%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN452-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:39:10 AM UTC 2025
% Result : Unsatisfiable 0.47s 0.63s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN452-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.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 12:35:10 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.47/0.63 % SZS status Unsatisfiable
% 0.47/0.63 % SZS output start Proof
% 0.47/0.63 tff(c0_1_type, type, (
% 0.47/0.63 c0_1: $i > $o)).
% 0.47/0.63 tff(a865_type, type, (
% 0.47/0.63 a865: $i)).
% 0.47/0.63 tff(c3_1_type, type, (
% 0.47/0.63 c3_1: $i > $o)).
% 0.47/0.63 tff(a828_type, type, (
% 0.47/0.63 a828: $i)).
% 0.47/0.63 tff(c1_1_type, type, (
% 0.47/0.63 c1_1: $i > $o)).
% 0.47/0.63 tff(a826_type, type, (
% 0.47/0.63 a826: $i)).
% 0.47/0.63 tff(c2_1_type, type, (
% 0.47/0.63 c2_1: $i > $o)).
% 0.47/0.63 tff(ndr1_0_type, type, (
% 0.47/0.63 ndr1_0: $o)).
% 0.47/0.63 tff(hskp7_type, type, (
% 0.47/0.63 hskp7: $o)).
% 0.47/0.63 tff(a860_type, type, (
% 0.47/0.63 a860: $i)).
% 0.47/0.63 tff(hskp22_type, type, (
% 0.47/0.63 hskp22: $o)).
% 0.47/0.63 tff(a821_type, type, (
% 0.47/0.63 a821: $i)).
% 0.47/0.63 tff(a816_type, type, (
% 0.47/0.63 a816: $i)).
% 0.47/0.63 tff(a830_type, type, (
% 0.47/0.63 a830: $i)).
% 0.47/0.63 tff(hskp8_type, type, (
% 0.47/0.63 hskp8: $o)).
% 0.47/0.63 tff(hskp1_type, type, (
% 0.47/0.63 hskp1: $o)).
% 0.47/0.63 tff(a842_type, type, (
% 0.47/0.63 a842: $i)).
% 0.47/0.63 tff(hskp14_type, type, (
% 0.47/0.63 hskp14: $o)).
% 0.47/0.63 tff(a878_type, type, (
% 0.47/0.63 a878: $i)).
% 0.47/0.63 tff(hskp24_type, type, (
% 0.47/0.63 hskp24: $o)).
% 0.47/0.63 tff(a815_type, type, (
% 0.47/0.63 a815: $i)).
% 0.47/0.63 tff(hskp0_type, type, (
% 0.47/0.63 hskp0: $o)).
% 0.47/0.63 tff(a833_type, type, (
% 0.47/0.63 a833: $i)).
% 0.47/0.63 tff(hskp28_type, type, (
% 0.47/0.63 hskp28: $o)).
% 0.47/0.63 tff(hskp20_type, type, (
% 0.47/0.63 hskp20: $o)).
% 0.47/0.63 tff(a817_type, type, (
% 0.47/0.63 a817: $i)).
% 0.47/0.63 tff(hskp2_type, type, (
% 0.47/0.63 hskp2: $o)).
% 0.47/0.63 tff(a831_type, type, (
% 0.47/0.63 a831: $i)).
% 0.47/0.63 tff(hskp9_type, type, (
% 0.47/0.63 hskp9: $o)).
% 0.47/0.63 tff(a856_type, type, (
% 0.47/0.63 a856: $i)).
% 0.47/0.63 tff(hskp29_type, type, (
% 0.47/0.63 hskp29: $o)).
% 0.47/0.63 tff(hskp4_type, type, (
% 0.47/0.63 hskp4: $o)).
% 0.47/0.63 tff(a825_type, type, (
% 0.47/0.63 a825: $i)).
% 0.47/0.63 tff(hskp5_type, type, (
% 0.47/0.63 hskp5: $o)).
% 0.47/0.63 tff(a855_type, type, (
% 0.47/0.63 a855: $i)).
% 0.47/0.63 tff(hskp19_type, type, (
% 0.47/0.63 hskp19: $o)).
% 0.47/0.63 tff(hskp27_type, type, (
% 0.47/0.63 hskp27: $o)).
% 0.47/0.63 tff(a839_type, type, (
% 0.47/0.63 a839: $i)).
% 0.47/0.63 tff(hskp13_type, type, (
% 0.47/0.63 hskp13: $o)).
% 0.47/0.63 tff(hskp16_type, type, (
% 0.47/0.63 hskp16: $o)).
% 0.47/0.63 tff(a848_type, type, (
% 0.47/0.63 a848: $i)).
% 0.47/0.63 tff(a857_type, type, (
% 0.47/0.63 a857: $i)).
% 0.47/0.63 tff(hskp21_type, type, (
% 0.47/0.63 hskp21: $o)).
% 0.47/0.63 tff(a827_type, type, (
% 0.47/0.63 a827: $i)).
% 0.47/0.63 tff(hskp6_type, type, (
% 0.47/0.63 hskp6: $o)).
% 0.47/0.63 tff(a844_type, type, (
% 0.47/0.63 a844: $i)).
% 0.47/0.63 tff(hskp15_type, type, (
% 0.47/0.63 hskp15: $o)).
% 0.47/0.63 tff(1,assumption,(~c3_1(a828)), introduced(assumption)).
% 0.47/0.63 tff(2,plain,
% 0.47/0.63 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(3,plain,
% 0.47/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_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)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[2])).
% 0.47/0.63 tff(4,plain,
% 0.47/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_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)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(5,plain,
% 0.47/0.63 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(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)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(6,plain,
% 0.47/0.63 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_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)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[5])).
% 0.47/0.63 tff(7,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.47/0.63 tff(8,plain,
% 0.47/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.47/0.63 tff(9,plain,
% 0.47/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.47/0.64 tff(10,plain,(
% 0.47/0.64 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.64 inference(skolemize,[status(sab)],[9])).
% 0.47/0.64 tff(11,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.47/0.64 tff(12,assumption,(~hskp7), introduced(assumption)).
% 0.47/0.64 tff(13,assumption,(~hskp22), introduced(assumption)).
% 0.47/0.64 tff(14,plain,
% 0.47/0.64 (^[U: $i] : refl((hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(15,plain,
% 0.47/0.64 (![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[14])).
% 0.47/0.64 tff(16,plain,
% 0.47/0.64 (![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(17,plain,
% 0.47/0.64 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp22) <=> ((hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp22))), rewrite(((hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp22) <=> (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp22) <=> (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(18,plain,
% 0.47/0.64 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp22) <=> ![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[17])).
% 0.47/0.64 tff(19,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 0.47/0.64 tff(20,plain,
% 0.47/0.64 (![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.47/0.64 tff(21,plain,
% 0.47/0.64 (![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.47/0.64 tff(22,plain,(
% 0.47/0.64 ![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.47/0.64 inference(skolemize,[status(sab)],[21])).
% 0.47/0.64 tff(23,plain,
% 0.47/0.64 (![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.47/0.64 tff(24,assumption,(~hskp1), introduced(assumption)).
% 0.47/0.64 tff(25,plain,
% 0.47/0.64 (^[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)) | c1_1(W) | 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)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(26,plain,
% 0.47/0.64 (![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)) | c1_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)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[25])).
% 0.47/0.64 tff(27,plain,
% 0.47/0.64 (![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)) | c1_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)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(28,plain,
% 0.47/0.64 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_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)) | (~c2_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) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(29,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[28])).
% 0.47/0.64 tff(30,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.47/0.64 tff(31,plain,
% 0.47/0.64 (![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.47/0.64 tff(32,plain,
% 0.47/0.64 (![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.47/0.64 tff(33,plain,(
% 0.47/0.64 ![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.47/0.64 inference(skolemize,[status(sab)],[32])).
% 0.47/0.64 tff(34,plain,
% 0.47/0.64 (![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.47/0.64 tff(35,plain,
% 0.47/0.64 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(36,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_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) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[35])).
% 0.47/0.64 tff(37,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_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) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(38,plain,
% 0.47/0.64 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_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) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(39,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) | c1_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) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[38])).
% 0.47/0.64 tff(40,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.47/0.64 tff(41,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.47/0.64 tff(42,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.47/0.64 tff(43,plain,(
% 0.47/0.64 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.47/0.64 inference(skolemize,[status(sab)],[42])).
% 0.47/0.64 tff(44,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.47/0.64 tff(45,assumption,(~hskp24), introduced(assumption)).
