | (~c2_1(a527)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1228,plain,
% 1.08/1.25 ((hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (hskp7 | c1_1(a527) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a527)) | (~c2_1(a527)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1229,plain,
% 1.08/1.25 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a527) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a527)) | (~c2_1(a527))))),
% 1.08/1.25 inference(monotonicity,[status(thm)],[1228])).
% 1.08/1.25 tff(1230,plain,
% 1.08/1.25 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a527) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a527)) | (~c2_1(a527)))),
% 1.08/1.25 inference(transitivity,[status(thm)],[1229, 1227])).
% 1.08/1.25 tff(1231,plain,
% 1.08/1.25 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(1232,plain,
% 1.08/1.25 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a527) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a527)) | (~c2_1(a527))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 1.08/1.25 tff(1233,plain,
% 1.08/1.25 (~c0_1(a527)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[1232, 106, 1139, 1226, 1199, 1225, 1198, 1207, 216])).
% 1.08/1.25 tff(1234,plain,
% 1.08/1.25 (~c3_1(a527)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[751, 1224])).
% 1.08/1.25 tff(1235,assumption,(c1_1(a502)), introduced(assumption)).
% 1.08/1.25 tff(1236,plain,
% 1.08/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1237,plain,
% 1.08/1.25 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536)) <=> (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(1238,plain,
% 1.08/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536))))),
% 1.08/1.25 inference(monotonicity,[status(thm)],[1237])).
% 1.08/1.25 tff(1239,plain,
% 1.08/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))),
% 1.08/1.25 inference(transitivity,[status(thm)],[1238, 1236])).
% 1.08/1.25 tff(1240,plain,
% 1.08/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(1241,plain,
% 1.08/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 1.08/1.25 tff(1242,plain,
% 1.08/1.25 (~c3_1(a536)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[1241, 106, 999, 998, 997, 996, 989, 239, 1235, 940, 21])).
% 1.08/1.25 tff(1243,assumption,(~c0_1(a527)), introduced(assumption)).
% 1.08/1.25 tff(1244,assumption,(~c3_1(a527)), introduced(assumption)).
% 1.08/1.25 tff(1245,assumption,(~c1_1(a527)), introduced(assumption)).
% 1.08/1.25 tff(1246,plain,
% 1.08/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c1_1(a527) | c3_1(a527) | (~ndr1_0) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c1_1(a527) | c3_1(a527) | (~ndr1_0) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(1247,plain,
% 1.08/1.26 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a527) | c1_1(a527) | c0_1(a527)) <=> (c0_1(a536) | c2_1(a536) | c3_1(a528) | c1_1(a527) | c3_1(a527) | (~ndr1_0) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(1248,plain,
% 1.08/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a527) | c1_1(a527) | c0_1(a527))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c1_1(a527) | c3_1(a527) | (~ndr1_0) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536)))),
% 1.08/1.26 inference(monotonicity,[status(thm)],[1247])).
% 1.08/1.26 tff(1249,plain,
% 1.08/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a527) | c1_1(a527) | c0_1(a527))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c1_1(a527) | c3_1(a527) | (~ndr1_0) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.08/1.26 inference(transitivity,[status(thm)],[1248, 1246])).
% 1.08/1.26 tff(1250,plain,
% 1.08/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a527) | c1_1(a527) | c0_1(a527))),
% 1.08/1.26 inference(quant_inst,[status(thm)],[])).
% 1.08/1.26 tff(1251,plain,
% 1.08/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c1_1(a527) | c3_1(a527) | (~ndr1_0) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536)),
% 1.08/1.26 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 1.08/1.26 tff(1252,plain,
% 1.08/1.26 (~c2_1(a528)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1251, 106, 998, 997, 996, 989, 1245, 1244, 709, 1243, 1242])).
% 1.08/1.26 tff(1253,plain,
% 1.08/1.26 ($false),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1020, 106, 999, 998, 997, 996, 989, 909, 1252, 1242])).
% 1.08/1.26 tff(1254,plain,((~hskp20) | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | c1_1(a527) | c3_1(a527) | c0_1(a527) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502)), inference(lemma,lemma(discharge,[]))).
% 1.08/1.26 tff(1255,plain,
% 1.08/1.26 (~hskp20),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1254, 1190, 1189, 1188, 1225, 1234, 1233, 239, 1138, 940])).
% 1.08/1.26 tff(1256,plain,
% 1.08/1.26 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a527) | c3_1(a527) | (~ndr1_0) | (~c2_1(a527)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a527) | c3_1(a527) | (~ndr1_0) | (~c2_1(a527)))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(1257,plain,
% 1.08/1.26 ((hskp20 | hskp12 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527))) <=> (hskp20 | hskp12 | c1_1(a527) | c3_1(a527) | (~ndr1_0) | (~c2_1(a527)))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(1258,plain,
% 1.08/1.26 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a527) | c3_1(a527) | (~ndr1_0) | (~c2_1(a527))))),
% 1.08/1.26 inference(monotonicity,[status(thm)],[1257])).
% 1.08/1.26 tff(1259,plain,
% 1.08/1.26 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a527) | c3_1(a527) | (~ndr1_0) | (~c2_1(a527)))),
% 1.08/1.26 inference(transitivity,[status(thm)],[1258, 1256])).
% 1.08/1.26 tff(1260,plain,
% 1.08/1.26 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)))),
% 1.08/1.26 inference(quant_inst,[status(thm)],[])).
% 1.08/1.26 tff(1261,plain,
% 1.08/1.26 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a527) | c3_1(a527) | (~ndr1_0) | (~c2_1(a527))),
% 1.08/1.26 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 1.08/1.26 tff(1262,plain,
% 1.08/1.26 (hskp20 | hskp12),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1261, 106, 1226, 1225, 1234, 1033])).
% 1.08/1.26 tff(1263,plain,
% 1.08/1.26 (hskp12),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1262, 1255])).
% 1.08/1.26 tff(1264,plain,
% 1.08/1.26 (~c2_1(a514)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[487, 1263])).
% 1.08/1.26 tff(1265,plain,
% 1.08/1.26 (c3_1(a514)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[495, 1263])).
% 1.08/1.26 tff(1266,plain,
% 1.08/1.26 (c1_1(a514)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[503, 1263])).
% 1.08/1.26 tff(1267,plain,
% 1.08/1.26 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c2_1(a514) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c2_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c2_1(a514) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c2_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(1268,plain,
% 1.08/1.26 ((hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a507) | (~c2_1(a507)) | (~c3_1(a507))) <=> (hskp20 | c2_1(a514) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c2_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(1269,plain,
% 1.08/1.26 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a507) | (~c2_1(a507)) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c2_1(a514) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c2_1(a507)) | (~c3_1(a514)) | (~c1_1(a514))))),
% 1.08/1.26 inference(monotonicity,[status(thm)],[1268])).
% 1.08/1.26 tff(1270,plain,
% 1.08/1.26 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a507) | (~c2_1(a507)) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c2_1(a514) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c2_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.08/1.26 inference(transitivity,[status(thm)],[1269, 1267])).
% 1.08/1.26 tff(1271,plain,
% 1.08/1.26 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a507) | (~c2_1(a507)) | (~c3_1(a507)))),
% 1.08/1.26 inference(quant_inst,[status(thm)],[])).
% 1.08/1.26 tff(1272,plain,
% 1.08/1.26 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c2_1(a514) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c2_1(a507)) | (~c3_1(a514)) | (~c1_1(a514))),
% 1.08/1.26 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 1.08/1.26 tff(1273,plain,
% 1.08/1.26 ($false),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1272, 106, 1255, 1266, 1265, 1199, 1264, 1207, 470, 1206])).
% 1.08/1.26 tff(1274,plain,(c3_1(a502) | c0_1(a502) | (~c0_1(a568)) | c1_1(a568) | hskp10 | (~c3_1(a568)) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.08/1.26 tff(1275,plain,
% 1.08/1.26 (c3_1(a502)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1274, 239, 368, 369, 11, 370, 371])).
% 1.08/1.26 tff(1276,plain,
% 1.08/1.26 (~hskp7),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[302, 1275])).
% 1.08/1.26 tff(1277,plain,
% 1.08/1.26 (~c2_1(a568)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1175, 1276])).
% 1.08/1.26 tff(1278,plain,
% 1.08/1.26 (hskp15),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[454, 1277])).
% 1.08/1.26 tff(1279,plain,
% 1.08/1.26 (~c3_1(a528)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[424, 1278])).
% 1.08/1.26 tff(1280,plain,
% 1.08/1.26 (c1_1(a528)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[432, 1278])).
% 1.08/1.26 tff(1281,plain,
% 1.08/1.26 (c0_1(a528)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[440, 1278])).
% 1.08/1.26 tff(1282,plain,
% 1.08/1.26 (hskp9),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1196, 106, 368, 1281, 1280, 369, 1279, 1186, 1277])).
% 1.08/1.26 tff(1283,plain,
% 1.08/1.26 (~c0_1(a507)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[846, 1282])).
% 1.08/1.26 tff(1284,plain,
% 1.08/1.26 (c3_1(a507)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[854, 1282])).
% 1.08/1.26 tff(1285,plain,
% 1.08/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c3_1(a528) | c0_1(a507) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a507) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(1286,plain,
% 1.08/1.26 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507)) <=> (c3_1(a528) | c0_1(a507) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(1287,plain,
% 1.08/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c3_1(a528) | c0_1(a507) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.08/1.26 inference(monotonicity,[status(thm)],[1286])).
% 1.08/1.26 tff(1288,plain,
% 1.08/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a507) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.08/1.26 inference(transitivity,[status(thm)],[1287, 1285])).
% 1.08/1.26 tff(1289,plain,
% 1.08/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))),
% 1.08/1.26 inference(quant_inst,[status(thm)],[])).
% 1.08/1.26 tff(1290,plain,
% 1.08/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a507) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.08/1.26 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 1.08/1.26 tff(1291,plain,
% 1.08/1.26 (c2_1(a507)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1290, 106, 1281, 1280, 1284, 948, 1279, 1283, 939, 933, 21])).
% 1.08/1.26 tff(1292,plain,
% 1.08/1.26 (~c1_1(a507)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[840, 1282])).
% 1.08/1.26 tff(1293,plain,
% 1.08/1.26 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 1.08/1.26 inference(bind,[status(th)],[])).
% 1.08/1.26 tff(1294,plain,
% 1.08/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.08/1.26 inference(quant_intro,[status(thm)],[1293])).
% 1.08/1.26 tff(1295,plain,
% 1.08/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(1296,plain,
% 1.08/1.26 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~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(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 1.08/1.26 inference(bind,[status(th)],[])).
% 1.08/1.26 tff(1297,plain,
% 1.08/1.26 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.08/1.26 inference(quant_intro,[status(thm)],[1296])).
% 1.08/1.26 tff(1298,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 1.08/1.26 tff(1299,plain,
% 1.08/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.08/1.26 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 1.08/1.26 tff(1300,plain,
% 1.08/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.08/1.26 inference(modus_ponens,[status(thm)],[1299, 1295])).
% 1.08/1.26 tff(1301,plain,(
% 1.08/1.26 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.08/1.26 inference(skolemize,[status(sab)],[1300])).
% 1.08/1.26 tff(1302,plain,
% 1.08/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.08/1.26 inference(modus_ponens,[status(thm)],[1301, 1294])).
% 1.08/1.26 tff(1303,plain,
% 1.08/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(1304,plain,
% 1.08/1.26 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a502) | (~c3_1(a502)) | (~c1_1(a502))) <=> (c1_1(a568) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(1305,plain,
% 1.08/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a502) | (~c3_1(a502)) | (~c1_1(a502)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.08/1.26 inference(monotonicity,[status(thm)],[1304])).
% 1.08/1.26 tff(1306,plain,
% 1.08/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a502) | (~c3_1(a502)) | (~c1_1(a502)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.08/1.26 inference(transitivity,[status(thm)],[1305, 1303])).
% 1.08/1.26 tff(1307,plain,
% 1.08/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a502) | (~c3_1(a502)) | (~c1_1(a502)))),
% 1.08/1.26 inference(quant_inst,[status(thm)],[])).
% 1.08/1.26 tff(1308,plain,
% 1.08/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.08/1.26 inference(modus_ponens,[status(thm)],[1307, 1306])).
% 1.08/1.26 tff(1309,plain,
% 1.08/1.26 (~c1_1(a502)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1308, 106, 368, 370, 1281, 1280, 369, 1279, 239, 1275, 1302])).
% 1.08/1.26 tff(1310,plain,
% 1.08/1.26 (hskp14),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1223, 106, 368, 974, 1066, 369, 980, 1217, 1277])).
% 1.08/1.26 tff(1311,plain,
% 1.08/1.26 (~c1_1(a527)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[757, 1310])).
% 1.08/1.26 tff(1312,plain,
% 1.08/1.26 (c2_1(a527)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[783, 1310])).
% 1.08/1.26 tff(1313,plain,
% 1.08/1.26 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a527) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a527)) | (~c2_1(a527)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a527) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a527)) | (~c2_1(a527)))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(1314,plain,
% 1.08/1.26 ((hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502))) <=> (hskp7 | c1_1(a527) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a527)) | (~c2_1(a527)))),
% 1.08/1.26 inference(rewrite,[status(thm)],[])).
% 1.08/1.26 tff(1315,plain,
% 1.08/1.26 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a527) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a527)) | (~c2_1(a527))))),
% 1.08/1.26 inference(monotonicity,[status(thm)],[1314])).
% 1.08/1.26 tff(1316,plain,
% 1.08/1.26 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a527) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a527)) | (~c2_1(a527)))),
% 1.08/1.26 inference(transitivity,[status(thm)],[1315, 1313])).
% 1.08/1.26 tff(1317,plain,
% 1.08/1.26 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502)))),
% 1.08/1.26 inference(quant_inst,[status(thm)],[])).
% 1.08/1.26 tff(1318,plain,
% 1.08/1.26 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a527) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a527)) | (~c2_1(a527))),
% 1.08/1.26 inference(modus_ponens,[status(thm)],[1317, 1316])).
% 1.08/1.26 tff(1319,plain,
% 1.08/1.26 (~c0_1(a527)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1318, 106, 1276, 1312, 1311, 239, 1309, 1275, 216])).
% 1.08/1.26 tff(1320,plain,
% 1.08/1.26 (~c3_1(a527)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[751, 1310])).
% 1.08/1.26 tff(1321,plain,
% 1.08/1.26 (~c2_1(a528)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1251, 106, 998, 997, 996, 989, 1245, 1244, 709, 1243, 1006])).
% 1.08/1.26 tff(1322,plain,
% 1.08/1.26 ($false),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1020, 106, 999, 998, 997, 996, 989, 909, 1321, 1006])).
% 1.08/1.26 tff(1323,plain,((~hskp20) | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | c1_1(a527) | c3_1(a527) | c0_1(a527) | (~c1_1(a495)) | c0_1(a495) | c3_1(a495)), inference(lemma,lemma(discharge,[]))).
% 1.08/1.26 tff(1324,plain,
% 1.08/1.26 (~hskp20),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1323, 1281, 1280, 1279, 1311, 1320, 1319, 948, 939, 933])).
% 1.08/1.26 tff(1325,plain,
% 1.08/1.26 (hskp20 | hskp12),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1261, 106, 1312, 1311, 1320, 1033])).
% 1.08/1.26 tff(1326,plain,
% 1.08/1.26 (hskp12),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1325, 1324])).
% 1.08/1.26 tff(1327,plain,
% 1.08/1.26 (~c2_1(a514)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[487, 1326])).
% 1.08/1.26 tff(1328,plain,
% 1.08/1.26 (c3_1(a514)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[495, 1326])).
% 1.08/1.26 tff(1329,plain,
% 1.08/1.26 (c1_1(a514)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[503, 1326])).
% 1.08/1.26 tff(1330,plain,
% 1.08/1.26 ($false),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1272, 106, 1324, 1329, 1328, 1284, 1327, 1292, 470, 1291])).
% 1.08/1.26 tff(1331,plain,(c0_1(a502) | (~c0_1(a568)) | c1_1(a568) | (~c3_1(a568)) | hskp10 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.08/1.26 tff(1332,plain,
% 1.08/1.26 (c0_1(a502)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1331, 371, 369, 370, 11, 368])).
% 1.08/1.26 tff(1333,plain,
% 1.08/1.26 (~hskp7),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[643, 1332])).
% 1.08/1.26 tff(1334,plain,
% 1.08/1.26 (~c2_1(a568)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1175, 1333])).
% 1.08/1.26 tff(1335,plain,
% 1.08/1.26 (hskp15),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[454, 1334])).
% 1.08/1.26 tff(1336,plain,
% 1.08/1.26 (~c3_1(a528)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[424, 1335])).
% 1.08/1.26 tff(1337,plain,
% 1.08/1.26 (c1_1(a528)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[432, 1335])).
% 1.08/1.26 tff(1338,plain,
% 1.08/1.26 (c0_1(a528)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[440, 1335])).
% 1.08/1.26 tff(1339,plain,
% 1.08/1.26 (hskp9),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1196, 106, 368, 1338, 1337, 369, 1336, 1186, 1334])).
% 1.08/1.26 tff(1340,plain,
% 1.08/1.26 (~c0_1(a507)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[846, 1339])).
% 1.08/1.26 tff(1341,plain,
% 1.08/1.26 (c3_1(a507)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[854, 1339])).
% 1.08/1.26 tff(1342,plain,
% 1.08/1.26 (c2_1(a507)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1290, 106, 1338, 1337, 1341, 948, 1336, 1340, 939, 933, 21])).
% 1.08/1.26 tff(1343,plain,
% 1.08/1.26 (~c1_1(a507)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[840, 1339])).
% 1.08/1.26 tff(1344,plain,
% 1.08/1.26 (hskp14),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1223, 106, 368, 974, 1066, 369, 980, 1217, 1334])).
% 1.08/1.26 tff(1345,plain,
% 1.08/1.26 (~c3_1(a527)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[751, 1344])).
% 1.08/1.26 tff(1346,plain,
% 1.08/1.26 (~c1_1(a527)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[757, 1344])).
% 1.08/1.26 tff(1347,plain,
% 1.08/1.26 (c2_1(a527)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[783, 1344])).
% 1.08/1.26 tff(1348,plain,
% 1.08/1.26 (~c0_1(a527)),
% 1.08/1.26 inference(unit_resolution,[status(thm)],[1232, 106, 1333, 1347, 1341, 1346, 1340, 1343, 216])).
% 1.08/1.27 tff(1349,plain,
% 1.08/1.27 (~hskp20),
% 1.08/1.27 inference(unit_resolution,[status(thm)],[1323, 1348, 1337, 1336, 1346, 1345, 1338, 948, 939, 933])).
% 1.08/1.27 tff(1350,plain,
% 1.08/1.27 (hskp20 | hskp12),
% 1.08/1.27 inference(unit_resolution,[status(thm)],[1261, 106, 1347, 1346, 1345, 1033])).
% 1.08/1.27 tff(1351,plain,
% 1.08/1.27 (hskp12),
% 1.08/1.27 inference(unit_resolution,[status(thm)],[1350, 1349])).
% 1.08/1.27 tff(1352,plain,
% 1.08/1.27 (~c2_1(a514)),
% 1.08/1.27 inference(unit_resolution,[status(thm)],[487, 1351])).
% 1.08/1.27 tff(1353,plain,
% 1.08/1.27 (c3_1(a514)),
% 1.08/1.27 inference(unit_resolution,[status(thm)],[495, 1351])).
% 1.08/1.27 tff(1354,plain,
% 1.08/1.27 (c1_1(a514)),
% 1.08/1.27 inference(unit_resolution,[status(thm)],[503, 1351])).
% 1.08/1.27 tff(1355,plain,
% 1.08/1.27 ($false),
% 1.08/1.27 inference(unit_resolution,[status(thm)],[1272, 106, 1349, 1354, 1353, 1341, 1352, 1343, 470, 1342])).
% 1.08/1.27 tff(1356,plain,(hskp13 | (~c0_1(a568)) | c1_1(a568) | hskp10 | (~c3_1(a568))), inference(lemma,lemma(discharge,[]))).
% 1.08/1.27 tff(1357,plain,
% 1.08/1.27 (hskp13),
% 1.08/1.27 inference(unit_resolution,[status(thm)],[1356, 198, 228, 11, 190])).
% 1.08/1.27 tff(1358,plain,
% 1.08/1.27 (((~hskp13) | (~c3_1(a520))) <=> ((~hskp13) | (~c3_1(a520)))),
% 1.08/1.27 inference(rewrite,[status(thm)],[])).
% 1.08/1.27 tff(1359,plain,
% 1.08/1.27 (((~c3_1(a520)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a520)))),
% 1.08/1.27 inference(rewrite,[status(thm)],[])).
% 1.08/1.27 tff(1360,axiom,((~c3_1(a520)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.08/1.27 tff(1361,plain,
% 1.08/1.27 ((~hskp13) | (~c3_1(a520))),
% 1.08/1.27 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 1.08/1.27 tff(1362,plain,
% 1.08/1.27 ((~hskp13) | (~c3_1(a520))),
% 1.08/1.27 inference(modus_ponens,[status(thm)],[1361, 1358])).
% 1.08/1.27 tff(1363,plain,
% 1.08/1.27 (~c3_1(a520)),
% 1.08/1.27 inference(unit_resolution,[status(thm)],[1362, 1357])).
% 1.08/1.27 tff(1364,plain,
% 1.08/1.27 (((~hskp13) | c2_1(a520)) <=> ((~hskp13) | c2_1(a520))),
% 1.08/1.27 inference(rewrite,[status(thm)],[])).
% 1.08/1.27 tff(1365,axiom,((~hskp13) | c2_1(a520)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.08/1.27 tff(1366,plain,
% 1.08/1.27 ((~hskp13) | c2_1(a520)),
% 1.08/1.27 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 1.08/1.27 tff(1367,plain,
% 1.08/1.27 ((~hskp13) | c2_1(a520)),
% 1.08/1.27 inference(modus_ponens,[status(thm)],[1366, 1364])).
% 1.08/1.27 tff(1368,plain,
% 1.08/1.27 ((~hskp13) | c2_1(a520)),
% 1.08/1.27 inference(modus_ponens,[status(thm)],[1367, 1364])).
% 1.08/1.27 tff(1369,plain,
% 1.08/1.27 ((~hskp13) | c2_1(a520)),
% 1.08/1.27 inference(modus_ponens,[status(thm)],[1368, 1364])).
% 1.08/1.27 tff(1370,plain,
% 1.08/1.27 ((~hskp13) | c2_1(a520)),
% 1.08/1.27 inference(modus_ponens,[status(thm)],[1369, 1364])).
% 1.08/1.27 tff(1371,plain,
% 1.08/1.27 (c2_1(a520)),
% 1.08/1.27 inference(unit_resolution,[status(thm)],[1370, 1357])).
% 1.08/1.27 tff(1372,plain,
% 1.08/1.27 (((~hskp13) | c0_1(a520)) <=> ((~hskp13) | c0_1(a520))),
% 1.08/1.27 inference(rewrite,[status(thm)],[])).
% 1.08/1.27 tff(1373,axiom,((~hskp13) | c0_1(a520)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.08/1.27 tff(1374,plain,
% 1.08/1.27 ((~hskp13) | c0_1(a520)),
% 1.08/1.27 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 1.08/1.27 tff(1375,plain,
% 1.08/1.27 ((~hskp13) | c0_1(a520)),
% 1.08/1.27 inference(modus_ponens,[status(thm)],[1374, 1372])).
% 1.08/1.27 tff(1376,plain,
% 1.08/1.27 ((~hskp13) | c0_1(a520)),
% 1.08/1.27 inference(modus_ponens,[status(thm)],[1375, 1372])).
% 1.08/1.27 tff(1377,plain,
% 1.08/1.27 ((~hskp13) | c0_1(a520)),
% 1.08/1.27 inference(modus_ponens,[status(thm)],[1376, 1372])).
% 1.08/1.27 tff(1378,plain,
% 1.08/1.27 ((~hskp13) | c0_1(a520)),
% 1.08/1.27 inference(modus_ponens,[status(thm)],[1377, 1372])).
% 1.08/1.27 tff(1379,plain,
% 1.08/1.27 (c0_1(a520)),
% 1.08/1.27 inference(unit_resolution,[status(thm)],[1378, 1357])).
% 1.08/1.27 tff(1380,plain,
% 1.08/1.27 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c3_1(a520) | c0_1(a502) | c1_1(a502) | (~ndr1_0) | (~c2_1(a502)) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a520) | c0_1(a502) | c1_1(a502) | (~ndr1_0) | (~c2_1(a502)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.08/1.27 inference(rewrite,[status(thm)],[])).
% 1.08/1.27 tff(1381,plain,
% 1.08/1.27 ((hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | (~c2_1(a502))) <=> (hskp4 | c3_1(a520) | c0_1(a502) | c1_1(a502) | (~ndr1_0) | (~c2_1(a502)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1382,plain,
% 1.11/1.27 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | (~c2_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c3_1(a520) | c0_1(a502) | c1_1(a502) | (~ndr1_0) | (~c2_1(a502)) | (~c0_1(a520)) | (~c2_1(a520))))),
% 1.11/1.27 inference(monotonicity,[status(thm)],[1381])).
% 1.11/1.27 tff(1383,plain,
% 1.11/1.27 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | (~c2_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a520) | c0_1(a502) | c1_1(a502) | (~ndr1_0) | (~c2_1(a502)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.11/1.27 inference(transitivity,[status(thm)],[1382, 1380])).
% 1.11/1.27 tff(1384,plain,
% 1.11/1.27 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | (~c2_1(a502)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(1385,plain,
% 1.11/1.27 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a520) | c0_1(a502) | c1_1(a502) | (~ndr1_0) | (~c2_1(a502)) | (~c0_1(a520)) | (~c2_1(a520))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 1.11/1.27 tff(1386,plain,
% 1.11/1.27 (hskp4),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1385, 106, 1379, 1371, 1363, 239, 309, 367, 357])).
% 1.11/1.27 tff(1387,plain,
% 1.11/1.27 (((~hskp4) | (~c0_1(a498))) <=> ((~hskp4) | (~c0_1(a498)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1388,plain,
% 1.11/1.27 (((~c0_1(a498)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a498)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1389,axiom,((~c0_1(a498)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.11/1.27 tff(1390,plain,
% 1.11/1.27 ((~hskp4) | (~c0_1(a498))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 1.11/1.27 tff(1391,plain,
% 1.11/1.27 ((~hskp4) | (~c0_1(a498))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1390, 1387])).
% 1.11/1.27 tff(1392,plain,
% 1.11/1.27 (~c0_1(a498)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1391, 1386])).
% 1.11/1.27 tff(1393,plain,
% 1.11/1.27 (((~hskp4) | c1_1(a498)) <=> ((~hskp4) | c1_1(a498))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1394,axiom,((~hskp4) | c1_1(a498)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.11/1.27 tff(1395,plain,
% 1.11/1.27 ((~hskp4) | c1_1(a498)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1394, 1393])).
% 1.11/1.27 tff(1396,plain,
% 1.11/1.27 ((~hskp4) | c1_1(a498)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1395, 1393])).
% 1.11/1.27 tff(1397,plain,
% 1.11/1.27 ((~hskp4) | c1_1(a498)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1396, 1393])).
% 1.11/1.27 tff(1398,plain,
% 1.11/1.27 ((~hskp4) | c1_1(a498)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1397, 1393])).
% 1.11/1.27 tff(1399,plain,
% 1.11/1.27 ((~hskp4) | c1_1(a498)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1398, 1393])).
% 1.11/1.27 tff(1400,plain,
% 1.11/1.27 (c1_1(a498)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1399, 1386])).
% 1.11/1.27 tff(1401,plain,
% 1.11/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a498) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a498)) | (~c1_1(a498)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a498) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a498)) | (~c1_1(a498)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1402,plain,
% 1.11/1.27 ((hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498))) <=> (hskp10 | c0_1(a498) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a498)) | (~c1_1(a498)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1403,plain,
% 1.11/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a498) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a498)) | (~c1_1(a498))))),
% 1.11/1.27 inference(monotonicity,[status(thm)],[1402])).
% 1.11/1.27 tff(1404,plain,
% 1.11/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a498) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a498)) | (~c1_1(a498)))),
% 1.11/1.27 inference(transitivity,[status(thm)],[1403, 1401])).
% 1.11/1.27 tff(1405,plain,
% 1.11/1.27 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(1406,plain,
% 1.11/1.27 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a498) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a498)) | (~c1_1(a498))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 1.11/1.27 tff(1407,plain,
% 1.11/1.27 (~c3_1(a498)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1406, 106, 11, 1400, 1392, 349, 336, 53, 343])).
% 1.11/1.27 tff(1408,plain,
% 1.11/1.27 (((~hskp4) | (~c2_1(a498))) <=> ((~hskp4) | (~c2_1(a498)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1409,plain,
% 1.11/1.27 (((~c2_1(a498)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a498)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1410,axiom,((~c2_1(a498)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.11/1.27 tff(1411,plain,
% 1.11/1.27 ((~hskp4) | (~c2_1(a498))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 1.11/1.27 tff(1412,plain,
% 1.11/1.27 ((~hskp4) | (~c2_1(a498))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1411, 1408])).
% 1.11/1.27 tff(1413,plain,
% 1.11/1.27 (~c2_1(a498)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1412, 1386])).
% 1.11/1.27 tff(1414,plain,
% 1.11/1.27 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1415,plain,
% 1.11/1.27 ((hskp11 | hskp10 | (~ndr1_0) | c3_1(a498) | c2_1(a498) | c0_1(a498)) <=> (hskp11 | hskp10 | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1416,plain,
% 1.11/1.27 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a498) | c2_1(a498) | c0_1(a498))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498)))),
% 1.11/1.27 inference(monotonicity,[status(thm)],[1415])).
% 1.11/1.27 tff(1417,plain,
% 1.11/1.27 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a498) | c2_1(a498) | c0_1(a498))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498))),
% 1.11/1.27 inference(transitivity,[status(thm)],[1416, 1414])).
% 1.11/1.27 tff(1418,plain,
% 1.11/1.27 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a498) | c2_1(a498) | c0_1(a498))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(1419,plain,
% 1.11/1.27 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498)),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 1.11/1.27 tff(1420,plain,
% 1.11/1.27 ($false),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1419, 106, 151, 11, 1392, 1413, 10, 1407])).
% 1.11/1.27 tff(1421,plain,(hskp15 | hskp10 | c0_1(a502) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.11/1.27 tff(1422,plain,
% 1.11/1.27 (hskp15),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1421, 239, 11, 32])).
% 1.11/1.27 tff(1423,plain,
% 1.11/1.27 (hskp13),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1356, 368, 369, 11, 370])).
% 1.11/1.27 tff(1424,plain,
% 1.11/1.27 (c0_1(a520)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1378, 1423])).
% 1.11/1.27 tff(1425,plain,
% 1.11/1.27 (~c3_1(a520)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1362, 1423])).
% 1.11/1.27 tff(1426,plain,
% 1.11/1.27 (c2_1(a520)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1370, 1423])).
% 1.11/1.27 tff(1427,assumption,(c2_1(a520)), introduced(assumption)).
% 1.11/1.27 tff(1428,assumption,(c0_1(a520)), introduced(assumption)).
% 1.11/1.27 tff(1429,plain,
% 1.11/1.27 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1430,plain,
% 1.11/1.27 ((hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1431,plain,
% 1.11/1.27 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520))))),
% 1.11/1.27 inference(monotonicity,[status(thm)],[1430])).
% 1.11/1.27 tff(1432,plain,
% 1.11/1.27 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.11/1.27 inference(transitivity,[status(thm)],[1431, 1429])).
% 1.11/1.27 tff(1433,plain,
% 1.11/1.27 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(1434,plain,
% 1.11/1.27 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1433, 1432])).
% 1.11/1.27 tff(1435,plain,
% 1.11/1.27 (hskp2 | c3_1(a502) | (~c1_1(a520))),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1434, 106, 1428, 1427, 239, 949, 290])).
% 1.11/1.27 tff(1436,plain,
% 1.11/1.27 (~c1_1(a520)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1435, 408, 940])).
% 1.11/1.27 tff(1437,assumption,(~c3_1(a520)), introduced(assumption)).
% 1.11/1.27 tff(1438,plain,
% 1.11/1.27 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1439,plain,
% 1.11/1.27 ((hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp1 | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1440,plain,
% 1.11/1.27 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520))))),
% 1.11/1.27 inference(monotonicity,[status(thm)],[1439])).
% 1.11/1.27 tff(1441,plain,
% 1.11/1.27 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.11/1.27 inference(transitivity,[status(thm)],[1440, 1438])).
% 1.11/1.27 tff(1442,plain,
% 1.11/1.27 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(1443,plain,
% 1.11/1.27 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 1.11/1.27 tff(1444,plain,
% 1.11/1.27 (hskp1 | c3_1(a502) | c1_1(a520)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1443, 106, 1428, 1437, 239, 949, 585])).
% 1.11/1.27 tff(1445,plain,
% 1.11/1.27 (hskp1),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1444, 1436, 940])).
% 1.11/1.27 tff(1446,assumption,(hskp1), introduced(assumption)).
% 1.11/1.27 tff(1447,plain,
% 1.11/1.27 (~c0_1(a495)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[938, 1446])).
% 1.11/1.27 tff(1448,plain,
% 1.11/1.27 (c1_1(a495)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[947, 1446])).
% 1.11/1.27 tff(1449,plain,
% 1.11/1.27 (~c3_1(a495)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[932, 1446])).
% 1.11/1.27 tff(1450,plain,
% 1.11/1.27 ($false),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1022, 1449, 1448, 239, 989, 998, 999, 949, 940, 990, 1447])).
% 1.11/1.27 tff(1451,plain,((~hskp1) | c0_1(a502) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a502) | c3_1(a502) | (~hskp20)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.27 tff(1452,plain,
% 1.11/1.27 (~hskp20),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1451, 1445, 989, 998, 999, 949, 940, 239])).
% 1.11/1.27 tff(1453,plain,
% 1.11/1.27 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1454,plain,
% 1.11/1.27 ((hskp20 | hskp12 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520))) <=> (hskp20 | hskp12 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1455,plain,
% 1.11/1.27 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c2_1(a520))))),
% 1.11/1.27 inference(monotonicity,[status(thm)],[1454])).
% 1.11/1.27 tff(1456,plain,
% 1.11/1.27 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)))),
% 1.11/1.27 inference(transitivity,[status(thm)],[1455, 1453])).
% 1.11/1.27 tff(1457,plain,
% 1.11/1.27 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)))),
% 1.11/1.27 inference(quant_inst,[status(thm)],[])).
% 1.11/1.27 tff(1458,plain,
% 1.11/1.27 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c2_1(a520))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1457, 1456])).
% 1.11/1.27 tff(1459,plain,
% 1.11/1.27 (hskp20 | hskp12 | c1_1(a520)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1458, 106, 1427, 1437, 1033])).
% 1.11/1.27 tff(1460,plain,
% 1.11/1.27 (hskp12),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1459, 1452, 1436])).
% 1.11/1.27 tff(1461,plain,
% 1.11/1.27 (c1_1(a514)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[503, 1460])).
% 1.11/1.27 tff(1462,plain,
% 1.11/1.27 (~c0_1(a495)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[938, 1445])).
% 1.11/1.27 tff(1463,plain,
% 1.11/1.27 (~c3_1(a495)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[932, 1445])).
% 1.11/1.27 tff(1464,plain,
% 1.11/1.27 (c1_1(a495)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[947, 1445])).
% 1.11/1.27 tff(1465,plain,
% 1.11/1.27 (hskp8),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[965, 106, 368, 370, 1464, 369, 1462, 1463, 959])).
% 1.11/1.27 tff(1466,plain,
% 1.11/1.27 (~c0_1(a505)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[979, 1465])).
% 1.11/1.27 tff(1467,plain,
% 1.11/1.27 (~c2_1(a514)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[487, 1460])).
% 1.11/1.27 tff(1468,plain,
% 1.11/1.27 (c3_1(a505)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1065, 1465])).
% 1.11/1.27 tff(1469,plain,
% 1.11/1.27 (c3_1(a514)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[495, 1460])).
% 1.11/1.27 tff(1470,plain,
% 1.11/1.27 (~c0_1(a514)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[547, 106, 408, 1461, 1469, 1467, 541])).
% 1.11/1.27 tff(1471,plain,
% 1.11/1.27 (c2_1(a505)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[973, 1465])).
% 1.11/1.27 tff(1472,plain,
% 1.11/1.27 ($false),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1107, 1471, 1470, 1469, 1468, 1464, 1467, 1466, 1462, 1461])).
% 1.11/1.27 tff(1473,plain,(hskp2 | (~c0_1(a568)) | (~c3_1(a568)) | c1_1(a568) | (~c2_1(a520)) | c3_1(a520) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a502) | c3_1(a502) | c0_1(a502) | (~c0_1(a520))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.27 tff(1474,plain,
% 1.11/1.27 (hskp2),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[1473, 940, 370, 369, 1426, 1425, 989, 998, 999, 949, 368, 239, 1424])).
% 1.11/1.27 tff(1475,plain,
% 1.11/1.27 (~c2_1(a496)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[335, 1474])).
% 1.11/1.27 tff(1476,plain,
% 1.11/1.27 (~c1_1(a496)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[348, 1474])).
% 1.11/1.27 tff(1477,plain,
% 1.11/1.27 (~c3_1(a496)),
% 1.11/1.27 inference(unit_resolution,[status(thm)],[329, 1474])).
% 1.11/1.27 tff(1478,assumption,(~hskp20), introduced(assumption)).
% 1.11/1.27 tff(1479,assumption,(c2_1(a568)), introduced(assumption)).
% 1.11/1.27 tff(1480,plain,
% 1.11/1.27 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.11/1.27 inference(bind,[status(th)],[])).
% 1.11/1.27 tff(1481,plain,
% 1.11/1.27 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.11/1.27 inference(quant_intro,[status(thm)],[1480])).
% 1.11/1.27 tff(1482,plain,
% 1.11/1.27 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1483,plain,
% 1.11/1.27 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_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))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_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))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_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))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp20) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_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))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.11/1.27 inference(bind,[status(th)],[])).
% 1.11/1.27 tff(1484,plain,
% 1.11/1.27 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.11/1.27 inference(quant_intro,[status(thm)],[1483])).
% 1.11/1.27 tff(1485,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.11/1.27 tff(1486,plain,
% 1.11/1.27 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 1.11/1.27 tff(1487,plain,
% 1.11/1.27 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1486, 1482])).
% 1.11/1.27 tff(1488,plain,(
% 1.11/1.27 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.11/1.27 inference(skolemize,[status(sab)],[1487])).
% 1.11/1.27 tff(1489,plain,
% 1.11/1.27 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.11/1.27 inference(modus_ponens,[status(thm)],[1488, 1481])).
% 1.11/1.27 tff(1490,plain,
% 1.11/1.27 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | c1_1(a568) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a568)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a568) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.11/1.27 inference(rewrite,[status(thm)],[])).
% 1.11/1.27 tff(1491,plain,
% 1.11/1.27 ((hskp20 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496))) <=> (hskp20 | c1_1(a568) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1492,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | c1_1(a568) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a568)) | (~c2_1(a568))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[1491])).
% 1.11/1.28 tff(1493,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a568) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[1492, 1490])).
% 1.11/1.28 tff(1494,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(1495,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a568) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a568)) | (~c2_1(a568))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 1.11/1.28 tff(1496,plain,
% 1.11/1.28 (hskp20 | (~c0_1(a496))),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1495, 106, 368, 369, 572, 574, 1489, 1479])).
% 1.11/1.28 tff(1497,plain,
% 1.11/1.28 (~c0_1(a496)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1496, 1478])).
% 1.11/1.28 tff(1498,plain,
% 1.11/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1499,plain,
% 1.11/1.28 (((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a502) | c1_1(a502) | c0_1(a502)) <=> (c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1500,plain,
% 1.11/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[1499])).
% 1.11/1.28 tff(1501,plain,
% 1.11/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[1500, 1498])).
% 1.11/1.28 tff(1502,plain,
% 1.11/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a502) | c1_1(a502) | c0_1(a502))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(1503,plain,
% 1.11/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1502, 1501])).
% 1.11/1.28 tff(1504,plain,
% 1.11/1.28 (c0_1(a496) | (~c1_1(a520))),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1503, 106, 1427, 1437, 239, 949, 940, 574, 573, 709])).
% 1.11/1.28 tff(1505,plain,
% 1.11/1.28 (~c1_1(a520)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1504, 1497])).
% 1.11/1.28 tff(1506,plain,
% 1.11/1.28 (hskp11 | c0_1(a496)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[342, 106, 11, 574, 573, 10])).
% 1.11/1.28 tff(1507,plain,
% 1.11/1.28 (hskp11),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1506, 1497])).
% 1.11/1.28 tff(1508,plain,
% 1.11/1.28 (~c2_1(a510)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[59, 1507])).
% 1.11/1.28 tff(1509,plain,
% 1.11/1.28 (~c1_1(a510)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[65, 1507])).
% 1.11/1.28 tff(1510,plain,
% 1.11/1.28 (c0_1(a510)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[73, 1507])).
% 1.11/1.28 tff(1511,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1512,plain,
% 1.11/1.28 ((hskp20 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510))) <=> (hskp20 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1513,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[1512])).
% 1.11/1.28 tff(1514,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[1513, 1511])).
% 1.11/1.28 tff(1515,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(1516,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 1.11/1.28 tff(1517,plain,
% 1.11/1.28 ($false),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1516, 106, 1478, 1428, 1427, 1510, 1509, 1508, 1489, 1505])).
% 1.11/1.28 tff(1518,plain,(hskp20 | (~c0_1(a520)) | (~c2_1(a520)) | hskp10 | c2_1(a496) | c3_1(a496) | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~c0_1(a568)) | c1_1(a568) | c1_1(a496) | (~c2_1(a568))), inference(lemma,lemma(discharge,[]))).
% 1.11/1.28 tff(1519,plain,
% 1.11/1.28 (~c2_1(a568)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1518, 1478, 1426, 11, 1424, 574, 1425, 239, 949, 940, 368, 369, 573, 572])).
% 1.11/1.28 tff(1520,plain,
% 1.11/1.28 (hskp9),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1196, 106, 368, 999, 998, 369, 989, 1186, 1519])).
% 1.11/1.28 tff(1521,plain,
% 1.11/1.28 (~c1_1(a507)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[840, 1520])).
% 1.11/1.28 tff(1522,plain,
% 1.11/1.28 (~c0_1(a507)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[846, 1520])).
% 1.11/1.28 tff(1523,plain,
% 1.11/1.28 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 1.11/1.28 inference(bind,[status(th)],[])).
% 1.11/1.28 tff(1524,plain,
% 1.11/1.28 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.11/1.28 inference(quant_intro,[status(thm)],[1523])).
% 1.11/1.28 tff(1525,plain,
% 1.11/1.28 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1526,plain,
% 1.11/1.28 (^[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(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~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)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~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)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | 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)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | 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)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp24) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp24))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp24) <=> (hskp24 | (~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)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 1.11/1.28 inference(bind,[status(th)],[])).
% 1.11/1.28 tff(1527,plain,
% 1.11/1.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.11/1.28 inference(quant_intro,[status(thm)],[1526])).
% 1.11/1.28 tff(1528,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 1.11/1.28 tff(1529,plain,
% 1.11/1.28 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1528, 1527])).
% 1.11/1.28 tff(1530,plain,
% 1.11/1.28 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1529, 1525])).
% 1.11/1.28 tff(1531,plain,(
% 1.11/1.28 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.11/1.28 inference(skolemize,[status(sab)],[1530])).
% 1.11/1.28 tff(1532,plain,
% 1.11/1.28 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1531, 1524])).
% 1.11/1.28 tff(1533,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1534,plain,
% 1.11/1.28 ((hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a568) | (~c0_1(a568)) | (~c3_1(a568))) <=> (hskp24 | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1535,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a568) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568)))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[1534])).
% 1.11/1.28 tff(1536,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a568) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))),
% 1.11/1.28 inference(transitivity,[status(thm)],[1535, 1533])).
% 1.11/1.28 tff(1537,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a568) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(1538,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 1.11/1.28 tff(1539,plain,
% 1.11/1.28 (hskp24),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1538, 106, 368, 370, 1424, 1426, 1425, 1532, 1519])).
% 1.11/1.28 tff(1540,plain,
% 1.11/1.28 (((~hskp24) | (~c2_1(a554))) <=> ((~hskp24) | (~c2_1(a554)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1541,plain,
% 1.11/1.28 (((~c2_1(a554)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a554)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1542,axiom,((~c2_1(a554)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.11/1.28 tff(1543,plain,
% 1.11/1.28 ((~hskp24) | (~c2_1(a554))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 1.11/1.28 tff(1544,plain,
% 1.11/1.28 ((~hskp24) | (~c2_1(a554))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1543, 1540])).
% 1.11/1.28 tff(1545,plain,
% 1.11/1.28 (~c2_1(a554)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1544, 1539])).
% 1.11/1.28 tff(1546,plain,
% 1.11/1.28 (c3_1(a507)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[854, 1520])).
% 1.11/1.28 tff(1547,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1548,plain,
% 1.11/1.28 ((hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (hskp28 | c1_1(a568) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1549,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[1548])).
% 1.11/1.28 tff(1550,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[1549, 1547])).
% 1.11/1.28 tff(1551,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(1552,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 1.11/1.28 tff(1553,plain,
% 1.11/1.28 (hskp28),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1552, 106, 368, 370, 1546, 369, 1522, 1521, 238])).
% 1.11/1.28 tff(1554,plain,
% 1.11/1.28 (c3_1(a500)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[390, 1553])).
% 1.11/1.28 tff(1555,plain,
% 1.11/1.28 (c2_1(a500)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[398, 1553])).
% 1.11/1.28 tff(1556,plain,
% 1.11/1.28 (c0_1(a500)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[406, 1553])).
% 1.11/1.28 tff(1557,plain,
% 1.11/1.28 (((~hskp24) | (~c3_1(a554))) <=> ((~hskp24) | (~c3_1(a554)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1558,plain,
% 1.11/1.28 (((~c3_1(a554)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a554)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1559,axiom,((~c3_1(a554)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.11/1.28 tff(1560,plain,
% 1.11/1.28 ((~hskp24) | (~c3_1(a554))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1559, 1558])).
% 1.11/1.28 tff(1561,plain,
% 1.11/1.28 ((~hskp24) | (~c3_1(a554))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1560, 1557])).
% 1.11/1.28 tff(1562,plain,
% 1.11/1.28 (~c3_1(a554)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1561, 1539])).
% 1.11/1.28 tff(1563,plain,
% 1.11/1.28 (((~hskp24) | c0_1(a554)) <=> ((~hskp24) | c0_1(a554))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1564,axiom,((~hskp24) | c0_1(a554)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.11/1.28 tff(1565,plain,
% 1.11/1.28 ((~hskp24) | c0_1(a554)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 1.11/1.28 tff(1566,plain,
% 1.11/1.28 ((~hskp24) | c0_1(a554)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1565, 1563])).
% 1.11/1.28 tff(1567,plain,
% 1.11/1.28 ((~hskp24) | c0_1(a554)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1566, 1563])).
% 1.11/1.28 tff(1568,plain,
% 1.11/1.28 ((~hskp24) | c0_1(a554)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1567, 1563])).
% 1.11/1.28 tff(1569,plain,
% 1.11/1.28 ((~hskp24) | c0_1(a554)),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1568, 1563])).
% 1.11/1.28 tff(1570,plain,
% 1.11/1.28 (c0_1(a554)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1569, 1539])).
% 1.11/1.28 tff(1571,plain,
% 1.11/1.28 (c1_1(a520)),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1459, 981, 1478])).
% 1.11/1.28 tff(1572,plain,
% 1.11/1.28 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.11/1.28 inference(bind,[status(th)],[])).
% 1.11/1.28 tff(1573,plain,
% 1.11/1.28 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.11/1.28 inference(quant_intro,[status(thm)],[1572])).
% 1.11/1.28 tff(1574,plain,
% 1.11/1.28 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1575,plain,
% 1.11/1.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_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))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp0))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.11/1.28 inference(bind,[status(th)],[])).
% 1.11/1.28 tff(1576,plain,
% 1.11/1.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.11/1.28 inference(quant_intro,[status(thm)],[1575])).
% 1.11/1.28 tff(1577,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.11/1.28 tff(1578,plain,
% 1.11/1.28 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1577, 1576])).
% 1.11/1.28 tff(1579,plain,
% 1.11/1.28 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1578, 1574])).
% 1.11/1.28 tff(1580,plain,(
% 1.11/1.28 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.11/1.28 inference(skolemize,[status(sab)],[1579])).
% 1.11/1.28 tff(1581,plain,
% 1.11/1.28 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1580, 1573])).
% 1.11/1.28 tff(1582,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp0 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1583,plain,
% 1.11/1.28 ((hskp0 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c2_1(a520))) <=> (hskp0 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1584,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c2_1(a520))))),
% 1.11/1.28 inference(monotonicity,[status(thm)],[1583])).
% 1.11/1.28 tff(1585,plain,
% 1.11/1.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp0 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.11/1.28 inference(transitivity,[status(thm)],[1584, 1582])).
% 1.11/1.28 tff(1586,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.11/1.28 inference(quant_inst,[status(thm)],[])).
% 1.11/1.28 tff(1587,plain,
% 1.11/1.28 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp0 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c2_1(a520))),
% 1.11/1.28 inference(modus_ponens,[status(thm)],[1586, 1585])).
% 1.11/1.28 tff(1588,plain,
% 1.11/1.28 (hskp0 | (~c1_1(a520))),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1587, 106, 444, 443, 442, 1427, 1437, 1581])).
% 1.11/1.28 tff(1589,plain,
% 1.11/1.28 (hskp0),
% 1.11/1.28 inference(unit_resolution,[status(thm)],[1588, 1571])).
% 1.11/1.28 tff(1590,plain,
% 1.11/1.28 (((~hskp0) | (~c2_1(a494))) <=> ((~hskp0) | (~c2_1(a494)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1591,plain,
% 1.11/1.28 (((~c2_1(a494)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a494)))),
% 1.11/1.28 inference(rewrite,[status(thm)],[])).
% 1.11/1.28 tff(1592,axiom,((~c2_1(a494)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.11/1.28 tff(1593,plain,
% 1.11/1.29 ((~hskp0) | (~c2_1(a494))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 1.11/1.29 tff(1594,plain,
% 1.11/1.29 ((~hskp0) | (~c2_1(a494))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[1593, 1590])).
% 1.11/1.29 tff(1595,plain,
% 1.11/1.29 (~c2_1(a494)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1594, 1589])).
% 1.11/1.29 tff(1596,plain,
% 1.11/1.29 (~c0_1(a494)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[797, 1589])).
% 1.11/1.29 tff(1597,plain,
% 1.11/1.29 (~c2_1(a502)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1040, 981, 940, 1478])).
% 1.11/1.29 tff(1598,assumption,(~c3_1(a554)), introduced(assumption)).
% 1.11/1.29 tff(1599,assumption,(~c2_1(a554)), introduced(assumption)).
% 1.11/1.29 tff(1600,assumption,(c0_1(a554)), introduced(assumption)).
% 1.11/1.29 tff(1601,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a554) | c3_1(a554) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a554)) | (~c0_1(a554)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a554) | c3_1(a554) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a554)) | (~c0_1(a554)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1602,plain,
% 1.11/1.29 (((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c2_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c3_1(a502) | c0_1(a502) | c2_1(a502)) <=> (c2_1(a554) | c3_1(a554) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a554)) | (~c0_1(a554)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1603,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c2_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a554) | c3_1(a554) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a554)) | (~c0_1(a554))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[1602])).
% 1.11/1.29 tff(1604,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c2_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a554) | c3_1(a554) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a554)) | (~c0_1(a554)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[1603, 1601])).
% 1.11/1.29 tff(1605,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c2_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c3_1(a502) | c0_1(a502) | c2_1(a502))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(1606,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a554) | c3_1(a554) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a554)) | (~c0_1(a554))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[1605, 1604])).
% 1.11/1.29 tff(1607,plain,
% 1.11/1.29 (c2_1(a502) | (~c1_1(a554))),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1606, 106, 1600, 1599, 1598, 239, 940, 909])).
% 1.11/1.29 tff(1608,plain,
% 1.11/1.29 (~c1_1(a554)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1607, 1597])).
% 1.11/1.29 tff(1609,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a554) | (~c0_1(a554)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a554) | (~c0_1(a554)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1610,plain,
% 1.11/1.29 ((hskp1 | (~ndr1_0) | c3_1(a554) | c1_1(a554) | (~c0_1(a554)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp1 | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a554) | (~c0_1(a554)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1611,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a554) | c1_1(a554) | (~c0_1(a554)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a554) | (~c0_1(a554))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[1610])).
% 1.11/1.29 tff(1612,plain,
% 1.11/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a554) | c1_1(a554) | (~c0_1(a554)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a554) | (~c0_1(a554)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[1611, 1609])).
% 1.11/1.29 tff(1613,plain,
% 1.11/1.29 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a554) | c1_1(a554) | (~c0_1(a554)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(1614,plain,
% 1.11/1.29 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a554) | (~c0_1(a554))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[1613, 1612])).
% 1.11/1.29 tff(1615,plain,
% 1.11/1.29 (hskp1 | c1_1(a554)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1614, 106, 1600, 1598, 239, 949, 940, 585])).
% 1.11/1.29 tff(1616,plain,
% 1.11/1.29 (hskp1),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1615, 1608])).
% 1.11/1.29 tff(1617,plain,
% 1.11/1.29 (~c3_1(a495)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[932, 1616])).
% 1.11/1.29 tff(1618,plain,
% 1.11/1.29 (~c0_1(a495)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[938, 1616])).
% 1.11/1.29 tff(1619,plain,
% 1.11/1.29 (c3_1(a494)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[809, 1589])).
% 1.11/1.29 tff(1620,plain,
% 1.11/1.29 (c1_1(a495)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[947, 1616])).
% 1.11/1.29 tff(1621,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c3_1(a528) | c0_1(a495) | c3_1(a495) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a495) | c3_1(a495) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1622,plain,
% 1.11/1.29 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494)) <=> (c3_1(a528) | c0_1(a495) | c3_1(a495) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1623,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c3_1(a528) | c0_1(a495) | c3_1(a495) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[1622])).
% 1.11/1.29 tff(1624,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a495) | c3_1(a495) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[1623, 1621])).
% 1.11/1.29 tff(1625,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(1626,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a495) | c3_1(a495) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[1625, 1624])).
% 1.11/1.29 tff(1627,plain,
% 1.11/1.29 ($false),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1626, 106, 999, 998, 1620, 1619, 989, 1618, 1617, 1596, 1595, 21])).
% 1.11/1.29 tff(1628,plain,(hskp12 | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | (~c0_1(a554)) | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c2_1(a520)) | c3_1(a520) | c2_1(a554) | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.11/1.29 tff(1629,plain,
% 1.11/1.29 (hskp12),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1628, 1570, 998, 989, 999, 1562, 239, 949, 940, 1556, 1555, 1554, 1426, 1425, 1545, 1478])).
% 1.11/1.29 tff(1630,plain,
% 1.11/1.29 (~c2_1(a514)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[487, 1629])).
% 1.11/1.29 tff(1631,plain,
% 1.11/1.29 (c3_1(a514)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[495, 1629])).
% 1.11/1.29 tff(1632,plain,
% 1.11/1.29 (c1_1(a514)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[503, 1629])).
% 1.11/1.29 tff(1633,plain,
% 1.11/1.29 (c0_1(a514)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[868, 106, 1632, 1631, 1546, 1630, 1522, 1521, 558])).
% 1.11/1.29 tff(1634,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a514) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a514) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1635,plain,
% 1.11/1.29 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a502) | c0_1(a502) | c2_1(a502)) <=> (c3_1(a528) | c2_1(a514) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1636,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a514) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[1635])).
% 1.11/1.29 tff(1637,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a514) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[1636, 1634])).
% 1.11/1.29 tff(1638,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a502) | c0_1(a502) | c2_1(a502))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(1639,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a514) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 1.11/1.29 tff(1640,plain,
% 1.11/1.29 (c2_1(a502) | (~c0_1(a514))),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1639, 106, 999, 998, 1632, 989, 1630, 239, 940, 909])).
% 1.11/1.29 tff(1641,plain,
% 1.11/1.29 (c2_1(a502)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1640, 1633])).
% 1.11/1.29 tff(1642,plain,
% 1.11/1.29 (hskp4 | (~c2_1(a502))),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1385, 106, 1424, 1426, 1425, 239, 949, 367])).
% 1.11/1.29 tff(1643,plain,
% 1.11/1.29 (hskp4),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1642, 1641])).
% 1.11/1.29 tff(1644,plain,
% 1.11/1.29 (~c0_1(a498)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1391, 1643])).
% 1.11/1.29 tff(1645,plain,
% 1.11/1.29 (c1_1(a498)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1399, 1643])).
% 1.11/1.29 tff(1646,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1647,plain,
% 1.11/1.29 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a498) | (~c3_1(a498)) | (~c1_1(a498))) <=> (c1_1(a568) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1648,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a498) | (~c3_1(a498)) | (~c1_1(a498)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[1647])).
% 1.11/1.29 tff(1649,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a498) | (~c3_1(a498)) | (~c1_1(a498)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[1648, 1646])).
% 1.11/1.29 tff(1650,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a498) | (~c3_1(a498)) | (~c1_1(a498)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(1651,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 1.11/1.29 tff(1652,plain,
% 1.11/1.29 (~c3_1(a498)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1651, 106, 368, 370, 999, 998, 1645, 369, 989, 1644, 1302])).
% 1.11/1.29 tff(1653,plain,
% 1.11/1.29 (~c2_1(a498)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1412, 1643])).
% 1.11/1.29 tff(1654,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1655,plain,
% 1.11/1.29 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c3_1(a528) | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1656,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[1655])).
% 1.11/1.29 tff(1657,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[1656, 1654])).
% 1.11/1.29 tff(1658,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(1659,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 1.11/1.29 tff(1660,plain,
% 1.11/1.29 (c0_1(a496) | (~c0_1(a514))),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1659, 106, 999, 998, 1632, 989, 1630, 574, 573, 909])).
% 1.11/1.29 tff(1661,plain,
% 1.11/1.29 (c0_1(a496)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1660, 1633])).
% 1.11/1.29 tff(1662,plain,
% 1.11/1.29 (hskp22 | (~c0_1(a496))),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[722, 106, 572, 574, 573, 31])).
% 1.11/1.29 tff(1663,plain,
% 1.11/1.29 (hskp22),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1662, 1661])).
% 1.11/1.29 tff(1664,plain,
% 1.11/1.29 (~c0_1(a540)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[125, 1663])).
% 1.11/1.29 tff(1665,plain,
% 1.11/1.29 (c1_1(a540)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[141, 1663])).
% 1.11/1.29 tff(1666,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a540) | c2_1(a514) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c1_1(a498)) | (~c3_1(a514)) | (~c1_1(a514)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c2_1(a514) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c1_1(a498)) | (~c3_1(a514)) | (~c1_1(a514)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1667,plain,
% 1.11/1.29 (((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498))) <=> (c0_1(a540) | c2_1(a514) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c1_1(a498)) | (~c3_1(a514)) | (~c1_1(a514)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1668,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a540) | c2_1(a514) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c1_1(a498)) | (~c3_1(a514)) | (~c1_1(a514)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[1667])).
% 1.11/1.29 tff(1669,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c2_1(a514) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c1_1(a498)) | (~c3_1(a514)) | (~c1_1(a514)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.11/1.29 inference(transitivity,[status(thm)],[1668, 1666])).
% 1.11/1.29 tff(1670,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498)))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(1671,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c2_1(a514) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c1_1(a498)) | (~c3_1(a514)) | (~c1_1(a514)) | (~c1_1(a540)) | (~c2_1(a540))),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 1.11/1.29 tff(1672,plain,
% 1.11/1.29 (~c2_1(a540)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[1671, 106, 1665, 1632, 1631, 1645, 1664, 1630, 1644, 1653, 1079])).
% 1.11/1.29 tff(1673,plain,
% 1.11/1.29 (c3_1(a540)),
% 1.11/1.29 inference(unit_resolution,[status(thm)],[133, 1663])).
% 1.11/1.29 tff(1674,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a540) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a540) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | c2_1(a540))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1675,plain,
% 1.11/1.29 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a498) | c3_1(a498) | (~c1_1(a498)) | c0_1(a540) | (~c3_1(a540)) | c2_1(a540)) <=> (c0_1(a540) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | c2_1(a540))),
% 1.11/1.29 inference(rewrite,[status(thm)],[])).
% 1.11/1.29 tff(1676,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a498) | c3_1(a498) | (~c1_1(a498)) | c0_1(a540) | (~c3_1(a540)) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a540) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | c2_1(a540)))),
% 1.11/1.29 inference(monotonicity,[status(thm)],[1675])).
% 1.11/1.29 tff(1677,plain,
% 1.11/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a498) | c3_1(a498) | (~c1_1(a498)) | c0_1(a540) | (~c3_1(a540)) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a540) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | c2_1(a540))),
% 1.11/1.29 inference(transitivity,[status(thm)],[1676, 1674])).
% 1.11/1.29 tff(1678,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a498) | c3_1(a498) | (~c1_1(a498)) | c0_1(a540) | (~c3_1(a540)) | c2_1(a540))),
% 1.11/1.29 inference(quant_inst,[status(thm)],[])).
% 1.11/1.29 tff(1679,plain,
% 1.11/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a540) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | c2_1(a540)),
% 1.11/1.29 inference(modus_ponens,[status(thm)],[1678, 1677])).
% 1.11/1.30 tff(1680,plain,
% 1.11/1.30 ($false),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1679, 106, 1673, 999, 998, 1645, 1664, 989, 1644, 21, 1672, 1652])).
% 1.11/1.30 tff(1681,plain,(hskp20 | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | (~c0_1(a568)) | (~c3_1(a568)) | c1_1(a568) | c1_1(a496) | c2_1(a496) | c3_1(a496) | c0_1(a502) | c1_1(a502) | c3_1(a502) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.11/1.30 tff(1682,plain,
% 1.11/1.30 (hskp20),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1681, 572, 998, 989, 368, 370, 369, 999, 574, 573, 239, 949, 940, 11])).
% 1.11/1.30 tff(1683,plain,
% 1.11/1.30 (~hskp1),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1451, 1682, 989, 998, 999, 949, 940, 239])).
% 1.11/1.30 tff(1684,plain,
% 1.11/1.30 (hskp1 | c3_1(a502) | c1_1(a520)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1443, 106, 1424, 1425, 239, 949, 585])).
% 1.11/1.30 tff(1685,plain,
% 1.11/1.30 (c1_1(a520)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1684, 1683, 940])).
% 1.11/1.30 tff(1686,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1687,plain,
% 1.11/1.30 ((hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1688,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[1687])).
% 1.11/1.30 tff(1689,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[1688, 1686])).
% 1.11/1.30 tff(1690,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(1691,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 1.11/1.30 tff(1692,plain,
% 1.11/1.30 (hskp1 | c1_1(a496) | (~c0_1(a496))),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1691, 106, 239, 949, 940, 573, 585])).
% 1.11/1.30 tff(1693,plain,
% 1.11/1.30 (~c0_1(a496)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1692, 1683, 572])).
% 1.11/1.30 tff(1694,plain,
% 1.11/1.30 (c3_1(a496) | c0_1(a496) | (~c1_1(a520))),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1503, 106, 1426, 1425, 239, 949, 940, 574, 709])).
% 1.11/1.30 tff(1695,plain,
% 1.11/1.30 ($false),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1694, 1693, 1685, 573])).
% 1.11/1.30 tff(1696,plain,(c1_1(a496) | c3_1(a496) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)) | c1_1(a568) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.11/1.30 tff(1697,plain,
% 1.11/1.30 ($false),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1696, 1477, 1476, 239, 949, 940, 1475, 989, 998, 999, 368, 370, 369, 11])).
% 1.11/1.30 tff(1698,plain,(c3_1(a502) | c0_1(a502) | c1_1(a502) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)) | c1_1(a568) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.11/1.30 tff(1699,plain,
% 1.11/1.30 (c1_1(a502)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1698, 940, 239, 425, 433, 441, 368, 370, 369, 11])).
% 1.11/1.30 tff(1700,plain,
% 1.11/1.30 (~hskp7),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[308, 1699])).
% 1.11/1.30 tff(1701,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a568) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a568) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1702,plain,
% 1.11/1.30 ((hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502))) <=> (hskp8 | c1_1(a568) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1703,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a568) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[1702])).
% 1.11/1.30 tff(1704,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a568) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[1703, 1701])).
% 1.11/1.30 tff(1705,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(1706,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a568) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[1705, 1704])).
% 1.11/1.30 tff(1707,plain,
% 1.11/1.30 (hskp8 | (~c1_1(a502)) | c3_1(a502)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1706, 106, 368, 370, 369, 239, 959])).
% 1.11/1.30 tff(1708,plain,
% 1.11/1.30 (hskp8),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1707, 1699, 940])).
% 1.11/1.30 tff(1709,plain,
% 1.11/1.30 (~c0_1(a505)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[979, 1708])).
% 1.11/1.30 tff(1710,plain,
% 1.11/1.30 (c3_1(a505)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1065, 1708])).
% 1.11/1.30 tff(1711,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c3_1(a528) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1712,plain,
% 1.11/1.30 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a505) | (~c3_1(a505)) | (~c1_1(a505))) <=> (c1_1(a568) | c3_1(a528) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1713,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a505) | (~c3_1(a505)) | (~c1_1(a505)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c3_1(a528) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[1712])).
% 1.11/1.30 tff(1714,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a505) | (~c3_1(a505)) | (~c1_1(a505)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[1713, 1711])).
% 1.11/1.30 tff(1715,plain,
% 1.11/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a505) | (~c3_1(a505)) | (~c1_1(a505)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(1716,plain,
% 1.11/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[1715, 1714])).
% 1.11/1.30 tff(1717,plain,
% 1.11/1.30 (~c1_1(a505)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1716, 106, 368, 370, 441, 433, 1710, 369, 425, 1709, 1302])).
% 1.11/1.30 tff(1718,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1719,plain,
% 1.11/1.30 ((hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505))) <=> (hskp28 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1720,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[1719])).
% 1.11/1.30 tff(1721,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[1720, 1718])).
% 1.11/1.30 tff(1722,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(1723,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[1722, 1721])).
% 1.11/1.30 tff(1724,plain,
% 1.11/1.30 (hskp28),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1723, 106, 368, 370, 1710, 369, 1709, 238, 1717])).
% 1.11/1.30 tff(1725,plain,
% 1.11/1.30 (c3_1(a500)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[390, 1724])).
% 1.11/1.30 tff(1726,plain,
% 1.11/1.30 (c0_1(a500)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[406, 1724])).
% 1.11/1.30 tff(1727,plain,
% 1.11/1.30 (c2_1(a500)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[398, 1724])).
% 1.11/1.30 tff(1728,plain,
% 1.11/1.30 (hskp2),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[452, 1727, 419, 1726, 1725])).
% 1.11/1.30 tff(1729,plain,
% 1.11/1.30 (~c3_1(a496)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[329, 1728])).
% 1.11/1.30 tff(1730,plain,
% 1.11/1.30 (~c2_1(a496)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[335, 1728])).
% 1.11/1.30 tff(1731,plain,
% 1.11/1.30 (~c1_1(a496)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[348, 1728])).
% 1.11/1.30 tff(1732,assumption,(hskp22), introduced(assumption)).
% 1.11/1.30 tff(1733,plain,
% 1.11/1.30 (~c0_1(a540)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[125, 1732])).
% 1.11/1.30 tff(1734,plain,
% 1.11/1.30 (c3_1(a540)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[133, 1732])).
% 1.11/1.30 tff(1735,plain,
% 1.11/1.30 (c1_1(a540)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[141, 1732])).
% 1.11/1.30 tff(1736,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1737,plain,
% 1.11/1.30 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540))) <=> (c1_1(a568) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1738,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[1737])).
% 1.11/1.30 tff(1739,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[1738, 1736])).
% 1.11/1.30 tff(1740,plain,
% 1.11/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(1741,plain,
% 1.11/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[1740, 1739])).
% 1.11/1.30 tff(1742,plain,
% 1.11/1.30 ($false),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1741, 106, 368, 370, 1735, 1734, 999, 998, 369, 1733, 989, 1302])).
% 1.11/1.30 tff(1743,plain,((~hskp22) | (~c0_1(a568)) | (~c3_1(a568)) | (~c0_1(a528)) | (~c1_1(a528)) | c1_1(a568) | c3_1(a528)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.30 tff(1744,plain,
% 1.11/1.30 (~hskp22),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1743, 441, 370, 368, 433, 369, 425])).
% 1.11/1.30 tff(1745,plain,
% 1.11/1.30 (~c0_1(a496)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[722, 106, 1744, 1731, 1730, 1729, 31])).
% 1.11/1.30 tff(1746,plain,
% 1.11/1.30 (~c2_1(a568)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1174, 106, 1700, 368, 1710, 369, 1709, 216, 1717])).
% 1.11/1.30 tff(1747,plain,
% 1.11/1.30 (c2_1(a505)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[973, 1708])).
% 1.11/1.30 tff(1748,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c3_1(a520) | c0_1(a505) | (~ndr1_0) | c1_1(a505) | (~c2_1(a505)) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a520) | c0_1(a505) | (~ndr1_0) | c1_1(a505) | (~c2_1(a505)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1749,plain,
% 1.11/1.30 ((hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a505) | c0_1(a505) | (~c2_1(a505))) <=> (hskp4 | c3_1(a520) | c0_1(a505) | (~ndr1_0) | c1_1(a505) | (~c2_1(a505)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1750,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a505) | c0_1(a505) | (~c2_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c3_1(a520) | c0_1(a505) | (~ndr1_0) | c1_1(a505) | (~c2_1(a505)) | (~c0_1(a520)) | (~c2_1(a520))))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[1749])).
% 1.11/1.30 tff(1751,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a505) | c0_1(a505) | (~c2_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a520) | c0_1(a505) | (~ndr1_0) | c1_1(a505) | (~c2_1(a505)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.11/1.30 inference(transitivity,[status(thm)],[1750, 1748])).
% 1.11/1.30 tff(1752,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a505) | c0_1(a505) | (~c2_1(a505)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(1753,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a520) | c0_1(a505) | (~ndr1_0) | c1_1(a505) | (~c2_1(a505)) | (~c0_1(a520)) | (~c2_1(a520))),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 1.11/1.30 tff(1754,plain,
% 1.11/1.30 (hskp4),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1753, 106, 1424, 1426, 1747, 1425, 1709, 367, 1717])).
% 1.11/1.30 tff(1755,plain,
% 1.11/1.30 (~c0_1(a498)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1391, 1754])).
% 1.11/1.30 tff(1756,plain,
% 1.11/1.30 (c1_1(a498)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1399, 1754])).
% 1.11/1.30 tff(1757,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a568) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c0_1(a568)) | c2_1(a568))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a568) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c0_1(a568)) | c2_1(a568))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1758,plain,
% 1.11/1.30 ((hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498))) <=> (hskp10 | c1_1(a568) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c0_1(a568)) | c2_1(a568))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1759,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a568) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c0_1(a568)) | c2_1(a568)))),
% 1.11/1.30 inference(monotonicity,[status(thm)],[1758])).
% 1.11/1.30 tff(1760,plain,
% 1.11/1.30 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a568) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c0_1(a568)) | c2_1(a568))),
% 1.11/1.30 inference(transitivity,[status(thm)],[1759, 1757])).
% 1.11/1.30 tff(1761,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498)))),
% 1.11/1.30 inference(quant_inst,[status(thm)],[])).
% 1.11/1.30 tff(1762,plain,
% 1.11/1.30 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a568) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c0_1(a568)) | c2_1(a568)),
% 1.11/1.30 inference(modus_ponens,[status(thm)],[1761, 1760])).
% 1.11/1.30 tff(1763,plain,
% 1.11/1.30 (~c3_1(a498)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1762, 106, 11, 368, 1756, 369, 1755, 53, 1746])).
% 1.11/1.30 tff(1764,plain,
% 1.11/1.30 (~c2_1(a498)),
% 1.11/1.30 inference(unit_resolution,[status(thm)],[1412, 1754])).