% 0.47/0.64 tff(46,plain,
% 0.47/0.64 ((hskp14 | hskp24) <=> (hskp14 | hskp24)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(47,axiom,(hskp14 | hskp24), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.47/0.64 tff(48,plain,
% 0.47/0.64 (hskp14 | hskp24),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.47/0.64 tff(49,plain,
% 0.47/0.64 (hskp14),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.47/0.64 tff(50,plain,
% 0.47/0.64 (((~hskp14) | (~c2_1(a842))) <=> ((~hskp14) | (~c2_1(a842)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(51,plain,
% 0.47/0.64 (((~c2_1(a842)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a842)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(52,axiom,((~c2_1(a842)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.47/0.64 tff(53,plain,
% 0.47/0.64 ((~hskp14) | (~c2_1(a842))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.47/0.64 tff(54,plain,
% 0.47/0.64 ((~hskp14) | (~c2_1(a842))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.47/0.64 tff(55,plain,
% 0.47/0.64 (~c2_1(a842)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[54, 49])).
% 0.47/0.64 tff(56,plain,
% 0.47/0.64 (((~hskp14) | c1_1(a842)) <=> ((~hskp14) | c1_1(a842))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(57,axiom,((~hskp14) | c1_1(a842)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.47/0.64 tff(58,plain,
% 0.47/0.64 ((~hskp14) | c1_1(a842)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.47/0.64 tff(59,plain,
% 0.47/0.64 ((~hskp14) | c1_1(a842)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[58, 56])).
% 0.47/0.64 tff(60,plain,
% 0.47/0.64 ((~hskp14) | c1_1(a842)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[59, 56])).
% 0.47/0.64 tff(61,plain,
% 0.47/0.64 ((~hskp14) | c1_1(a842)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.47/0.64 tff(62,plain,
% 0.47/0.64 ((~hskp14) | c1_1(a842)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[61, 56])).
% 0.47/0.64 tff(63,plain,
% 0.47/0.64 (c1_1(a842)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[62, 49])).
% 0.47/0.64 tff(64,plain,
% 0.47/0.64 (((~hskp14) | c0_1(a842)) <=> ((~hskp14) | c0_1(a842))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(65,axiom,((~hskp14) | c0_1(a842)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.47/0.64 tff(66,plain,
% 0.47/0.64 ((~hskp14) | c0_1(a842)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.47/0.64 tff(67,plain,
% 0.47/0.64 ((~hskp14) | c0_1(a842)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[66, 64])).
% 0.47/0.64 tff(68,plain,
% 0.47/0.64 ((~hskp14) | c0_1(a842)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[67, 64])).
% 0.47/0.64 tff(69,plain,
% 0.47/0.64 ((~hskp14) | c0_1(a842)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.47/0.64 tff(70,plain,
% 0.47/0.64 ((~hskp14) | c0_1(a842)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[69, 64])).
% 0.47/0.64 tff(71,plain,
% 0.47/0.64 (c0_1(a842)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[70, 49])).
% 0.47/0.64 tff(72,plain,
% 0.47/0.64 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(73,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[72])).
% 0.47/0.64 tff(74,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(75,plain,
% 0.47/0.64 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(76,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[75])).
% 0.47/0.64 tff(77,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 0.47/0.64 tff(78,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.47/0.64 tff(79,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.47/0.64 tff(80,plain,(
% 0.47/0.64 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.47/0.64 inference(skolemize,[status(sab)],[79])).
% 0.47/0.64 tff(81,plain,
% 0.47/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.47/0.64 tff(82,plain,
% 0.47/0.64 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(83,plain,
% 0.47/0.64 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[82])).
% 0.47/0.64 tff(84,plain,
% 0.47/0.64 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(85,plain,
% 0.47/0.64 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(86,plain,
% 0.47/0.64 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[85])).
% 0.47/0.64 tff(87,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 0.47/0.64 tff(88,plain,
% 0.47/0.64 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.47/0.64 tff(89,plain,
% 0.47/0.64 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.47/0.64 tff(90,plain,(
% 0.47/0.64 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.47/0.64 inference(skolemize,[status(sab)],[89])).
% 0.47/0.64 tff(91,plain,
% 0.47/0.64 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.47/0.64 tff(92,assumption,(~c2_1(a842)), introduced(assumption)).
% 0.47/0.64 tff(93,assumption,(hskp20), introduced(assumption)).
% 0.47/0.64 tff(94,plain,
% 0.47/0.64 (((~hskp20) | (~c2_1(a856))) <=> ((~hskp20) | (~c2_1(a856)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(95,plain,
% 0.47/0.64 (((~c2_1(a856)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a856)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(96,axiom,((~c2_1(a856)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.47/0.64 tff(97,plain,
% 0.47/0.64 ((~hskp20) | (~c2_1(a856))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.47/0.64 tff(98,plain,
% 0.47/0.64 ((~hskp20) | (~c2_1(a856))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[97, 94])).
% 0.47/0.64 tff(99,plain,
% 0.47/0.64 (~c2_1(a856)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[98, 93])).
% 0.47/0.64 tff(100,assumption,(c1_1(a842)), introduced(assumption)).
% 0.47/0.64 tff(101,assumption,(c0_1(a842)), introduced(assumption)).
% 0.47/0.64 tff(102,plain,
% 0.47/0.64 (((~hskp20) | (~c1_1(a856))) <=> ((~hskp20) | (~c1_1(a856)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(103,plain,
% 0.47/0.64 (((~c1_1(a856)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a856)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(104,axiom,((~c1_1(a856)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.47/0.65 tff(105,plain,
% 0.47/0.65 ((~hskp20) | (~c1_1(a856))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.47/0.65 tff(106,plain,
% 0.47/0.65 ((~hskp20) | (~c1_1(a856))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[105, 102])).
% 0.47/0.65 tff(107,plain,
% 0.47/0.65 (~c1_1(a856)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[106, 93])).
% 0.47/0.65 tff(108,plain,
% 0.47/0.65 (((~hskp20) | c3_1(a856)) <=> ((~hskp20) | c3_1(a856))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(109,axiom,((~hskp20) | c3_1(a856)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.47/0.65 tff(110,plain,
% 0.47/0.65 ((~hskp20) | c3_1(a856)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.47/0.65 tff(111,plain,
% 0.47/0.65 ((~hskp20) | c3_1(a856)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[110, 108])).
% 0.47/0.65 tff(112,plain,
% 0.47/0.65 ((~hskp20) | c3_1(a856)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[111, 108])).
% 0.47/0.65 tff(113,plain,
% 0.47/0.65 ((~hskp20) | c3_1(a856)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.47/0.65 tff(114,plain,
% 0.47/0.65 ((~hskp20) | c3_1(a856)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[113, 108])).
% 0.47/0.65 tff(115,plain,
% 0.47/0.65 (c3_1(a856)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[114, 93])).
% 0.47/0.65 tff(116,assumption,(~c0_1(a856)), introduced(assumption)).
% 0.47/0.65 tff(117,assumption,(~c2_1(a856)), introduced(assumption)).
% 0.47/0.65 tff(118,assumption,(~c1_1(a856)), introduced(assumption)).
% 0.47/0.65 tff(119,assumption,(c3_1(a856)), introduced(assumption)).
% 0.47/0.65 tff(120,assumption,(~ndr1_0), introduced(assumption)).
% 0.47/0.65 tff(121,plain,
% 0.47/0.65 ((ndr1_0 | (~hskp20)) <=> (ndr1_0 | (~hskp20))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(122,plain,
% 0.47/0.65 (((~hskp20) | ndr1_0) <=> (ndr1_0 | (~hskp20))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(123,axiom,((~hskp20) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause11')).
% 0.47/0.65 tff(124,plain,
% 0.47/0.65 (ndr1_0 | (~hskp20)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.47/0.65 tff(125,plain,
% 0.47/0.65 (ndr1_0 | (~hskp20)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[124, 121])).
% 0.47/0.65 tff(126,plain,
% 0.47/0.65 (~hskp20),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[125, 120])).
% 0.47/0.65 tff(127,plain,
% 0.47/0.65 ((ndr1_0 | (~hskp28)) <=> (ndr1_0 | (~hskp28))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(128,plain,
% 0.47/0.65 (((~hskp28) | ndr1_0) <=> (ndr1_0 | (~hskp28))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(129,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.47/0.65 tff(130,plain,
% 0.47/0.65 (ndr1_0 | (~hskp28)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.47/0.65 tff(131,plain,
% 0.47/0.65 (ndr1_0 | (~hskp28)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[130, 127])).
% 0.47/0.65 tff(132,plain,
% 0.47/0.65 (~hskp28),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[131, 120])).
% 0.47/0.65 tff(133,plain,
% 0.47/0.65 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(134,plain,
% 0.47/0.65 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(135,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.47/0.65 tff(136,plain,
% 0.47/0.65 (ndr1_0 | (~hskp24)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.47/0.65 tff(137,plain,
% 0.47/0.65 (ndr1_0 | (~hskp24)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[136, 133])).