% 1.11/1.30 tff(1765,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a520) | c0_1(a498) | c2_1(a498) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c3_1(a498) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c0_1(a498) | c2_1(a498) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c3_1(a498) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1766,plain,
% 1.11/1.30 (((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a496) | c1_1(a496) | c0_1(a496)) <=> (c3_1(a520) | c0_1(a498) | c2_1(a498) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c3_1(a498) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.11/1.30 inference(rewrite,[status(thm)],[])).
% 1.11/1.30 tff(1767,plain,
% 1.11/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a520) | c0_1(a498) | c2_1(a498) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c3_1(a498) | (~c1_1(a520)) | (~c2_1(a520))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[1766])).
% 1.11/1.31 tff(1768,plain,
% 1.11/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c0_1(a498) | c2_1(a498) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c3_1(a498) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[1767, 1765])).
% 1.11/1.31 tff(1769,plain,
% 1.11/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a496) | c1_1(a496) | c0_1(a496))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(1770,plain,
% 1.11/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c0_1(a498) | c2_1(a498) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c3_1(a498) | (~c1_1(a520)) | (~c2_1(a520))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1769, 1768])).
% 1.11/1.31 tff(1771,plain,
% 1.11/1.31 (c0_1(a496) | (~c1_1(a520))),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1770, 106, 1426, 1425, 1755, 1764, 1731, 1729, 709, 1763])).
% 1.11/1.31 tff(1772,plain,
% 1.11/1.31 (~c1_1(a520)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1771, 1745])).
% 1.11/1.31 tff(1773,plain,
% 1.11/1.31 (^[U: $i] : refl((hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.11/1.31 inference(bind,[status(th)],[])).
% 1.11/1.31 tff(1774,plain,
% 1.11/1.31 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.11/1.31 inference(quant_intro,[status(thm)],[1773])).
% 1.11/1.31 tff(1775,plain,
% 1.11/1.31 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1776,plain,
% 1.11/1.31 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp5) | hskp7) <=> ((hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp7))), rewrite(((hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp7) <=> (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp5) | hskp7) <=> (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.11/1.31 inference(bind,[status(th)],[])).
% 1.11/1.31 tff(1777,plain,
% 1.11/1.31 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp5) | hskp7) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.11/1.31 inference(quant_intro,[status(thm)],[1776])).
% 1.11/1.31 tff(1778,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp5) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 1.11/1.31 tff(1779,plain,
% 1.11/1.31 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 1.11/1.31 tff(1780,plain,
% 1.11/1.31 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1779, 1775])).
% 1.11/1.31 tff(1781,plain,(
% 1.11/1.31 ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.11/1.31 inference(skolemize,[status(sab)],[1780])).
% 1.11/1.31 tff(1782,plain,
% 1.11/1.31 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1781, 1774])).
% 1.11/1.31 tff(1783,plain,
% 1.11/1.31 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp7 | hskp5 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp7 | hskp5 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1784,plain,
% 1.11/1.31 ((hskp7 | hskp5 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520))) <=> (hskp7 | hskp5 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1785,plain,
% 1.11/1.31 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp7 | hskp5 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[1784])).
% 1.11/1.31 tff(1786,plain,
% 1.11/1.31 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp7 | hskp5 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[1785, 1783])).
% 1.11/1.31 tff(1787,plain,
% 1.11/1.31 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(1788,plain,
% 1.11/1.31 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp7 | hskp5 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1787, 1786])).
% 1.11/1.31 tff(1789,plain,
% 1.11/1.31 (hskp7 | hskp5 | c1_1(a520)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1788, 106, 1424, 1425, 1782])).
% 1.11/1.31 tff(1790,plain,
% 1.11/1.31 (hskp5),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1789, 1772, 1700])).
% 1.11/1.31 tff(1791,plain,
% 1.11/1.31 (((~hskp5) | c0_1(a499)) <=> ((~hskp5) | c0_1(a499))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1792,axiom,((~hskp5) | c0_1(a499)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.11/1.31 tff(1793,plain,
% 1.11/1.31 ((~hskp5) | c0_1(a499)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1792, 1791])).
% 1.11/1.31 tff(1794,plain,
% 1.11/1.31 ((~hskp5) | c0_1(a499)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1793, 1791])).
% 1.11/1.31 tff(1795,plain,
% 1.11/1.31 ((~hskp5) | c0_1(a499)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1794, 1791])).
% 1.11/1.31 tff(1796,plain,
% 1.11/1.31 ((~hskp5) | c0_1(a499)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1795, 1791])).
% 1.11/1.31 tff(1797,plain,
% 1.11/1.31 ((~hskp5) | c0_1(a499)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1796, 1791])).
% 1.11/1.31 tff(1798,plain,
% 1.11/1.31 (c0_1(a499)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1797, 1790])).
% 1.11/1.31 tff(1799,plain,
% 1.11/1.31 (((~hskp5) | c2_1(a499)) <=> ((~hskp5) | c2_1(a499))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1800,axiom,((~hskp5) | c2_1(a499)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.11/1.31 tff(1801,plain,
% 1.11/1.31 ((~hskp5) | c2_1(a499)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.11/1.31 tff(1802,plain,
% 1.11/1.31 ((~hskp5) | c2_1(a499)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1801, 1799])).
% 1.11/1.31 tff(1803,plain,
% 1.11/1.31 ((~hskp5) | c2_1(a499)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1802, 1799])).
% 1.11/1.31 tff(1804,plain,
% 1.11/1.31 ((~hskp5) | c2_1(a499)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1803, 1799])).
% 1.11/1.31 tff(1805,plain,
% 1.11/1.31 ((~hskp5) | c2_1(a499)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1804, 1799])).
% 1.11/1.31 tff(1806,plain,
% 1.11/1.31 (c2_1(a499)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1805, 1790])).
% 1.11/1.31 tff(1807,plain,
% 1.11/1.31 (((~hskp5) | (~c1_1(a499))) <=> ((~hskp5) | (~c1_1(a499)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1808,plain,
% 1.11/1.31 (((~c1_1(a499)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a499)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1809,axiom,((~c1_1(a499)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.11/1.31 tff(1810,plain,
% 1.11/1.31 ((~hskp5) | (~c1_1(a499))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1809, 1808])).
% 1.11/1.31 tff(1811,plain,
% 1.11/1.31 ((~hskp5) | (~c1_1(a499))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1810, 1807])).
% 1.11/1.31 tff(1812,plain,
% 1.11/1.31 (~c1_1(a499)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1811, 1790])).
% 1.11/1.31 tff(1813,assumption,(~c1_1(a505)), introduced(assumption)).
% 1.11/1.31 tff(1814,assumption,(~c1_1(a499)), introduced(assumption)).
% 1.11/1.31 tff(1815,assumption,(c2_1(a499)), introduced(assumption)).
% 1.11/1.31 tff(1816,assumption,(c0_1(a499)), introduced(assumption)).
% 1.11/1.31 tff(1817,assumption,(~hskp7), introduced(assumption)).
% 1.11/1.31 tff(1818,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a505) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a505)) | c1_1(a505))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a505) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a505)) | c1_1(a505))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1819,plain,
% 1.11/1.31 ((hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505))) <=> (hskp7 | c0_1(a505) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a505)) | c1_1(a505))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1820,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a505) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a505)) | c1_1(a505)))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[1819])).
% 1.11/1.31 tff(1821,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a505) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a505)) | c1_1(a505))),
% 1.11/1.31 inference(transitivity,[status(thm)],[1820, 1818])).
% 1.11/1.31 tff(1822,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(1823,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a505) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a505)) | c1_1(a505)),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1822, 1821])).
% 1.11/1.31 tff(1824,plain,
% 1.11/1.31 ($false),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1823, 106, 1817, 1099, 1816, 1815, 1080, 1814, 216, 1813])).
% 1.11/1.31 tff(1825,plain,(c1_1(a505) | hskp7 | (~c3_1(a505)) | (~c0_1(a499)) | (~c2_1(a499)) | c0_1(a505) | c1_1(a499)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.31 tff(1826,plain,
% 1.11/1.31 ($false),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1825, 1812, 1806, 1700, 1710, 1717, 1709, 1798])).
% 1.11/1.31 tff(1827,plain,(c3_1(a502) | hskp10 | (~c0_1(a568)) | c1_1(a568) | (~hskp15) | (~c3_1(a568)) | c0_1(a502)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.31 tff(1828,plain,
% 1.11/1.31 (c3_1(a502)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1827, 1422, 198, 228, 11, 190, 239])).
% 1.11/1.31 tff(1829,plain,
% 1.11/1.31 (~c3_1(a528)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[424, 1422])).
% 1.11/1.31 tff(1830,plain,
% 1.11/1.31 (c1_1(a528)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[432, 1422])).
% 1.11/1.31 tff(1831,plain,
% 1.11/1.31 (c0_1(a528)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[440, 1422])).
% 1.11/1.31 tff(1832,plain,
% 1.11/1.31 ((~c1_1(a502)) | (~c3_1(a502))),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1308, 106, 198, 190, 1831, 1830, 228, 1829, 239, 1302])).
% 1.11/1.31 tff(1833,plain,
% 1.11/1.31 (~c1_1(a502)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1832, 1828])).
% 1.11/1.31 tff(1834,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1835,plain,
% 1.11/1.31 ((hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502))) <=> (hskp28 | c1_1(a568) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1836,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[1835])).
% 1.11/1.31 tff(1837,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[1836, 1834])).
% 1.11/1.31 tff(1838,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502)))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(1839,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1838, 1837])).
% 1.11/1.31 tff(1840,plain,
% 1.11/1.31 (hskp28),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1839, 106, 198, 190, 228, 239, 1833, 1828, 238])).
% 1.11/1.31 tff(1841,plain,
% 1.11/1.31 (c3_1(a500)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[390, 1840])).
% 1.11/1.31 tff(1842,plain,
% 1.11/1.31 (c0_1(a500)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[406, 1840])).
% 1.11/1.31 tff(1843,plain,
% 1.11/1.31 (c2_1(a500)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[398, 1840])).
% 1.11/1.31 tff(1844,plain,
% 1.11/1.31 (hskp2),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[452, 1843, 1422, 1842, 1841])).
% 1.11/1.31 tff(1845,plain,
% 1.11/1.31 (~c3_1(a496)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[329, 1844])).
% 1.11/1.31 tff(1846,plain,
% 1.11/1.31 (~c2_1(a496)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[335, 1844])).
% 1.11/1.31 tff(1847,plain,
% 1.11/1.31 (~c1_1(a496)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[348, 1844])).
% 1.11/1.31 tff(1848,plain,
% 1.11/1.31 (~hskp22),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1743, 1831, 190, 198, 1830, 228, 1829])).
% 1.11/1.31 tff(1849,plain,
% 1.11/1.31 (~c0_1(a496)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[722, 106, 1848, 1847, 1846, 1845, 31])).
% 1.11/1.31 tff(1850,plain,
% 1.11/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a520) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1851,plain,
% 1.11/1.31 (((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496)) <=> (c3_1(a520) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1852,plain,
% 1.11/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a520) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[1851])).
% 1.11/1.31 tff(1853,plain,
% 1.11/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[1852, 1850])).
% 1.11/1.31 tff(1854,plain,
% 1.11/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(1855,plain,
% 1.11/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 1.11/1.31 tff(1856,plain,
% 1.11/1.31 (c0_1(a496) | (~c1_1(a520))),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1855, 106, 1371, 1363, 1847, 1846, 1845, 709])).
% 1.11/1.31 tff(1857,plain,
% 1.11/1.31 (~c1_1(a520)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1856, 1849])).
% 1.11/1.31 tff(1858,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c3_1(a520) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a520) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c2_1(a520)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1859,plain,
% 1.11/1.31 ((hskp0 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)) | c2_1(a496) | c1_1(a496) | c0_1(a496)) <=> (hskp0 | c3_1(a520) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c2_1(a520)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1860,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)) | c2_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c3_1(a520) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c2_1(a520))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[1859])).
% 1.11/1.31 tff(1861,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)) | c2_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a520) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c2_1(a520)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[1860, 1858])).
% 1.11/1.31 tff(1862,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)) | c2_1(a496) | c1_1(a496) | c0_1(a496))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(1863,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a520) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c2_1(a520))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 1.11/1.31 tff(1864,plain,
% 1.11/1.31 (hskp0 | c0_1(a496) | c1_1(a520)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1863, 106, 1371, 1363, 1847, 1846, 776])).
% 1.11/1.31 tff(1865,plain,
% 1.11/1.31 (hskp0),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1864, 1849, 1857])).
% 1.11/1.31 tff(1866,plain,
% 1.11/1.31 (~c2_1(a494)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1594, 1865])).
% 1.11/1.31 tff(1867,plain,
% 1.11/1.31 (~c0_1(a494)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[797, 1865])).
% 1.11/1.31 tff(1868,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a520) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a520) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c0_1(a520)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1869,plain,
% 1.11/1.31 ((hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a496) | c0_1(a496) | c3_1(a496)) <=> (hskp1 | c3_1(a520) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c0_1(a520)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1870,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a520) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c0_1(a520))))),
% 1.11/1.31 inference(monotonicity,[status(thm)],[1869])).
% 1.11/1.31 tff(1871,plain,
% 1.11/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a520) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c0_1(a520)))),
% 1.11/1.31 inference(transitivity,[status(thm)],[1870, 1868])).
% 1.11/1.31 tff(1872,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a496) | c0_1(a496) | c3_1(a496))),
% 1.11/1.31 inference(quant_inst,[status(thm)],[])).
% 1.11/1.31 tff(1873,plain,
% 1.11/1.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a520) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c0_1(a520))),
% 1.11/1.31 inference(modus_ponens,[status(thm)],[1872, 1871])).
% 1.11/1.31 tff(1874,plain,
% 1.11/1.31 (hskp1 | c1_1(a520)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1873, 106, 1379, 1363, 1847, 1845, 585, 1849])).
% 1.11/1.31 tff(1875,plain,
% 1.11/1.31 (hskp1),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1874, 1857])).
% 1.11/1.31 tff(1876,plain,
% 1.11/1.31 (~c3_1(a495)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[932, 1875])).
% 1.11/1.31 tff(1877,plain,
% 1.11/1.31 (~c0_1(a495)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[938, 1875])).
% 1.11/1.31 tff(1878,plain,
% 1.11/1.31 (c3_1(a494)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[809, 1865])).
% 1.11/1.31 tff(1879,plain,
% 1.11/1.31 (c1_1(a495)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[947, 1875])).
% 1.11/1.31 tff(1880,plain,
% 1.11/1.31 ($false),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1626, 106, 1831, 1830, 1879, 1878, 1829, 1877, 1876, 1867, 1866, 21])).
% 1.11/1.31 tff(1881,plain,(c0_1(a502) | hskp10 | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.11/1.31 tff(1882,plain,
% 1.11/1.31 (c0_1(a502)),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1881, 11, 32])).
% 1.11/1.31 tff(1883,plain,
% 1.11/1.31 (~hskp7),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[643, 1882])).
% 1.11/1.31 tff(1884,plain,
% 1.11/1.31 ($false),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[296, 106, 1883, 198, 174, 228, 222, 216, 206, 181])).
% 1.11/1.31 tff(1885,plain,(hskp15 | hskp10 | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.11/1.31 tff(1886,plain,
% 1.11/1.31 (hskp15),
% 1.11/1.31 inference(unit_resolution,[status(thm)],[1885, 11, 32])).
% 1.11/1.31 tff(1887,plain,
% 1.11/1.31 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.11/1.31 inference(bind,[status(th)],[])).
% 1.11/1.31 tff(1888,plain,
% 1.11/1.31 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.11/1.31 inference(quant_intro,[status(thm)],[1887])).
% 1.11/1.31 tff(1889,plain,
% 1.11/1.31 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.11/1.31 inference(rewrite,[status(thm)],[])).
% 1.11/1.31 tff(1890,plain,
% 1.11/1.31 (^[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)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_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))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp23))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_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))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.11/1.32 inference(bind,[status(th)],[])).
% 1.11/1.32 tff(1891,plain,
% 1.11/1.32 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.11/1.32 inference(quant_intro,[status(thm)],[1890])).
% 1.11/1.32 tff(1892,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 1.11/1.32 tff(1893,plain,
% 1.11/1.32 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1892, 1891])).
% 1.11/1.32 tff(1894,plain,
% 1.11/1.32 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1893, 1889])).
% 1.11/1.32 tff(1895,plain,(
% 1.11/1.32 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.11/1.32 inference(skolemize,[status(sab)],[1894])).
% 1.11/1.32 tff(1896,plain,
% 1.11/1.32 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1895, 1888])).
% 1.11/1.32 tff(1897,assumption,(hskp28), introduced(assumption)).
% 1.11/1.32 tff(1898,plain,
% 1.11/1.32 (c3_1(a500)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[390, 1897])).
% 1.11/1.32 tff(1899,plain,
% 1.11/1.32 (c0_1(a500)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[406, 1897])).
% 1.11/1.32 tff(1900,plain,
% 1.11/1.32 (c2_1(a500)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[398, 1897])).
% 1.11/1.32 tff(1901,plain,
% 1.11/1.32 ($false),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[452, 1900, 1899, 419, 408, 1898])).
% 1.11/1.32 tff(1902,plain,((~hskp28) | (~hskp15) | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.11/1.32 tff(1903,plain,
% 1.11/1.32 (~hskp28),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1902, 408, 419])).
% 1.11/1.32 tff(1904,plain,
% 1.11/1.32 (~c1_1(a536)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[516, 990])).
% 1.11/1.32 tff(1905,assumption,(~hskp28), introduced(assumption)).
% 1.11/1.32 tff(1906,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c3_1(a536)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c3_1(a536)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1907,plain,
% 1.11/1.32 ((hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536))) <=> (hskp28 | c1_1(a568) | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c3_1(a536)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1908,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c3_1(a536)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[1907])).
% 1.11/1.32 tff(1909,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c3_1(a536)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.32 inference(transitivity,[status(thm)],[1908, 1906])).
% 1.11/1.32 tff(1910,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(1911,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c3_1(a536)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 1.11/1.32 tff(1912,plain,
% 1.11/1.32 (~c3_1(a536)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1911, 106, 1905, 368, 370, 369, 997, 1904, 238])).
% 1.11/1.32 tff(1913,plain,
% 1.11/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a536) | c1_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c1_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1914,plain,
% 1.11/1.32 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a536) | c1_1(a536) | c0_1(a536)) <=> (c0_1(a536) | c1_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1915,plain,
% 1.11/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a536) | c1_1(a536) | c0_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a536) | c1_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536)))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[1914])).
% 1.11/1.32 tff(1916,plain,
% 1.11/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a536) | c1_1(a536) | c0_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c1_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.11/1.32 inference(transitivity,[status(thm)],[1915, 1913])).
% 1.11/1.32 tff(1917,plain,
% 1.11/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a536) | c1_1(a536) | c0_1(a536))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(1918,plain,
% 1.11/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c1_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1917, 1916])).
% 1.11/1.32 tff(1919,plain,
% 1.11/1.32 (~c2_1(a528)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1918, 106, 998, 997, 1904, 996, 989, 709, 1912])).
% 1.11/1.32 tff(1920,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)) | c3_1(a536))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)) | c3_1(a536))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1921,plain,
% 1.11/1.32 ((hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a536) | c0_1(a536) | c3_1(a536)) <=> (hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)) | c3_1(a536))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1922,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a536) | c0_1(a536) | c3_1(a536))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)) | c3_1(a536)))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[1921])).
% 1.11/1.32 tff(1923,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a536) | c0_1(a536) | c3_1(a536))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)) | c3_1(a536))),
% 1.11/1.32 inference(transitivity,[status(thm)],[1922, 1920])).
% 1.11/1.32 tff(1924,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a536) | c0_1(a536) | c3_1(a536))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(1925,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)) | c3_1(a536)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1924, 1923])).
% 1.11/1.32 tff(1926,plain,
% 1.11/1.32 (~c1_1(a520)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1925, 106, 408, 1428, 1427, 997, 1904, 290, 1912])).
% 1.11/1.32 tff(1927,plain,
% 1.11/1.32 (~hskp22),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1743, 999, 370, 368, 998, 369, 989])).
% 1.11/1.32 tff(1928,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a528)) | c2_1(a528))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a528)) | c2_1(a528))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1929,plain,
% 1.11/1.32 ((hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520))) <=> (hskp22 | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a528)) | c2_1(a528))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1930,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a528)) | c2_1(a528)))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[1929])).
% 1.11/1.32 tff(1931,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a528)) | c2_1(a528))),
% 1.11/1.32 inference(transitivity,[status(thm)],[1930, 1928])).
% 1.11/1.32 tff(1932,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(1933,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a528)) | c2_1(a528)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 1.11/1.32 tff(1934,plain,
% 1.11/1.32 ($false),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1933, 106, 1927, 999, 1428, 989, 1437, 31, 1926, 1919])).
% 1.11/1.32 tff(1935,plain,((~hskp20) | (~c0_1(a528)) | (~c0_1(a520)) | c3_1(a528) | c3_1(a520) | (~c1_1(a528)) | hskp2 | (~c2_1(a520)) | hskp28 | (~c0_1(a568)) | (~c3_1(a568)) | c1_1(a568)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.32 tff(1936,plain,
% 1.11/1.32 (~hskp20),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1935, 408, 1428, 425, 1437, 433, 441, 1427, 1903, 368, 370, 369])).
% 1.11/1.32 tff(1937,plain,
% 1.11/1.32 ((hskp28 | hskp21 | hskp20) <=> (hskp28 | hskp21 | hskp20)),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1938,plain,
% 1.11/1.32 (((hskp28 | hskp21) | hskp20) <=> (hskp28 | hskp21 | hskp20)),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1939,plain,
% 1.11/1.32 ((hskp28 | hskp21) <=> (hskp28 | hskp21)),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1940,plain,
% 1.11/1.32 (((hskp28 | hskp21) | hskp20) <=> ((hskp28 | hskp21) | hskp20)),
% 1.11/1.32 inference(monotonicity,[status(thm)],[1939])).
% 1.11/1.32 tff(1941,plain,
% 1.11/1.32 (((hskp28 | hskp21) | hskp20) <=> (hskp28 | hskp21 | hskp20)),
% 1.11/1.32 inference(transitivity,[status(thm)],[1940, 1938])).
% 1.11/1.32 tff(1942,axiom,((hskp28 | hskp21) | hskp20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 1.11/1.32 tff(1943,plain,
% 1.11/1.32 (hskp28 | hskp21 | hskp20),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1942, 1941])).
% 1.11/1.32 tff(1944,plain,
% 1.11/1.32 (hskp28 | hskp21 | hskp20),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1943, 1937])).
% 1.11/1.32 tff(1945,plain,
% 1.11/1.32 (hskp28 | hskp21 | hskp20),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1944, 1937])).
% 1.11/1.32 tff(1946,plain,
% 1.11/1.32 (hskp28 | hskp21 | hskp20),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1945, 1937])).
% 1.11/1.32 tff(1947,plain,
% 1.11/1.32 (hskp28 | hskp21 | hskp20),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1946, 1937])).
% 1.11/1.32 tff(1948,plain,
% 1.11/1.32 (hskp21),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1947, 1936, 1903])).
% 1.11/1.32 tff(1949,plain,
% 1.11/1.32 (((~hskp21) | (~c3_1(a538))) <=> ((~hskp21) | (~c3_1(a538)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1950,plain,
% 1.11/1.32 (((~c3_1(a538)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a538)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1951,axiom,((~c3_1(a538)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.11/1.32 tff(1952,plain,
% 1.11/1.32 ((~hskp21) | (~c3_1(a538))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 1.11/1.32 tff(1953,plain,
% 1.11/1.32 ((~hskp21) | (~c3_1(a538))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1952, 1949])).
% 1.11/1.32 tff(1954,plain,
% 1.11/1.32 (~c3_1(a538)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1953, 1948])).
% 1.11/1.32 tff(1955,plain,
% 1.11/1.32 (((~hskp21) | (~c1_1(a538))) <=> ((~hskp21) | (~c1_1(a538)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1956,plain,
% 1.11/1.32 (((~c1_1(a538)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a538)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1957,axiom,((~c1_1(a538)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.11/1.32 tff(1958,plain,
% 1.11/1.32 ((~hskp21) | (~c1_1(a538))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 1.11/1.32 tff(1959,plain,
% 1.11/1.32 ((~hskp21) | (~c1_1(a538))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1958, 1955])).
% 1.11/1.32 tff(1960,plain,
% 1.11/1.32 (~c1_1(a538)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1959, 1948])).
% 1.11/1.32 tff(1961,plain,
% 1.11/1.32 (((~hskp21) | c0_1(a538)) <=> ((~hskp21) | c0_1(a538))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1962,axiom,((~hskp21) | c0_1(a538)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.11/1.32 tff(1963,plain,
% 1.11/1.32 ((~hskp21) | c0_1(a538)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1962, 1961])).
% 1.11/1.32 tff(1964,plain,
% 1.11/1.32 ((~hskp21) | c0_1(a538)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1963, 1961])).
% 1.11/1.32 tff(1965,plain,
% 1.11/1.32 ((~hskp21) | c0_1(a538)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1964, 1961])).
% 1.11/1.32 tff(1966,plain,
% 1.11/1.32 ((~hskp21) | c0_1(a538)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1965, 1961])).
% 1.11/1.32 tff(1967,plain,
% 1.11/1.32 ((~hskp21) | c0_1(a538)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1966, 1961])).
% 1.11/1.32 tff(1968,plain,
% 1.11/1.32 (c0_1(a538)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1967, 1948])).
% 1.11/1.32 tff(1969,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a538) | c3_1(a538) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a538) | c3_1(a538) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a538)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1970,plain,
% 1.11/1.32 ((hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538))) <=> (hskp23 | c1_1(a538) | c3_1(a538) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a538)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1971,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a538) | c3_1(a538) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a538))))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[1970])).
% 1.11/1.32 tff(1972,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a538) | c3_1(a538) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a538)))),
% 1.11/1.32 inference(transitivity,[status(thm)],[1971, 1969])).
% 1.11/1.32 tff(1973,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(1974,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a538) | c3_1(a538) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a538))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1973, 1972])).
% 1.11/1.32 tff(1975,plain,
% 1.11/1.32 (hskp23),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1974, 106, 1968, 441, 433, 1960, 1954, 425, 1896])).
% 1.11/1.32 tff(1976,plain,
% 1.11/1.32 (((~hskp23) | (~c2_1(a541))) <=> ((~hskp23) | (~c2_1(a541)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1977,plain,
% 1.11/1.32 (((~c2_1(a541)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a541)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1978,axiom,((~c2_1(a541)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.11/1.32 tff(1979,plain,
% 1.11/1.32 ((~hskp23) | (~c2_1(a541))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1978, 1977])).
% 1.11/1.32 tff(1980,plain,
% 1.11/1.32 ((~hskp23) | (~c2_1(a541))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1979, 1976])).
% 1.11/1.32 tff(1981,plain,
% 1.11/1.32 (~c2_1(a541)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1980, 1975])).
% 1.11/1.32 tff(1982,plain,
% 1.11/1.32 (((~hskp23) | c1_1(a541)) <=> ((~hskp23) | c1_1(a541))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1983,axiom,((~hskp23) | c1_1(a541)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.11/1.32 tff(1984,plain,
% 1.11/1.32 ((~hskp23) | c1_1(a541)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1983, 1982])).
% 1.11/1.32 tff(1985,plain,
% 1.11/1.32 ((~hskp23) | c1_1(a541)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1984, 1982])).
% 1.11/1.32 tff(1986,plain,
% 1.11/1.32 ((~hskp23) | c1_1(a541)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1985, 1982])).
% 1.11/1.32 tff(1987,plain,
% 1.11/1.32 ((~hskp23) | c1_1(a541)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1986, 1982])).
% 1.11/1.32 tff(1988,plain,
% 1.11/1.32 ((~hskp23) | c1_1(a541)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1987, 1982])).
% 1.11/1.32 tff(1989,plain,
% 1.11/1.32 (c1_1(a541)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1988, 1975])).
% 1.11/1.32 tff(1990,plain,
% 1.11/1.32 (((~hskp23) | c0_1(a541)) <=> ((~hskp23) | c0_1(a541))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1991,axiom,((~hskp23) | c0_1(a541)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.11/1.32 tff(1992,plain,
% 1.11/1.32 ((~hskp23) | c0_1(a541)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 1.11/1.32 tff(1993,plain,
% 1.11/1.32 ((~hskp23) | c0_1(a541)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1992, 1990])).
% 1.11/1.32 tff(1994,plain,
% 1.11/1.32 ((~hskp23) | c0_1(a541)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1993, 1990])).
% 1.11/1.32 tff(1995,plain,
% 1.11/1.32 ((~hskp23) | c0_1(a541)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1994, 1990])).
% 1.11/1.32 tff(1996,plain,
% 1.11/1.32 ((~hskp23) | c0_1(a541)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[1995, 1990])).
% 1.11/1.32 tff(1997,plain,
% 1.11/1.32 (c0_1(a541)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[1996, 1975])).
% 1.11/1.32 tff(1998,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a541) | (~ndr1_0) | (~c3_1(a541)) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a541) | (~ndr1_0) | (~c3_1(a541)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(1999,plain,
% 1.11/1.32 ((hskp2 | (~ndr1_0) | c2_1(a541) | (~c3_1(a541)) | (~c0_1(a541)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541))) <=> (hskp2 | c2_1(a541) | (~ndr1_0) | (~c3_1(a541)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2000,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a541) | (~c3_1(a541)) | (~c0_1(a541)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a541) | (~ndr1_0) | (~c3_1(a541)) | (~c1_1(a541)) | (~c0_1(a541))))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[1999])).
% 1.11/1.32 tff(2001,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a541) | (~c3_1(a541)) | (~c0_1(a541)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a541) | (~ndr1_0) | (~c3_1(a541)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.11/1.32 inference(transitivity,[status(thm)],[2000, 1998])).
% 1.11/1.32 tff(2002,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a541) | (~c3_1(a541)) | (~c0_1(a541)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(2003,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a541) | (~ndr1_0) | (~c3_1(a541)) | (~c1_1(a541)) | (~c0_1(a541))),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2002, 2001])).
% 1.11/1.32 tff(2004,plain,
% 1.11/1.32 (~c3_1(a541)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2003, 106, 408, 1997, 1989, 1981, 541])).
% 1.11/1.32 tff(2005,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c0_1(a538)) | c2_1(a538))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c0_1(a538)) | c2_1(a538))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2006,plain,
% 1.11/1.32 ((hskp22 | (~ndr1_0) | c3_1(a538) | c2_1(a538) | (~c0_1(a538)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538))) <=> (hskp22 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c0_1(a538)) | c2_1(a538))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2007,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a538) | c2_1(a538) | (~c0_1(a538)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c0_1(a538)) | c2_1(a538)))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[2006])).
% 1.11/1.32 tff(2008,plain,
% 1.11/1.32 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a538) | c2_1(a538) | (~c0_1(a538)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c0_1(a538)) | c2_1(a538))),
% 1.11/1.32 inference(transitivity,[status(thm)],[2007, 2005])).
% 1.11/1.32 tff(2009,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a538) | c2_1(a538) | (~c0_1(a538)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))),
% 1.11/1.32 inference(quant_inst,[status(thm)],[])).
% 1.11/1.32 tff(2010,plain,
% 1.11/1.32 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c0_1(a538)) | c2_1(a538)),
% 1.11/1.32 inference(modus_ponens,[status(thm)],[2009, 2008])).
% 1.11/1.32 tff(2011,plain,
% 1.11/1.32 (c2_1(a538)),
% 1.11/1.32 inference(unit_resolution,[status(thm)],[2010, 106, 1744, 1968, 1960, 1954, 31])).
% 1.11/1.32 tff(2012,plain,
% 1.11/1.32 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c2_1(a538)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c2_1(a538)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2013,plain,
% 1.11/1.32 ((hskp20 | hskp12 | (~ndr1_0) | c3_1(a538) | c1_1(a538) | (~c2_1(a538))) <=> (hskp20 | hskp12 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c2_1(a538)))),
% 1.11/1.32 inference(rewrite,[status(thm)],[])).
% 1.11/1.32 tff(2014,plain,
% 1.11/1.32 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a538) | c1_1(a538) | (~c2_1(a538)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c2_1(a538))))),
% 1.11/1.32 inference(monotonicity,[status(thm)],[2013])).
% 1.11/1.32 tff(2015,plain,
% 1.11/1.32 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a538) | c1_1(a538) | (~c2_1(a538)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c2_1(a538)))),
% 1.11/1.33 inference(transitivity,[status(thm)],[2014, 2012])).
% 1.11/1.33 tff(2016,plain,
% 1.11/1.33 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a538) | c1_1(a538) | (~c2_1(a538)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(2017,plain,
% 1.11/1.33 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c2_1(a538))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 1.11/1.33 tff(2018,plain,
% 1.11/1.33 (hskp12),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2017, 106, 1936, 1960, 1954, 1033, 2011])).
% 1.11/1.33 tff(2019,plain,
% 1.11/1.33 (~c2_1(a514)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[487, 2018])).
% 1.11/1.33 tff(2020,plain,
% 1.11/1.33 (c3_1(a514)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[495, 2018])).
% 1.11/1.33 tff(2021,plain,
% 1.11/1.33 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a541) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a541) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2022,plain,
% 1.11/1.33 ((hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541))) <=> (hskp2 | c2_1(a541) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2023,plain,
% 1.11/1.33 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a541) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)) | (~c1_1(a541)) | (~c0_1(a541))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[2022])).
% 1.11/1.33 tff(2024,plain,
% 1.11/1.33 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a541) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.11/1.33 inference(transitivity,[status(thm)],[2023, 2021])).
% 1.11/1.33 tff(2025,plain,
% 1.11/1.33 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(2026,plain,
% 1.11/1.33 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a541) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)) | (~c1_1(a541)) | (~c0_1(a541))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 1.11/1.33 tff(2027,plain,
% 1.11/1.33 (~c0_1(a514)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2026, 106, 408, 1997, 1989, 2020, 1981, 2019, 541])).
% 1.11/1.33 tff(2028,plain,
% 1.11/1.33 (c1_1(a514)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[503, 2018])).
% 1.11/1.33 tff(2029,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2030,plain,
% 1.11/1.33 (((~ndr1_0) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a514) | (~c3_1(a514)) | (~c1_1(a514))) <=> (c1_1(a568) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2031,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a514) | (~c3_1(a514)) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[2030])).
% 1.11/1.33 tff(2032,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a514) | (~c3_1(a514)) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.11/1.33 inference(transitivity,[status(thm)],[2031, 2029])).
% 1.11/1.33 tff(2033,plain,
% 1.11/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a514) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(2034,plain,
% 1.11/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2033, 2032])).
% 1.11/1.33 tff(2035,plain,
% 1.11/1.33 ($false),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2034, 106, 368, 370, 1997, 1989, 2028, 2020, 369, 1302, 2027, 2004])).
% 1.11/1.33 tff(2036,plain,(hskp2 | (~c0_1(a568)) | (~c3_1(a568)) | c1_1(a568) | (~c0_1(a520)) | c3_1(a520) | (~c2_1(a520)) | (~hskp15)), inference(lemma,lemma(discharge,[]))).
% 1.11/1.33 tff(2037,plain,
% 1.11/1.33 (hskp2),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2036, 198, 190, 228, 1379, 1363, 1371, 1886])).
% 1.11/1.33 tff(2038,plain,
% 1.11/1.33 (~c3_1(a496)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[329, 2037])).
% 1.11/1.33 tff(2039,plain,
% 1.11/1.33 (~c2_1(a496)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[335, 2037])).
% 1.11/1.33 tff(2040,plain,
% 1.11/1.33 (~c1_1(a496)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[348, 2037])).
% 1.11/1.33 tff(2041,plain,
% 1.11/1.33 (~c3_1(a528)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[424, 1886])).
% 1.11/1.33 tff(2042,plain,
% 1.11/1.33 (c1_1(a528)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[432, 1886])).
% 1.11/1.33 tff(2043,plain,
% 1.11/1.33 (c0_1(a528)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[440, 1886])).
% 1.11/1.33 tff(2044,plain,
% 1.11/1.33 (~hskp22),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[1743, 2043, 190, 198, 2042, 228, 2041])).
% 1.11/1.33 tff(2045,plain,
% 1.11/1.33 (~c0_1(a496)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[722, 106, 2044, 2040, 2039, 2038, 31])).
% 1.11/1.33 tff(2046,plain,
% 1.11/1.33 (c0_1(a496) | (~c1_1(a520))),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[1855, 106, 1371, 1363, 2040, 2039, 2038, 709])).
% 1.11/1.33 tff(2047,plain,
% 1.11/1.33 (~c1_1(a520)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2046, 2045])).
% 1.11/1.33 tff(2048,plain,
% 1.11/1.33 (hskp0 | c1_1(a520)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[1863, 106, 1371, 1363, 2040, 2039, 776, 2045])).
% 1.11/1.33 tff(2049,plain,
% 1.11/1.33 (hskp0),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2048, 2047])).
% 1.11/1.33 tff(2050,plain,
% 1.11/1.33 (~c2_1(a494)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[1594, 2049])).
% 1.11/1.33 tff(2051,plain,
% 1.11/1.33 (~c0_1(a494)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[797, 2049])).
% 1.11/1.33 tff(2052,plain,
% 1.11/1.33 (hskp1 | c1_1(a520)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[1873, 106, 1379, 1363, 2040, 2038, 585, 2045])).
% 1.11/1.33 tff(2053,plain,
% 1.11/1.33 (hskp1),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2052, 2047])).
% 1.11/1.33 tff(2054,plain,
% 1.11/1.33 (~c3_1(a495)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[932, 2053])).
% 1.11/1.33 tff(2055,plain,
% 1.11/1.33 (~c0_1(a495)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[938, 2053])).
% 1.11/1.33 tff(2056,plain,
% 1.11/1.33 (c3_1(a494)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[809, 2049])).
% 1.11/1.33 tff(2057,plain,
% 1.11/1.33 (c1_1(a495)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[947, 2053])).
% 1.11/1.33 tff(2058,plain,
% 1.11/1.33 ($false),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[1626, 106, 2043, 2042, 2057, 2056, 2041, 2055, 2054, 2051, 2050, 21])).
% 1.11/1.33 tff(2059,plain,(hskp10 | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.11/1.33 tff(2060,plain,
% 1.11/1.33 (hskp26),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2059, 11])).
% 1.11/1.33 tff(2061,plain,
% 1.11/1.33 (((~hskp26) | (~c3_1(a559))) <=> ((~hskp26) | (~c3_1(a559)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2062,plain,
% 1.11/1.33 (((~c3_1(a559)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a559)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2063,axiom,((~c3_1(a559)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.11/1.33 tff(2064,plain,
% 1.11/1.33 ((~hskp26) | (~c3_1(a559))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2063, 2062])).
% 1.11/1.33 tff(2065,plain,
% 1.11/1.33 ((~hskp26) | (~c3_1(a559))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2064, 2061])).
% 1.11/1.33 tff(2066,plain,
% 1.11/1.33 (~c3_1(a559)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2065, 2060])).
% 1.11/1.33 tff(2067,plain,
% 1.11/1.33 (((~hskp26) | (~c2_1(a559))) <=> ((~hskp26) | (~c2_1(a559)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2068,plain,
% 1.11/1.33 (((~c2_1(a559)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a559)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2069,axiom,((~c2_1(a559)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.11/1.33 tff(2070,plain,
% 1.11/1.33 ((~hskp26) | (~c2_1(a559))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 1.11/1.33 tff(2071,plain,
% 1.11/1.33 ((~hskp26) | (~c2_1(a559))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2070, 2067])).
% 1.11/1.33 tff(2072,plain,
% 1.11/1.33 (~c2_1(a559)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2071, 2060])).
% 1.11/1.33 tff(2073,plain,
% 1.11/1.33 (((~hskp26) | (~c0_1(a559))) <=> ((~hskp26) | (~c0_1(a559)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2074,plain,
% 1.11/1.33 (((~c0_1(a559)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a559)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2075,axiom,((~c0_1(a559)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 1.11/1.33 tff(2076,plain,
% 1.11/1.33 ((~hskp26) | (~c0_1(a559))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2075, 2074])).
% 1.11/1.33 tff(2077,plain,
% 1.11/1.33 ((~hskp26) | (~c0_1(a559))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2076, 2073])).
% 1.11/1.33 tff(2078,plain,
% 1.11/1.33 (~c0_1(a559)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2077, 2060])).
% 1.11/1.33 tff(2079,plain,
% 1.11/1.33 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a559) | c2_1(a559) | c3_1(a559) | (~ndr1_0))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a559) | c2_1(a559) | c3_1(a559) | (~ndr1_0))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2080,plain,
% 1.11/1.33 ((hskp11 | hskp10 | (~ndr1_0) | c3_1(a559) | c2_1(a559) | c0_1(a559)) <=> (hskp11 | hskp10 | c0_1(a559) | c2_1(a559) | c3_1(a559) | (~ndr1_0))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2081,plain,
% 1.11/1.33 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a559) | c2_1(a559) | c0_1(a559))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a559) | c2_1(a559) | c3_1(a559) | (~ndr1_0)))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[2080])).
% 1.11/1.33 tff(2082,plain,
% 1.11/1.33 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a559) | c2_1(a559) | c0_1(a559))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a559) | c2_1(a559) | c3_1(a559) | (~ndr1_0))),
% 1.11/1.33 inference(transitivity,[status(thm)],[2081, 2079])).
% 1.11/1.33 tff(2083,plain,
% 1.11/1.33 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a559) | c2_1(a559) | c0_1(a559))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(2084,plain,
% 1.11/1.33 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a559) | c2_1(a559) | c3_1(a559) | (~ndr1_0)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2083, 2082])).
% 1.11/1.33 tff(2085,plain,
% 1.11/1.33 (hskp11),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2084, 106, 11, 2078, 2072, 2066, 10])).
% 1.11/1.33 tff(2086,plain,
% 1.11/1.33 (~c2_1(a510)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[59, 2085])).
% 1.11/1.33 tff(2087,plain,
% 1.11/1.33 (~c1_1(a510)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[65, 2085])).
% 1.11/1.33 tff(2088,plain,
% 1.11/1.33 (c0_1(a510)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[73, 2085])).
% 1.11/1.33 tff(2089,plain,
% 1.11/1.33 (hskp15),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[150, 2085, 11])).
% 1.11/1.33 tff(2090,plain,
% 1.11/1.33 (~c3_1(a528)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[424, 2089])).
% 1.11/1.33 tff(2091,plain,
% 1.11/1.33 (c1_1(a528)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[432, 2089])).
% 1.11/1.33 tff(2092,plain,
% 1.11/1.33 (c0_1(a528)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[440, 2089])).
% 1.11/1.33 tff(2093,assumption,(c2_1(a528)), introduced(assumption)).
% 1.11/1.33 tff(2094,assumption,(~c3_1(a559)), introduced(assumption)).
% 1.11/1.33 tff(2095,assumption,(~c2_1(a559)), introduced(assumption)).
% 1.11/1.33 tff(2096,assumption,(~c0_1(a559)), introduced(assumption)).
% 1.11/1.33 tff(2097,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c1_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c1_1(a559))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2098,plain,
% 1.11/1.33 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a559) | c0_1(a559) | c3_1(a559) | c3_1(a559) | c1_1(a559) | c0_1(a559)) <=> (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c1_1(a559))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2099,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a559) | c0_1(a559) | c3_1(a559) | c3_1(a559) | c1_1(a559) | c0_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c1_1(a559)))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[2098])).
% 1.11/1.33 tff(2100,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a559) | c0_1(a559) | c3_1(a559) | c3_1(a559) | c1_1(a559) | c0_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c1_1(a559))),
% 1.11/1.33 inference(transitivity,[status(thm)],[2099, 2097])).
% 1.11/1.33 tff(2101,plain,
% 1.11/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a559) | c0_1(a559) | c3_1(a559) | c3_1(a559) | c1_1(a559) | c0_1(a559))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(2102,plain,
% 1.11/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c1_1(a559)),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2101, 2100])).
% 1.11/1.33 tff(2103,plain,
% 1.11/1.33 ((~c2_1(a528)) | c1_1(a559)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2102, 106, 998, 2096, 2095, 2094, 989, 709])).
% 1.11/1.33 tff(2104,plain,
% 1.11/1.33 (c1_1(a559)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2103, 2093])).
% 1.11/1.33 tff(2105,assumption,(~c2_1(a510)), introduced(assumption)).
% 1.11/1.33 tff(2106,assumption,(~c1_1(a510)), introduced(assumption)).
% 1.11/1.33 tff(2107,assumption,(c0_1(a510)), introduced(assumption)).
% 1.11/1.33 tff(2108,plain,
% 1.11/1.33 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2109,plain,
% 1.11/1.33 ((hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510))) <=> (hskp9 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.11/1.33 inference(rewrite,[status(thm)],[])).
% 1.11/1.33 tff(2110,plain,
% 1.11/1.33 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.11/1.33 inference(monotonicity,[status(thm)],[2109])).
% 1.11/1.33 tff(2111,plain,
% 1.11/1.33 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.11/1.33 inference(transitivity,[status(thm)],[2110, 2108])).
% 1.11/1.33 tff(2112,plain,
% 1.11/1.33 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))),
% 1.11/1.33 inference(quant_inst,[status(thm)],[])).
% 1.11/1.33 tff(2113,plain,
% 1.11/1.33 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.11/1.33 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 1.11/1.33 tff(2114,plain,
% 1.11/1.33 (hskp9),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[2113, 106, 999, 998, 2107, 989, 2106, 2105, 1186])).
% 1.11/1.33 tff(2115,plain,
% 1.11/1.33 (~c0_1(a507)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[846, 2114])).
% 1.11/1.33 tff(2116,plain,
% 1.11/1.33 (c3_1(a507)),
% 1.11/1.33 inference(unit_resolution,[status(thm)],[854, 2114])).
% 1.11/1.33 tff(2117,plain,
% 1.11/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a559) | c3_1(a559) | c3_1(a528) | c0_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a559)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a559) | c3_1(a559) | c3_1(a528) | c0_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a559)))),
% 1.18/1.33 inference(rewrite,[status(thm)],[])).
% 1.18/1.33 tff(2118,plain,
% 1.18/1.33 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a559) | c3_1(a559) | (~c1_1(a559)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507)) <=> (c0_1(a559) | c3_1(a559) | c3_1(a528) | c0_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a559)))),
% 1.18/1.33 inference(rewrite,[status(thm)],[])).
% 1.18/1.33 tff(2119,plain,
% 1.18/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a559) | c3_1(a559) | (~c1_1(a559)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a559) | c3_1(a559) | c3_1(a528) | c0_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a559))))),
% 1.18/1.33 inference(monotonicity,[status(thm)],[2118])).
% 1.18/1.33 tff(2120,plain,
% 1.18/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a559) | c3_1(a559) | (~c1_1(a559)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a559) | c3_1(a559) | c3_1(a528) | c0_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a559)))),
% 1.18/1.33 inference(transitivity,[status(thm)],[2119, 2117])).
% 1.18/1.33 tff(2121,plain,
% 1.18/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a559) | c3_1(a559) | (~c1_1(a559)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))),
% 1.18/1.33 inference(quant_inst,[status(thm)],[])).
% 1.18/1.33 tff(2122,plain,
% 1.18/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a559) | c3_1(a559) | c3_1(a528) | c0_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a559))),
% 1.18/1.33 inference(modus_ponens,[status(thm)],[2121, 2120])).
% 1.18/1.33 tff(2123,plain,
% 1.18/1.33 (c2_1(a507) | (~c1_1(a559))),
% 1.18/1.33 inference(unit_resolution,[status(thm)],[2122, 106, 999, 998, 2116, 2096, 2094, 989, 2115, 21])).
% 1.18/1.33 tff(2124,plain,
% 1.18/1.33 (c2_1(a507)),
% 1.18/1.33 inference(unit_resolution,[status(thm)],[2123, 2104])).
% 1.18/1.33 tff(2125,plain,
% 1.18/1.33 (~c1_1(a507)),
% 1.18/1.33 inference(unit_resolution,[status(thm)],[840, 2114])).
% 1.18/1.33 tff(2126,plain,
% 1.18/1.33 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c3_1(a528) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c2_1(a507)) | (~c0_1(a528)) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a528) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c2_1(a507)) | (~c0_1(a528)) | (~c2_1(a528)))),
% 1.18/1.33 inference(rewrite,[status(thm)],[])).
% 1.18/1.33 tff(2127,plain,
% 1.18/1.33 ((hskp4 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c1_1(a507) | c0_1(a507) | (~c2_1(a507))) <=> (hskp4 | c3_1(a528) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c2_1(a507)) | (~c0_1(a528)) | (~c2_1(a528)))),
% 1.18/1.33 inference(rewrite,[status(thm)],[])).
% 1.18/1.33 tff(2128,plain,
% 1.18/1.33 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c1_1(a507) | c0_1(a507) | (~c2_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c3_1(a528) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c2_1(a507)) | (~c0_1(a528)) | (~c2_1(a528))))),
% 1.18/1.33 inference(monotonicity,[status(thm)],[2127])).
% 1.18/1.33 tff(2129,plain,
% 1.18/1.33 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c1_1(a507) | c0_1(a507) | (~c2_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a528) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c2_1(a507)) | (~c0_1(a528)) | (~c2_1(a528)))),
% 1.18/1.33 inference(transitivity,[status(thm)],[2128, 2126])).
% 1.18/1.33 tff(2130,plain,
% 1.18/1.33 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c1_1(a507) | c0_1(a507) | (~c2_1(a507)))),
% 1.18/1.33 inference(quant_inst,[status(thm)],[])).
% 1.18/1.33 tff(2131,plain,
% 1.18/1.33 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a528) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c2_1(a507)) | (~c0_1(a528)) | (~c2_1(a528))),
% 1.18/1.33 inference(modus_ponens,[status(thm)],[2130, 2129])).
% 1.18/1.33 tff(2132,plain,
% 1.18/1.33 (hskp4 | (~c2_1(a507)) | (~c2_1(a528))),
% 1.18/1.33 inference(unit_resolution,[status(thm)],[2131, 106, 999, 989, 2115, 2125, 367])).
% 1.18/1.33 tff(2133,plain,
% 1.18/1.33 (hskp4),
% 1.18/1.33 inference(unit_resolution,[status(thm)],[2132, 2124, 2093])).
% 1.18/1.33 tff(2134,plain,
% 1.18/1.33 (~c2_1(a498)),
% 1.18/1.33 inference(unit_resolution,[status(thm)],[1412, 2133])).
% 1.18/1.33 tff(2135,plain,
% 1.18/1.33 (~c0_1(a498)),
% 1.18/1.33 inference(unit_resolution,[status(thm)],[1391, 2133])).
% 1.18/1.33 tff(2136,plain,
% 1.18/1.33 (c1_1(a498)),
% 1.18/1.33 inference(unit_resolution,[status(thm)],[1399, 2133])).
% 1.18/1.33 tff(2137,plain,
% 1.18/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a507) | c1_1(a507) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a507) | c1_1(a507) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c3_1(a507)))),
% 1.18/1.33 inference(rewrite,[status(thm)],[])).
% 1.18/1.33 tff(2138,plain,
% 1.18/1.33 (((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c2_1(a498) | c0_1(a498) | (~c1_1(a498)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (c0_1(a507) | c1_1(a507) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c3_1(a507)))),
% 1.18/1.33 inference(rewrite,[status(thm)],[])).
% 1.18/1.33 tff(2139,plain,
% 1.18/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c2_1(a498) | c0_1(a498) | (~c1_1(a498)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a507) | c1_1(a507) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c3_1(a507))))),
% 1.18/1.33 inference(monotonicity,[status(thm)],[2138])).
% 1.18/1.33 tff(2140,plain,
% 1.18/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c2_1(a498) | c0_1(a498) | (~c1_1(a498)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a507) | c1_1(a507) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c3_1(a507)))),
% 1.18/1.33 inference(transitivity,[status(thm)],[2139, 2137])).
% 1.18/1.33 tff(2141,plain,
% 1.18/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c2_1(a498) | c0_1(a498) | (~c1_1(a498)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 1.18/1.34 inference(quant_inst,[status(thm)],[])).
% 1.18/1.34 tff(2142,plain,
% 1.18/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a507) | c1_1(a507) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c3_1(a507))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2141, 2140])).
% 1.18/1.34 tff(2143,plain,
% 1.18/1.34 (~c3_1(a498)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[2142, 106, 2116, 2136, 2115, 2125, 2135, 2134, 558])).
% 1.18/1.34 tff(2144,plain,
% 1.18/1.34 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.18/1.34 inference(bind,[status(th)],[])).
% 1.18/1.34 tff(2145,plain,
% 1.18/1.34 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(quant_intro,[status(thm)],[2144])).
% 1.18/1.34 tff(2146,plain,
% 1.18/1.34 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2147,plain,
% 1.18/1.34 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_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)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c1_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)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.18/1.34 inference(bind,[status(th)],[])).
% 1.18/1.34 tff(2148,plain,
% 1.18/1.34 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(quant_intro,[status(thm)],[2147])).
% 1.18/1.34 tff(2149,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.18/1.34 tff(2150,plain,
% 1.18/1.34 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2149, 2148])).
% 1.18/1.34 tff(2151,plain,
% 1.18/1.34 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2150, 2146])).
% 1.18/1.34 tff(2152,plain,(
% 1.18/1.34 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(skolemize,[status(sab)],[2151])).
% 1.18/1.34 tff(2153,plain,
% 1.18/1.34 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2152, 2145])).
% 1.18/1.34 tff(2154,plain,
% 1.18/1.34 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2155,plain,
% 1.18/1.34 ((hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510))) <=> (hskp21 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2156,plain,
% 1.18/1.34 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c2_1(a528))))),
% 1.18/1.34 inference(monotonicity,[status(thm)],[2155])).
% 1.18/1.34 tff(2157,plain,
% 1.18/1.34 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.18/1.34 inference(transitivity,[status(thm)],[2156, 2154])).
% 1.18/1.34 tff(2158,plain,
% 1.18/1.34 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))),
% 1.18/1.34 inference(quant_inst,[status(thm)],[])).
% 1.18/1.34 tff(2159,plain,
% 1.18/1.34 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c2_1(a528))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2158, 2157])).
% 1.18/1.34 tff(2160,plain,
% 1.18/1.34 (hskp21 | (~c2_1(a528))),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[2159, 106, 998, 2107, 989, 2106, 2105, 2153])).
% 1.18/1.34 tff(2161,plain,
% 1.18/1.34 (hskp21),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[2160, 2093])).
% 1.18/1.34 tff(2162,plain,
% 1.18/1.34 (~c3_1(a538)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1953, 2161])).
% 1.18/1.34 tff(2163,plain,
% 1.18/1.34 (~c1_1(a538)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1959, 2161])).
% 1.18/1.34 tff(2164,plain,
% 1.18/1.34 (c0_1(a538)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1967, 2161])).
% 1.18/1.34 tff(2165,plain,
% 1.18/1.34 (hskp23),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1974, 106, 2164, 999, 998, 2163, 2162, 989, 1896])).
% 1.18/1.34 tff(2166,plain,
% 1.18/1.34 (~c2_1(a541)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1980, 2165])).
% 1.18/1.34 tff(2167,plain,
% 1.18/1.34 (c1_1(a541)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1988, 2165])).
% 1.18/1.34 tff(2168,plain,
% 1.18/1.34 (c0_1(a541)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1996, 2165])).
% 1.18/1.34 tff(2169,plain,
% 1.18/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a541) | c3_1(a528) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a541) | c3_1(a528) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2170,plain,
% 1.18/1.34 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a498) | c0_1(a498) | c2_1(a498)) <=> (c2_1(a541) | c3_1(a528) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2171,plain,
% 1.18/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a498) | c0_1(a498) | c2_1(a498))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a541) | c3_1(a528) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541))))),
% 1.18/1.34 inference(monotonicity,[status(thm)],[2170])).
% 1.18/1.34 tff(2172,plain,
% 1.18/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a498) | c0_1(a498) | c2_1(a498))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a541) | c3_1(a528) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.18/1.34 inference(transitivity,[status(thm)],[2171, 2169])).
% 1.18/1.34 tff(2173,plain,
% 1.18/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a498) | c0_1(a498) | c2_1(a498))),
% 1.18/1.34 inference(quant_inst,[status(thm)],[])).
% 1.18/1.34 tff(2174,plain,
% 1.18/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a541) | c3_1(a528) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2173, 2172])).
% 1.18/1.34 tff(2175,plain,
% 1.18/1.34 ($false),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[2174, 106, 2168, 2167, 999, 998, 2166, 989, 2135, 2134, 909, 2143])).
% 1.18/1.34 tff(2176,plain,((~c2_1(a528)) | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | c0_1(a559) | c3_1(a559) | c2_1(a559) | (~c0_1(a510)) | c1_1(a510) | c2_1(a510)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.34 tff(2177,plain,
% 1.18/1.34 (~c2_1(a528)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[2176, 2092, 2091, 2090, 2078, 2066, 2072, 2088, 2087, 2086])).
% 1.18/1.34 tff(2178,plain,
% 1.18/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2179,plain,
% 1.18/1.34 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a559) | c0_1(a559) | c2_1(a559)) <=> (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2180,plain,
% 1.18/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a559) | c0_1(a559) | c2_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528)))),
% 1.18/1.34 inference(monotonicity,[status(thm)],[2179])).
% 1.18/1.34 tff(2181,plain,
% 1.18/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a559) | c0_1(a559) | c2_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.18/1.34 inference(transitivity,[status(thm)],[2180, 2178])).
% 1.18/1.34 tff(2182,plain,
% 1.18/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a559) | c0_1(a559) | c2_1(a559))),
% 1.18/1.34 inference(quant_inst,[status(thm)],[])).
% 1.18/1.34 tff(2183,plain,
% 1.18/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528)),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 1.18/1.34 tff(2184,plain,
% 1.18/1.34 ($false),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[2183, 106, 2092, 2091, 2078, 2072, 2066, 2090, 909, 2177])).
% 1.18/1.34 tff(2185,plain,(hskp10), inference(lemma,lemma(discharge,[]))).
% 1.18/1.34 tff(2186,plain,
% 1.18/1.34 (((~hskp10) | (~c2_1(a509))) <=> ((~hskp10) | (~c2_1(a509)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2187,plain,
% 1.18/1.34 (((~c2_1(a509)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a509)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2188,axiom,((~c2_1(a509)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.18/1.34 tff(2189,plain,
% 1.18/1.34 ((~hskp10) | (~c2_1(a509))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 1.18/1.34 tff(2190,plain,
% 1.18/1.34 ((~hskp10) | (~c2_1(a509))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2189, 2186])).
% 1.18/1.34 tff(2191,plain,
% 1.18/1.34 (~c2_1(a509)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[2190, 2185])).
% 1.18/1.34 tff(2192,plain,
% 1.18/1.34 (((~hskp10) | c3_1(a509)) <=> ((~hskp10) | c3_1(a509))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2193,axiom,((~hskp10) | c3_1(a509)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.18/1.34 tff(2194,plain,
% 1.18/1.34 ((~hskp10) | c3_1(a509)),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2193, 2192])).
% 1.18/1.34 tff(2195,plain,
% 1.18/1.34 ((~hskp10) | c3_1(a509)),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2194, 2192])).
% 1.18/1.34 tff(2196,plain,
% 1.18/1.34 ((~hskp10) | c3_1(a509)),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2195, 2192])).
% 1.18/1.34 tff(2197,plain,
% 1.18/1.34 ((~hskp10) | c3_1(a509)),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2196, 2192])).
% 1.18/1.34 tff(2198,plain,
% 1.18/1.34 ((~hskp10) | c3_1(a509)),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2197, 2192])).
% 1.18/1.34 tff(2199,plain,
% 1.18/1.34 (c3_1(a509)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[2198, 2185])).
% 1.18/1.34 tff(2200,plain,
% 1.18/1.34 (((~hskp10) | c0_1(a509)) <=> ((~hskp10) | c0_1(a509))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2201,axiom,((~hskp10) | c0_1(a509)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.18/1.34 tff(2202,plain,
% 1.18/1.34 ((~hskp10) | c0_1(a509)),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 1.18/1.34 tff(2203,plain,
% 1.18/1.34 ((~hskp10) | c0_1(a509)),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2202, 2200])).
% 1.18/1.34 tff(2204,plain,
% 1.18/1.34 ((~hskp10) | c0_1(a509)),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2203, 2200])).
% 1.18/1.34 tff(2205,plain,
% 1.18/1.34 ((~hskp10) | c0_1(a509)),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2204, 2200])).
% 1.18/1.34 tff(2206,plain,
% 1.18/1.34 ((~hskp10) | c0_1(a509)),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2205, 2200])).
% 1.18/1.34 tff(2207,plain,
% 1.18/1.34 (c0_1(a509)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[2206, 2185])).
% 1.18/1.34 tff(2208,plain,
% 1.18/1.34 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c0_1(a509)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2209,plain,
% 1.18/1.34 ((hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509))) <=> (hskp2 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c0_1(a509)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2210,plain,
% 1.18/1.34 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c0_1(a509))))),
% 1.18/1.34 inference(monotonicity,[status(thm)],[2209])).
% 1.18/1.34 tff(2211,plain,
% 1.18/1.34 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c0_1(a509)))),
% 1.18/1.34 inference(transitivity,[status(thm)],[2210, 2208])).
% 1.18/1.34 tff(2212,plain,
% 1.18/1.34 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)))),
% 1.18/1.34 inference(quant_inst,[status(thm)],[])).
% 1.18/1.34 tff(2213,plain,
% 1.18/1.34 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c0_1(a509))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2212, 2211])).
% 1.18/1.34 tff(2214,plain,
% 1.18/1.34 (hskp2 | (~c1_1(a509))),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[2213, 106, 2207, 2199, 2191, 541])).
% 1.18/1.34 tff(2215,plain,
% 1.18/1.34 (~c1_1(a509)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[2214, 408])).
% 1.18/1.34 tff(2216,plain,
% 1.18/1.34 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.18/1.34 inference(bind,[status(th)],[])).
% 1.18/1.34 tff(2217,plain,
% 1.18/1.34 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(quant_intro,[status(thm)],[2216])).
% 1.18/1.34 tff(2218,plain,
% 1.18/1.34 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2219,plain,
% 1.18/1.34 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.18/1.34 inference(bind,[status(th)],[])).
% 1.18/1.34 tff(2220,plain,
% 1.18/1.34 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(quant_intro,[status(thm)],[2219])).
% 1.18/1.34 tff(2221,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 1.18/1.34 tff(2222,plain,
% 1.18/1.34 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 1.18/1.34 tff(2223,plain,
% 1.18/1.34 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2222, 2218])).
% 1.18/1.34 tff(2224,plain,(
% 1.18/1.34 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(skolemize,[status(sab)],[2223])).
% 1.18/1.34 tff(2225,plain,
% 1.18/1.34 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2224, 2217])).
% 1.18/1.34 tff(2226,plain,
% 1.18/1.34 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2227,plain,
% 1.18/1.34 ((hskp9 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c3_1(a509)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509))) <=> (hskp9 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2228,plain,
% 1.18/1.34 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c3_1(a509)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509))))),
% 1.18/1.34 inference(monotonicity,[status(thm)],[2227])).
% 1.18/1.34 tff(2229,plain,
% 1.18/1.34 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c3_1(a509)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))),
% 1.18/1.34 inference(transitivity,[status(thm)],[2228, 2226])).
% 1.18/1.34 tff(2230,plain,
% 1.18/1.34 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c3_1(a509)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))),
% 1.18/1.34 inference(quant_inst,[status(thm)],[])).
% 1.18/1.34 tff(2231,plain,
% 1.18/1.34 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 1.18/1.34 tff(2232,plain,
% 1.18/1.34 (hskp9 | c1_1(a509)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[2231, 106, 2207, 2199, 2191, 2225])).
% 1.18/1.34 tff(2233,plain,
% 1.18/1.34 (hskp9),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[2232, 2215])).
% 1.18/1.34 tff(2234,plain,
% 1.18/1.34 (~c1_1(a507)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[840, 2233])).
% 1.18/1.34 tff(2235,plain,
% 1.18/1.34 (~c0_1(a507)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[846, 2233])).
% 1.18/1.34 tff(2236,plain,
% 1.18/1.34 (c3_1(a507)),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[854, 2233])).
% 1.18/1.34 tff(2237,plain,
% 1.18/1.34 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2238,plain,
% 1.18/1.34 ((hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (hskp28 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(2239,plain,
% 1.18/1.34 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[2238])).
% 1.18/1.35 tff(2240,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))),
% 1.18/1.35 inference(transitivity,[status(thm)],[2239, 2237])).
% 1.18/1.35 tff(2241,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(2242,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 1.18/1.35 tff(2243,plain,
% 1.18/1.35 (hskp28),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2242, 106, 2207, 2199, 2236, 2235, 2234, 238, 2215])).
% 1.18/1.35 tff(2244,plain,
% 1.18/1.35 (c0_1(a500)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[406, 2243])).
% 1.18/1.35 tff(2245,plain,
% 1.18/1.35 (c3_1(a500)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[390, 2243])).
% 1.18/1.35 tff(2246,plain,
% 1.18/1.35 (c2_1(a500)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[398, 2243])).
% 1.18/1.35 tff(2247,plain,
% 1.18/1.35 (~hskp15),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1902, 2243, 408])).
% 1.18/1.35 tff(2248,plain,
% 1.18/1.35 ($false),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[547, 106, 408, 862, 861, 859, 541, 869])).
% 1.18/1.35 tff(2249,plain,((~hskp12) | hskp2 | (~c3_1(a507)) | c0_1(a507) | c1_1(a507)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.35 tff(2250,plain,
% 1.18/1.35 (~hskp12),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2249, 408, 860, 857, 856])).
% 1.18/1.35 tff(2251,plain,
% 1.18/1.35 (hskp13),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[481, 2250, 43])).
% 1.18/1.35 tff(2252,plain,
% 1.18/1.35 (~c3_1(a520)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1362, 2251])).
% 1.18/1.35 tff(2253,plain,
% 1.18/1.35 (c0_1(a520)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1378, 2251])).
% 1.18/1.35 tff(2254,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c0_1(a520)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(2255,plain,
% 1.18/1.35 ((hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520))) <=> (hskp2 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c0_1(a520)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(2256,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c0_1(a520))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[2255])).
% 1.18/1.35 tff(2257,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c0_1(a520)))),
% 1.18/1.35 inference(transitivity,[status(thm)],[2256, 2254])).
% 1.18/1.35 tff(2258,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(2259,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c0_1(a520))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[2258, 2257])).
% 1.18/1.35 tff(2260,plain,
% 1.18/1.35 (~c1_1(a520)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2259, 106, 408, 444, 443, 442, 2253, 2252, 418])).
% 1.18/1.35 tff(2261,assumption,(~c2_1(a509)), introduced(assumption)).
% 1.18/1.35 tff(2262,assumption,(c3_1(a509)), introduced(assumption)).
% 1.18/1.35 tff(2263,assumption,(c0_1(a509)), introduced(assumption)).
% 1.18/1.35 tff(2264,plain,
% 1.18/1.35 (c2_1(a520)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1370, 2251])).
% 1.18/1.35 tff(2265,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | c3_1(a520) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a520) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(2266,plain,
% 1.18/1.35 ((hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509))) <=> (hskp24 | c3_1(a520) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(2267,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | c3_1(a520) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a520)) | (~c2_1(a520))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[2266])).
% 1.18/1.35 tff(2268,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a520) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.18/1.35 inference(transitivity,[status(thm)],[2267, 2265])).
% 1.18/1.35 tff(2269,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509)))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(2270,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a520) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a520)) | (~c2_1(a520))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[2269, 2268])).
% 1.18/1.35 tff(2271,plain,
% 1.18/1.35 (hskp24),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2270, 106, 2253, 2264, 2263, 2262, 2252, 2261, 1532])).
% 1.18/1.35 tff(2272,plain,
% 1.18/1.35 (~c3_1(a554)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1561, 2271])).
% 1.18/1.35 tff(2273,plain,
% 1.18/1.35 (~c2_1(a554)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1544, 2271])).
% 1.18/1.35 tff(2274,plain,
% 1.18/1.35 (c0_1(a554)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1569, 2271])).
% 1.18/1.35 tff(2275,assumption,(~hskp22), introduced(assumption)).
% 1.18/1.35 tff(2276,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a554) | c3_1(a554) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a554)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a554) | c3_1(a554) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a554)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(2277,plain,
% 1.18/1.35 ((hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520))) <=> (hskp22 | c2_1(a554) | c3_1(a554) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a554)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(2278,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a554) | c3_1(a554) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a554))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[2277])).
% 1.18/1.35 tff(2279,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a554) | c3_1(a554) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a554)))),
% 1.18/1.35 inference(transitivity,[status(thm)],[2278, 2276])).
% 1.18/1.35 tff(2280,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520)))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(2281,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a554) | c3_1(a554) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a554))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[2280, 2279])).
% 1.18/1.35 tff(2282,plain,
% 1.18/1.35 ($false),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2281, 106, 2275, 2274, 2253, 2273, 2272, 2252, 31, 2260])).
% 1.18/1.35 tff(2283,plain,(hskp2 | hskp22 | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | hskp15 | (~c3_1(a507)) | c0_1(a507) | c1_1(a507)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.35 tff(2284,plain,
% 1.18/1.35 (hskp22),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2283, 2247, 2207, 2199, 2191, 408, 2246, 2245, 2244, 2236, 2235, 2234])).
% 1.18/1.35 tff(2285,plain,
% 1.18/1.35 (c3_1(a540)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[133, 2284])).
% 1.18/1.35 tff(2286,plain,
% 1.18/1.35 (c1_1(a540)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[141, 2284])).
% 1.18/1.35 tff(2287,plain,
% 1.18/1.35 (~c0_1(a540)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[125, 2284])).
% 1.18/1.35 tff(2288,assumption,(c1_1(a540)), introduced(assumption)).
% 1.18/1.35 tff(2289,assumption,(hskp9), introduced(assumption)).
% 1.18/1.35 tff(2290,plain,
% 1.18/1.35 (~c0_1(a507)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[846, 2289])).
% 1.18/1.35 tff(2291,assumption,(~c0_1(a540)), introduced(assumption)).
% 1.18/1.35 tff(2292,plain,
% 1.18/1.35 (c3_1(a507)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[854, 2289])).
% 1.18/1.35 tff(2293,assumption,(c3_1(a540)), introduced(assumption)).
% 1.18/1.35 tff(2294,plain,
% 1.18/1.35 (~c1_1(a507)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[840, 2289])).
% 1.18/1.35 tff(2295,assumption,(~c2_1(a540)), introduced(assumption)).
% 1.18/1.35 tff(2296,plain,
% 1.18/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a540) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a540) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(2297,plain,
% 1.18/1.35 (((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (c0_1(a540) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(2298,plain,
% 1.18/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a540) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540)))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[2297])).
% 1.18/1.35 tff(2299,plain,
% 1.18/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a540) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))),
% 1.18/1.35 inference(transitivity,[status(thm)],[2298, 2296])).
% 1.18/1.35 tff(2300,plain,
% 1.18/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(2301,plain,
% 1.18/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a540) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540)),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[2300, 2299])).
% 1.18/1.35 tff(2302,plain,
% 1.18/1.35 ($false),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2301, 106, 2288, 2293, 860, 2291, 857, 856, 558, 2295])).
% 1.18/1.35 tff(2303,plain,(c2_1(a540) | (~c1_1(a540)) | (~c3_1(a540)) | (~c3_1(a507)) | c0_1(a540) | c0_1(a507) | c1_1(a507)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.35 tff(2304,plain,
% 1.18/1.35 (c2_1(a540)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2303, 2294, 2293, 2292, 2291, 2290, 2288])).
% 1.18/1.35 tff(2305,plain,
% 1.18/1.35 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.18/1.35 inference(bind,[status(th)],[])).
% 1.18/1.35 tff(2306,plain,
% 1.18/1.35 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.18/1.35 inference(quant_intro,[status(thm)],[2305])).
% 1.18/1.35 tff(2307,plain,
% 1.18/1.35 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(2308,plain,
% 1.18/1.35 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.18/1.35 inference(bind,[status(th)],[])).
% 1.18/1.35 tff(2309,plain,
% 1.18/1.35 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.18/1.35 inference(quant_intro,[status(thm)],[2308])).