% 0.47/0.65 tff(138,plain,
% 0.47/0.65 (~hskp24),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[137, 120])).
% 0.47/0.65 tff(139,plain,
% 0.47/0.65 ((hskp24 | hskp28 | hskp20) <=> (hskp24 | hskp28 | hskp20)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(140,plain,
% 0.47/0.65 (((hskp24 | hskp28) | hskp20) <=> (hskp24 | hskp28 | hskp20)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(141,plain,
% 0.47/0.65 ((hskp28 | hskp24) <=> (hskp24 | hskp28)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(142,plain,
% 0.47/0.65 (((hskp28 | hskp24) | hskp20) <=> ((hskp24 | hskp28) | hskp20)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[141])).
% 0.47/0.65 tff(143,plain,
% 0.47/0.65 (((hskp28 | hskp24) | hskp20) <=> (hskp24 | hskp28 | hskp20)),
% 0.47/0.65 inference(transitivity,[status(thm)],[142, 140])).
% 0.47/0.65 tff(144,axiom,((hskp28 | hskp24) | hskp20), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.47/0.65 tff(145,plain,
% 0.47/0.65 (hskp24 | hskp28 | hskp20),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.47/0.65 tff(146,plain,
% 0.47/0.65 (hskp24 | hskp28 | hskp20),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[145, 139])).
% 0.47/0.65 tff(147,plain,
% 0.47/0.65 (hskp24 | hskp28 | hskp20),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.47/0.65 tff(148,plain,
% 0.47/0.65 (hskp24 | hskp28 | hskp20),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[147, 139])).
% 0.47/0.65 tff(149,plain,
% 0.47/0.65 (hskp24 | hskp28 | hskp20),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[148, 139])).
% 0.47/0.65 tff(150,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[149, 138, 132, 126])).
% 0.47/0.65 tff(151,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(152,plain,
% 0.47/0.65 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | c0_1(a856) | (~c3_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | c0_1(a856) | (~c3_1(a856)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(153,plain,
% 0.47/0.65 ((hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a856) | c0_1(a856) | (~c3_1(a856))) <=> (hskp2 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | c0_1(a856) | (~c3_1(a856)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(154,plain,
% 0.47/0.65 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | c0_1(a856) | (~c3_1(a856))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[153])).
% 0.47/0.65 tff(155,plain,
% 0.47/0.65 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | c0_1(a856) | (~c3_1(a856)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[154, 152])).
% 0.47/0.65 tff(156,plain,
% 0.47/0.65 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(157,plain,
% 0.47/0.65 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | c0_1(a856) | (~c3_1(a856))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.47/0.65 tff(158,plain,
% 0.47/0.65 (hskp2 | c0_1(a856)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[157, 151, 119, 118, 117, 91])).
% 0.47/0.65 tff(159,plain,
% 0.47/0.65 (hskp2),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[158, 116])).
% 0.47/0.65 tff(160,plain,
% 0.47/0.65 (((~hskp2) | (~c0_1(a817))) <=> ((~hskp2) | (~c0_1(a817)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(161,plain,
% 0.47/0.65 (((~c0_1(a817)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a817)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(162,axiom,((~c0_1(a817)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.47/0.65 tff(163,plain,
% 0.47/0.65 ((~hskp2) | (~c0_1(a817))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.47/0.65 tff(164,plain,
% 0.47/0.65 ((~hskp2) | (~c0_1(a817))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[163, 160])).
% 0.47/0.65 tff(165,plain,
% 0.47/0.65 (~c0_1(a817)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[164, 159])).
% 0.47/0.65 tff(166,plain,
% 0.47/0.65 (((~hskp2) | c2_1(a817)) <=> ((~hskp2) | c2_1(a817))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(167,axiom,((~hskp2) | c2_1(a817)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.47/0.65 tff(168,plain,
% 0.47/0.65 ((~hskp2) | c2_1(a817)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.47/0.65 tff(169,plain,
% 0.47/0.65 ((~hskp2) | c2_1(a817)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[168, 166])).
% 0.47/0.65 tff(170,plain,
% 0.47/0.65 ((~hskp2) | c2_1(a817)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[169, 166])).
% 0.47/0.65 tff(171,plain,
% 0.47/0.65 ((~hskp2) | c2_1(a817)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.47/0.65 tff(172,plain,
% 0.47/0.65 ((~hskp2) | c2_1(a817)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[171, 166])).
% 0.47/0.65 tff(173,plain,
% 0.47/0.65 (c2_1(a817)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[172, 159])).
% 0.47/0.65 tff(174,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a856) | c2_1(a856) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a856)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a856) | c2_1(a856) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a856)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(175,plain,
% 0.47/0.65 (((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817))) <=> (c1_1(a856) | c2_1(a856) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a856)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(176,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a856) | c2_1(a856) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a856))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[175])).
% 0.47/0.65 tff(177,plain,
% 0.47/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a856) | c2_1(a856) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a856)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[176, 174])).
% 0.47/0.65 tff(178,plain,
% 0.47/0.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(179,plain,
% 0.47/0.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a856) | c2_1(a856) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a856))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.47/0.65 tff(180,plain,
% 0.47/0.65 (~c1_1(a817)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[179, 151, 119, 101, 100, 173, 118, 117, 92, 165, 81])).
% 0.47/0.65 tff(181,plain,
% 0.47/0.65 (^[V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(182,plain,
% 0.47/0.65 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[181])).
% 0.47/0.65 tff(183,plain,
% 0.47/0.65 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(184,plain,
% 0.47/0.65 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(185,plain,
% 0.47/0.65 (![V: $i, U: $i] : (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[184])).
% 0.47/0.65 tff(186,axiom,(![V: $i, U: $i] : (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 0.47/0.65 tff(187,plain,
% 0.47/0.65 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.47/0.65 tff(188,plain,
% 0.47/0.65 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.47/0.65 tff(189,plain,(
% 0.47/0.65 ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.65 inference(skolemize,[status(sab)],[188])).
% 0.47/0.65 tff(190,plain,
% 0.47/0.65 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.47/0.65 tff(191,plain,
% 0.47/0.65 (((~hskp2) | (~c3_1(a817))) <=> ((~hskp2) | (~c3_1(a817)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(192,plain,
% 0.47/0.65 (((~c3_1(a817)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a817)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(193,axiom,((~c3_1(a817)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.47/0.65 tff(194,plain,
% 0.47/0.65 ((~hskp2) | (~c3_1(a817))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.47/0.65 tff(195,plain,
% 0.47/0.65 ((~hskp2) | (~c3_1(a817))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[194, 191])).
% 0.47/0.65 tff(196,plain,
% 0.47/0.65 (~c3_1(a817)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[195, 159])).
% 0.47/0.65 tff(197,plain,
% 0.47/0.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c1_1(a856) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | c0_1(a856) | (~c3_1(a856)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c1_1(a856) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | c0_1(a856) | (~c3_1(a856)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(198,plain,
% 0.47/0.65 (((~ndr1_0) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)) | c1_1(a817) | c0_1(a817) | c3_1(a817)) <=> (c1_1(a856) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | c0_1(a856) | (~c3_1(a856)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(199,plain,
% 0.47/0.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)) | c1_1(a817) | c0_1(a817) | c3_1(a817))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c1_1(a856) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | c0_1(a856) | (~c3_1(a856))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[198])).
% 0.47/0.65 tff(200,plain,
% 0.47/0.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)) | c1_1(a817) | c0_1(a817) | c3_1(a817))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c1_1(a856) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | c0_1(a856) | (~c3_1(a856)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[199, 197])).
% 0.47/0.65 tff(201,plain,
% 0.47/0.65 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)) | c1_1(a817) | c0_1(a817) | c3_1(a817))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(202,plain,
% 0.47/0.65 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c1_1(a856) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | c0_1(a856) | (~c3_1(a856))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.47/0.65 tff(203,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[202, 151, 119, 118, 165, 196, 190, 116, 180])).
% 0.47/0.65 tff(204,plain,(c0_1(a856) | (~c3_1(a856)) | c1_1(a856) | (~c0_1(a842)) | (~c1_1(a842)) | c2_1(a856) | c2_1(a842)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(205,plain,
% 0.47/0.65 (c0_1(a856)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[204, 115, 107, 101, 100, 99, 92])).
% 0.47/0.65 tff(206,plain,
% 0.47/0.65 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(207,plain,
% 0.47/0.65 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[206])).
% 0.47/0.65 tff(208,plain,
% 0.47/0.65 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(209,plain,
% 0.47/0.65 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(210,plain,
% 0.47/0.65 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[209])).