% 1.18/1.35 tff(2310,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.18/1.35 tff(2311,plain,
% 1.18/1.35 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[2310, 2309])).
% 1.18/1.35 tff(2312,plain,
% 1.18/1.35 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[2311, 2307])).
% 1.18/1.35 tff(2313,plain,(
% 1.18/1.35 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.18/1.35 inference(skolemize,[status(sab)],[2312])).
% 1.18/1.35 tff(2314,plain,
% 1.18/1.35 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[2313, 2306])).
% 1.18/1.35 tff(2315,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c3_1(a540)) | (~c2_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(2316,plain,
% 1.18/1.35 ((hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540))) <=> (hskp15 | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(2317,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c3_1(a540)) | (~c2_1(a540))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[2316])).
% 1.18/1.35 tff(2318,plain,
% 1.18/1.35 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 1.18/1.35 inference(transitivity,[status(thm)],[2317, 2315])).
% 1.18/1.35 tff(2319,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(2320,plain,
% 1.18/1.35 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c3_1(a540)) | (~c2_1(a540))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[2319, 2318])).
% 1.18/1.35 tff(2321,plain,
% 1.18/1.35 ((~c1_1(a509)) | (~c2_1(a540))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2320, 106, 43, 2293, 2263, 2291, 2261, 2314])).
% 1.18/1.35 tff(2322,plain,
% 1.18/1.35 (~c1_1(a509)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2321, 2304])).
% 1.18/1.35 tff(2323,plain,
% 1.18/1.35 (c2_1(a540)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[2303, 856, 2293, 860, 2291, 857, 2288])).
% 1.18/1.35 tff(2324,assumption,(~c1_1(a509)), introduced(assumption)).
% 1.18/1.35 tff(2325,assumption,(hskp13), introduced(assumption)).
% 1.18/1.35 tff(2326,plain,
% 1.18/1.35 (~c3_1(a520)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1362, 2325])).
% 1.18/1.35 tff(2327,plain,
% 1.18/1.35 (c0_1(a520)),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1378, 2325])).
% 1.18/1.35 tff(2328,plain,
% 1.18/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a540) | c3_1(a520) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a520) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(2329,plain,
% 1.18/1.35 (((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540))) <=> (c0_1(a540) | c3_1(a520) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(2330,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a540) | c3_1(a520) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c3_1(a540)) | (~c1_1(a540))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[2329])).
% 1.18/1.36 tff(2331,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a520) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.18/1.36 inference(transitivity,[status(thm)],[2330, 2328])).
% 1.18/1.36 tff(2332,plain,
% 1.18/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(2333,plain,
% 1.18/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a520) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c3_1(a540)) | (~c1_1(a540))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[2332, 2331])).
% 1.18/1.36 tff(2334,plain,
% 1.18/1.36 (~c1_1(a520)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[2333, 106, 2288, 2293, 2327, 2263, 2262, 2291, 2326, 1302, 2324])).
% 1.18/1.36 tff(2335,plain,
% 1.18/1.36 (c2_1(a520)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1370, 2325])).
% 1.18/1.36 tff(2336,plain,
% 1.18/1.36 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(2337,plain,
% 1.18/1.36 ((hskp7 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (hskp7 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(2338,plain,
% 1.18/1.36 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[2337])).
% 1.18/1.36 tff(2339,plain,
% 1.18/1.36 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.18/1.36 inference(transitivity,[status(thm)],[2338, 2336])).
% 1.18/1.36 tff(2340,plain,
% 1.18/1.36 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(2341,plain,
% 1.18/1.36 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[2340, 2339])).
% 1.18/1.36 tff(2342,plain,
% 1.18/1.36 (hskp7),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[2341, 106, 2327, 2335, 860, 857, 856, 216, 2334])).
% 1.18/1.36 tff(2343,plain,
% 1.18/1.36 (~c3_1(a502)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[302, 2342])).
% 1.18/1.36 tff(2344,plain,
% 1.18/1.36 (~c0_1(a502)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[643, 2342])).
% 1.18/1.36 tff(2345,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(2346,plain,
% 1.18/1.36 (((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a502) | c0_1(a502) | c2_1(a502)) <=> (c0_1(a540) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(2347,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[2346])).
% 1.18/1.36 tff(2348,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.18/1.36 inference(transitivity,[status(thm)],[2347, 2345])).
% 1.18/1.36 tff(2349,plain,
% 1.18/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a502) | c0_1(a502) | c2_1(a502))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(2350,plain,
% 1.18/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[2349, 2348])).
% 1.18/1.36 tff(2351,plain,
% 1.18/1.36 (c2_1(a502)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[2350, 106, 2288, 2293, 2291, 2344, 2343, 1150, 2323])).
% 1.18/1.36 tff(2352,plain,
% 1.18/1.36 (~c1_1(a502)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[308, 2342])).
% 1.18/1.36 tff(2353,plain,
% 1.18/1.36 (hskp4 | (~c2_1(a502))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1385, 106, 2327, 2335, 2326, 2344, 2352, 367])).
% 1.18/1.36 tff(2354,plain,
% 1.18/1.36 (hskp4),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[2353, 2351])).
% 1.18/1.36 tff(2355,plain,
% 1.18/1.36 (~c2_1(a498)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1412, 2354])).
% 1.18/1.36 tff(2356,plain,
% 1.18/1.36 (~c0_1(a498)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1391, 2354])).
% 1.18/1.36 tff(2357,plain,
% 1.18/1.36 (c1_1(a498)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1399, 2354])).
% 1.18/1.36 tff(2358,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a540) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(2359,plain,
% 1.18/1.36 (((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498))) <=> (c0_1(a540) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(2360,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a540) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[2359])).
% 1.18/1.36 tff(2361,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.18/1.36 inference(transitivity,[status(thm)],[2360, 2358])).
% 1.18/1.36 tff(2362,plain,
% 1.18/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498)))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(2363,plain,
% 1.18/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a540)) | (~c2_1(a540))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[2362, 2361])).
% 1.18/1.36 tff(2364,plain,
% 1.18/1.36 (~c3_1(a498)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[2363, 106, 2288, 2357, 2291, 2356, 2355, 1079, 2323])).
% 1.18/1.36 tff(2365,plain,
% 1.18/1.36 (hskp24),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[2270, 106, 2327, 2335, 2263, 2262, 2326, 2261, 1532])).
% 1.18/1.36 tff(2366,plain,
% 1.18/1.36 (~c3_1(a554)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1561, 2365])).
% 1.18/1.36 tff(2367,plain,
% 1.18/1.36 (c0_1(a554)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1569, 2365])).
% 1.18/1.36 tff(2368,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a554) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c1_1(a554)) | (~c0_1(a554)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a554) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c1_1(a554)) | (~c0_1(a554)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(2369,plain,
% 1.18/1.36 (((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540))) <=> (c3_1(a554) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c1_1(a554)) | (~c0_1(a554)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(2370,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a554) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c1_1(a554)) | (~c0_1(a554))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[2369])).
% 1.18/1.36 tff(2371,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a554) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c1_1(a554)) | (~c0_1(a554)))),
% 1.18/1.36 inference(transitivity,[status(thm)],[2370, 2368])).
% 1.18/1.36 tff(2372,plain,
% 1.18/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(2373,plain,
% 1.18/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a554) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c1_1(a554)) | (~c0_1(a554))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[2372, 2371])).
% 1.18/1.36 tff(2374,plain,
% 1.18/1.36 (~c1_1(a554)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[2373, 106, 2367, 2288, 2293, 2263, 2262, 2366, 2291, 1302, 2324])).
% 1.18/1.36 tff(2375,plain,
% 1.18/1.36 (hskp1),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1614, 106, 2367, 2366, 2344, 2352, 2343, 585, 2374])).
% 1.18/1.36 tff(2376,plain,
% 1.18/1.36 (~c3_1(a495)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[932, 2375])).
% 1.18/1.36 tff(2377,plain,
% 1.18/1.36 (c1_1(a495)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[947, 2375])).
% 1.18/1.36 tff(2378,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a502) | c1_1(a502) | c3_1(a502) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(2379,plain,
% 1.18/1.36 (((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a502) | c1_1(a502) | c0_1(a502)) <=> (c0_1(a502) | c1_1(a502) | c3_1(a502) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(2380,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a502) | c1_1(a502) | c3_1(a502) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498)))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[2379])).
% 1.18/1.36 tff(2381,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))),
% 1.18/1.36 inference(transitivity,[status(thm)],[2380, 2378])).
% 1.18/1.36 tff(2382,plain,
% 1.18/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a502) | c1_1(a502) | c0_1(a502))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(2383,plain,
% 1.18/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498)),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[2382, 2381])).
% 1.18/1.36 tff(2384,plain,
% 1.18/1.36 (~c2_1(a495)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[2383, 106, 2377, 2344, 2352, 2343, 2356, 2355, 2376, 709, 2364])).
% 1.18/1.36 tff(2385,plain,
% 1.18/1.36 (~c0_1(a495)),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[938, 2375])).
% 1.18/1.36 tff(2386,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | c2_1(a495) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | c2_1(a495) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(2387,plain,
% 1.18/1.36 (((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a495) | c0_1(a495) | c2_1(a495)) <=> (c0_1(a540) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | c2_1(a495) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(2388,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a495) | c0_1(a495) | c2_1(a495))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | c2_1(a495) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[2387])).
% 1.18/1.36 tff(2389,plain,
% 1.18/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a495) | c0_1(a495) | c2_1(a495))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | c2_1(a495) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.36 inference(transitivity,[status(thm)],[2388, 2386])).
% 1.21/1.36 tff(2390,plain,
% 1.21/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a495) | c0_1(a495) | c2_1(a495))),
% 1.21/1.36 inference(quant_inst,[status(thm)],[])).
% 1.21/1.36 tff(2391,plain,
% 1.21/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | c2_1(a495) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 1.21/1.36 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 1.21/1.36 tff(2392,plain,
% 1.21/1.36 ($false),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[2391, 106, 2288, 2293, 2291, 2385, 2376, 1150, 2323, 2384])).
% 1.21/1.36 tff(2393,plain,((~hskp13) | (~c1_1(a540)) | (~c3_1(a540)) | c0_1(a540) | (~c0_1(a509)) | (~c3_1(a509)) | c1_1(a509) | (~c3_1(a507)) | c0_1(a507) | c1_1(a507) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.36 tff(2394,plain,
% 1.21/1.36 (~hskp13),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[2393, 2322, 2293, 2291, 2263, 2262, 2288, 2292, 2290, 2294, 2261])).
% 1.21/1.36 tff(2395,plain,
% 1.21/1.36 (hskp12),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[481, 2394, 43])).
% 1.21/1.36 tff(2396,plain,
% 1.21/1.36 (~c2_1(a514)),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[487, 2395])).
% 1.21/1.36 tff(2397,plain,
% 1.21/1.36 (c3_1(a514)),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[495, 2395])).
% 1.21/1.36 tff(2398,plain,
% 1.21/1.36 (c1_1(a514)),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[503, 2395])).
% 1.21/1.36 tff(2399,plain,
% 1.21/1.36 (c0_1(a514)),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[868, 106, 2398, 2397, 2292, 2396, 2290, 2294, 558])).
% 1.21/1.36 tff(2400,plain,
% 1.21/1.36 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a540) | c2_1(a514) | (~ndr1_0) | (~c1_1(a514)) | (~c0_1(a514)) | (~c3_1(a540)) | (~c2_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a514) | (~ndr1_0) | (~c1_1(a514)) | (~c0_1(a514)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 1.21/1.36 inference(rewrite,[status(thm)],[])).
% 1.21/1.36 tff(2401,plain,
% 1.21/1.36 ((hskp15 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540))) <=> (hskp15 | c0_1(a540) | c2_1(a514) | (~ndr1_0) | (~c1_1(a514)) | (~c0_1(a514)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 1.21/1.36 inference(rewrite,[status(thm)],[])).
% 1.21/1.36 tff(2402,plain,
% 1.21/1.36 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a540) | c2_1(a514) | (~ndr1_0) | (~c1_1(a514)) | (~c0_1(a514)) | (~c3_1(a540)) | (~c2_1(a540))))),
% 1.21/1.36 inference(monotonicity,[status(thm)],[2401])).
% 1.21/1.36 tff(2403,plain,
% 1.21/1.36 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a514) | (~ndr1_0) | (~c1_1(a514)) | (~c0_1(a514)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 1.21/1.36 inference(transitivity,[status(thm)],[2402, 2400])).
% 1.21/1.36 tff(2404,plain,
% 1.21/1.36 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))),
% 1.21/1.36 inference(quant_inst,[status(thm)],[])).
% 1.21/1.36 tff(2405,plain,
% 1.21/1.36 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a514) | (~ndr1_0) | (~c1_1(a514)) | (~c0_1(a514)) | (~c3_1(a540)) | (~c2_1(a540))),
% 1.21/1.36 inference(modus_ponens,[status(thm)],[2404, 2403])).
% 1.21/1.36 tff(2406,plain,
% 1.21/1.36 ($false),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[2405, 106, 43, 2293, 2398, 2291, 2396, 2314, 2399, 2304])).
% 1.21/1.36 tff(2407,plain,((~hskp9) | hskp15 | (~c3_1(a540)) | c0_1(a540) | (~c0_1(a509)) | (~c3_1(a509)) | (~c1_1(a540)) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.36 tff(2408,plain,
% 1.21/1.36 ($false),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[2407, 2287, 2286, 2247, 2233, 2207, 2199, 2285, 2191])).
% 1.21/1.36 tff(2409,plain,(hskp2), inference(lemma,lemma(discharge,[]))).
% 1.21/1.36 tff(2410,plain,
% 1.21/1.36 (~c2_1(a496)),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[335, 2409])).
% 1.21/1.36 tff(2411,plain,
% 1.21/1.36 (~c3_1(a496)),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[329, 2409])).
% 1.21/1.36 tff(2412,plain,
% 1.21/1.36 (~hskp9),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[2407, 1735, 43, 1733, 2207, 2199, 1734, 2191])).
% 1.21/1.36 tff(2413,plain,
% 1.21/1.36 (c1_1(a509)),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[2232, 2412])).
% 1.21/1.36 tff(2414,plain,
% 1.21/1.36 (~c2_1(a540)),
% 1.21/1.36 inference(unit_resolution,[status(thm)],[2320, 106, 43, 1734, 2207, 1733, 2191, 2314, 2413])).
% 1.21/1.36 tff(2415,assumption,(c1_1(a509)), introduced(assumption)).
% 1.21/1.36 tff(2416,plain,
% 1.21/1.36 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)))),
% 1.21/1.36 inference(rewrite,[status(thm)],[])).
% 1.21/1.36 tff(2417,plain,
% 1.21/1.36 ((hskp6 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c2_1(a496) | c0_1(a496) | c3_1(a496)) <=> (hskp6 | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)))),
% 1.21/1.36 inference(rewrite,[status(thm)],[])).
% 1.21/1.36 tff(2418,plain,
% 1.21/1.36 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c2_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509))))),
% 1.21/1.36 inference(monotonicity,[status(thm)],[2417])).
% 1.21/1.36 tff(2419,plain,
% 1.21/1.36 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c2_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)))),
% 1.21/1.36 inference(transitivity,[status(thm)],[2418, 2416])).
% 1.21/1.36 tff(2420,plain,
% 1.21/1.36 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c2_1(a496) | c0_1(a496) | c3_1(a496))),
% 1.21/1.36 inference(quant_inst,[status(thm)],[])).
% 1.21/1.36 tff(2421,plain,
% 1.21/1.36 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509))),
% 1.21/1.36 inference(modus_ponens,[status(thm)],[2420, 2419])).
% 1.21/1.37 tff(2422,plain,
% 1.21/1.37 (hskp6 | c3_1(a496) | c0_1(a496) | (~c1_1(a509))),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2421, 106, 2263, 2261, 574, 879])).
% 1.21/1.37 tff(2423,plain,
% 1.21/1.37 (hskp6),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2422, 2415, 573, 575])).
% 1.21/1.37 tff(2424,plain,
% 1.21/1.37 (hskp2 | (~c1_1(a509))),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2213, 106, 2263, 2262, 2261, 541])).
% 1.21/1.37 tff(2425,plain,
% 1.21/1.37 (hskp2),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2424, 2415])).
% 1.21/1.37 tff(2426,plain,
% 1.21/1.37 (~c1_1(a496)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[348, 2425])).
% 1.21/1.37 tff(2427,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[715, 106, 608, 600, 592, 572, 574, 573, 709, 575])).
% 1.21/1.37 tff(2428,plain,((~hskp6) | c1_1(a496) | c2_1(a496) | c3_1(a496) | c0_1(a496)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(2429,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2428, 2426, 2423, 574, 573, 575])).
% 1.21/1.37 tff(2430,plain,((~c1_1(a509)) | c2_1(a496) | c3_1(a496) | c0_1(a496) | (~c0_1(a509)) | c2_1(a509) | (~c3_1(a509))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(2431,plain,
% 1.21/1.37 (~c1_1(a509)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2430, 575, 573, 574, 2263, 2261, 2262])).
% 1.21/1.37 tff(2432,plain,
% 1.21/1.37 (hskp9 | c1_1(a509)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2231, 106, 2263, 2262, 2261, 2225])).
% 1.21/1.37 tff(2433,plain,
% 1.21/1.37 (hskp9),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2432, 2431])).
% 1.21/1.37 tff(2434,plain,
% 1.21/1.37 (c3_1(a507)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[854, 2433])).
% 1.21/1.37 tff(2435,plain,
% 1.21/1.37 (~c0_1(a507)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[846, 2433])).
% 1.21/1.37 tff(2436,plain,
% 1.21/1.37 (~c1_1(a507)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[840, 2433])).
% 1.21/1.37 tff(2437,plain,
% 1.21/1.37 (c2_1(a540)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2303, 2436, 2288, 2293, 2291, 2435, 2434])).
% 1.21/1.37 tff(2438,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(2439,plain,
% 1.21/1.37 (((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(2440,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[2439])).
% 1.21/1.37 tff(2441,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[2440, 2438])).
% 1.21/1.37 tff(2442,plain,
% 1.21/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(2443,plain,
% 1.21/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[2442, 2441])).
% 1.21/1.37 tff(2444,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2443, 106, 2288, 2293, 2291, 574, 573, 1150, 575, 2437])).
% 1.21/1.37 tff(2445,plain,(c0_1(a496) | (~c1_1(a540)) | (~c3_1(a540)) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(2446,plain,
% 1.21/1.37 (c0_1(a496)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2445, 1733, 2191, 2207, 574, 573, 1734, 2199, 1735])).
% 1.21/1.37 tff(2447,plain,
% 1.21/1.37 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.21/1.37 inference(bind,[status(th)],[])).
% 1.21/1.37 tff(2448,plain,
% 1.21/1.37 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.37 inference(quant_intro,[status(thm)],[2447])).
% 1.21/1.37 tff(2449,plain,
% 1.21/1.37 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(2450,plain,
% 1.21/1.37 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.21/1.37 inference(bind,[status(th)],[])).
% 1.21/1.37 tff(2451,plain,
% 1.21/1.37 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.37 inference(quant_intro,[status(thm)],[2450])).
% 1.21/1.37 tff(2452,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.21/1.37 tff(2453,plain,
% 1.21/1.37 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[2452, 2451])).
% 1.21/1.37 tff(2454,plain,
% 1.21/1.37 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[2453, 2449])).
% 1.21/1.37 tff(2455,plain,(
% 1.21/1.37 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.37 inference(skolemize,[status(sab)],[2454])).
% 1.21/1.37 tff(2456,plain,
% 1.21/1.37 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[2455, 2448])).
% 1.21/1.37 tff(2457,plain,
% 1.21/1.37 (hskp2),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2214, 2413])).
% 1.21/1.37 tff(2458,plain,
% 1.21/1.37 (~c1_1(a496)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[348, 2457])).
% 1.21/1.37 tff(2459,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a540)) | c2_1(a540))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a540)) | c2_1(a540))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(2460,plain,
% 1.21/1.37 ((hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540))) <=> (hskp9 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a540)) | c2_1(a540))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(2461,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a540)) | c2_1(a540)))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[2460])).
% 1.21/1.37 tff(2462,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a540)) | c2_1(a540))),
% 1.21/1.37 inference(transitivity,[status(thm)],[2461, 2459])).
% 1.21/1.37 tff(2463,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(2464,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a540)) | c2_1(a540)),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 1.21/1.37 tff(2465,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2464, 106, 2412, 1735, 1733, 2458, 574, 2456, 2446, 2414])).
% 1.21/1.37 tff(2466,plain,((~hskp22) | c2_1(a496) | hskp15 | c3_1(a496)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(2467,plain,
% 1.21/1.37 (~hskp22),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2466, 43, 574, 573])).
% 1.21/1.37 tff(2468,assumption,(c0_1(a496)), introduced(assumption)).
% 1.21/1.37 tff(2469,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[722, 106, 2275, 572, 574, 573, 31, 2468])).
% 1.21/1.37 tff(2470,plain,(c1_1(a496) | hskp22 | c2_1(a496) | c3_1(a496) | (~c0_1(a496))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(2471,plain,
% 1.21/1.37 (c1_1(a496)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2470, 2468, 574, 573, 2275])).
% 1.21/1.37 tff(2472,plain,
% 1.21/1.37 (~hskp2),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[348, 2471])).
% 1.21/1.37 tff(2473,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a509)) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a509)) | (~c0_1(a509)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(2474,plain,
% 1.21/1.37 ((hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a496) | (~c1_1(a496)) | (~c0_1(a496))) <=> (hskp2 | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a509)) | (~c0_1(a509)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(2475,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a496) | (~c1_1(a496)) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a509)) | (~c0_1(a509))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[2474])).
% 1.21/1.37 tff(2476,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a496) | (~c1_1(a496)) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a509)) | (~c0_1(a509)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[2475, 2473])).
% 1.21/1.37 tff(2477,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a496) | (~c1_1(a496)) | (~c0_1(a496)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(2478,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a509)) | (~c0_1(a509))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[2477, 2476])).
% 1.21/1.37 tff(2479,plain,
% 1.21/1.37 (hskp2 | (~c1_1(a496)) | (~c0_1(a496))),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2478, 106, 2263, 2262, 2261, 574, 541])).
% 1.21/1.37 tff(2480,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2479, 2472, 2471, 2468])).
% 1.21/1.37 tff(2481,plain,((~c0_1(a496)) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | c2_1(a496) | c3_1(a496) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(2482,plain,
% 1.21/1.37 (~c0_1(a496)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2481, 2467, 2199, 2191, 574, 573, 2207])).
% 1.21/1.37 tff(2483,plain,
% 1.21/1.37 (~c1_1(a509)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2430, 2482, 2199, 573, 2207, 2191, 574])).
% 1.21/1.37 tff(2484,plain,
% 1.21/1.37 (hskp9),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2232, 2483])).
% 1.21/1.37 tff(2485,plain,
% 1.21/1.37 (~c1_1(a507)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[840, 2484])).
% 1.21/1.37 tff(2486,plain,
% 1.21/1.37 (~c0_1(a507)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[846, 2484])).
% 1.21/1.37 tff(2487,plain,
% 1.21/1.37 (c3_1(a507)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[854, 2484])).
% 1.21/1.37 tff(2488,plain,
% 1.21/1.37 (hskp28),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2242, 106, 2207, 2199, 2487, 2486, 2485, 238, 2483])).
% 1.21/1.37 tff(2489,plain,
% 1.21/1.37 (c3_1(a500)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[390, 2488])).
% 1.21/1.37 tff(2490,plain,
% 1.21/1.37 (c2_1(a500)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[398, 2488])).
% 1.21/1.37 tff(2491,plain,
% 1.21/1.37 (c0_1(a500)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[406, 2488])).
% 1.21/1.37 tff(2492,plain,
% 1.21/1.37 (hskp2),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2283, 2491, 2207, 2199, 2191, 43, 2490, 2489, 2467, 2487, 2486, 2485])).
% 1.21/1.37 tff(2493,plain,
% 1.21/1.37 (~c1_1(a496)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[348, 2492])).
% 1.21/1.37 tff(2494,plain,
% 1.21/1.37 (~hskp6),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2428, 2493, 574, 573, 2482])).
% 1.21/1.37 tff(2495,plain,
% 1.21/1.37 (~hskp12),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[888, 2494, 2482, 574, 573, 2487, 2486, 2485])).
% 1.21/1.37 tff(2496,plain,
% 1.21/1.37 (hskp13),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[481, 2495, 43])).
% 1.21/1.37 tff(2497,plain,
% 1.21/1.37 (~c3_1(a520)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1362, 2496])).
% 1.21/1.37 tff(2498,plain,
% 1.21/1.37 (c2_1(a520)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1370, 2496])).
% 1.21/1.37 tff(2499,plain,
% 1.21/1.37 (~c1_1(a520)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1855, 106, 2498, 2497, 2493, 574, 573, 709, 2482])).
% 1.21/1.37 tff(2500,plain,
% 1.21/1.37 (c0_1(a520)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1378, 2496])).
% 1.21/1.37 tff(2501,plain,
% 1.21/1.37 (hskp24),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2270, 106, 2500, 2498, 2207, 2199, 2497, 2191, 1532])).
% 1.21/1.37 tff(2502,plain,
% 1.21/1.37 (~c3_1(a554)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1561, 2501])).
% 1.21/1.37 tff(2503,plain,
% 1.21/1.37 (~c2_1(a554)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1544, 2501])).
% 1.21/1.37 tff(2504,plain,
% 1.21/1.37 (c0_1(a554)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1569, 2501])).
% 1.21/1.37 tff(2505,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2281, 106, 2467, 2504, 2500, 2503, 2502, 2497, 31, 2499])).
% 1.21/1.37 tff(2506,plain,(hskp15 | c2_1(a496) | c3_1(a496)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(2507,plain,
% 1.21/1.37 (hskp15),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2506, 573, 574])).
% 1.21/1.37 tff(2508,plain,
% 1.21/1.37 (c1_1(a528)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[432, 2507])).
% 1.21/1.37 tff(2509,plain,
% 1.21/1.37 (c0_1(a528)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[440, 2507])).
% 1.21/1.37 tff(2510,plain,
% 1.21/1.37 (~c3_1(a528)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[424, 2507])).
% 1.21/1.37 tff(2511,plain,
% 1.21/1.37 (hskp10),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2059, 32])).
% 1.21/1.37 tff(2512,plain,
% 1.21/1.37 (c3_1(a509)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2198, 2511])).
% 1.21/1.37 tff(2513,plain,
% 1.21/1.37 (~c2_1(a509)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2190, 2511])).
% 1.21/1.37 tff(2514,plain,
% 1.21/1.37 (c0_1(a509)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2206, 2511])).
% 1.21/1.37 tff(2515,plain,
% 1.21/1.37 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.21/1.37 inference(bind,[status(th)],[])).
% 1.21/1.37 tff(2516,plain,
% 1.21/1.37 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.37 inference(quant_intro,[status(thm)],[2515])).
% 1.21/1.37 tff(2517,plain,
% 1.21/1.37 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(2518,plain,
% 1.21/1.37 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.21/1.37 inference(bind,[status(th)],[])).
% 1.21/1.37 tff(2519,plain,
% 1.21/1.37 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.37 inference(quant_intro,[status(thm)],[2518])).
% 1.21/1.37 tff(2520,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 1.21/1.37 tff(2521,plain,
% 1.21/1.37 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[2520, 2519])).
% 1.21/1.37 tff(2522,plain,
% 1.21/1.37 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[2521, 2517])).
% 1.21/1.37 tff(2523,plain,(
% 1.21/1.37 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.37 inference(skolemize,[status(sab)],[2522])).
% 1.21/1.37 tff(2524,plain,
% 1.21/1.37 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[2523, 2516])).
% 1.21/1.37 tff(2525,assumption,(~c1_1(a528)), introduced(assumption)).
% 1.21/1.37 tff(2526,plain,
% 1.21/1.37 (~hskp15),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[432, 2525])).
% 1.21/1.37 tff(2527,assumption,(~c0_1(a528)), introduced(assumption)).
% 1.21/1.37 tff(2528,plain,
% 1.21/1.37 (~c1_1(a509)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2424, 408])).
% 1.21/1.37 tff(2529,plain,
% 1.21/1.37 (hskp9),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2432, 2528])).
% 1.21/1.37 tff(2530,plain,
% 1.21/1.37 (~c1_1(a507)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[840, 2529])).
% 1.21/1.37 tff(2531,plain,
% 1.21/1.37 (~c0_1(a507)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[846, 2529])).
% 1.21/1.37 tff(2532,plain,
% 1.21/1.37 (c3_1(a507)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[854, 2529])).
% 1.21/1.37 tff(2533,plain,
% 1.21/1.37 (~hskp12),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2249, 408, 2532, 2531, 2530])).
% 1.21/1.37 tff(2534,plain,
% 1.21/1.37 (hskp13),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[481, 2533, 2526])).
% 1.21/1.37 tff(2535,plain,
% 1.21/1.37 (c2_1(a520)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1370, 2534])).
% 1.21/1.37 tff(2536,plain,
% 1.21/1.37 (c0_1(a520)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1378, 2534])).
% 1.21/1.37 tff(2537,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(2538,plain,
% 1.21/1.37 ((hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528)) <=> (hskp2 | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(2539,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[2538])).
% 1.21/1.37 tff(2540,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[2539, 2537])).
% 1.21/1.37 tff(2541,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(2542,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[2541, 2540])).
% 1.21/1.37 tff(2543,plain,
% 1.21/1.37 (~c1_1(a520)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2542, 106, 408, 2527, 2525, 2536, 2535, 989, 290])).
% 1.21/1.37 tff(2544,plain,
% 1.21/1.37 (~c3_1(a520)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1362, 2534])).
% 1.21/1.37 tff(2545,plain,
% 1.21/1.37 (hskp24),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2270, 106, 2536, 2535, 2263, 2262, 2544, 2261, 1532])).
% 1.21/1.37 tff(2546,plain,
% 1.21/1.37 (~c3_1(a554)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1561, 2545])).
% 1.21/1.37 tff(2547,plain,
% 1.21/1.37 (~c2_1(a554)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1544, 2545])).
% 1.21/1.37 tff(2548,plain,
% 1.21/1.37 (c0_1(a554)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1569, 2545])).
% 1.21/1.37 tff(2549,plain,
% 1.21/1.37 (hskp22),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2281, 106, 2548, 2536, 2547, 2546, 2544, 31, 2543])).
% 1.21/1.37 tff(2550,plain,
% 1.21/1.37 (~c0_1(a540)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[125, 2549])).
% 1.21/1.37 tff(2551,plain,
% 1.21/1.37 (c1_1(a540)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[141, 2549])).
% 1.21/1.37 tff(2552,plain,
% 1.21/1.37 (c3_1(a540)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[133, 2549])).
% 1.21/1.37 tff(2553,plain,
% 1.21/1.37 (c2_1(a540)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2303, 2552, 2530, 2532, 2550, 2531, 2551])).
% 1.21/1.37 tff(2554,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(2555,plain,
% 1.21/1.37 ((hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528)) <=> (hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(2556,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[2555])).
% 1.21/1.37 tff(2557,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[2556, 2554])).
% 1.21/1.37 tff(2558,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(2559,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[2558, 2557])).
% 1.21/1.37 tff(2560,plain,
% 1.21/1.37 (hskp1),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[2559, 106, 2527, 2525, 2536, 989, 2544, 585, 2543])).
% 1.21/1.37 tff(2561,plain,
% 1.21/1.37 (~c3_1(a495)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[932, 2560])).
% 1.21/1.37 tff(2562,plain,
% 1.21/1.37 (c1_1(a495)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[947, 2560])).
% 1.21/1.38 tff(2563,plain,
% 1.21/1.38 (~c0_1(a495)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[938, 2560])).
% 1.21/1.38 tff(2564,plain,
% 1.21/1.38 (c2_1(a495)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2391, 106, 2551, 2552, 2550, 2563, 2561, 1150, 2553])).
% 1.21/1.38 tff(2565,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a528) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | c2_1(a528) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a528) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | c2_1(a528) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(2566,plain,
% 1.21/1.38 (((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a528) | c0_1(a528) | c2_1(a528)) <=> (c0_1(a528) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | c2_1(a528) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(2567,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a528) | c0_1(a528) | c2_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a528) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | c2_1(a528) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[2566])).
% 1.21/1.38 tff(2568,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a528) | c0_1(a528) | c2_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a528) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | c2_1(a528) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[2567, 2565])).
% 1.21/1.38 tff(2569,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a528) | c0_1(a528) | c2_1(a528))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(2570,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a528) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | c2_1(a528) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 1.21/1.38 tff(2571,plain,
% 1.21/1.38 (c2_1(a528)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2570, 106, 2551, 2552, 2527, 2550, 989, 1150, 2553])).
% 1.21/1.38 tff(2572,assumption,(~hskp4), introduced(assumption)).
% 1.21/1.38 tff(2573,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a528) | c1_1(a528) | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a528) | c1_1(a528) | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c2_1(a528)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(2574,plain,
% 1.21/1.38 ((hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | (~c2_1(a528))) <=> (hskp4 | c0_1(a528) | c1_1(a528) | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c2_1(a528)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(2575,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a528) | c1_1(a528) | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c2_1(a528))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[2574])).
% 1.21/1.38 tff(2576,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a528) | c1_1(a528) | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c2_1(a528)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[2575, 2573])).
% 1.21/1.38 tff(2577,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | (~c2_1(a528)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(2578,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a528) | c1_1(a528) | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c2_1(a528))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[2577, 2576])).
% 1.21/1.38 tff(2579,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2578, 106, 2572, 2527, 2525, 2327, 2335, 2326, 367, 2093])).
% 1.21/1.38 tff(2580,plain,((~hskp13) | hskp4 | c0_1(a528) | c1_1(a528) | (~c2_1(a528))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(2581,plain,
% 1.21/1.38 (hskp4),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2580, 2571, 2527, 2525, 2534])).
% 1.21/1.38 tff(2582,assumption,(c2_1(a540)), introduced(assumption)).
% 1.21/1.38 tff(2583,assumption,(hskp4), introduced(assumption)).
% 1.21/1.38 tff(2584,plain,
% 1.21/1.38 (~c2_1(a498)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1412, 2583])).
% 1.21/1.38 tff(2585,plain,
% 1.21/1.38 (~c0_1(a498)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1391, 2583])).
% 1.21/1.38 tff(2586,plain,
% 1.21/1.38 (c1_1(a498)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1399, 2583])).
% 1.21/1.38 tff(2587,plain,
% 1.21/1.38 (~c3_1(a498)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2363, 106, 2288, 2586, 2291, 2585, 2584, 1079, 2582])).
% 1.21/1.38 tff(2588,assumption,(c2_1(a495)), introduced(assumption)).
% 1.21/1.38 tff(2589,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a528) | c1_1(a528) | c3_1(a528) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(2590,plain,
% 1.21/1.38 (((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a528) | c1_1(a528) | c0_1(a528)) <=> (c0_1(a528) | c1_1(a528) | c3_1(a528) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(2591,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a528) | c1_1(a528) | c0_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a528) | c1_1(a528) | c3_1(a528) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498)))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[2590])).
% 1.21/1.38 tff(2592,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a528) | c1_1(a528) | c0_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))),
% 1.21/1.38 inference(transitivity,[status(thm)],[2591, 2589])).
% 1.21/1.38 tff(2593,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a528) | c1_1(a528) | c0_1(a528))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(2594,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498)),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[2593, 2592])).
% 1.21/1.38 tff(2595,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2594, 106, 2527, 2525, 984, 989, 2585, 2584, 982, 709, 2588, 2587])).
% 1.21/1.38 tff(2596,plain,((~hskp4) | c0_1(a528) | c1_1(a528) | (~c1_1(a495)) | c3_1(a528) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a540)) | c0_1(a540) | (~c2_1(a540))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(2597,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2596, 2581, 2564, 2525, 2562, 989, 2561, 2553, 2551, 2550, 2527])).
% 1.21/1.38 tff(2598,plain,(hskp2 | c1_1(a528) | c3_1(a528) | c0_1(a528) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(2599,plain,
% 1.21/1.38 (hskp2),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2598, 2527, 989, 2525, 2263, 2262, 2261])).
% 1.21/1.38 tff(2600,plain,
% 1.21/1.38 (~c2_1(a496)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[335, 2599])).
% 1.21/1.38 tff(2601,plain,
% 1.21/1.38 (~c3_1(a496)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[329, 2599])).
% 1.21/1.38 tff(2602,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(2603,plain,
% 1.21/1.38 (((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528)) <=> (c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(2604,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[2603])).
% 1.21/1.38 tff(2605,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[2604, 2602])).
% 1.21/1.38 tff(2606,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(2607,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[2606, 2605])).
% 1.21/1.38 tff(2608,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2607, 106, 2527, 2525, 608, 600, 989, 592, 574, 573, 709, 575])).
% 1.21/1.38 tff(2609,plain,((~hskp6) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c2_1(a496) | c3_1(a496) | c0_1(a496)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(2610,plain,
% 1.21/1.38 (~hskp6),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2609, 575, 2525, 989, 574, 573, 2527])).
% 1.21/1.38 tff(2611,plain,
% 1.21/1.38 (~c1_1(a509)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2422, 575, 573, 2610])).
% 1.21/1.38 tff(2612,plain,
% 1.21/1.38 (hskp9),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2432, 2611])).
% 1.21/1.38 tff(2613,plain,
% 1.21/1.38 (~c1_1(a507)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[840, 2612])).
% 1.21/1.38 tff(2614,plain,
% 1.21/1.38 (~c0_1(a507)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[846, 2612])).
% 1.21/1.38 tff(2615,plain,
% 1.21/1.38 (~c0_1(a496)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2481, 2275, 2262, 2261, 574, 573, 2263])).
% 1.21/1.38 tff(2616,plain,
% 1.21/1.38 (~hskp6),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2609, 2615, 2525, 989, 574, 573, 2527])).
% 1.21/1.38 tff(2617,plain,
% 1.21/1.38 (~c1_1(a509)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2422, 2616, 573, 2615])).
% 1.21/1.38 tff(2618,plain,
% 1.21/1.38 (hskp9),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2432, 2617])).
% 1.21/1.38 tff(2619,plain,
% 1.21/1.38 (~c1_1(a507)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[840, 2618])).
% 1.21/1.38 tff(2620,plain,
% 1.21/1.38 (~c0_1(a507)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[846, 2618])).
% 1.21/1.38 tff(2621,plain,
% 1.21/1.38 (c3_1(a507)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[854, 2618])).
% 1.21/1.38 tff(2622,plain,
% 1.21/1.38 (~hskp12),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[888, 2621, 574, 573, 2615, 2616, 2620, 2619])).
% 1.21/1.38 tff(2623,plain,
% 1.21/1.38 (hskp13),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[481, 2622, 2526])).
% 1.21/1.38 tff(2624,plain,
% 1.21/1.38 (~c3_1(a520)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1362, 2623])).
% 1.21/1.38 tff(2625,plain,
% 1.21/1.38 (c2_1(a520)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1370, 2623])).
% 1.21/1.38 tff(2626,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(2627,plain,
% 1.21/1.38 (((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528)) <=> (c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(2628,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[2627])).
% 1.21/1.38 tff(2629,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[2628, 2626])).
% 1.21/1.38 tff(2630,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(2631,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[2630, 2629])).
% 1.21/1.38 tff(2632,plain,
% 1.21/1.38 (~c1_1(a520)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2631, 106, 2527, 2525, 2625, 989, 2624, 574, 573, 709, 2615])).
% 1.21/1.38 tff(2633,plain,
% 1.21/1.38 (c0_1(a520)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1378, 2623])).
% 1.21/1.38 tff(2634,plain,
% 1.21/1.38 (hskp24),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2270, 106, 2633, 2625, 2263, 2262, 2624, 2261, 1532])).
% 1.21/1.38 tff(2635,plain,
% 1.21/1.38 (~c3_1(a554)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1561, 2634])).
% 1.21/1.38 tff(2636,plain,
% 1.21/1.38 (~c2_1(a554)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1544, 2634])).
% 1.21/1.38 tff(2637,plain,
% 1.21/1.38 (c0_1(a554)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1569, 2634])).
% 1.21/1.38 tff(2638,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2281, 106, 2275, 2637, 2633, 2636, 2635, 2624, 31, 2632])).
% 1.21/1.38 tff(2639,plain,(hskp22 | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c2_1(a496) | c3_1(a496)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(2640,plain,
% 1.21/1.38 (hskp22),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2639, 573, 2262, 2261, 2527, 2525, 989, 574, 2263])).
% 1.21/1.38 tff(2641,plain,
% 1.21/1.38 (~c0_1(a540)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[125, 2640])).
% 1.21/1.38 tff(2642,plain,
% 1.21/1.38 (c1_1(a540)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[141, 2640])).
% 1.21/1.38 tff(2643,plain,
% 1.21/1.38 (c3_1(a540)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[133, 2640])).
% 1.21/1.38 tff(2644,plain,
% 1.21/1.38 (c3_1(a507)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[854, 2612])).
% 1.21/1.38 tff(2645,plain,
% 1.21/1.38 (c2_1(a540)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2303, 2644, 2643, 2642, 2641, 2614, 2613])).
% 1.21/1.38 tff(2646,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2443, 106, 2642, 2643, 2641, 574, 573, 1150, 575, 2645])).
% 1.21/1.38 tff(2647,plain,(c0_1(a496) | c2_1(a496) | c3_1(a496) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | c1_1(a528) | c3_1(a528) | c0_1(a528)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(2648,plain,
% 1.21/1.38 (c0_1(a496)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2647, 573, 574, 2263, 2262, 2261, 2525, 989, 2527])).
% 1.21/1.38 tff(2649,assumption,(~hskp27), introduced(assumption)).
% 1.21/1.38 tff(2650,assumption,(~hskp19), introduced(assumption)).
% 1.21/1.38 tff(2651,plain,
% 1.21/1.38 (^[U: $i] : refl((hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(2652,plain,
% 1.21/1.38 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[2651])).
% 1.21/1.38 tff(2653,plain,
% 1.21/1.38 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(2654,plain,
% 1.21/1.38 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19) <=> ((hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp19))), rewrite(((hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(2655,plain,
% 1.21/1.38 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[2654])).
% 1.21/1.38 tff(2656,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 1.21/1.38 tff(2657,plain,
% 1.21/1.38 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[2656, 2655])).
% 1.21/1.38 tff(2658,plain,
% 1.21/1.38 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[2657, 2653])).
% 1.21/1.38 tff(2659,plain,(
% 1.21/1.38 ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.38 inference(skolemize,[status(sab)],[2658])).
% 1.21/1.38 tff(2660,plain,
% 1.21/1.38 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[2659, 2652])).
% 1.21/1.38 tff(2661,plain,
% 1.21/1.38 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(2662,plain,
% 1.21/1.38 ((hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540))) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(2663,plain,
% 1.21/1.38 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[2662])).
% 1.21/1.38 tff(2664,plain,
% 1.21/1.38 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[2663, 2661])).
% 1.21/1.38 tff(2665,plain,
% 1.21/1.38 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(2666,plain,
% 1.21/1.38 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[2665, 2664])).
% 1.21/1.38 tff(2667,plain,
% 1.21/1.38 (hskp27 | hskp19 | (~c2_1(a540))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[2666, 106, 2288, 2293, 2660])).
% 1.21/1.39 tff(2668,plain,
% 1.21/1.39 (~c2_1(a540)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2667, 2650, 2649])).
% 1.21/1.39 tff(2669,plain,
% 1.21/1.39 (^[U: $i] : refl((hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 1.21/1.39 inference(bind,[status(th)],[])).
% 1.21/1.39 tff(2670,plain,
% 1.21/1.39 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.21/1.39 inference(quant_intro,[status(thm)],[2669])).
% 1.21/1.39 tff(2671,plain,
% 1.21/1.39 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2672,plain,
% 1.21/1.39 (^[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) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19) <=> ((hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp19))), rewrite(((hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 1.21/1.39 inference(bind,[status(th)],[])).
% 1.21/1.39 tff(2673,plain,
% 1.21/1.39 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.21/1.39 inference(quant_intro,[status(thm)],[2672])).
% 1.21/1.39 tff(2674,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.21/1.39 tff(2675,plain,
% 1.21/1.39 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2674, 2673])).
% 1.21/1.39 tff(2676,plain,
% 1.21/1.39 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2675, 2671])).
% 1.21/1.39 tff(2677,plain,(
% 1.21/1.39 ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.21/1.39 inference(skolemize,[status(sab)],[2676])).
% 1.21/1.39 tff(2678,plain,
% 1.21/1.39 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2677, 2670])).
% 1.21/1.39 tff(2679,plain,
% 1.21/1.39 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp18 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp18 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2680,plain,
% 1.21/1.39 ((hskp19 | hskp18 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c1_1(a496)) <=> (hskp19 | hskp18 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2681,plain,
% 1.21/1.39 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c1_1(a496))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp18 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[2680])).
% 1.21/1.39 tff(2682,plain,
% 1.21/1.39 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c1_1(a496))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp18 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0))),
% 1.21/1.39 inference(transitivity,[status(thm)],[2681, 2679])).
% 1.21/1.39 tff(2683,plain,
% 1.21/1.39 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c1_1(a496))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(2684,plain,
% 1.21/1.39 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp18 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2683, 2682])).
% 1.21/1.39 tff(2685,plain,
% 1.21/1.39 (hskp19 | hskp18 | c1_1(a496) | c3_1(a496)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2684, 106, 574, 2678])).
% 1.21/1.39 tff(2686,plain,
% 1.21/1.39 (hskp18),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2685, 2650, 572, 573])).
% 1.21/1.39 tff(2687,plain,
% 1.21/1.39 (((~hskp18) | (~c0_1(a533))) <=> ((~hskp18) | (~c0_1(a533)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2688,plain,
% 1.21/1.39 (((~c0_1(a533)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a533)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2689,axiom,((~c0_1(a533)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.21/1.39 tff(2690,plain,
% 1.21/1.39 ((~hskp18) | (~c0_1(a533))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2689, 2688])).
% 1.21/1.39 tff(2691,plain,
% 1.21/1.39 ((~hskp18) | (~c0_1(a533))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2690, 2687])).
% 1.21/1.39 tff(2692,plain,
% 1.21/1.39 (~c0_1(a533)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2691, 2686])).
% 1.21/1.39 tff(2693,plain,
% 1.21/1.39 (((~hskp18) | c2_1(a533)) <=> ((~hskp18) | c2_1(a533))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2694,axiom,((~hskp18) | c2_1(a533)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 1.21/1.39 tff(2695,plain,
% 1.21/1.39 ((~hskp18) | c2_1(a533)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2694, 2693])).
% 1.21/1.39 tff(2696,plain,
% 1.21/1.39 ((~hskp18) | c2_1(a533)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2695, 2693])).
% 1.21/1.39 tff(2697,plain,
% 1.21/1.39 ((~hskp18) | c2_1(a533)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2696, 2693])).
% 1.21/1.39 tff(2698,plain,
% 1.21/1.39 ((~hskp18) | c2_1(a533)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2697, 2693])).
% 1.21/1.39 tff(2699,plain,
% 1.21/1.39 ((~hskp18) | c2_1(a533)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2698, 2693])).
% 1.21/1.39 tff(2700,plain,
% 1.21/1.39 (c2_1(a533)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2699, 2686])).
% 1.21/1.39 tff(2701,plain,
% 1.21/1.39 (((~hskp18) | c1_1(a533)) <=> ((~hskp18) | c1_1(a533))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2702,axiom,((~hskp18) | c1_1(a533)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.21/1.39 tff(2703,plain,
% 1.21/1.39 ((~hskp18) | c1_1(a533)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2702, 2701])).
% 1.21/1.39 tff(2704,plain,
% 1.21/1.39 ((~hskp18) | c1_1(a533)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2703, 2701])).
% 1.21/1.39 tff(2705,plain,
% 1.21/1.39 ((~hskp18) | c1_1(a533)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2704, 2701])).
% 1.21/1.39 tff(2706,plain,
% 1.21/1.39 ((~hskp18) | c1_1(a533)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2705, 2701])).
% 1.21/1.39 tff(2707,plain,
% 1.21/1.39 ((~hskp18) | c1_1(a533)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2706, 2701])).
% 1.21/1.39 tff(2708,plain,
% 1.21/1.39 (c1_1(a533)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2707, 2686])).
% 1.21/1.39 tff(2709,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a540) | c0_1(a533) | (~ndr1_0) | (~c1_1(a533)) | (~c2_1(a533)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c0_1(a533) | (~ndr1_0) | (~c1_1(a533)) | (~c2_1(a533)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2710,plain,
% 1.21/1.39 (((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a533) | (~c1_1(a533)) | (~c2_1(a533)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540))) <=> (c0_1(a540) | c0_1(a533) | (~ndr1_0) | (~c1_1(a533)) | (~c2_1(a533)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2711,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a533) | (~c1_1(a533)) | (~c2_1(a533)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a540) | c0_1(a533) | (~ndr1_0) | (~c1_1(a533)) | (~c2_1(a533)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[2710])).
% 1.21/1.39 tff(2712,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a533) | (~c1_1(a533)) | (~c2_1(a533)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c0_1(a533) | (~ndr1_0) | (~c1_1(a533)) | (~c2_1(a533)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))),
% 1.21/1.39 inference(transitivity,[status(thm)],[2711, 2709])).
% 1.21/1.39 tff(2713,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a533) | (~c1_1(a533)) | (~c2_1(a533)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(2714,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c0_1(a533) | (~ndr1_0) | (~c1_1(a533)) | (~c2_1(a533)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2713, 2712])).
% 1.21/1.39 tff(2715,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2714, 106, 2288, 2293, 2708, 2700, 2291, 2692, 1079, 2668])).
% 1.21/1.39 tff(2716,plain,(hskp19 | (~c1_1(a540)) | (~c3_1(a540)) | c0_1(a540) | hskp27 | c1_1(a496) | c3_1(a496) | c2_1(a496)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(2717,plain,
% 1.21/1.39 (hskp19),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2716, 572, 2643, 2641, 2649, 2642, 573, 574])).
% 1.21/1.39 tff(2718,plain,
% 1.21/1.39 (((~hskp19) | (~c2_1(a534))) <=> ((~hskp19) | (~c2_1(a534)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2719,plain,
% 1.21/1.39 (((~c2_1(a534)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a534)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2720,axiom,((~c2_1(a534)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.21/1.39 tff(2721,plain,
% 1.21/1.39 ((~hskp19) | (~c2_1(a534))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2720, 2719])).
% 1.21/1.39 tff(2722,plain,
% 1.21/1.39 ((~hskp19) | (~c2_1(a534))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2721, 2718])).
% 1.21/1.39 tff(2723,plain,
% 1.21/1.39 (~c2_1(a534)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2722, 2717])).
% 1.21/1.39 tff(2724,plain,
% 1.21/1.39 (((~hskp19) | (~c3_1(a534))) <=> ((~hskp19) | (~c3_1(a534)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2725,plain,
% 1.21/1.39 (((~c3_1(a534)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a534)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2726,axiom,((~c3_1(a534)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.21/1.39 tff(2727,plain,
% 1.21/1.39 ((~hskp19) | (~c3_1(a534))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2726, 2725])).
% 1.21/1.39 tff(2728,plain,
% 1.21/1.39 ((~hskp19) | (~c3_1(a534))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2727, 2724])).
% 1.21/1.39 tff(2729,plain,
% 1.21/1.39 (~c3_1(a534)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2728, 2717])).
% 1.21/1.39 tff(2730,plain,
% 1.21/1.39 (((~hskp19) | c1_1(a534)) <=> ((~hskp19) | c1_1(a534))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2731,axiom,((~hskp19) | c1_1(a534)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.21/1.39 tff(2732,plain,
% 1.21/1.39 ((~hskp19) | c1_1(a534)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2731, 2730])).
% 1.21/1.39 tff(2733,plain,
% 1.21/1.39 ((~hskp19) | c1_1(a534)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2732, 2730])).
% 1.21/1.39 tff(2734,plain,
% 1.21/1.39 ((~hskp19) | c1_1(a534)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2733, 2730])).
% 1.21/1.39 tff(2735,plain,
% 1.21/1.39 ((~hskp19) | c1_1(a534)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2734, 2730])).
% 1.21/1.39 tff(2736,plain,
% 1.21/1.39 ((~hskp19) | c1_1(a534)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2735, 2730])).
% 1.21/1.39 tff(2737,plain,
% 1.21/1.39 (c1_1(a534)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2736, 2717])).
% 1.21/1.39 tff(2738,assumption,(~c3_1(a534)), introduced(assumption)).
% 1.21/1.39 tff(2739,assumption,(~c2_1(a534)), introduced(assumption)).
% 1.21/1.39 tff(2740,assumption,(c1_1(a534)), introduced(assumption)).
% 1.21/1.39 tff(2741,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a534) | c3_1(a534) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a534)) | (~c0_1(a534)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a534) | c3_1(a534) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a534)) | (~c0_1(a534)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2742,plain,
% 1.21/1.39 (((~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c2_1(a534) | c3_1(a534) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a534)) | (~c0_1(a534)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2743,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a534) | c3_1(a534) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a534)) | (~c0_1(a534))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[2742])).
% 1.21/1.39 tff(2744,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a534) | c3_1(a534) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a534)) | (~c0_1(a534)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[2743, 2741])).
% 1.21/1.39 tff(2745,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(2746,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a534) | c3_1(a534) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a534)) | (~c0_1(a534))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2745, 2744])).
% 1.21/1.39 tff(2747,plain,
% 1.21/1.39 (c0_1(a496) | (~c0_1(a534))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2746, 106, 2740, 2739, 2738, 574, 573, 909])).
% 1.21/1.39 tff(2748,plain,
% 1.21/1.39 (~c0_1(a534)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2747, 575])).
% 1.21/1.39 tff(2749,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c2_1(a534) | c3_1(a534) | (~ndr1_0) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c2_1(a534) | c3_1(a534) | (~ndr1_0) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2750,plain,
% 1.21/1.39 (((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a534) | c0_1(a534) | c2_1(a534)) <=> (c0_1(a540) | c2_1(a534) | c3_1(a534) | (~ndr1_0) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2751,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a534) | c0_1(a534) | c2_1(a534))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c2_1(a534) | c3_1(a534) | (~ndr1_0) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[2750])).
% 1.21/1.39 tff(2752,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a534) | c0_1(a534) | c2_1(a534))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c2_1(a534) | c3_1(a534) | (~ndr1_0) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[2751, 2749])).
% 1.21/1.39 tff(2753,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a534) | c0_1(a534) | c2_1(a534))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(2754,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c2_1(a534) | c3_1(a534) | (~ndr1_0) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2753, 2752])).
% 1.21/1.39 tff(2755,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2754, 106, 2642, 2643, 2641, 2739, 2738, 1150, 2645, 2748])).
% 1.21/1.39 tff(2756,plain,(c0_1(a496) | c2_1(a534) | c3_1(a534) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | (~c1_1(a534)) | c2_1(a496) | c3_1(a496) | c1_1(a528) | c3_1(a528) | c0_1(a528)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(2757,plain,
% 1.21/1.39 (c0_1(a496)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2756, 2723, 2729, 2263, 2262, 2261, 2737, 574, 573, 2525, 989, 2527])).
% 1.21/1.39 tff(2758,assumption,(~hskp9), introduced(assumption)).
% 1.21/1.39 tff(2759,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | c0_1(a534))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | c0_1(a534))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2760,plain,
% 1.21/1.39 ((hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a534) | c0_1(a534) | (~c1_1(a534))) <=> (hskp9 | c2_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | c0_1(a534))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2761,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a534) | c0_1(a534) | (~c1_1(a534)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | c0_1(a534)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[2760])).
% 1.21/1.39 tff(2762,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a534) | c0_1(a534) | (~c1_1(a534)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | c0_1(a534))),
% 1.21/1.39 inference(transitivity,[status(thm)],[2761, 2759])).
% 1.21/1.39 tff(2763,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a534) | c0_1(a534) | (~c1_1(a534)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(2764,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | c0_1(a534)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2763, 2762])).
% 1.21/1.39 tff(2765,plain,
% 1.21/1.39 (hskp9 | (~c0_1(a496)) | c0_1(a534)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2764, 106, 2740, 2739, 572, 574, 2456])).
% 1.21/1.39 tff(2766,plain,
% 1.21/1.39 (c0_1(a534)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2765, 2758, 2468])).
% 1.21/1.39 tff(2767,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | (~c0_1(a534)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | (~c0_1(a534)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2768,plain,
% 1.21/1.39 ((hskp9 | (~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496))) <=> (hskp9 | c3_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | (~c0_1(a534)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2769,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | (~c0_1(a534))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[2768])).
% 1.21/1.39 tff(2770,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | (~c0_1(a534)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[2769, 2767])).
% 1.21/1.39 tff(2771,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(2772,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | (~c0_1(a534))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2771, 2770])).
% 1.21/1.39 tff(2773,plain,
% 1.21/1.39 (hskp9 | (~c0_1(a496)) | (~c0_1(a534))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2772, 106, 2740, 2738, 572, 574, 1186])).
% 1.21/1.39 tff(2774,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2773, 2766, 2758, 2468])).
% 1.21/1.39 tff(2775,plain,(hskp9 | (~c0_1(a496)) | (~c1_1(a534)) | c3_1(a534) | c1_1(a496) | c2_1(a496) | c2_1(a534)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(2776,plain,
% 1.21/1.39 (hskp9),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2775, 2757, 2737, 2729, 572, 574, 2723])).
% 1.21/1.39 tff(2777,plain,
% 1.21/1.39 (~c1_1(a507)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[840, 2776])).
% 1.21/1.39 tff(2778,plain,
% 1.21/1.39 (~c0_1(a507)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[846, 2776])).
% 1.21/1.39 tff(2779,plain,
% 1.21/1.39 (c3_1(a507)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[854, 2776])).
% 1.21/1.39 tff(2780,plain,
% 1.21/1.39 (c2_1(a540)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2303, 2779, 2643, 2642, 2641, 2778, 2777])).
% 1.21/1.39 tff(2781,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a540) | c2_1(a534) | (~ndr1_0) | (~c1_1(a534)) | (~c0_1(a534)) | (~c3_1(a540)) | (~c2_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a534) | (~ndr1_0) | (~c1_1(a534)) | (~c0_1(a534)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2782,plain,
% 1.21/1.39 ((hskp15 | (~ndr1_0) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540))) <=> (hskp15 | c0_1(a540) | c2_1(a534) | (~ndr1_0) | (~c1_1(a534)) | (~c0_1(a534)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2783,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a540) | c2_1(a534) | (~ndr1_0) | (~c1_1(a534)) | (~c0_1(a534)) | (~c3_1(a540)) | (~c2_1(a540))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[2782])).
% 1.21/1.39 tff(2784,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a534) | (~ndr1_0) | (~c1_1(a534)) | (~c0_1(a534)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[2783, 2781])).
% 1.21/1.39 tff(2785,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(2786,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a534) | (~ndr1_0) | (~c1_1(a534)) | (~c0_1(a534)) | (~c3_1(a540)) | (~c2_1(a540))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2785, 2784])).
% 1.21/1.39 tff(2787,plain,
% 1.21/1.39 ((~c0_1(a534)) | (~c2_1(a540))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2786, 106, 2526, 2643, 2737, 2641, 2723, 2314])).
% 1.21/1.39 tff(2788,plain,
% 1.21/1.39 (~c0_1(a534)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2787, 2780])).
% 1.21/1.39 tff(2789,plain,
% 1.21/1.39 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2790,plain,
% 1.21/1.40 ((hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a528) | c0_1(a528) | c3_1(a528)) <=> (hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2791,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a528) | c0_1(a528) | c3_1(a528))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2790])).
% 1.21/1.40 tff(2792,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a528) | c0_1(a528) | c3_1(a528))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2791, 2789])).
% 1.21/1.40 tff(2793,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a528) | c0_1(a528) | c3_1(a528))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2794,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2793, 2792])).
% 1.21/1.40 tff(2795,plain,
% 1.21/1.40 (hskp1 | c1_1(a496) | (~c0_1(a496))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2794, 106, 2527, 2525, 989, 573, 585])).
% 1.21/1.40 tff(2796,plain,
% 1.21/1.40 (hskp1),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2795, 2757, 572])).
% 1.21/1.40 tff(2797,plain,
% 1.21/1.40 (~c0_1(a495)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[938, 2796])).
% 1.21/1.40 tff(2798,plain,
% 1.21/1.40 (c1_1(a495)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[947, 2796])).
% 1.21/1.40 tff(2799,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a534) | c3_1(a534) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a534) | c3_1(a534) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2800,plain,
% 1.21/1.40 (((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a534) | c0_1(a534) | c2_1(a534)) <=> (c2_1(a534) | c3_1(a534) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2801,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a534) | c0_1(a534) | c2_1(a534))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a534) | c3_1(a534) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2800])).
% 1.21/1.40 tff(2802,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a534) | c0_1(a534) | c2_1(a534))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a534) | c3_1(a534) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2801, 2799])).
% 1.21/1.40 tff(2803,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a534) | c0_1(a534) | c2_1(a534))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2804,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a534) | c3_1(a534) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2803, 2802])).
% 1.21/1.40 tff(2805,plain,
% 1.21/1.40 (~c2_1(a495)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2804, 106, 2642, 2643, 2798, 2723, 2729, 2797, 1150, 2780, 2788])).
% 1.21/1.40 tff(2806,plain,
% 1.21/1.40 (~c3_1(a495)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[932, 2796])).
% 1.21/1.40 tff(2807,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2391, 106, 2642, 2643, 2641, 2797, 2806, 1150, 2780, 2805])).
% 1.21/1.40 tff(2808,plain,(c1_1(a496) | c2_1(a496) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a496) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(2809,plain,
% 1.21/1.40 (c1_1(a496)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2808, 2649, 2527, 2525, 989, 573, 2263, 2262, 2261, 574])).
% 1.21/1.40 tff(2810,plain,
% 1.21/1.40 (~hskp2),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[348, 2809])).
% 1.21/1.40 tff(2811,plain,
% 1.21/1.40 (~c1_1(a509)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2424, 2810])).
% 1.21/1.40 tff(2812,plain,
% 1.21/1.40 (hskp9),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2432, 2811])).
% 1.21/1.40 tff(2813,plain,
% 1.21/1.40 (~c1_1(a507)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[840, 2812])).
% 1.21/1.40 tff(2814,plain,
% 1.21/1.40 (~c0_1(a507)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[846, 2812])).
% 1.21/1.40 tff(2815,plain,
% 1.21/1.40 (c3_1(a507)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[854, 2812])).
% 1.21/1.40 tff(2816,plain,
% 1.21/1.40 (c2_1(a540)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2303, 2815, 2643, 2642, 2641, 2814, 2813])).
% 1.21/1.40 tff(2817,plain,
% 1.21/1.40 (hskp27 | hskp19 | (~c2_1(a540))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2666, 106, 2642, 2643, 2660])).
% 1.21/1.40 tff(2818,plain,
% 1.21/1.40 (hskp19),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2817, 2816, 2649])).
% 1.21/1.40 tff(2819,plain,
% 1.21/1.40 (c1_1(a534)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2736, 2818])).
% 1.21/1.40 tff(2820,plain,
% 1.21/1.40 (~c0_1(a496)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2479, 2810, 2809])).
% 1.21/1.40 tff(2821,plain,
% 1.21/1.40 (~c2_1(a534)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2722, 2818])).
% 1.21/1.40 tff(2822,plain,
% 1.21/1.40 (~c3_1(a534)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2728, 2818])).
% 1.21/1.40 tff(2823,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2756, 2822, 2821, 2820, 2263, 2262, 2261, 2819, 574, 573, 2525, 989, 2527])).
% 1.21/1.40 tff(2824,plain,(hskp27 | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | c2_1(a496) | c3_1(a496) | c1_1(a528) | c3_1(a528) | c0_1(a528)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(2825,plain,
% 1.21/1.40 (hskp27),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2824, 573, 2262, 2261, 574, 2263, 2525, 989, 2527])).
% 1.21/1.40 tff(2826,plain,
% 1.21/1.40 (~c1_1(a568)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[227, 2825])).
% 1.21/1.40 tff(2827,plain,
% 1.21/1.40 (c3_1(a568)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[189, 2825])).
% 1.21/1.40 tff(2828,plain,
% 1.21/1.40 (c0_1(a568)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[197, 2825])).
% 1.21/1.40 tff(2829,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c0_1(a540) | (~c1_1(a496)) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c0_1(a540) | (~c1_1(a496)) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2830,plain,
% 1.21/1.40 (((~ndr1_0) | c3_1(a496) | (~c1_1(a496)) | (~c0_1(a496)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540))) <=> (c1_1(a568) | c0_1(a540) | (~c1_1(a496)) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2831,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a496) | (~c1_1(a496)) | (~c0_1(a496)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c0_1(a540) | (~c1_1(a496)) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2830])).
% 1.21/1.40 tff(2832,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a496) | (~c1_1(a496)) | (~c0_1(a496)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c0_1(a540) | (~c1_1(a496)) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2831, 2829])).
% 1.21/1.40 tff(2833,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a496) | (~c1_1(a496)) | (~c0_1(a496)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2834,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c0_1(a540) | (~c1_1(a496)) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2833, 2832])).
% 1.21/1.40 tff(2835,plain,
% 1.21/1.40 ((~c1_1(a496)) | (~c0_1(a496))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2834, 106, 2828, 2827, 2642, 2643, 2826, 2641, 573, 1302])).
% 1.21/1.40 tff(2836,plain,
% 1.21/1.40 (~c1_1(a496)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2835, 2648])).
% 1.21/1.40 tff(2837,plain,
% 1.21/1.40 (hskp1),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2795, 2836, 2648])).
% 1.21/1.40 tff(2838,plain,
% 1.21/1.40 (~c3_1(a495)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[932, 2837])).
% 1.21/1.40 tff(2839,plain,
% 1.21/1.40 (~c0_1(a495)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[938, 2837])).
% 1.21/1.40 tff(2840,plain,
% 1.21/1.40 (c1_1(a495)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[947, 2837])).
% 1.21/1.40 tff(2841,plain,
% 1.21/1.40 (hskp8),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[965, 106, 2828, 2827, 2840, 2826, 2839, 2838, 959])).
% 1.21/1.40 tff(2842,plain,
% 1.21/1.40 (~c0_1(a505)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[979, 2841])).
% 1.21/1.40 tff(2843,plain,
% 1.21/1.40 (c3_1(a505)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1065, 2841])).
% 1.21/1.40 tff(2844,plain,
% 1.21/1.40 (c2_1(a505)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[973, 2841])).
% 1.21/1.40 tff(2845,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c1_1(a509)) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c1_1(a509)) | (~c0_1(a509)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2846,plain,
% 1.21/1.40 ((hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505))) <=> (hskp15 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c1_1(a509)) | (~c0_1(a509)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2847,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c1_1(a509)) | (~c0_1(a509))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2846])).
% 1.21/1.40 tff(2848,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c1_1(a509)) | (~c0_1(a509)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2847, 2845])).
% 1.21/1.40 tff(2849,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2850,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c1_1(a509)) | (~c0_1(a509))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2849, 2848])).
% 1.21/1.40 tff(2851,plain,
% 1.21/1.40 (~c1_1(a509)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2850, 106, 2526, 2263, 2844, 2843, 2261, 2842, 2314])).
% 1.21/1.40 tff(2852,plain,
% 1.21/1.40 (hskp9),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2432, 2851])).
% 1.21/1.40 tff(2853,plain,
% 1.21/1.40 (~c1_1(a507)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[840, 2852])).
% 1.21/1.40 tff(2854,plain,
% 1.21/1.40 (~c0_1(a507)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[846, 2852])).
% 1.21/1.40 tff(2855,plain,
% 1.21/1.40 (c3_1(a507)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[854, 2852])).
% 1.21/1.40 tff(2856,plain,
% 1.21/1.40 (c2_1(a540)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2303, 2855, 2643, 2642, 2641, 2854, 2853])).
% 1.21/1.40 tff(2857,plain,
% 1.21/1.40 (c2_1(a528)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2570, 106, 2642, 2643, 2527, 2641, 989, 1150, 2856])).
% 1.21/1.40 tff(2858,plain,
% 1.21/1.40 (c2_1(a495)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2391, 106, 2642, 2643, 2641, 2839, 2838, 1150, 2856])).
% 1.21/1.40 tff(2859,plain,
% 1.21/1.40 (~hskp4),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2596, 2840, 2525, 2527, 989, 2838, 2858, 2642, 2641, 2856])).
% 1.21/1.40 tff(2860,plain,
% 1.21/1.40 (~hskp13),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2580, 2859, 2527, 2525, 2857])).
% 1.21/1.40 tff(2861,plain,
% 1.21/1.40 (hskp12),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[481, 2860, 2526])).
% 1.21/1.40 tff(2862,plain,
% 1.21/1.40 (c1_1(a514)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[503, 2861])).
% 1.21/1.40 tff(2863,plain,
% 1.21/1.40 (~c2_1(a514)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[487, 2861])).
% 1.21/1.40 tff(2864,plain,
% 1.21/1.40 (c3_1(a514)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[495, 2861])).
% 1.21/1.40 tff(2865,plain,
% 1.21/1.40 (c0_1(a514)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1107, 2864, 2844, 2843, 2840, 2863, 2842, 2839, 2862])).
% 1.21/1.40 tff(2866,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2405, 106, 2526, 2643, 2862, 2641, 2863, 2314, 2865, 2856])).
% 1.21/1.40 tff(2867,plain,(c3_1(a496) | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | c2_1(a496)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(2868,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2867, 2601, 2600, 2525, 989, 2263, 2262, 2261, 2527])).
% 1.21/1.40 tff(2869,plain,(c0_1(a528) | c1_1(a528) | c3_1(a528) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(2870,plain,
% 1.21/1.40 (c0_1(a528)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2869, 2525, 989, 2263, 2262, 2261])).
% 1.21/1.40 tff(2871,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | c2_1(a528))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | c2_1(a528))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2872,plain,
% 1.21/1.40 ((hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528))) <=> (hskp22 | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | c2_1(a528))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2873,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | c2_1(a528)))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2872])).
% 1.21/1.40 tff(2874,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | c2_1(a528))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2873, 2871])).
% 1.21/1.40 tff(2875,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2876,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | c2_1(a528)),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2875, 2874])).
% 1.21/1.40 tff(2877,plain,
% 1.21/1.40 (hskp22 | (~c0_1(a528)) | c2_1(a528)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2876, 106, 2525, 989, 31])).
% 1.21/1.40 tff(2878,plain,
% 1.21/1.40 (c2_1(a528)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2877, 2275, 2870])).
% 1.21/1.40 tff(2879,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a528)) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a528)) | (~c2_1(a528)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2880,plain,
% 1.21/1.40 ((hskp24 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509))) <=> (hskp24 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a528)) | (~c2_1(a528)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2881,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a528)) | (~c2_1(a528))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2880])).
% 1.21/1.40 tff(2882,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a528)) | (~c2_1(a528)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2881, 2879])).
% 1.21/1.40 tff(2883,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2884,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a528)) | (~c2_1(a528))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2883, 2882])).
% 1.21/1.40 tff(2885,plain,
% 1.21/1.40 (hskp24 | (~c0_1(a528)) | (~c2_1(a528))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2884, 106, 2263, 2262, 989, 2261, 1532])).
% 1.21/1.40 tff(2886,plain,
% 1.21/1.40 (hskp24),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2885, 2878, 2870])).
% 1.21/1.40 tff(2887,plain,
% 1.21/1.40 (~c3_1(a554)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1561, 2886])).
% 1.21/1.40 tff(2888,plain,
% 1.21/1.40 (~c2_1(a554)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1544, 2886])).
% 1.21/1.40 tff(2889,plain,
% 1.21/1.40 (c0_1(a554)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1569, 2886])).
% 1.21/1.40 tff(2890,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a528) | c2_1(a554) | c3_1(a554) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | (~c0_1(a554)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a528) | c2_1(a554) | c3_1(a554) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | (~c0_1(a554)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2891,plain,
% 1.21/1.40 ((hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528))) <=> (hskp22 | c1_1(a528) | c2_1(a554) | c3_1(a554) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | (~c0_1(a554)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2892,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a528) | c2_1(a554) | c3_1(a554) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | (~c0_1(a554))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2891])).
% 1.21/1.40 tff(2893,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a528) | c2_1(a554) | c3_1(a554) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | (~c0_1(a554)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2892, 2890])).