% 0.47/0.65 tff(211,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 0.47/0.65 tff(212,plain,
% 0.47/0.65 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.47/0.65 tff(213,plain,
% 0.47/0.65 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[212, 208])).
% 0.47/0.65 tff(214,plain,(
% 0.47/0.65 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.47/0.65 inference(skolemize,[status(sab)],[213])).
% 0.47/0.65 tff(215,plain,
% 0.47/0.65 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[214, 207])).
% 0.47/0.65 tff(216,plain,
% 0.47/0.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | (~c0_1(a856)) | (~c3_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | (~c0_1(a856)) | (~c3_1(a856)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(217,plain,
% 0.47/0.65 ((hskp9 | (~ndr1_0) | c2_1(a856) | (~c3_1(a856)) | (~c0_1(a856)) | c2_1(a856) | c1_1(a856) | (~c0_1(a856))) <=> (hskp9 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | (~c0_1(a856)) | (~c3_1(a856)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(218,plain,
% 0.47/0.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a856) | (~c3_1(a856)) | (~c0_1(a856)) | c2_1(a856) | c1_1(a856) | (~c0_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | (~c0_1(a856)) | (~c3_1(a856))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[217])).
% 0.47/0.65 tff(219,plain,
% 0.47/0.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a856) | (~c3_1(a856)) | (~c0_1(a856)) | c2_1(a856) | c1_1(a856) | (~c0_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | (~c0_1(a856)) | (~c3_1(a856)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[218, 216])).
% 0.47/0.65 tff(220,plain,
% 0.47/0.65 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a856) | (~c3_1(a856)) | (~c0_1(a856)) | c2_1(a856) | c1_1(a856) | (~c0_1(a856)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(221,plain,
% 0.47/0.65 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | (~c0_1(a856)) | (~c3_1(a856))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.47/0.65 tff(222,plain,
% 0.47/0.65 (hskp9 | (~c0_1(a856))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[221, 151, 115, 107, 99, 215])).
% 0.47/0.65 tff(223,plain,
% 0.47/0.65 (hskp9),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[222, 205])).
% 0.47/0.65 tff(224,plain,
% 0.47/0.65 (((~hskp9) | (~c1_1(a831))) <=> ((~hskp9) | (~c1_1(a831)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(225,plain,
% 0.47/0.65 (((~c1_1(a831)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a831)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(226,axiom,((~c1_1(a831)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.47/0.65 tff(227,plain,
% 0.47/0.65 ((~hskp9) | (~c1_1(a831))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.47/0.65 tff(228,plain,
% 0.47/0.65 ((~hskp9) | (~c1_1(a831))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[227, 224])).
% 0.47/0.65 tff(229,plain,
% 0.47/0.65 (~c1_1(a831)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[228, 223])).
% 0.47/0.65 tff(230,plain,
% 0.47/0.65 (((~hskp9) | (~c0_1(a831))) <=> ((~hskp9) | (~c0_1(a831)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(231,plain,
% 0.47/0.65 (((~c0_1(a831)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a831)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(232,axiom,((~c0_1(a831)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.47/0.65 tff(233,plain,
% 0.47/0.65 ((~hskp9) | (~c0_1(a831))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.47/0.65 tff(234,plain,
% 0.47/0.65 ((~hskp9) | (~c0_1(a831))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[233, 230])).
% 0.47/0.65 tff(235,plain,
% 0.47/0.65 (~c0_1(a831)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[234, 223])).
% 0.47/0.65 tff(236,plain,
% 0.47/0.65 (((~hskp9) | c3_1(a831)) <=> ((~hskp9) | c3_1(a831))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(237,axiom,((~hskp9) | c3_1(a831)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.47/0.65 tff(238,plain,
% 0.47/0.65 ((~hskp9) | c3_1(a831)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.47/0.65 tff(239,plain,
% 0.47/0.65 ((~hskp9) | c3_1(a831)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[238, 236])).
% 0.47/0.65 tff(240,plain,
% 0.47/0.65 ((~hskp9) | c3_1(a831)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[239, 236])).
% 0.47/0.65 tff(241,plain,
% 0.47/0.65 ((~hskp9) | c3_1(a831)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[240, 236])).
% 0.47/0.65 tff(242,plain,
% 0.47/0.65 ((~hskp9) | c3_1(a831)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[241, 236])).
% 0.47/0.65 tff(243,plain,
% 0.47/0.65 (c3_1(a831)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[242, 223])).
% 0.47/0.65 tff(244,plain,
% 0.47/0.65 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a856) | c2_1(a856) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a856) | c2_1(a856) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a856)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(245,plain,
% 0.47/0.66 ((hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831))) <=> (hskp2 | c1_1(a856) | c2_1(a856) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a856)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(246,plain,
% 0.47/0.66 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a856) | c2_1(a856) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a856))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[245])).
% 0.47/0.66 tff(247,plain,
% 0.47/0.66 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a856) | c2_1(a856) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a856)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[246, 244])).
% 0.47/0.66 tff(248,plain,
% 0.47/0.66 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(249,plain,
% 0.47/0.66 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a856) | c2_1(a856) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a856))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.47/0.66 tff(250,plain,
% 0.47/0.66 (hskp2),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[249, 151, 115, 243, 107, 99, 235, 229, 91])).
% 0.47/0.66 tff(251,plain,
% 0.47/0.66 (~c0_1(a817)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[164, 250])).
% 0.47/0.66 tff(252,plain,
% 0.47/0.66 (c2_1(a817)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[172, 250])).
% 0.47/0.66 tff(253,plain,
% 0.47/0.66 (~c1_1(a817)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[179, 151, 115, 101, 100, 252, 107, 99, 92, 251, 81])).
% 0.47/0.66 tff(254,plain,
% 0.47/0.66 (~c3_1(a817)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[195, 250])).
% 0.47/0.66 tff(255,plain,
% 0.47/0.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a831) | c1_1(a831) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a831) | c1_1(a831) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a831)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(256,plain,
% 0.47/0.66 (((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a817) | c0_1(a817) | c3_1(a817)) <=> (c0_1(a831) | c1_1(a831) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a831)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(257,plain,
% 0.47/0.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a817) | c0_1(a817) | c3_1(a817))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a831) | c1_1(a831) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a831))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[256])).
% 0.47/0.66 tff(258,plain,
% 0.47/0.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a817) | c0_1(a817) | c3_1(a817))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a831) | c1_1(a831) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a831)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[257, 255])).
% 0.47/0.66 tff(259,plain,
% 0.47/0.66 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a817) | c0_1(a817) | c3_1(a817))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(260,plain,
% 0.47/0.66 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a831) | c1_1(a831) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a831))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.47/0.66 tff(261,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[260, 151, 243, 235, 229, 251, 254, 190, 253])).
% 0.47/0.66 tff(262,plain,((~hskp20) | (~c0_1(a842)) | (~c1_1(a842)) | c2_1(a842)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.66 tff(263,plain,
% 0.47/0.66 (~hskp20),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[262, 71, 63, 55])).
% 0.47/0.66 tff(264,plain,
% 0.47/0.66 (hskp28),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[149, 263, 45])).
% 0.47/0.66 tff(265,plain,
% 0.47/0.66 (((~hskp28) | c3_1(a833)) <=> ((~hskp28) | c3_1(a833))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(266,axiom,((~hskp28) | c3_1(a833)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.47/0.66 tff(267,plain,
% 0.47/0.66 ((~hskp28) | c3_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.47/0.66 tff(268,plain,
% 0.47/0.66 ((~hskp28) | c3_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[267, 265])).
% 0.47/0.66 tff(269,plain,
% 0.47/0.66 ((~hskp28) | c3_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[268, 265])).
% 0.47/0.66 tff(270,plain,
% 0.47/0.66 ((~hskp28) | c3_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[269, 265])).
% 0.47/0.66 tff(271,plain,
% 0.47/0.66 ((~hskp28) | c3_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[270, 265])).
% 0.47/0.66 tff(272,plain,
% 0.47/0.66 (c3_1(a833)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[271, 264])).
% 0.47/0.66 tff(273,plain,
% 0.47/0.66 (((~hskp28) | c1_1(a833)) <=> ((~hskp28) | c1_1(a833))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(274,axiom,((~hskp28) | c1_1(a833)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.47/0.66 tff(275,plain,
% 0.47/0.66 ((~hskp28) | c1_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.47/0.66 tff(276,plain,
% 0.47/0.66 ((~hskp28) | c1_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[275, 273])).
% 0.47/0.66 tff(277,plain,
% 0.47/0.66 ((~hskp28) | c1_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[276, 273])).
% 0.47/0.66 tff(278,plain,
% 0.47/0.66 ((~hskp28) | c1_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.47/0.66 tff(279,plain,
% 0.47/0.66 ((~hskp28) | c1_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[278, 273])).
% 0.47/0.66 tff(280,plain,
% 0.47/0.66 (c1_1(a833)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[279, 264])).
% 0.47/0.66 tff(281,plain,
% 0.47/0.66 (((~hskp28) | c0_1(a833)) <=> ((~hskp28) | c0_1(a833))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(282,axiom,((~hskp28) | c0_1(a833)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.47/0.66 tff(283,plain,
% 0.47/0.66 ((~hskp28) | c0_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.47/0.66 tff(284,plain,
% 0.47/0.66 ((~hskp28) | c0_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[283, 281])).
% 0.47/0.66 tff(285,plain,
% 0.47/0.66 ((~hskp28) | c0_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[284, 281])).
% 0.47/0.66 tff(286,plain,
% 0.47/0.66 ((~hskp28) | c0_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[285, 281])).
% 0.47/0.66 tff(287,plain,
% 0.47/0.66 ((~hskp28) | c0_1(a833)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[286, 281])).
% 0.47/0.66 tff(288,plain,
% 0.47/0.66 (c0_1(a833)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[287, 264])).
% 0.47/0.66 tff(289,plain,
% 0.47/0.66 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | c3_1(a842))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | c3_1(a842))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(290,plain,
% 0.47/0.66 ((hskp22 | hskp1 | (~ndr1_0) | c3_1(a842) | c2_1(a842) | (~c1_1(a842))) <=> (hskp22 | hskp1 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | c3_1(a842))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(291,plain,
% 0.47/0.66 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a842) | c2_1(a842) | (~c1_1(a842)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | c3_1(a842)))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[290])).
% 0.47/0.66 tff(292,plain,
% 0.47/0.66 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a842) | c2_1(a842) | (~c1_1(a842)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | c3_1(a842))),
% 0.47/0.66 inference(transitivity,[status(thm)],[291, 289])).
% 0.47/0.66 tff(293,plain,
% 0.47/0.66 ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a842) | c2_1(a842) | (~c1_1(a842)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(294,plain,
% 0.47/0.66 ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | c3_1(a842)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.47/0.66 tff(295,plain,
% 0.47/0.66 (hskp1 | c3_1(a842)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[294, 151, 13, 100, 92, 23])).
% 0.47/0.66 tff(296,plain,
% 0.47/0.66 (c3_1(a842)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[295, 24])).
% 0.47/0.66 tff(297,plain,
% 0.47/0.66 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(298,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | 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) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[297])).
% 0.47/0.66 tff(299,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | 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) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(300,plain,
% 0.47/0.66 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(301,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_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)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[300])).
% 0.47/0.66 tff(302,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.47/0.66 tff(303,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.47/0.66 tff(304,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[303, 299])).
% 0.47/0.66 tff(305,plain,(
% 0.47/0.66 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.47/0.66 inference(skolemize,[status(sab)],[304])).
% 0.47/0.66 tff(306,plain,
% 0.47/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[305, 298])).
% 0.47/0.66 tff(307,plain,
% 0.47/0.66 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(308,plain,
% 0.47/0.66 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[307])).
% 0.47/0.66 tff(309,plain,
% 0.47/0.66 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(310,plain,
% 0.47/0.66 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_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))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_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))) | (~c3_1(V))) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_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))) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(311,plain,
% 0.47/0.66 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[310])).
% 0.47/0.66 tff(312,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.47/0.66 tff(313,plain,
% 0.47/0.66 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.47/0.66 tff(314,plain,
% 0.47/0.66 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[313, 309])).
% 0.47/0.66 tff(315,plain,(
% 0.47/0.66 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.47/0.66 inference(skolemize,[status(sab)],[314])).
% 0.47/0.66 tff(316,plain,
% 0.47/0.66 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[315, 308])).
% 0.47/0.66 tff(317,plain,
% 0.47/0.66 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(318,plain,
% 0.47/0.66 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[317])).
% 0.47/0.66 tff(319,plain,
% 0.47/0.66 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(320,plain,
% 0.47/0.66 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp29))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(321,plain,
% 0.47/0.67 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[320])).
% 0.47/0.67 tff(322,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 0.47/0.67 tff(323,plain,
% 0.47/0.67 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.47/0.67 tff(324,plain,
% 0.47/0.67 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[323, 319])).
% 0.47/0.67 tff(325,plain,(
% 0.47/0.67 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.47/0.67 inference(skolemize,[status(sab)],[324])).
% 0.47/0.67 tff(326,plain,
% 0.47/0.67 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[325, 318])).
% 0.47/0.67 tff(327,assumption,(c3_1(a833)), introduced(assumption)).
% 0.47/0.67 tff(328,assumption,(c1_1(a833)), introduced(assumption)).
% 0.47/0.67 tff(329,assumption,(c0_1(a833)), introduced(assumption)).
% 0.47/0.67 tff(330,plain,
% 0.47/0.67 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a842) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a842)) | (~c3_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a842) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(331,plain,
% 0.47/0.67 ((hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842))) <=> (hskp29 | c2_1(a842) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(332,plain,
% 0.47/0.67 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a842) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a842)) | (~c3_1(a842))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[331])).
% 0.47/0.67 tff(333,plain,
% 0.47/0.67 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a842) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.47/0.67 inference(transitivity,[status(thm)],[332, 330])).
% 0.47/0.67 tff(334,plain,
% 0.47/0.67 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(335,plain,
% 0.47/0.67 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a842) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a842)) | (~c3_1(a842))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.47/0.67 tff(336,plain,
% 0.47/0.67 (hskp29 | (~c3_1(a842))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[335, 151, 329, 328, 327, 101, 92, 326])).
% 0.47/0.67 tff(337,plain,
% 0.47/0.67 (hskp29),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[336, 296])).
% 0.47/0.67 tff(338,plain,
% 0.47/0.67 (((~hskp29) | c3_1(a865)) <=> ((~hskp29) | c3_1(a865))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(339,axiom,((~hskp29) | c3_1(a865)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.47/0.67 tff(340,plain,
% 0.47/0.67 ((~hskp29) | c3_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.47/0.67 tff(341,plain,
% 0.47/0.67 ((~hskp29) | c3_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[340, 338])).
% 0.47/0.67 tff(342,plain,
% 0.47/0.67 ((~hskp29) | c3_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[341, 338])).
% 0.47/0.67 tff(343,plain,
% 0.47/0.67 ((~hskp29) | c3_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[342, 338])).
% 0.47/0.67 tff(344,plain,
% 0.47/0.67 ((~hskp29) | c3_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[343, 338])).
% 0.47/0.67 tff(345,plain,
% 0.47/0.67 (c3_1(a865)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[344, 337])).
% 0.47/0.67 tff(346,plain,
% 0.47/0.67 (((~hskp29) | c2_1(a865)) <=> ((~hskp29) | c2_1(a865))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(347,axiom,((~hskp29) | c2_1(a865)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.47/0.67 tff(348,plain,
% 0.47/0.67 ((~hskp29) | c2_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.47/0.67 tff(349,plain,
% 0.47/0.67 ((~hskp29) | c2_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[348, 346])).
% 0.47/0.67 tff(350,plain,
% 0.47/0.67 ((~hskp29) | c2_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[349, 346])).
% 0.47/0.67 tff(351,plain,
% 0.47/0.67 ((~hskp29) | c2_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[350, 346])).
% 0.47/0.67 tff(352,plain,
% 0.47/0.67 ((~hskp29) | c2_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[351, 346])).
% 0.47/0.67 tff(353,plain,
% 0.47/0.67 (c2_1(a865)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[352, 337])).
% 0.47/0.67 tff(354,plain,
% 0.47/0.67 (((~hskp29) | c1_1(a865)) <=> ((~hskp29) | c1_1(a865))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(355,axiom,((~hskp29) | c1_1(a865)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.47/0.67 tff(356,plain,
% 0.47/0.67 ((~hskp29) | c1_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.47/0.67 tff(357,plain,
% 0.47/0.67 ((~hskp29) | c1_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[356, 354])).
% 0.47/0.67 tff(358,plain,
% 0.47/0.67 ((~hskp29) | c1_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[357, 354])).
% 0.47/0.67 tff(359,plain,
% 0.47/0.67 ((~hskp29) | c1_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[358, 354])).
% 0.47/0.67 tff(360,plain,
% 0.47/0.67 ((~hskp29) | c1_1(a865)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[359, 354])).
% 0.47/0.67 tff(361,plain,
% 0.47/0.67 (c1_1(a865)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[360, 337])).
% 0.47/0.67 tff(362,plain,
% 0.47/0.67 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(363,plain,
% 0.47/0.67 ((hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842))) <=> (hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(364,plain,
% 0.47/0.67 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[363])).