% 1.21/1.40 tff(2894,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2895,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a528) | c2_1(a554) | c3_1(a554) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | (~c0_1(a554))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2894, 2893])).
% 1.21/1.40 tff(2896,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2895, 106, 2275, 2889, 2870, 2525, 2888, 2887, 989, 31])).
% 1.21/1.40 tff(2897,plain,(hskp22 | c1_1(a528) | c3_1(a528) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(2898,plain,
% 1.21/1.40 (hskp22),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2897, 2525, 989, 2514, 2512, 2513])).
% 1.21/1.40 tff(2899,plain,
% 1.21/1.40 (c3_1(a540)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[133, 2898])).
% 1.21/1.40 tff(2900,plain,
% 1.21/1.40 (~c0_1(a540)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[125, 2898])).
% 1.21/1.40 tff(2901,plain,
% 1.21/1.40 (c1_1(a540)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[141, 2898])).
% 1.21/1.40 tff(2902,plain,
% 1.21/1.40 (~hskp9),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2407, 2526, 2899, 2900, 2514, 2512, 2901, 2513])).
% 1.21/1.40 tff(2903,plain,
% 1.21/1.40 (hskp9 | c1_1(a509)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2231, 106, 2514, 2512, 2513, 2225])).
% 1.21/1.40 tff(2904,plain,
% 1.21/1.40 (c1_1(a509)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2903, 2902])).
% 1.21/1.40 tff(2905,plain,
% 1.21/1.40 (hskp2 | (~c1_1(a509))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2213, 106, 2514, 2512, 2513, 541])).
% 1.21/1.40 tff(2906,plain,
% 1.21/1.40 (hskp2),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2905, 2904])).
% 1.21/1.40 tff(2907,plain,
% 1.21/1.40 (~c2_1(a496)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[335, 2906])).
% 1.21/1.40 tff(2908,plain,
% 1.21/1.40 (~c3_1(a496)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[329, 2906])).
% 1.21/1.40 tff(2909,plain,
% 1.21/1.40 (c1_1(a509)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2903, 2758])).
% 1.21/1.40 tff(2910,plain,
% 1.21/1.40 ((~c1_1(a509)) | (~c2_1(a540))),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2320, 106, 43, 2293, 2514, 2291, 2513, 2314])).
% 1.21/1.40 tff(2911,plain,
% 1.21/1.40 (~c2_1(a540)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2910, 2909])).
% 1.21/1.40 tff(2912,plain,
% 1.21/1.40 (^[U: $i] : refl((hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.21/1.40 inference(bind,[status(th)],[])).
% 1.21/1.40 tff(2913,plain,
% 1.21/1.40 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.40 inference(quant_intro,[status(thm)],[2912])).
% 1.21/1.40 tff(2914,plain,
% 1.21/1.40 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2915,plain,
% 1.21/1.40 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp26) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp26))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp26) <=> (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp26) <=> (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.21/1.41 inference(bind,[status(th)],[])).
% 1.21/1.41 tff(2916,plain,
% 1.21/1.41 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp26) <=> ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.41 inference(quant_intro,[status(thm)],[2915])).
% 1.21/1.41 tff(2917,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 1.21/1.41 tff(2918,plain,
% 1.21/1.41 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2917, 2916])).
% 1.21/1.41 tff(2919,plain,
% 1.21/1.41 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2918, 2914])).
% 1.21/1.41 tff(2920,plain,(
% 1.21/1.41 ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.41 inference(skolemize,[status(sab)],[2919])).
% 1.21/1.41 tff(2921,plain,
% 1.21/1.41 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2920, 2913])).
% 1.21/1.41 tff(2922,plain,
% 1.21/1.41 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp26 | hskp25 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp26 | hskp25 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2923,plain,
% 1.21/1.41 ((hskp26 | hskp25 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509))) <=> (hskp26 | hskp25 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2924,plain,
% 1.21/1.41 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp26 | hskp25 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp26 | hskp25 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[2923])).
% 1.21/1.41 tff(2925,plain,
% 1.21/1.41 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp26 | hskp25 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp26 | hskp25 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[2924, 2922])).
% 1.21/1.41 tff(2926,plain,
% 1.21/1.41 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp26 | hskp25 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(2927,plain,
% 1.21/1.41 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp26 | hskp25 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2926, 2925])).
% 1.21/1.41 tff(2928,plain,
% 1.21/1.41 (hskp25 | (~c1_1(a509))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2927, 106, 32, 2512, 2513, 2921])).
% 1.21/1.41 tff(2929,plain,
% 1.21/1.41 (hskp25),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2928, 2909])).
% 1.21/1.41 tff(2930,plain,
% 1.21/1.41 (((~hskp25) | (~c0_1(a558))) <=> ((~hskp25) | (~c0_1(a558)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2931,plain,
% 1.21/1.41 (((~c0_1(a558)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a558)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2932,axiom,((~c0_1(a558)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.21/1.41 tff(2933,plain,
% 1.21/1.41 ((~hskp25) | (~c0_1(a558))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2932, 2931])).
% 1.21/1.41 tff(2934,plain,
% 1.21/1.41 ((~hskp25) | (~c0_1(a558))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2933, 2930])).
% 1.21/1.41 tff(2935,plain,
% 1.21/1.41 (~c0_1(a558)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2934, 2929])).
% 1.21/1.41 tff(2936,plain,
% 1.21/1.41 (((~hskp25) | c2_1(a558)) <=> ((~hskp25) | c2_1(a558))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2937,axiom,((~hskp25) | c2_1(a558)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.21/1.41 tff(2938,plain,
% 1.21/1.41 ((~hskp25) | c2_1(a558)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2937, 2936])).
% 1.21/1.41 tff(2939,plain,
% 1.21/1.41 ((~hskp25) | c2_1(a558)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2938, 2936])).
% 1.21/1.41 tff(2940,plain,
% 1.21/1.41 ((~hskp25) | c2_1(a558)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2939, 2936])).
% 1.21/1.41 tff(2941,plain,
% 1.21/1.41 ((~hskp25) | c2_1(a558)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2940, 2936])).
% 1.21/1.41 tff(2942,plain,
% 1.21/1.41 ((~hskp25) | c2_1(a558)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2941, 2936])).
% 1.21/1.41 tff(2943,plain,
% 1.21/1.41 (c2_1(a558)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2942, 2929])).
% 1.21/1.41 tff(2944,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a558) | c0_1(a540) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | (~c1_1(a558)) | (~c2_1(a558)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a558) | c0_1(a540) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | (~c1_1(a558)) | (~c2_1(a558)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2945,plain,
% 1.21/1.41 (((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a558) | (~c1_1(a558)) | (~c2_1(a558)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540))) <=> (c0_1(a558) | c0_1(a540) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | (~c1_1(a558)) | (~c2_1(a558)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2946,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a558) | (~c1_1(a558)) | (~c2_1(a558)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a558) | c0_1(a540) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | (~c1_1(a558)) | (~c2_1(a558))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[2945])).
% 1.21/1.41 tff(2947,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a558) | (~c1_1(a558)) | (~c2_1(a558)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a558) | c0_1(a540) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | (~c1_1(a558)) | (~c2_1(a558)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[2946, 2944])).
% 1.21/1.41 tff(2948,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a558) | (~c1_1(a558)) | (~c2_1(a558)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(2949,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a558) | c0_1(a540) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | (~c1_1(a558)) | (~c2_1(a558))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2948, 2947])).
% 1.21/1.41 tff(2950,plain,
% 1.21/1.41 (~c1_1(a558)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2949, 106, 2943, 2288, 2293, 2935, 2291, 1079, 2911])).
% 1.21/1.41 tff(2951,plain,
% 1.21/1.41 (hskp2),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2905, 2909])).
% 1.21/1.41 tff(2952,plain,
% 1.21/1.41 (~c1_1(a496)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[348, 2951])).
% 1.21/1.41 tff(2953,plain,
% 1.21/1.41 (~c0_1(a496)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2464, 106, 2758, 2288, 2291, 2952, 574, 2456, 2911])).
% 1.21/1.41 tff(2954,plain,
% 1.21/1.41 (hskp6 | c3_1(a496) | c0_1(a496) | (~c1_1(a509))),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2421, 106, 2514, 2513, 574, 879])).
% 1.21/1.41 tff(2955,plain,
% 1.21/1.41 (hskp6),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2954, 2953, 573, 2909])).
% 1.21/1.41 tff(2956,plain,
% 1.21/1.41 (~c3_1(a501)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[591, 2955])).
% 1.21/1.41 tff(2957,plain,
% 1.21/1.41 (((~hskp25) | (~c3_1(a558))) <=> ((~hskp25) | (~c3_1(a558)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2958,plain,
% 1.21/1.41 (((~c3_1(a558)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a558)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2959,axiom,((~c3_1(a558)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 1.21/1.41 tff(2960,plain,
% 1.21/1.41 ((~hskp25) | (~c3_1(a558))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2959, 2958])).
% 1.21/1.41 tff(2961,plain,
% 1.21/1.41 ((~hskp25) | (~c3_1(a558))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2960, 2957])).
% 1.21/1.41 tff(2962,plain,
% 1.21/1.41 (~c3_1(a558)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2961, 2929])).
% 1.21/1.41 tff(2963,plain,
% 1.21/1.41 (c2_1(a501)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[599, 2955])).
% 1.21/1.41 tff(2964,plain,
% 1.21/1.41 (c1_1(a501)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[607, 2955])).
% 1.21/1.41 tff(2965,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a558) | c3_1(a558) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c1_1(a558))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a558) | c3_1(a558) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c1_1(a558))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2966,plain,
% 1.21/1.41 (((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a558) | c1_1(a558) | c0_1(a558)) <=> (c0_1(a558) | c3_1(a558) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c1_1(a558))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2967,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a558) | c1_1(a558) | c0_1(a558))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a558) | c3_1(a558) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c1_1(a558)))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[2966])).
% 1.21/1.41 tff(2968,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a558) | c1_1(a558) | c0_1(a558))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a558) | c3_1(a558) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c1_1(a558))),
% 1.21/1.41 inference(transitivity,[status(thm)],[2967, 2965])).
% 1.21/1.41 tff(2969,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a558) | c1_1(a558) | c0_1(a558))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(2970,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a558) | c3_1(a558) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c1_1(a558)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2969, 2968])).
% 1.21/1.41 tff(2971,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2970, 106, 2964, 2963, 2935, 2962, 2956, 574, 573, 709, 2953, 2950])).
% 1.21/1.41 tff(2972,plain,(hskp9 | c2_1(a496) | c3_1(a496) | (~c1_1(a540)) | c0_1(a540) | (~c3_1(a540)) | hskp15 | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(2973,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2972, 2908, 2907, 2902, 2901, 2900, 2899, 2526, 32])).
% 1.21/1.41 tff(2974,plain,(c1_1(a528) | hskp26 | c3_1(a528)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(2975,plain,
% 1.21/1.41 (c1_1(a528)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2974, 989, 32])).
% 1.21/1.41 tff(2976,assumption,(~c1_1(a540)), introduced(assumption)).
% 1.21/1.41 tff(2977,assumption,(~c3_1(a540)), introduced(assumption)).
% 1.21/1.41 tff(2978,plain,
% 1.21/1.41 (~hskp22),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[141, 2976])).
% 1.21/1.41 tff(2979,plain,
% 1.21/1.41 (~c0_1(a496)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2481, 2978, 2512, 2513, 574, 573, 2514])).
% 1.21/1.41 tff(2980,plain,
% 1.21/1.41 (hskp6),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2954, 2415, 573, 2979])).
% 1.21/1.41 tff(2981,plain,
% 1.21/1.41 (~c3_1(a501)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[591, 2980])).
% 1.21/1.41 tff(2982,plain,
% 1.21/1.41 (hskp25),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2928, 2415])).
% 1.21/1.41 tff(2983,plain,
% 1.21/1.41 (~c3_1(a558)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2961, 2982])).
% 1.21/1.41 tff(2984,plain,
% 1.21/1.41 (~c0_1(a558)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2934, 2982])).
% 1.21/1.41 tff(2985,plain,
% 1.21/1.41 (c2_1(a501)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[599, 2980])).
% 1.21/1.41 tff(2986,plain,
% 1.21/1.41 (c1_1(a501)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[607, 2980])).
% 1.21/1.41 tff(2987,plain,
% 1.21/1.41 (c1_1(a558)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2970, 106, 2986, 2985, 2984, 2983, 2981, 574, 573, 709, 2979])).
% 1.21/1.41 tff(2988,plain,
% 1.21/1.41 (c2_1(a558)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2942, 2982])).
% 1.21/1.41 tff(2989,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a540) | c3_1(a540) | c3_1(a558) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a558)) | (~c2_1(a558)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c3_1(a558) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a558)) | (~c2_1(a558)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2990,plain,
% 1.21/1.41 (((~ndr1_0) | c3_1(a558) | (~c2_1(a558)) | (~c1_1(a558)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540)) <=> (c1_1(a540) | c3_1(a540) | c3_1(a558) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a558)) | (~c2_1(a558)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2991,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a558) | (~c2_1(a558)) | (~c1_1(a558)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a540) | c3_1(a540) | c3_1(a558) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a558)) | (~c2_1(a558))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[2990])).
% 1.21/1.41 tff(2992,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a558) | (~c2_1(a558)) | (~c1_1(a558)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c3_1(a558) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a558)) | (~c2_1(a558)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[2991, 2989])).
% 1.21/1.41 tff(2993,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a558) | (~c2_1(a558)) | (~c1_1(a558)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(2994,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c3_1(a558) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a558)) | (~c2_1(a558))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2993, 2992])).
% 1.21/1.41 tff(2995,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2994, 106, 2988, 2976, 2977, 2983, 2291, 574, 573, 709, 2979, 2987])).
% 1.21/1.41 tff(2996,plain,((~c1_1(a509)) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c2_1(a496) | c3_1(a496) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(2997,plain,
% 1.21/1.41 (~c1_1(a509)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2996, 2977, 2976, 2291, 574, 573, 32])).
% 1.21/1.41 tff(2998,plain,
% 1.21/1.41 (hskp9),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2903, 2997])).
% 1.21/1.41 tff(2999,plain,
% 1.21/1.41 (~c1_1(a507)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[840, 2998])).
% 1.21/1.41 tff(3000,plain,
% 1.21/1.41 (~c0_1(a507)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[846, 2998])).
% 1.21/1.41 tff(3001,plain,
% 1.21/1.41 (c3_1(a507)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[854, 2998])).
% 1.21/1.41 tff(3002,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3003,plain,
% 1.21/1.41 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540)) <=> (c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3004,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[3003])).
% 1.21/1.41 tff(3005,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[3004, 3002])).
% 1.21/1.41 tff(3006,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(3007,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3006, 3005])).
% 1.21/1.41 tff(3008,plain,
% 1.21/1.41 (~c2_1(a528)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3007, 106, 2976, 2977, 2975, 2291, 989, 574, 573, 709, 2979])).
% 1.21/1.41 tff(3009,plain,
% 1.21/1.41 (~c0_1(a528)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[916, 106, 2975, 989, 574, 573, 909, 2979, 3008])).
% 1.21/1.41 tff(3010,plain,
% 1.21/1.41 (~hskp15),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[440, 3009])).
% 1.21/1.41 tff(3011,plain,
% 1.21/1.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3012,plain,
% 1.21/1.41 ((hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a540) | c0_1(a540) | c3_1(a540)) <=> (hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(3013,plain,
% 1.21/1.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a540) | c0_1(a540) | c3_1(a540))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[3012])).
% 1.21/1.41 tff(3014,plain,
% 1.21/1.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a540) | c0_1(a540) | c3_1(a540))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[3013, 3011])).
% 1.21/1.41 tff(3015,plain,
% 1.21/1.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a540) | c0_1(a540) | c3_1(a540))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(3016,plain,
% 1.21/1.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[3015, 3014])).
% 1.21/1.41 tff(3017,plain,
% 1.21/1.41 (~c1_1(a520)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3016, 106, 408, 2976, 2977, 2327, 2335, 2291, 290])).
% 1.21/1.41 tff(3018,plain,
% 1.21/1.41 (~c2_1(a554)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1544, 2365])).
% 1.21/1.41 tff(3019,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2281, 106, 2978, 2367, 2327, 3018, 2366, 2326, 31, 3017])).
% 1.21/1.41 tff(3020,plain,((~hskp13) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(3021,plain,
% 1.21/1.41 (~hskp13),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[3020, 408, 2262, 2261, 2976, 2977, 2263, 2291])).
% 1.21/1.41 tff(3022,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[481, 3021, 2250, 43])).
% 1.21/1.41 tff(3023,plain,(hskp2 | hskp15 | (~c3_1(a509)) | c2_1(a509) | c1_1(a540) | c3_1(a540) | (~c0_1(a509)) | c0_1(a540) | (~c3_1(a507)) | c0_1(a507) | c1_1(a507)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(3024,plain,
% 1.21/1.42 (hskp2),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3023, 3010, 2512, 2513, 2976, 2977, 2514, 2291, 3001, 3000, 2999])).
% 1.21/1.42 tff(3025,plain,
% 1.21/1.42 (~c1_1(a496)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[348, 3024])).
% 1.21/1.42 tff(3026,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a528) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a528) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3027,plain,
% 1.21/1.42 ((hskp8 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528))) <=> (hskp8 | c0_1(a528) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3028,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a528) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3027])).
% 1.21/1.42 tff(3029,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a528) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3028, 3026])).
% 1.21/1.42 tff(3030,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3031,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a528) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3030, 3029])).
% 1.21/1.42 tff(3032,plain,
% 1.21/1.42 (hskp8),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3031, 106, 3009, 2975, 2514, 2512, 989, 959, 2997])).
% 1.21/1.42 tff(3033,plain,
% 1.21/1.42 (~c0_1(a505)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[979, 3032])).
% 1.21/1.42 tff(3034,plain,
% 1.21/1.42 (c3_1(a505)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1065, 3032])).
% 1.21/1.42 tff(3035,plain,
% 1.21/1.42 (c2_1(a505)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[973, 3032])).
% 1.21/1.42 tff(3036,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | c1_1(a509) | (~c0_1(a509)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3037,plain,
% 1.21/1.42 ((hskp14 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505))) <=> (hskp14 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | c1_1(a509) | (~c0_1(a509)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3038,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | c1_1(a509) | (~c0_1(a509))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3037])).
% 1.21/1.42 tff(3039,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | c1_1(a509) | (~c0_1(a509)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3038, 3036])).
% 1.21/1.42 tff(3040,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3041,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | c1_1(a509) | (~c0_1(a509))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3040, 3039])).
% 1.21/1.42 tff(3042,plain,
% 1.21/1.42 (hskp14),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3041, 106, 2514, 3035, 3034, 2513, 3033, 1217, 2997])).
% 1.21/1.42 tff(3043,plain,
% 1.21/1.42 (~c3_1(a527)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[751, 3042])).
% 1.21/1.42 tff(3044,plain,
% 1.21/1.42 (~c1_1(a527)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[757, 3042])).
% 1.21/1.42 tff(3045,plain,
% 1.21/1.42 (c2_1(a527)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[783, 3042])).
% 1.21/1.42 tff(3046,plain,
% 1.21/1.42 (hskp0 | c1_1(a496)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[790, 106, 3045, 3044, 3043, 574, 776, 2979])).
% 1.21/1.42 tff(3047,plain,
% 1.21/1.42 (hskp0),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3046, 3025])).
% 1.21/1.42 tff(3048,plain,
% 1.21/1.42 (~c2_1(a494)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1594, 3047])).
% 1.21/1.42 tff(3049,plain,
% 1.21/1.42 (~c0_1(a494)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[797, 3047])).
% 1.21/1.42 tff(3050,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3051,plain,
% 1.21/1.42 (((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540)) <=> (c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3052,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3051])).
% 1.21/1.42 tff(3053,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3052, 3050])).
% 1.21/1.42 tff(3054,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3055,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3054, 3053])).
% 1.21/1.42 tff(3056,plain,
% 1.21/1.42 ($false),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3055, 106, 2976, 2977, 608, 600, 2291, 592, 574, 573, 709, 575])).
% 1.21/1.42 tff(3057,plain,((~hskp6) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c2_1(a496) | c3_1(a496) | c0_1(a496)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(3058,plain,
% 1.21/1.42 (~hskp6),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3057, 2977, 2976, 2291, 574, 573, 2979])).
% 1.21/1.42 tff(3059,plain,
% 1.21/1.42 (~hskp12),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[888, 3058, 574, 573, 2979, 3000, 3001, 2999])).
% 1.21/1.42 tff(3060,plain,
% 1.21/1.42 (hskp13),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[481, 3059, 3010])).
% 1.21/1.42 tff(3061,plain,
% 1.21/1.42 (~c3_1(a520)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1362, 3060])).
% 1.21/1.42 tff(3062,plain,
% 1.21/1.42 (c3_1(a494)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[809, 3047])).
% 1.21/1.42 tff(3063,plain,
% 1.21/1.42 (c0_1(a520)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1378, 3060])).
% 1.21/1.42 tff(3064,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a528) | c3_1(a528) | c3_1(a520) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c1_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a528) | c3_1(a528) | c3_1(a520) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c1_1(a528)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3065,plain,
% 1.21/1.42 (((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494)) <=> (c0_1(a528) | c3_1(a528) | c3_1(a520) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c1_1(a528)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3066,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a528) | c3_1(a528) | c3_1(a520) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c1_1(a528))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3065])).
% 1.21/1.42 tff(3067,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a528) | c3_1(a528) | c3_1(a520) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c1_1(a528)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3066, 3064])).
% 1.21/1.42 tff(3068,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3069,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a528) | c3_1(a528) | c3_1(a520) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c1_1(a528))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3068, 3067])).
% 1.21/1.42 tff(3070,plain,
% 1.21/1.42 (~c1_1(a520)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3069, 106, 3009, 2975, 3063, 3062, 989, 3061, 3049, 3048, 21])).
% 1.21/1.42 tff(3071,plain,
% 1.21/1.42 (c2_1(a520)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1370, 3060])).
% 1.21/1.42 tff(3072,plain,
% 1.21/1.42 (hskp24),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2270, 106, 3063, 3071, 2514, 2512, 3061, 2513, 1532])).
% 1.21/1.42 tff(3073,plain,
% 1.21/1.42 (~c3_1(a554)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1561, 3072])).
% 1.21/1.42 tff(3074,plain,
% 1.21/1.42 (~c2_1(a554)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1544, 3072])).
% 1.21/1.42 tff(3075,plain,
% 1.21/1.42 (c0_1(a554)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1569, 3072])).
% 1.21/1.42 tff(3076,plain,
% 1.21/1.42 ($false),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2281, 106, 2978, 3075, 3063, 3074, 3073, 3061, 31, 3070])).
% 1.21/1.42 tff(3077,plain,(c3_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | c1_1(a540) | c0_1(a540) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(3078,plain,
% 1.21/1.42 (c3_1(a540)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3077, 2976, 574, 573, 989, 2291, 32])).
% 1.21/1.42 tff(3079,plain,
% 1.21/1.42 (~c0_1(a496)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2481, 2978, 2262, 2261, 574, 573, 2263])).
% 1.21/1.42 tff(3080,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a540) | c0_1(a540) | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a509)) | (~c1_1(a509)) | (~c3_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a540) | c0_1(a540) | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a509)) | (~c1_1(a509)) | (~c3_1(a540)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3081,plain,
% 1.21/1.42 (((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a496) | c0_1(a496) | (~c1_1(a496)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540))) <=> (c1_1(a540) | c0_1(a540) | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a509)) | (~c1_1(a509)) | (~c3_1(a540)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3082,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a496) | c0_1(a496) | (~c1_1(a496)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a540) | c0_1(a540) | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a509)) | (~c1_1(a509)) | (~c3_1(a540))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3081])).
% 1.21/1.42 tff(3083,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a496) | c0_1(a496) | (~c1_1(a496)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a540) | c0_1(a540) | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a509)) | (~c1_1(a509)) | (~c3_1(a540)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3082, 3080])).
% 1.21/1.42 tff(3084,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a496) | c0_1(a496) | (~c1_1(a496)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3085,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a540) | c0_1(a540) | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a509)) | (~c1_1(a509)) | (~c3_1(a540))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3084, 3083])).
% 1.21/1.42 tff(3086,plain,
% 1.21/1.42 ((~c1_1(a496)) | (~c1_1(a509)) | (~c3_1(a540))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3085, 106, 2976, 2262, 2291, 2261, 574, 558, 3079])).
% 1.21/1.42 tff(3087,plain,
% 1.21/1.42 (~c1_1(a496)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3086, 2415, 2293])).
% 1.21/1.42 tff(3088,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a528) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3089,plain,
% 1.21/1.42 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496)) <=> (c3_1(a528) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3090,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a528) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3089])).
% 1.21/1.42 tff(3091,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3090, 3088])).
% 1.21/1.42 tff(3092,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3093,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3092, 3091])).
% 1.21/1.42 tff(3094,plain,
% 1.21/1.42 (c1_1(a496) | c0_1(a496) | (~c2_1(a528))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3093, 106, 998, 989, 574, 573, 709])).
% 1.21/1.42 tff(3095,plain,
% 1.21/1.42 (~c2_1(a528)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3094, 3087, 3079])).
% 1.21/1.42 tff(3096,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3097,plain,
% 1.21/1.42 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c3_1(a528) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3098,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3097])).
% 1.21/1.42 tff(3099,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3098, 3096])).
% 1.21/1.42 tff(3100,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3101,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3100, 3099])).
% 1.21/1.42 tff(3102,plain,
% 1.21/1.42 (c0_1(a496) | (~c1_1(a509)) | (~c0_1(a528))),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3101, 106, 998, 2263, 989, 2261, 574, 573, 909])).
% 1.21/1.42 tff(3103,plain,
% 1.21/1.42 (~c0_1(a528)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3102, 2415, 3079])).
% 1.21/1.42 tff(3104,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a540) | c0_1(a528) | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c1_1(a528)) | c2_1(a528) | (~c3_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a540) | c0_1(a528) | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c1_1(a528)) | c2_1(a528) | (~c3_1(a540)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3105,plain,
% 1.21/1.42 (((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a528) | c0_1(a528) | (~c1_1(a528)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540))) <=> (c1_1(a540) | c0_1(a528) | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c1_1(a528)) | c2_1(a528) | (~c3_1(a540)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3106,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a528) | c0_1(a528) | (~c1_1(a528)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a540) | c0_1(a528) | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c1_1(a528)) | c2_1(a528) | (~c3_1(a540))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[3105])).
% 1.21/1.42 tff(3107,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a528) | c0_1(a528) | (~c1_1(a528)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a540) | c0_1(a528) | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c1_1(a528)) | c2_1(a528) | (~c3_1(a540)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[3106, 3104])).
% 1.21/1.42 tff(3108,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a528) | c0_1(a528) | (~c1_1(a528)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(3109,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a540) | c0_1(a528) | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c1_1(a528)) | c2_1(a528) | (~c3_1(a540))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[3108, 3107])).
% 1.21/1.42 tff(3110,plain,
% 1.21/1.42 ($false),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3109, 106, 2976, 2293, 3103, 998, 2262, 2291, 2261, 558, 2415, 3095])).
% 1.21/1.42 tff(3111,plain,((~c1_1(a509)) | c1_1(a540) | (~c3_1(a540)) | (~c1_1(a528)) | (~c3_1(a509)) | c0_1(a540) | c2_1(a509) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~c0_1(a509))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(3112,plain,
% 1.21/1.42 (~c1_1(a509)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[3111, 2976, 3078, 2975, 2512, 2291, 2513, 989, 574, 573, 2514])).
% 1.21/1.42 tff(3113,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a540) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a540) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3114,plain,
% 1.21/1.42 ((hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540))) <=> (hskp28 | c1_1(a540) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(3115,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a540) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540))))),
% 1.27/1.43 inference(monotonicity,[status(thm)],[3114])).
% 1.27/1.43 tff(3116,plain,
% 1.27/1.43 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a540) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)))),
% 1.27/1.43 inference(transitivity,[status(thm)],[3115, 3113])).
% 1.27/1.43 tff(3117,plain,
% 1.27/1.43 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))),
% 1.27/1.43 inference(quant_inst,[status(thm)],[])).
% 1.27/1.43 tff(3118,plain,
% 1.27/1.43 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a540) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540))),
% 1.27/1.43 inference(modus_ponens,[status(thm)],[3117, 3116])).
% 1.27/1.43 tff(3119,plain,
% 1.27/1.43 (hskp28),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3118, 106, 2976, 3078, 2514, 2512, 2291, 238, 3112])).
% 1.27/1.43 tff(3120,plain,
% 1.27/1.43 (c3_1(a500)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[390, 3119])).
% 1.27/1.43 tff(3121,plain,
% 1.27/1.43 (c2_1(a500)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[398, 3119])).
% 1.27/1.43 tff(3122,plain,
% 1.27/1.43 (c0_1(a500)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[406, 3119])).
% 1.27/1.43 tff(3123,plain,
% 1.27/1.43 (hskp9),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[2432, 2324])).
% 1.27/1.43 tff(3124,plain,
% 1.27/1.43 (~c1_1(a507)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[840, 3123])).
% 1.27/1.43 tff(3125,plain,
% 1.27/1.43 (~c0_1(a507)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[846, 3123])).
% 1.27/1.43 tff(3126,plain,
% 1.27/1.43 (c3_1(a507)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[854, 3123])).
% 1.27/1.43 tff(3127,plain,
% 1.27/1.43 (~hskp15),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[440, 2527])).
% 1.27/1.43 tff(3128,plain,
% 1.27/1.43 (hskp2),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[2283, 3127, 2263, 2262, 2261, 444, 443, 442, 2275, 3126, 3125, 3124])).
% 1.27/1.43 tff(3129,plain,
% 1.27/1.43 (~c1_1(a496)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[348, 3128])).
% 1.27/1.43 tff(3130,plain,
% 1.27/1.43 (hskp8),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3031, 106, 2527, 998, 2263, 2262, 989, 959, 2324])).
% 1.27/1.43 tff(3131,plain,
% 1.27/1.43 (~c0_1(a505)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[979, 3130])).
% 1.27/1.43 tff(3132,plain,
% 1.27/1.43 (c3_1(a505)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1065, 3130])).
% 1.27/1.43 tff(3133,plain,
% 1.27/1.43 (c2_1(a505)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[973, 3130])).
% 1.27/1.43 tff(3134,plain,
% 1.27/1.43 (hskp14),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3041, 106, 2263, 3133, 3132, 2261, 3131, 1217, 2324])).
% 1.27/1.43 tff(3135,plain,
% 1.27/1.43 (~c3_1(a527)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[751, 3134])).
% 1.27/1.43 tff(3136,plain,
% 1.27/1.43 (~c1_1(a527)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[757, 3134])).
% 1.27/1.43 tff(3137,plain,
% 1.27/1.43 (c2_1(a527)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[783, 3134])).
% 1.27/1.43 tff(3138,plain,
% 1.27/1.43 (hskp0 | c1_1(a496)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[790, 106, 3137, 3136, 3135, 574, 776, 2615])).
% 1.27/1.43 tff(3139,plain,
% 1.27/1.43 (hskp0),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3138, 3129])).
% 1.27/1.43 tff(3140,plain,
% 1.27/1.43 (~c2_1(a494)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1594, 3139])).
% 1.27/1.43 tff(3141,plain,
% 1.27/1.43 (~c0_1(a494)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[797, 3139])).
% 1.27/1.43 tff(3142,plain,
% 1.27/1.43 (~hskp6),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[2428, 3129, 574, 573, 2615])).
% 1.27/1.43 tff(3143,plain,
% 1.27/1.43 (~hskp12),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[888, 3142, 574, 573, 2615, 3125, 3126, 3124])).
% 1.27/1.43 tff(3144,plain,
% 1.27/1.43 (hskp13),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[481, 3143, 3127])).
% 1.27/1.43 tff(3145,plain,
% 1.27/1.43 (~c3_1(a520)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1362, 3144])).
% 1.27/1.43 tff(3146,plain,
% 1.27/1.43 (c3_1(a494)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[809, 3139])).
% 1.27/1.43 tff(3147,plain,
% 1.27/1.43 (c0_1(a520)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1378, 3144])).
% 1.27/1.43 tff(3148,plain,
% 1.27/1.43 (~c1_1(a520)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3069, 106, 2527, 998, 3147, 3146, 989, 3145, 3141, 3140, 21])).
% 1.27/1.43 tff(3149,plain,
% 1.27/1.43 (c2_1(a520)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1370, 3144])).
% 1.27/1.43 tff(3150,plain,
% 1.27/1.43 (hskp24),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[2270, 106, 3147, 3149, 2263, 2262, 3145, 2261, 1532])).
% 1.27/1.43 tff(3151,plain,
% 1.27/1.43 (~c3_1(a554)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1561, 3150])).
% 1.27/1.43 tff(3152,plain,
% 1.27/1.43 (~c2_1(a554)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1544, 3150])).
% 1.27/1.43 tff(3153,plain,
% 1.27/1.43 (c0_1(a554)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1569, 3150])).
% 1.27/1.43 tff(3154,plain,
% 1.27/1.43 ($false),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[2281, 106, 2275, 3153, 3147, 3152, 3151, 3145, 31, 3148])).
% 1.27/1.43 tff(3155,plain,(c0_1(a528) | hskp22 | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | (~c1_1(a528)) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | c1_1(a509)), inference(lemma,lemma(discharge,[]))).
% 1.27/1.43 tff(3156,plain,
% 1.27/1.43 (c0_1(a528)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3155, 2978, 2514, 2512, 2513, 2975, 989, 574, 573, 3122, 3121, 3120, 3112])).
% 1.27/1.43 tff(3157,assumption,(hskp21), introduced(assumption)).
% 1.27/1.43 tff(3158,plain,
% 1.27/1.43 (~c3_1(a538)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1953, 3157])).
% 1.27/1.43 tff(3159,plain,
% 1.27/1.43 (~c1_1(a538)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1959, 3157])).
% 1.27/1.43 tff(3160,plain,
% 1.27/1.43 (c0_1(a538)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1967, 3157])).
% 1.27/1.43 tff(3161,plain,
% 1.27/1.43 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a538) | c3_1(a538) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a538) | c3_1(a538) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a538)))),
% 1.27/1.43 inference(rewrite,[status(thm)],[])).
% 1.27/1.43 tff(3162,plain,
% 1.27/1.43 ((hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538))) <=> (hskp22 | c1_1(a538) | c3_1(a538) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a538)))),
% 1.27/1.43 inference(rewrite,[status(thm)],[])).
% 1.27/1.43 tff(3163,plain,
% 1.27/1.43 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a538) | c3_1(a538) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a538))))),
% 1.27/1.43 inference(monotonicity,[status(thm)],[3162])).
% 1.27/1.43 tff(3164,plain,
% 1.27/1.43 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a538) | c3_1(a538) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a538)))),
% 1.27/1.43 inference(transitivity,[status(thm)],[3163, 3161])).
% 1.27/1.43 tff(3165,plain,
% 1.27/1.43 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))),
% 1.27/1.43 inference(quant_inst,[status(thm)],[])).
% 1.27/1.43 tff(3166,plain,
% 1.27/1.43 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a538) | c3_1(a538) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a538))),
% 1.27/1.43 inference(modus_ponens,[status(thm)],[3165, 3164])).
% 1.27/1.43 tff(3167,plain,
% 1.27/1.43 (~c0_1(a496)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3166, 106, 2275, 3160, 3159, 3158, 574, 573, 31])).
% 1.27/1.43 tff(3168,plain,
% 1.27/1.43 (hskp23),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1974, 106, 3160, 999, 998, 3159, 3158, 989, 1896])).
% 1.27/1.43 tff(3169,plain,
% 1.27/1.43 (~c2_1(a541)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1980, 3168])).
% 1.27/1.43 tff(3170,plain,
% 1.27/1.43 (c1_1(a541)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1988, 3168])).
% 1.27/1.43 tff(3171,plain,
% 1.27/1.43 (c0_1(a541)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[1996, 3168])).
% 1.27/1.43 tff(3172,plain,
% 1.27/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a541) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a541) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.27/1.43 inference(rewrite,[status(thm)],[])).
% 1.27/1.43 tff(3173,plain,
% 1.27/1.43 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c2_1(a541) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.27/1.43 inference(rewrite,[status(thm)],[])).