% 0.47/0.67 tff(365,plain,
% 0.47/0.67 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.47/0.67 inference(transitivity,[status(thm)],[364, 362])).
% 0.47/0.67 tff(366,plain,
% 0.47/0.67 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(367,plain,
% 0.47/0.67 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.47/0.67 tff(368,plain,
% 0.47/0.67 (hskp8),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[367, 151, 361, 353, 345, 101, 100, 316, 296])).
% 0.47/0.67 tff(369,plain,
% 0.47/0.67 (((~hskp8) | (~c2_1(a830))) <=> ((~hskp8) | (~c2_1(a830)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(370,plain,
% 0.47/0.67 (((~c2_1(a830)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a830)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(371,axiom,((~c2_1(a830)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.47/0.67 tff(372,plain,
% 0.47/0.67 ((~hskp8) | (~c2_1(a830))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.47/0.67 tff(373,plain,
% 0.47/0.67 ((~hskp8) | (~c2_1(a830))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[372, 369])).
% 0.47/0.67 tff(374,plain,
% 0.47/0.67 (~c2_1(a830)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[373, 368])).
% 0.47/0.67 tff(375,plain,
% 0.47/0.67 (((~hskp8) | (~c0_1(a830))) <=> ((~hskp8) | (~c0_1(a830)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(376,plain,
% 0.47/0.67 (((~c0_1(a830)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a830)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(377,axiom,((~c0_1(a830)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.47/0.67 tff(378,plain,
% 0.47/0.67 ((~hskp8) | (~c0_1(a830))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.47/0.67 tff(379,plain,
% 0.47/0.67 ((~hskp8) | (~c0_1(a830))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[378, 375])).
% 0.47/0.67 tff(380,plain,
% 0.47/0.67 (~c0_1(a830)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[379, 368])).
% 0.47/0.67 tff(381,plain,
% 0.47/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a842) | c0_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a830)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a842) | c0_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a830)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(382,plain,
% 0.47/0.67 (((~ndr1_0) | c2_1(a842) | (~c3_1(a842)) | (~c1_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830))) <=> (c2_1(a842) | c0_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a830)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(383,plain,
% 0.47/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c3_1(a842)) | (~c1_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a842) | c0_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a830)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[382])).
% 0.47/0.67 tff(384,plain,
% 0.47/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c3_1(a842)) | (~c1_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a842) | c0_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a830)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.47/0.67 inference(transitivity,[status(thm)],[383, 381])).
% 0.47/0.67 tff(385,plain,
% 0.47/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c3_1(a842)) | (~c1_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830)))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(386,plain,
% 0.47/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a842) | c0_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a830)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.47/0.67 tff(387,plain,
% 0.47/0.67 (~c1_1(a830)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[386, 151, 101, 100, 92, 380, 374, 306, 296])).
% 0.47/0.67 tff(388,plain,
% 0.47/0.67 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(389,plain,
% 0.47/0.67 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[388])).
% 0.47/0.67 tff(390,plain,
% 0.47/0.67 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(391,plain,
% 0.47/0.67 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | 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))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c0_1(V)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | 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))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_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)))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | 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))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | 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)))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(392,plain,
% 0.47/0.67 (![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[391])).
% 0.47/0.67 tff(393,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.47/0.67 tff(394,plain,
% 0.47/0.67 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.47/0.67 tff(395,plain,
% 0.47/0.67 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[394, 390])).
% 0.47/0.67 tff(396,plain,(
% 0.47/0.67 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.47/0.67 inference(skolemize,[status(sab)],[395])).
% 0.47/0.67 tff(397,plain,
% 0.47/0.67 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[396, 389])).
% 0.47/0.67 tff(398,plain,
% 0.47/0.67 (((~hskp8) | (~c3_1(a830))) <=> ((~hskp8) | (~c3_1(a830)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(399,plain,
% 0.47/0.67 (((~c3_1(a830)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a830)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(400,axiom,((~c3_1(a830)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.47/0.67 tff(401,plain,
% 0.47/0.67 ((~hskp8) | (~c3_1(a830))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.47/0.67 tff(402,plain,
% 0.47/0.67 ((~hskp8) | (~c3_1(a830))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[401, 398])).
% 0.47/0.67 tff(403,plain,
% 0.47/0.67 (~c3_1(a830)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[402, 368])).
% 0.47/0.67 tff(404,plain,
% 0.47/0.67 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(405,plain,
% 0.47/0.67 ((hskp0 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c1_1(a830) | c2_1(a830) | c1_1(a830) | c0_1(a830)) <=> (hskp0 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(406,plain,
% 0.47/0.67 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c1_1(a830) | c2_1(a830) | c1_1(a830) | c0_1(a830))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830)))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[405])).
% 0.47/0.67 tff(407,plain,
% 0.47/0.67 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c1_1(a830) | c2_1(a830) | c1_1(a830) | c0_1(a830))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830))),
% 0.47/0.67 inference(transitivity,[status(thm)],[406, 404])).
% 0.47/0.67 tff(408,plain,
% 0.47/0.67 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c1_1(a830) | c2_1(a830) | c1_1(a830) | c0_1(a830))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(409,plain,
% 0.47/0.67 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.47/0.67 tff(410,plain,
% 0.47/0.67 (hskp0),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[409, 151, 380, 374, 403, 397, 387])).
% 0.47/0.67 tff(411,plain,
% 0.47/0.67 (((~hskp0) | (~c3_1(a815))) <=> ((~hskp0) | (~c3_1(a815)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(412,plain,
% 0.47/0.67 (((~c3_1(a815)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a815)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(413,axiom,((~c3_1(a815)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.47/0.67 tff(414,plain,
% 0.47/0.67 ((~hskp0) | (~c3_1(a815))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.47/0.67 tff(415,plain,
% 0.47/0.67 ((~hskp0) | (~c3_1(a815))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[414, 411])).
% 0.47/0.67 tff(416,plain,
% 0.47/0.67 (~c3_1(a815)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[415, 410])).
% 0.47/0.67 tff(417,plain,
% 0.47/0.67 (((~hskp0) | c1_1(a815)) <=> ((~hskp0) | c1_1(a815))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(418,axiom,((~hskp0) | c1_1(a815)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.47/0.67 tff(419,plain,
% 0.47/0.67 ((~hskp0) | c1_1(a815)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.47/0.67 tff(420,plain,
% 0.47/0.67 ((~hskp0) | c1_1(a815)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[419, 417])).
% 0.47/0.67 tff(421,plain,
% 0.47/0.67 ((~hskp0) | c1_1(a815)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[420, 417])).
% 0.47/0.67 tff(422,plain,
% 0.47/0.67 ((~hskp0) | c1_1(a815)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[421, 417])).
% 0.47/0.67 tff(423,plain,
% 0.47/0.67 ((~hskp0) | c1_1(a815)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[422, 417])).
% 0.47/0.67 tff(424,plain,
% 0.47/0.67 (c1_1(a815)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[423, 410])).
% 0.47/0.67 tff(425,plain,
% 0.47/0.67 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c1_1(a815)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c1_1(a815)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(426,plain,
% 0.47/0.67 ((hskp22 | hskp1 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c1_1(a815))) <=> (hskp22 | hskp1 | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c1_1(a815)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(427,plain,
% 0.47/0.67 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c1_1(a815)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c1_1(a815))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[426])).
% 0.47/0.67 tff(428,plain,
% 0.47/0.67 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c1_1(a815)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c1_1(a815)))),
% 0.47/0.67 inference(transitivity,[status(thm)],[427, 425])).
% 0.47/0.67 tff(429,plain,
% 0.47/0.67 ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c1_1(a815)))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(430,plain,
% 0.47/0.67 ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c1_1(a815))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.47/0.68 tff(431,plain,
% 0.47/0.68 (c2_1(a815)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[430, 151, 13, 24, 424, 416, 23])).
% 0.47/0.68 tff(432,plain,
% 0.47/0.68 (^[U: $i] : refl((hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))),
% 0.47/0.68 inference(bind,[status(th)],[])).
% 0.47/0.68 tff(433,plain,
% 0.47/0.68 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.47/0.68 inference(quant_intro,[status(thm)],[432])).
% 0.47/0.68 tff(434,plain,
% 0.47/0.68 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(435,plain,
% 0.47/0.68 (^[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)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp4) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp4))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp4) <=> (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp4) <=> (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))))),
% 0.47/0.68 inference(bind,[status(th)],[])).
% 0.47/0.68 tff(436,plain,
% 0.47/0.68 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp4) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.47/0.68 inference(quant_intro,[status(thm)],[435])).
% 0.47/0.68 tff(437,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 0.47/0.68 tff(438,plain,
% 0.47/0.68 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.47/0.68 tff(439,plain,
% 0.47/0.68 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[438, 434])).