% 1.27/1.43 tff(3174,plain,
% 1.27/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a541) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541))))),
% 1.27/1.43 inference(monotonicity,[status(thm)],[3173])).
% 1.27/1.43 tff(3175,plain,
% 1.27/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a541) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.27/1.43 inference(transitivity,[status(thm)],[3174, 3172])).
% 1.27/1.43 tff(3176,plain,
% 1.27/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 1.27/1.43 inference(quant_inst,[status(thm)],[])).
% 1.27/1.43 tff(3177,plain,
% 1.27/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a541) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541))),
% 1.27/1.43 inference(modus_ponens,[status(thm)],[3176, 3175])).
% 1.27/1.43 tff(3178,plain,
% 1.27/1.43 ($false),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3177, 106, 3171, 3170, 999, 998, 3169, 989, 574, 573, 909, 3167])).
% 1.27/1.43 tff(3179,plain,((~hskp21) | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | c2_1(a496) | c3_1(a496) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.27/1.43 tff(3180,plain,
% 1.27/1.43 (~hskp21),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3179, 3156, 2975, 989, 574, 573, 2978])).
% 1.27/1.43 tff(3181,plain,
% 1.27/1.43 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.27/1.43 inference(rewrite,[status(thm)],[])).
% 1.27/1.43 tff(3182,plain,
% 1.27/1.43 ((hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509))) <=> (hskp21 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.27/1.43 inference(rewrite,[status(thm)],[])).
% 1.27/1.43 tff(3183,plain,
% 1.27/1.43 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c2_1(a528))))),
% 1.27/1.43 inference(monotonicity,[status(thm)],[3182])).
% 1.27/1.43 tff(3184,plain,
% 1.27/1.43 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.27/1.43 inference(transitivity,[status(thm)],[3183, 3181])).
% 1.27/1.43 tff(3185,plain,
% 1.27/1.43 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))),
% 1.27/1.43 inference(quant_inst,[status(thm)],[])).
% 1.27/1.43 tff(3186,plain,
% 1.27/1.43 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c2_1(a528))),
% 1.27/1.43 inference(modus_ponens,[status(thm)],[3185, 3184])).
% 1.27/1.43 tff(3187,plain,
% 1.27/1.43 (hskp21 | c1_1(a509) | (~c1_1(a528)) | (~c2_1(a528))),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3186, 106, 2514, 989, 2513, 2153])).
% 1.27/1.43 tff(3188,plain,
% 1.27/1.43 (~c2_1(a528)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3187, 3180, 2975, 3112])).
% 1.27/1.43 tff(3189,plain,
% 1.27/1.43 ($false),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[916, 106, 3156, 2975, 989, 574, 573, 909, 2979, 3188])).
% 1.27/1.43 tff(3190,plain,(c1_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | c0_1(a540) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.27/1.43 tff(3191,plain,
% 1.27/1.43 (c1_1(a540)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3190, 2291, 574, 573, 989, 32])).
% 1.27/1.43 tff(3192,plain,
% 1.27/1.43 (~hskp22),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[133, 2977])).
% 1.27/1.43 tff(3193,plain,
% 1.27/1.43 (~c0_1(a496)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[2481, 3192, 2262, 2261, 574, 573, 2263])).
% 1.27/1.43 tff(3194,plain,
% 1.27/1.43 (~c1_1(a509)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[2430, 3193, 573, 574, 2263, 2261, 2262])).
% 1.27/1.43 tff(3195,plain,
% 1.27/1.43 (hskp28),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[2242, 106, 2263, 2262, 3126, 3125, 3124, 238, 2324])).
% 1.27/1.43 tff(3196,plain,
% 1.27/1.43 (c3_1(a500)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[390, 3195])).
% 1.27/1.43 tff(3197,plain,
% 1.27/1.43 (c0_1(a500)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[406, 3195])).
% 1.27/1.43 tff(3198,plain,
% 1.27/1.43 (c2_1(a500)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[398, 3195])).
% 1.27/1.43 tff(3199,plain,
% 1.27/1.43 ($false),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3155, 3198, 3197, 2263, 2262, 2261, 998, 989, 574, 573, 2275, 2527, 3196, 2324])).
% 1.27/1.43 tff(3200,plain,(c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | (~c1_1(a528)) | c3_1(a528) | c2_1(a496) | c3_1(a496) | hskp22 | c0_1(a528)), inference(lemma,lemma(discharge,[]))).
% 1.27/1.43 tff(3201,plain,
% 1.27/1.43 (c0_1(a528)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3200, 3194, 2262, 2261, 998, 989, 574, 573, 3192, 2263])).
% 1.27/1.43 tff(3202,plain,
% 1.27/1.43 (~hskp21),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3179, 3201, 998, 989, 574, 573, 3192])).
% 1.27/1.43 tff(3203,plain,
% 1.27/1.43 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a540) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a540) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.27/1.43 inference(rewrite,[status(thm)],[])).
% 1.27/1.43 tff(3204,plain,
% 1.27/1.43 ((hskp21 | (~ndr1_0) | c3_1(a540) | (~c2_1(a540)) | (~c1_1(a540)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509))) <=> (hskp21 | c3_1(a540) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.27/1.43 inference(rewrite,[status(thm)],[])).
% 1.27/1.43 tff(3205,plain,
% 1.27/1.43 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a540) | (~c2_1(a540)) | (~c1_1(a540)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a540) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 1.27/1.43 inference(monotonicity,[status(thm)],[3204])).
% 1.27/1.43 tff(3206,plain,
% 1.27/1.43 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a540) | (~c2_1(a540)) | (~c1_1(a540)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a540) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.27/1.43 inference(transitivity,[status(thm)],[3205, 3203])).
% 1.27/1.43 tff(3207,plain,
% 1.27/1.43 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a540) | (~c2_1(a540)) | (~c1_1(a540)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))),
% 1.27/1.43 inference(quant_inst,[status(thm)],[])).
% 1.27/1.43 tff(3208,plain,
% 1.27/1.43 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a540) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a540)) | (~c2_1(a540))),
% 1.27/1.43 inference(modus_ponens,[status(thm)],[3207, 3206])).
% 1.27/1.43 tff(3209,plain,
% 1.27/1.43 (hskp21 | c1_1(a509) | (~c2_1(a540))),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3208, 106, 2288, 2977, 2263, 2261, 2153])).
% 1.27/1.43 tff(3210,plain,
% 1.27/1.43 (~c2_1(a540)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3209, 3202, 3194])).
% 1.27/1.43 tff(3211,plain,
% 1.27/1.43 (hskp21 | c1_1(a509) | (~c1_1(a528)) | (~c2_1(a528))),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3186, 106, 2263, 989, 2261, 2153])).
% 1.27/1.43 tff(3212,plain,
% 1.27/1.43 (~c2_1(a528)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3211, 3202, 998, 3194])).
% 1.27/1.43 tff(3213,plain,
% 1.27/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a540) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a540) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c2_1(a540))),
% 1.27/1.43 inference(rewrite,[status(thm)],[])).
% 1.27/1.43 tff(3214,plain,
% 1.27/1.43 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a540) | c0_1(a540) | c2_1(a540)) <=> (c3_1(a540) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c2_1(a540))),
% 1.27/1.43 inference(rewrite,[status(thm)],[])).
% 1.27/1.43 tff(3215,plain,
% 1.27/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a540) | c0_1(a540) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a540) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c2_1(a540)))),
% 1.27/1.43 inference(monotonicity,[status(thm)],[3214])).
% 1.27/1.43 tff(3216,plain,
% 1.27/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a540) | c0_1(a540) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a540) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c2_1(a540))),
% 1.27/1.43 inference(transitivity,[status(thm)],[3215, 3213])).
% 1.27/1.43 tff(3217,plain,
% 1.27/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a540) | c0_1(a540) | c2_1(a540))),
% 1.27/1.43 inference(quant_inst,[status(thm)],[])).
% 1.27/1.43 tff(3218,plain,
% 1.27/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a540) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c2_1(a540)),
% 1.27/1.43 inference(modus_ponens,[status(thm)],[3217, 3216])).
% 1.27/1.43 tff(3219,plain,
% 1.27/1.43 ($false),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3218, 106, 2977, 3201, 998, 2291, 989, 909, 3212, 3210])).
% 1.27/1.43 tff(3220,plain,(c3_1(a540) | (~c1_1(a528)) | c0_1(a540) | c3_1(a528) | (~c1_1(a540)) | (~c0_1(a509)) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~c3_1(a509))), inference(lemma,lemma(discharge,[]))).
% 1.27/1.43 tff(3221,plain,
% 1.27/1.43 (c3_1(a540)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[3220, 2291, 2975, 989, 3191, 2514, 2513, 574, 573, 2512])).
% 1.27/1.43 tff(3222,plain,
% 1.27/1.43 (c0_1(a496)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[2445, 3191, 3221, 2291, 574, 573, 2514, 2512, 2513])).
% 1.27/1.43 tff(3223,plain,
% 1.27/1.43 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.27/1.43 inference(bind,[status(th)],[])).
% 1.27/1.43 tff(3224,plain,
% 1.27/1.43 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.27/1.43 inference(quant_intro,[status(thm)],[3223])).
% 1.27/1.43 tff(3225,plain,
% 1.27/1.43 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.27/1.43 inference(rewrite,[status(thm)],[])).
% 1.27/1.43 tff(3226,plain,
% 1.27/1.43 (^[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))) | 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))) | (~c2_1(U))) | (~ndr1_0)) | (~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))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.27/1.43 inference(bind,[status(th)],[])).
% 1.27/1.43 tff(3227,plain,
% 1.27/1.43 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.27/1.43 inference(quant_intro,[status(thm)],[3226])).
% 1.27/1.43 tff(3228,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.27/1.43 tff(3229,plain,
% 1.27/1.43 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.27/1.43 inference(modus_ponens,[status(thm)],[3228, 3227])).
% 1.27/1.43 tff(3230,plain,
% 1.27/1.43 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.27/1.43 inference(modus_ponens,[status(thm)],[3229, 3225])).
% 1.27/1.43 tff(3231,plain,(
% 1.27/1.43 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.27/1.43 inference(skolemize,[status(sab)],[3230])).
% 1.27/1.43 tff(3232,plain,
% 1.27/1.43 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.27/1.43 inference(modus_ponens,[status(thm)],[3231, 3224])).
% 1.27/1.43 tff(3233,plain,
% 1.27/1.43 (hskp15),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[2407, 3123, 2288, 2291, 2263, 2262, 2293, 2261])).
% 1.27/1.43 tff(3234,plain,
% 1.27/1.43 (c0_1(a528)),
% 1.27/1.43 inference(unit_resolution,[status(thm)],[440, 3233])).
% 1.27/1.43 tff(3235,plain,
% 1.27/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.27/1.43 inference(rewrite,[status(thm)],[])).
% 1.27/1.43 tff(3236,plain,
% 1.27/1.43 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540))) <=> (c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3237,plain,
% 1.27/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540))))),
% 1.27/1.44 inference(monotonicity,[status(thm)],[3236])).
% 1.27/1.44 tff(3238,plain,
% 1.27/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.27/1.44 inference(transitivity,[status(thm)],[3237, 3235])).
% 1.27/1.44 tff(3239,plain,
% 1.27/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.27/1.44 inference(quant_inst,[status(thm)],[])).
% 1.27/1.44 tff(3240,plain,
% 1.27/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540))),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3239, 3238])).
% 1.27/1.44 tff(3241,plain,
% 1.27/1.44 ($false),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[3240, 106, 2288, 2293, 3234, 998, 2263, 2262, 2291, 989, 1302, 2324])).
% 1.27/1.44 tff(3242,plain,(c1_1(a509) | (~c1_1(a540)) | (~c3_1(a540)) | (~c1_1(a528)) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | c3_1(a528) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 1.27/1.44 tff(3243,plain,
% 1.27/1.44 (c1_1(a509)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[3242, 3191, 3221, 2975, 2514, 2512, 2291, 989, 2513])).
% 1.27/1.44 tff(3244,plain,
% 1.27/1.44 (hskp2),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[2905, 3243])).
% 1.27/1.44 tff(3245,plain,
% 1.27/1.44 (~c1_1(a496)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[348, 3244])).
% 1.27/1.44 tff(3246,plain,
% 1.27/1.44 (~hskp9),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[2407, 43, 2288, 2291, 2514, 2512, 2293, 2513])).
% 1.27/1.44 tff(3247,plain,
% 1.27/1.44 ($false),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[2972, 3246, 43, 574, 573, 2291, 2288, 2293, 32])).
% 1.27/1.44 tff(3248,plain,(hskp15 | c2_1(a496) | c3_1(a496) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.27/1.44 tff(3249,plain,
% 1.27/1.44 (hskp15),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[3248, 2291, 573, 574, 3191, 3221, 32])).
% 1.27/1.44 tff(3250,plain,
% 1.27/1.44 (c0_1(a528)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[440, 3249])).
% 1.27/1.44 tff(3251,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a528) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a528) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3252,plain,
% 1.27/1.44 ((hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496))) <=> (hskp9 | c3_1(a528) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3253,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a528) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.27/1.44 inference(monotonicity,[status(thm)],[3252])).
% 1.27/1.44 tff(3254,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a528) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.27/1.44 inference(transitivity,[status(thm)],[3253, 3251])).
% 1.27/1.44 tff(3255,plain,
% 1.27/1.44 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))),
% 1.27/1.44 inference(quant_inst,[status(thm)],[])).
% 1.27/1.44 tff(3256,plain,
% 1.27/1.44 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a528) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3255, 3254])).
% 1.27/1.44 tff(3257,plain,
% 1.27/1.44 (hskp9 | c1_1(a496) | (~c0_1(a496)) | (~c0_1(a528))),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[3256, 106, 2975, 989, 574, 1186])).
% 1.27/1.44 tff(3258,plain,
% 1.27/1.44 (hskp9),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[3257, 3250, 3245, 3222])).
% 1.27/1.44 tff(3259,plain,
% 1.27/1.44 (c3_1(a507)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[854, 3258])).
% 1.27/1.44 tff(3260,plain,
% 1.27/1.44 (~c0_1(a507)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[846, 3258])).
% 1.27/1.44 tff(3261,plain,
% 1.27/1.44 (~c1_1(a507)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[840, 3258])).
% 1.27/1.44 tff(3262,plain,
% 1.27/1.44 (c2_1(a540)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[2303, 3261, 3191, 3221, 2291, 3260, 3259])).
% 1.27/1.44 tff(3263,plain,
% 1.27/1.44 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.27/1.44 inference(bind,[status(th)],[])).
% 1.27/1.44 tff(3264,plain,
% 1.27/1.44 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.27/1.44 inference(quant_intro,[status(thm)],[3263])).
% 1.27/1.44 tff(3265,plain,
% 1.27/1.44 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3266,plain,
% 1.27/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp31) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp31))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.27/1.44 inference(bind,[status(th)],[])).
% 1.27/1.44 tff(3267,plain,
% 1.27/1.44 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.27/1.44 inference(quant_intro,[status(thm)],[3266])).
% 1.27/1.44 tff(3268,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 1.27/1.44 tff(3269,plain,
% 1.27/1.44 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3268, 3267])).
% 1.27/1.44 tff(3270,plain,
% 1.27/1.44 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3269, 3265])).
% 1.27/1.44 tff(3271,plain,(
% 1.27/1.44 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.27/1.44 inference(skolemize,[status(sab)],[3270])).
% 1.27/1.44 tff(3272,plain,
% 1.27/1.44 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3271, 3264])).
% 1.27/1.44 tff(3273,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3274,plain,
% 1.27/1.44 ((hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496))) <=> (hskp23 | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3275,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.27/1.44 inference(monotonicity,[status(thm)],[3274])).
% 1.27/1.44 tff(3276,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.27/1.44 inference(transitivity,[status(thm)],[3275, 3273])).
% 1.27/1.44 tff(3277,plain,
% 1.27/1.44 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496)))),
% 1.27/1.44 inference(quant_inst,[status(thm)],[])).
% 1.27/1.44 tff(3278,plain,
% 1.27/1.44 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3277, 3276])).
% 1.27/1.44 tff(3279,plain,
% 1.27/1.44 (hskp23 | (~c0_1(a528))),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[3278, 106, 2975, 989, 3245, 573, 1896, 3222])).
% 1.27/1.44 tff(3280,plain,
% 1.27/1.44 (hskp23),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[3279, 3250])).
% 1.27/1.44 tff(3281,plain,
% 1.27/1.44 (~c2_1(a541)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[1980, 3280])).
% 1.27/1.44 tff(3282,plain,
% 1.27/1.44 (c1_1(a541)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[1988, 3280])).
% 1.27/1.44 tff(3283,plain,
% 1.27/1.44 (c0_1(a541)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[1996, 3280])).
% 1.27/1.44 tff(3284,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp31 | c2_1(a541) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp31 | c2_1(a541) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3285,plain,
% 1.27/1.44 ((hskp31 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541))) <=> (hskp31 | c2_1(a541) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3286,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp31 | c2_1(a541) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c1_1(a541)) | (~c0_1(a541))))),
% 1.27/1.44 inference(monotonicity,[status(thm)],[3285])).
% 1.27/1.44 tff(3287,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp31 | c2_1(a541) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.27/1.44 inference(transitivity,[status(thm)],[3286, 3284])).
% 1.27/1.44 tff(3288,plain,
% 1.27/1.44 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.27/1.44 inference(quant_inst,[status(thm)],[])).
% 1.27/1.44 tff(3289,plain,
% 1.27/1.44 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp31 | c2_1(a541) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c1_1(a541)) | (~c0_1(a541))),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3288, 3287])).
% 1.27/1.44 tff(3290,plain,
% 1.27/1.44 (hskp31),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[3289, 106, 3283, 3282, 3191, 3221, 3281, 3272, 3262])).
% 1.27/1.44 tff(3291,plain,
% 1.27/1.44 (c2_1(a522)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[670, 3290])).
% 1.27/1.44 tff(3292,plain,
% 1.27/1.44 (c1_1(a522)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[678, 3290])).
% 1.27/1.44 tff(3293,plain,
% 1.27/1.44 (c0_1(a522)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[686, 3290])).
% 1.27/1.44 tff(3294,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3295,plain,
% 1.27/1.44 ((hskp3 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496))) <=> (hskp3 | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3296,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522))))),
% 1.27/1.44 inference(monotonicity,[status(thm)],[3295])).
% 1.27/1.44 tff(3297,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))),
% 1.27/1.44 inference(transitivity,[status(thm)],[3296, 3294])).
% 1.27/1.44 tff(3298,plain,
% 1.27/1.44 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))),
% 1.27/1.44 inference(quant_inst,[status(thm)],[])).
% 1.27/1.44 tff(3299,plain,
% 1.27/1.44 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522))),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3298, 3297])).
% 1.27/1.44 tff(3300,plain,
% 1.27/1.44 (hskp3),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[3299, 106, 3293, 3292, 3291, 3245, 574, 3232, 3222])).
% 1.27/1.44 tff(3301,plain,
% 1.27/1.44 (((~hskp3) | (~c1_1(a497))) <=> ((~hskp3) | (~c1_1(a497)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3302,plain,
% 1.27/1.44 (((~c1_1(a497)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a497)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3303,axiom,((~c1_1(a497)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.27/1.44 tff(3304,plain,
% 1.27/1.44 ((~hskp3) | (~c1_1(a497))),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3303, 3302])).
% 1.27/1.44 tff(3305,plain,
% 1.27/1.44 ((~hskp3) | (~c1_1(a497))),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3304, 3301])).
% 1.27/1.44 tff(3306,plain,
% 1.27/1.44 (~c1_1(a497)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[3305, 3300])).
% 1.27/1.44 tff(3307,plain,
% 1.27/1.44 (((~hskp3) | (~c0_1(a497))) <=> ((~hskp3) | (~c0_1(a497)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3308,plain,
% 1.27/1.44 (((~c0_1(a497)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a497)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3309,axiom,((~c0_1(a497)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.27/1.44 tff(3310,plain,
% 1.27/1.44 ((~hskp3) | (~c0_1(a497))),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3309, 3308])).
% 1.27/1.44 tff(3311,plain,
% 1.27/1.44 ((~hskp3) | (~c0_1(a497))),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3310, 3307])).
% 1.27/1.44 tff(3312,plain,
% 1.27/1.44 (~c0_1(a497)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[3311, 3300])).
% 1.27/1.44 tff(3313,plain,
% 1.27/1.44 (((~hskp3) | c2_1(a497)) <=> ((~hskp3) | c2_1(a497))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3314,axiom,((~hskp3) | c2_1(a497)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.27/1.44 tff(3315,plain,
% 1.27/1.44 ((~hskp3) | c2_1(a497)),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3314, 3313])).
% 1.27/1.44 tff(3316,plain,
% 1.27/1.44 ((~hskp3) | c2_1(a497)),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3315, 3313])).
% 1.27/1.44 tff(3317,plain,
% 1.27/1.44 ((~hskp3) | c2_1(a497)),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3316, 3313])).
% 1.27/1.44 tff(3318,plain,
% 1.27/1.44 ((~hskp3) | c2_1(a497)),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3317, 3313])).
% 1.27/1.44 tff(3319,plain,
% 1.27/1.44 ((~hskp3) | c2_1(a497)),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3318, 3313])).
% 1.27/1.44 tff(3320,plain,
% 1.27/1.44 (c2_1(a497)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[3319, 3300])).
% 1.27/1.44 tff(3321,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a497) | c1_1(a497) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | (~c2_1(a497)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a497) | c1_1(a497) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | (~c2_1(a497)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3322,plain,
% 1.27/1.44 ((hskp5 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a497) | c0_1(a497) | (~c2_1(a497))) <=> (hskp5 | c0_1(a497) | c1_1(a497) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | (~c2_1(a497)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3323,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a497) | c0_1(a497) | (~c2_1(a497)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a497) | c1_1(a497) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | (~c2_1(a497))))),
% 1.27/1.44 inference(monotonicity,[status(thm)],[3322])).
% 1.27/1.44 tff(3324,plain,
% 1.27/1.44 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a497) | c0_1(a497) | (~c2_1(a497)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a497) | c1_1(a497) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | (~c2_1(a497)))),
% 1.27/1.44 inference(transitivity,[status(thm)],[3323, 3321])).
% 1.27/1.44 tff(3325,plain,
% 1.27/1.44 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a497) | c0_1(a497) | (~c2_1(a497)))),
% 1.27/1.44 inference(quant_inst,[status(thm)],[])).
% 1.27/1.44 tff(3326,plain,
% 1.27/1.44 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a497) | c1_1(a497) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | (~c2_1(a497))),
% 1.27/1.44 inference(modus_ponens,[status(thm)],[3325, 3324])).
% 1.27/1.44 tff(3327,plain,
% 1.27/1.44 (hskp5),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[3326, 106, 3293, 3292, 3291, 3320, 3312, 3306, 2524])).
% 1.27/1.44 tff(3328,plain,
% 1.27/1.44 (~c1_1(a499)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[1811, 3327])).
% 1.27/1.44 tff(3329,plain,
% 1.27/1.44 (c0_1(a499)),
% 1.27/1.44 inference(unit_resolution,[status(thm)],[1797, 3327])).
% 1.27/1.44 tff(3330,plain,
% 1.27/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a540) | c3_1(a528) | c1_1(a499) | (~ndr1_0) | (~c3_1(a499)) | (~c0_1(a499)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a528) | c1_1(a499) | (~ndr1_0) | (~c3_1(a499)) | (~c0_1(a499)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3331,plain,
% 1.27/1.44 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a499) | (~c0_1(a499)) | (~c3_1(a499)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540))) <=> (c0_1(a540) | c3_1(a528) | c1_1(a499) | (~ndr1_0) | (~c3_1(a499)) | (~c0_1(a499)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.27/1.44 inference(rewrite,[status(thm)],[])).
% 1.27/1.44 tff(3332,plain,
% 1.27/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a499) | (~c0_1(a499)) | (~c3_1(a499)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a540) | c3_1(a528) | c1_1(a499) | (~ndr1_0) | (~c3_1(a499)) | (~c0_1(a499)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540))))),
% 1.27/1.44 inference(monotonicity,[status(thm)],[3331])).
% 1.27/1.44 tff(3333,plain,
% 1.27/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a499) | (~c0_1(a499)) | (~c3_1(a499)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a528) | c1_1(a499) | (~ndr1_0) | (~c3_1(a499)) | (~c0_1(a499)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.27/1.44 inference(transitivity,[status(thm)],[3332, 3330])).
% 1.27/1.44 tff(3334,plain,
% 1.27/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a499) | (~c0_1(a499)) | (~c3_1(a499)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.27/1.45 inference(quant_inst,[status(thm)],[])).
% 1.27/1.45 tff(3335,plain,
% 1.27/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a528) | c1_1(a499) | (~ndr1_0) | (~c3_1(a499)) | (~c0_1(a499)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540))),
% 1.27/1.45 inference(modus_ponens,[status(thm)],[3334, 3333])).
% 1.27/1.45 tff(3336,plain,
% 1.27/1.45 (~c3_1(a499)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[3335, 106, 3191, 3221, 3250, 2975, 3329, 2291, 989, 3328, 1302])).
% 1.27/1.45 tff(3337,plain,
% 1.27/1.45 (c2_1(a499)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[1805, 3327])).
% 1.27/1.45 tff(3338,plain,
% 1.27/1.45 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a507) | c1_1(a507) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a507) | c1_1(a507) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a507)))),
% 1.27/1.45 inference(rewrite,[status(thm)],[])).
% 1.27/1.45 tff(3339,plain,
% 1.27/1.45 ((hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (hskp7 | c0_1(a507) | c1_1(a507) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a507)))),
% 1.27/1.45 inference(rewrite,[status(thm)],[])).
% 1.27/1.45 tff(3340,plain,
% 1.27/1.45 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a507) | c1_1(a507) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a507))))),
% 1.27/1.45 inference(monotonicity,[status(thm)],[3339])).
% 1.27/1.45 tff(3341,plain,
% 1.27/1.45 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a507) | c1_1(a507) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a507)))),
% 1.27/1.45 inference(transitivity,[status(thm)],[3340, 3338])).
% 1.27/1.45 tff(3342,plain,
% 1.27/1.45 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 1.27/1.45 inference(quant_inst,[status(thm)],[])).
% 1.27/1.45 tff(3343,plain,
% 1.27/1.45 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a507) | c1_1(a507) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a507))),
% 1.27/1.45 inference(modus_ponens,[status(thm)],[3342, 3341])).
% 1.27/1.45 tff(3344,plain,
% 1.27/1.45 (hskp7),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[3343, 106, 3259, 3329, 3337, 3260, 3261, 3328, 216])).
% 1.27/1.45 tff(3345,plain,
% 1.27/1.45 (~c3_1(a502)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[302, 3344])).
% 1.27/1.45 tff(3346,plain,
% 1.27/1.45 (~c1_1(a502)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[308, 3344])).
% 1.27/1.45 tff(3347,plain,
% 1.27/1.45 (~c0_1(a502)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[643, 3344])).
% 1.27/1.45 tff(3348,plain,
% 1.27/1.45 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | c1_1(a499) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a499)) | (~c0_1(a499)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a499) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a499)) | (~c0_1(a499)))),
% 1.27/1.45 inference(rewrite,[status(thm)],[])).
% 1.27/1.45 tff(3349,plain,
% 1.27/1.45 ((hskp20 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496))) <=> (hskp20 | c1_1(a499) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a499)) | (~c0_1(a499)))),
% 1.27/1.45 inference(rewrite,[status(thm)],[])).
% 1.27/1.45 tff(3350,plain,
% 1.27/1.45 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | c1_1(a499) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a499)) | (~c0_1(a499))))),
% 1.27/1.45 inference(monotonicity,[status(thm)],[3349])).
% 1.27/1.45 tff(3351,plain,
% 1.27/1.45 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a499) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a499)) | (~c0_1(a499)))),
% 1.27/1.45 inference(transitivity,[status(thm)],[3350, 3348])).
% 1.27/1.45 tff(3352,plain,
% 1.27/1.45 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))),
% 1.27/1.45 inference(quant_inst,[status(thm)],[])).
% 1.27/1.45 tff(3353,plain,
% 1.27/1.45 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a499) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a499)) | (~c0_1(a499))),
% 1.27/1.45 inference(modus_ponens,[status(thm)],[3352, 3351])).
% 1.27/1.45 tff(3354,plain,
% 1.27/1.45 (hskp20),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[3353, 106, 3329, 3337, 3328, 3245, 574, 1489, 3222])).
% 1.27/1.45 tff(3355,plain,
% 1.27/1.45 (~hskp1),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[1451, 3345, 2975, 989, 3250, 3346, 3354, 3347])).
% 1.27/1.45 tff(3356,plain,
% 1.27/1.45 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a499) | (~ndr1_0) | c3_1(a499) | (~c0_1(a499)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a499) | (~ndr1_0) | c3_1(a499) | (~c0_1(a499)))),
% 1.27/1.45 inference(rewrite,[status(thm)],[])).
% 1.27/1.45 tff(3357,plain,
% 1.27/1.45 ((hskp1 | (~ndr1_0) | c3_1(a499) | c1_1(a499) | (~c0_1(a499)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a499) | (~ndr1_0) | c3_1(a499) | (~c0_1(a499)))),
% 1.27/1.45 inference(rewrite,[status(thm)],[])).
% 1.27/1.45 tff(3358,plain,
% 1.27/1.45 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a499) | c1_1(a499) | (~c0_1(a499)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a499) | (~ndr1_0) | c3_1(a499) | (~c0_1(a499))))),
% 1.27/1.45 inference(monotonicity,[status(thm)],[3357])).
% 1.27/1.45 tff(3359,plain,
% 1.27/1.45 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a499) | c1_1(a499) | (~c0_1(a499)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a499) | (~ndr1_0) | c3_1(a499) | (~c0_1(a499)))),
% 1.27/1.45 inference(transitivity,[status(thm)],[3358, 3356])).
% 1.27/1.45 tff(3360,plain,
% 1.27/1.45 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a499) | c1_1(a499) | (~c0_1(a499)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 1.27/1.45 inference(quant_inst,[status(thm)],[])).
% 1.27/1.45 tff(3361,plain,
% 1.27/1.45 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a499) | (~ndr1_0) | c3_1(a499) | (~c0_1(a499))),
% 1.27/1.45 inference(modus_ponens,[status(thm)],[3360, 3359])).
% 1.27/1.45 tff(3362,plain,
% 1.27/1.45 ($false),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[3361, 106, 3355, 3329, 3347, 3346, 3345, 3328, 585, 3336])).
% 1.27/1.45 tff(3363,plain,(c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.27/1.45 tff(3364,plain,
% 1.27/1.45 (c0_1(a540)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[3363, 573, 574, 989, 32])).
% 1.27/1.45 tff(3365,plain,
% 1.27/1.45 (~hskp22),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[125, 3364])).
% 1.27/1.45 tff(3366,plain,
% 1.27/1.45 (~c0_1(a496)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[2481, 3365, 2512, 2513, 574, 573, 2514])).
% 1.27/1.45 tff(3367,plain,
% 1.27/1.45 (~c1_1(a509)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[2430, 3366, 573, 574, 2514, 2513, 2512])).
% 1.27/1.45 tff(3368,plain,
% 1.27/1.45 (c0_1(a528)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[3200, 3367, 2512, 2513, 2975, 989, 574, 573, 3365, 2514])).
% 1.27/1.45 tff(3369,plain,
% 1.27/1.45 (~hskp21),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[3179, 3368, 2975, 989, 574, 573, 3365])).
% 1.27/1.45 tff(3370,plain,
% 1.27/1.45 (~c2_1(a528)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[3187, 3369, 2975, 3367])).
% 1.27/1.45 tff(3371,plain,
% 1.27/1.45 ($false),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[916, 106, 3368, 2975, 989, 574, 573, 909, 3366, 3370])).
% 1.27/1.45 tff(3372,plain,(c3_1(a496) | c3_1(a528) | c2_1(a496) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.27/1.45 tff(3373,plain,
% 1.27/1.45 (hskp26),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[3372, 2510, 573, 574])).
% 1.27/1.45 tff(3374,plain,
% 1.27/1.45 (~c3_1(a559)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[2065, 3373])).
% 1.27/1.45 tff(3375,plain,
% 1.27/1.45 (~c2_1(a559)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[2071, 3373])).
% 1.27/1.45 tff(3376,plain,
% 1.27/1.45 (~c0_1(a559)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[2077, 3373])).
% 1.27/1.45 tff(3377,assumption,(~c2_1(a528)), introduced(assumption)).
% 1.27/1.45 tff(3378,plain,
% 1.27/1.45 ($false),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[2183, 106, 999, 998, 2096, 2095, 2094, 989, 909, 3377])).
% 1.27/1.45 tff(3379,plain,(c2_1(a528) | (~c0_1(a528)) | (~c1_1(a528)) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528)), inference(lemma,lemma(discharge,[]))).
% 1.27/1.45 tff(3380,plain,
% 1.27/1.45 (c2_1(a528)),
% 1.27/1.45 inference(unit_resolution,[status(thm)],[3379, 2509, 2508, 3376, 3375, 3374, 2510])).
% 1.27/1.45 tff(3381,plain,
% 1.27/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.27/1.45 inference(rewrite,[status(thm)],[])).
% 1.27/1.45 tff(3382,plain,
% 1.27/1.45 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a559) | c0_1(a559) | c2_1(a559)) <=> (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.27/1.45 inference(rewrite,[status(thm)],[])).
% 1.27/1.45 tff(3383,plain,
% 1.27/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a559) | c0_1(a559) | c2_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.27/1.45 inference(monotonicity,[status(thm)],[3382])).
% 1.27/1.45 tff(3384,plain,
% 1.27/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a559) | c0_1(a559) | c2_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.27/1.45 inference(transitivity,[status(thm)],[3383, 3381])).
% 1.27/1.45 tff(3385,plain,
% 1.27/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a559) | c0_1(a559) | c2_1(a559))),
% 1.27/1.46 inference(quant_inst,[status(thm)],[])).
% 1.27/1.46 tff(3386,plain,
% 1.27/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.27/1.46 inference(modus_ponens,[status(thm)],[3385, 3384])).
% 1.27/1.46 tff(3387,plain,
% 1.27/1.46 (~c1_1(a509)),
% 1.27/1.46 inference(unit_resolution,[status(thm)],[3386, 106, 2509, 2508, 2207, 3376, 3375, 3374, 2510, 2191, 909])).
% 1.27/1.46 tff(3388,plain,
% 1.27/1.46 (hskp21 | (~c2_1(a528))),
% 1.27/1.46 inference(unit_resolution,[status(thm)],[3186, 106, 2508, 2207, 2510, 2191, 2153, 3387])).
% 1.27/1.46 tff(3389,plain,
% 1.27/1.46 (hskp21),
% 1.27/1.46 inference(unit_resolution,[status(thm)],[3388, 3380])).
% 1.27/1.46 tff(3390,plain,
% 1.27/1.46 (hskp22),
% 1.27/1.46 inference(unit_resolution,[status(thm)],[3179, 3389, 574, 2510, 2509, 2508, 573])).
% 1.27/1.46 tff(3391,plain,
% 1.27/1.46 (~c0_1(a540)),
% 1.27/1.46 inference(unit_resolution,[status(thm)],[125, 3390])).
% 1.27/1.46 tff(3392,plain,
% 1.27/1.46 (c1_1(a540)),
% 1.27/1.46 inference(unit_resolution,[status(thm)],[141, 3390])).
% 1.27/1.46 tff(3393,plain,
% 1.27/1.46 (c3_1(a540)),
% 1.27/1.46 inference(unit_resolution,[status(thm)],[133, 3390])).
% 1.27/1.46 tff(3394,plain,
% 1.27/1.46 ($false),
% 1.27/1.46 inference(unit_resolution,[status(thm)],[3242, 3393, 3392, 2191, 2207, 2508, 2199, 3387, 2510, 3391])).
% 1.27/1.46 tff(3395,plain,(c3_1(a496) | c2_1(a496)), inference(lemma,lemma(discharge,[]))).
% 1.27/1.46 tff(3396,plain,
% 1.27/1.46 ($false),
% 1.27/1.46 inference(unit_resolution,[status(thm)],[3395, 2411, 2410])).
% 1.27/1.46 % SZS output end Proof
% 1.27/1.46 % E exiting
%------------------------------------------------------------------------------