% 0.47/0.68 tff(440,plain,(
% 0.47/0.68 ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.47/0.68 inference(skolemize,[status(sab)],[439])).
% 0.47/0.68 tff(441,plain,
% 0.47/0.68 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[440, 433])).
% 0.47/0.68 tff(442,plain,
% 0.47/0.68 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(443,plain,
% 0.47/0.68 ((hskp7 | hskp4 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c0_1(a830)) <=> (hskp7 | hskp4 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(444,plain,
% 0.47/0.68 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c0_1(a830))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0)))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[443])).
% 0.47/0.68 tff(445,plain,
% 0.47/0.68 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c0_1(a830))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0))),
% 0.47/0.68 inference(transitivity,[status(thm)],[444, 442])).
% 0.47/0.68 tff(446,plain,
% 0.47/0.68 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c0_1(a830))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(447,plain,
% 0.47/0.68 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.47/0.68 tff(448,plain,
% 0.47/0.68 (hskp4),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[447, 151, 12, 380, 374, 403, 441])).
% 0.47/0.68 tff(449,plain,
% 0.47/0.68 (((~hskp4) | (~c1_1(a821))) <=> ((~hskp4) | (~c1_1(a821)))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(450,plain,
% 0.47/0.68 (((~c1_1(a821)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a821)))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(451,axiom,((~c1_1(a821)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.47/0.68 tff(452,plain,
% 0.47/0.68 ((~hskp4) | (~c1_1(a821))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.47/0.68 tff(453,plain,
% 0.47/0.68 ((~hskp4) | (~c1_1(a821))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[452, 449])).
% 0.47/0.68 tff(454,plain,
% 0.47/0.68 (~c1_1(a821)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[453, 448])).
% 0.47/0.68 tff(455,plain,
% 0.47/0.68 (((~hskp4) | (~c0_1(a821))) <=> ((~hskp4) | (~c0_1(a821)))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(456,plain,
% 0.47/0.68 (((~c0_1(a821)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a821)))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(457,axiom,((~c0_1(a821)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.47/0.68 tff(458,plain,
% 0.47/0.68 ((~hskp4) | (~c0_1(a821))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.47/0.68 tff(459,plain,
% 0.47/0.68 ((~hskp4) | (~c0_1(a821))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[458, 455])).
% 0.47/0.68 tff(460,plain,
% 0.47/0.68 (~c0_1(a821)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[459, 448])).
% 0.47/0.68 tff(461,plain,
% 0.47/0.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a830) | c3_1(a830) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c1_1(a830))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a830) | c3_1(a830) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c1_1(a830))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(462,plain,
% 0.47/0.68 (((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a830) | c0_1(a830) | c3_1(a830)) <=> (c0_1(a830) | c3_1(a830) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c1_1(a830))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(463,plain,
% 0.47/0.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a830) | c0_1(a830) | c3_1(a830))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a830) | c3_1(a830) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c1_1(a830)))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[462])).
% 0.47/0.68 tff(464,plain,
% 0.47/0.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a830) | c0_1(a830) | c3_1(a830))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a830) | c3_1(a830) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c1_1(a830))),
% 0.47/0.68 inference(transitivity,[status(thm)],[463, 461])).
% 0.47/0.68 tff(465,plain,
% 0.47/0.68 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a830) | c0_1(a830) | c3_1(a830))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(466,plain,
% 0.47/0.68 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a830) | c3_1(a830) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c1_1(a830)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.47/0.68 tff(467,plain,
% 0.47/0.68 (~c3_1(a821)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[466, 151, 380, 403, 460, 454, 190, 387])).
% 0.47/0.68 tff(468,plain,
% 0.47/0.68 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))),
% 0.47/0.68 inference(bind,[status(th)],[])).
% 0.47/0.68 tff(469,plain,
% 0.47/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.68 inference(quant_intro,[status(thm)],[468])).
% 0.47/0.68 tff(470,plain,
% 0.47/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(471,plain,
% 0.47/0.68 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))))),
% 0.47/0.68 inference(bind,[status(th)],[])).
% 0.47/0.68 tff(472,plain,
% 0.47/0.68 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.68 inference(quant_intro,[status(thm)],[471])).
% 0.47/0.68 tff(473,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 0.47/0.68 tff(474,plain,
% 0.47/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.47/0.68 tff(475,plain,
% 0.47/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[474, 470])).
% 0.47/0.68 tff(476,plain,(
% 0.47/0.68 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.68 inference(skolemize,[status(sab)],[475])).
% 0.47/0.68 tff(477,plain,
% 0.47/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[476, 469])).
% 0.47/0.68 tff(478,plain,
% 0.47/0.68 (((~hskp4) | c2_1(a821)) <=> ((~hskp4) | c2_1(a821))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(479,axiom,((~hskp4) | c2_1(a821)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.47/0.68 tff(480,plain,
% 0.47/0.68 ((~hskp4) | c2_1(a821)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.47/0.68 tff(481,plain,
% 0.47/0.68 ((~hskp4) | c2_1(a821)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[480, 478])).
% 0.47/0.68 tff(482,plain,
% 0.47/0.68 ((~hskp4) | c2_1(a821)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[481, 478])).
% 0.47/0.68 tff(483,plain,
% 0.47/0.68 ((~hskp4) | c2_1(a821)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[482, 478])).
% 0.47/0.68 tff(484,plain,
% 0.47/0.68 ((~hskp4) | c2_1(a821)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[483, 478])).
% 0.47/0.68 tff(485,plain,
% 0.47/0.68 (c2_1(a821)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[484, 448])).
% 0.47/0.68 tff(486,plain,
% 0.47/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a830) | c3_1(a830) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c1_1(a830))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a830) | c3_1(a830) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c1_1(a830))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(487,plain,
% 0.47/0.68 (((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a830) | c2_1(a830) | c1_1(a830)) <=> (c2_1(a830) | c3_1(a830) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c1_1(a830))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(488,plain,
% 0.47/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a830) | c2_1(a830) | c1_1(a830))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a830) | c3_1(a830) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c1_1(a830)))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[487])).
% 0.47/0.68 tff(489,plain,
% 0.47/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a830) | c2_1(a830) | c1_1(a830))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a830) | c3_1(a830) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c1_1(a830))),
% 0.47/0.68 inference(transitivity,[status(thm)],[488, 486])).
% 0.47/0.68 tff(490,plain,
% 0.47/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a830) | c2_1(a830) | c1_1(a830))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(491,plain,
% 0.47/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a830) | c3_1(a830) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c1_1(a830)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.47/0.68 tff(492,plain,
% 0.47/0.68 ($false),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[491, 151, 485, 424, 374, 403, 460, 416, 477, 387, 467, 431])).
% 0.47/0.68 tff(493,plain,(hskp1 | hskp22 | (~c0_1(a842)) | (~c1_1(a842)) | c2_1(a842) | hskp7 | (~c0_1(a833)) | (~c1_1(a833)) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.68 tff(494,plain,
% 0.47/0.68 (hskp1),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[493, 71, 13, 63, 55, 12, 288, 280, 272])).
% 0.47/0.68 tff(495,plain,
% 0.47/0.68 (((~hskp1) | (~c2_1(a816))) <=> ((~hskp1) | (~c2_1(a816)))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(496,plain,
% 0.47/0.68 (((~c2_1(a816)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a816)))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(497,axiom,((~c2_1(a816)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.47/0.68 tff(498,plain,
% 0.47/0.68 ((~hskp1) | (~c2_1(a816))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.47/0.68 tff(499,plain,
% 0.47/0.68 ((~hskp1) | (~c2_1(a816))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[498, 495])).
% 0.47/0.68 tff(500,plain,
% 0.47/0.68 (~c2_1(a816)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[499, 494])).
% 0.47/0.68 tff(501,plain,
% 0.47/0.68 (((~hskp1) | c3_1(a816)) <=> ((~hskp1) | c3_1(a816))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(502,axiom,((~hskp1) | c3_1(a816)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.47/0.68 tff(503,plain,
% 0.47/0.68 ((~hskp1) | c3_1(a816)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.47/0.68 tff(504,plain,
% 0.47/0.68 ((~hskp1) | c3_1(a816)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[503, 501])).
% 0.47/0.68 tff(505,plain,
% 0.47/0.68 ((~hskp1) | c3_1(a816)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[504, 501])).
% 0.47/0.68 tff(506,plain,
% 0.47/0.68 ((~hskp1) | c3_1(a816)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[505, 501])).
% 0.47/0.68 tff(507,plain,
% 0.47/0.68 ((~hskp1) | c3_1(a816)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[506, 501])).
% 0.47/0.68 tff(508,plain,
% 0.47/0.68 (c3_1(a816)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[507, 494])).
% 0.47/0.68 tff(509,plain,
% 0.47/0.68 (((~hskp1) | c0_1(a816)) <=> ((~hskp1) | c0_1(a816))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(510,axiom,((~hskp1) | c0_1(a816)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.47/0.68 tff(511,plain,
% 0.47/0.68 ((~hskp1) | c0_1(a816)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.47/0.68 tff(512,plain,
% 0.47/0.68 ((~hskp1) | c0_1(a816)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[511, 509])).
% 0.47/0.68 tff(513,plain,
% 0.47/0.68 ((~hskp1) | c0_1(a816)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[512, 509])).
% 0.47/0.68 tff(514,plain,
% 0.47/0.68 ((~hskp1) | c0_1(a816)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[513, 509])).
% 0.47/0.68 tff(515,plain,
% 0.47/0.68 ((~hskp1) | c0_1(a816)),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[514, 509])).
% 0.47/0.68 tff(516,plain,
% 0.47/0.68 (c0_1(a816)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[515, 494])).
% 0.47/0.68 tff(517,plain,
% 0.47/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(518,plain,
% 0.47/0.68 (((~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816))) <=> (c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(519,plain,
% 0.47/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816))))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[518])).
% 0.47/0.68 tff(520,plain,
% 0.47/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))),
% 0.47/0.68 inference(transitivity,[status(thm)],[519, 517])).
% 0.47/0.68 tff(521,plain,
% 0.47/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816)))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(522,plain,
% 0.47/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[521, 520])).
% 0.47/0.69 tff(523,plain,
% 0.47/0.69 (c1_1(a816)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[522, 151, 288, 280, 272, 516, 508, 500, 44])).
% 0.47/0.69 tff(524,plain,
% 0.47/0.69 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | (~c0_1(a816)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(525,plain,
% 0.47/0.69 ((hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816))) <=> (hskp29 | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | (~c0_1(a816)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(526,plain,
% 0.47/0.69 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | (~c0_1(a816))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[525])).
% 0.47/0.69 tff(527,plain,
% 0.47/0.69 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | (~c0_1(a816)))),
% 0.47/0.69 inference(transitivity,[status(thm)],[526, 524])).
% 0.47/0.69 tff(528,plain,
% 0.47/0.69 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(529,plain,
% 0.47/0.69 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | (~c0_1(a816))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.47/0.69 tff(530,plain,
% 0.47/0.69 (hskp29),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[529, 151, 288, 280, 272, 516, 508, 500, 326])).
% 0.47/0.69 tff(531,plain,
% 0.47/0.69 (c3_1(a865)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[344, 530])).
% 0.47/0.69 tff(532,plain,
% 0.47/0.69 (c2_1(a865)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[352, 530])).
% 0.47/0.69 tff(533,plain,
% 0.47/0.69 (c1_1(a865)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[360, 530])).
% 0.47/0.69 tff(534,plain,
% 0.47/0.69 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(535,plain,
% 0.47/0.69 ((hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833))) <=> (hskp8 | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(536,plain,
% 0.47/0.69 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[535])).
% 0.47/0.69 tff(537,plain,
% 0.47/0.69 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))),
% 0.47/0.69 inference(transitivity,[status(thm)],[536, 534])).
% 0.47/0.69 tff(538,plain,
% 0.47/0.69 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(539,plain,
% 0.47/0.69 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.47/0.69 tff(540,plain,
% 0.47/0.69 (hskp8),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[539, 151, 533, 532, 531, 288, 280, 272, 316])).
% 0.47/0.69 tff(541,plain,
% 0.47/0.69 (~c2_1(a830)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[373, 540])).
% 0.47/0.69 tff(542,plain,
% 0.47/0.69 (~c0_1(a830)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[379, 540])).
% 0.47/0.69 tff(543,plain,
% 0.47/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a830) | c2_1(a830) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c1_1(a830)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a830) | c2_1(a830) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c1_1(a830)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(544,plain,
% 0.47/0.69 (((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830))) <=> (c0_1(a830) | c2_1(a830) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c1_1(a830)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(545,plain,
% 0.47/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a830) | c2_1(a830) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c1_1(a830))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[544])).
% 0.47/0.69 tff(546,plain,
% 0.47/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a830) | c2_1(a830) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c1_1(a830)))),
% 0.47/0.69 inference(transitivity,[status(thm)],[545, 543])).
% 0.47/0.69 tff(547,plain,
% 0.47/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830)))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(548,plain,
% 0.47/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a830) | c2_1(a830) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c1_1(a830))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.47/0.69 tff(549,plain,
% 0.47/0.69 (~c1_1(a830)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[548, 151, 516, 508, 542, 541, 500, 306, 523])).
% 0.47/0.69 tff(550,plain,
% 0.47/0.69 (~c3_1(a830)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[402, 540])).
% 0.47/0.69 tff(551,plain,
% 0.47/0.69 (hskp0),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[409, 151, 542, 541, 550, 397, 549])).
% 0.47/0.69 tff(552,plain,
% 0.47/0.69 (~c3_1(a815)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[415, 551])).
% 0.47/0.69 tff(553,plain,
% 0.47/0.69 (hskp4),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[447, 151, 12, 542, 541, 550, 441])).
% 0.47/0.69 tff(554,plain,
% 0.47/0.69 (~c1_1(a821)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[453, 553])).
% 0.47/0.69 tff(555,plain,
% 0.47/0.69 (~c0_1(a821)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[459, 553])).
% 0.47/0.69 tff(556,plain,
% 0.47/0.69 (~c3_1(a821)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[466, 151, 542, 550, 555, 554, 190, 549])).
% 0.47/0.69 tff(557,plain,
% 0.47/0.69 (c1_1(a815)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[423, 551])).
% 0.47/0.69 tff(558,plain,
% 0.47/0.69 (c2_1(a821)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[484, 553])).
% 0.47/0.69 tff(559,plain,
% 0.47/0.69 (~c2_1(a815)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[491, 151, 558, 557, 541, 550, 555, 552, 477, 549, 556])).
% 0.47/0.69 tff(560,plain,
% 0.47/0.69 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 0.47/0.69 inference(bind,[status(th)],[])).
% 0.47/0.69 tff(561,plain,
% 0.47/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.69 inference(quant_intro,[status(thm)],[560])).
% 0.47/0.69 tff(562,plain,
% 0.47/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(563,plain,
% 0.47/0.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_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)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_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)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 0.47/0.69 inference(bind,[status(th)],[])).
% 0.47/0.69 tff(564,plain,
% 0.47/0.69 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.69 inference(quant_intro,[status(thm)],[563])).
% 0.47/0.69 tff(565,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 0.47/0.69 tff(566,plain,
% 0.47/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.47/0.69 tff(567,plain,
% 0.47/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[566, 562])).
% 0.47/0.69 tff(568,plain,(
% 0.47/0.69 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.69 inference(skolemize,[status(sab)],[567])).
% 0.47/0.69 tff(569,plain,
% 0.47/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[568, 561])).
% 0.47/0.69 tff(570,plain,
% 0.47/0.69 (((~hskp0) | c0_1(a815)) <=> ((~hskp0) | c0_1(a815))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(571,axiom,((~hskp0) | c0_1(a815)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.47/0.69 tff(572,plain,
% 0.47/0.69 ((~hskp0) | c0_1(a815)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.47/0.69 tff(573,plain,
% 0.47/0.69 ((~hskp0) | c0_1(a815)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[572, 570])).
% 0.47/0.69 tff(574,plain,
% 0.47/0.69 ((~hskp0) | c0_1(a815)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[573, 570])).
% 0.47/0.69 tff(575,plain,
% 0.47/0.69 ((~hskp0) | c0_1(a815)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[574, 570])).
% 0.47/0.69 tff(576,plain,
% 0.47/0.69 ((~hskp0) | c0_1(a815)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[575, 570])).
% 0.47/0.69 tff(577,plain,
% 0.47/0.69 (c0_1(a815)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[576, 551])).
% 0.47/0.69 tff(578,plain,
% 0.47/0.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a830) | c2_1(a830) | c3_1(a830) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a830) | c2_1(a830) | c3_1(a830) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(579,plain,
% 0.47/0.69 ((hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a830) | c0_1(a830) | c3_1(a830)) <=> (hskp5 | c0_1(a830) | c2_1(a830) | c3_1(a830) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(580,plain,
% 0.47/0.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a830) | c0_1(a830) | c3_1(a830))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a830) | c2_1(a830) | c3_1(a830) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[579])).
% 0.47/0.69 tff(581,plain,
% 0.47/0.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a830) | c0_1(a830) | c3_1(a830))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a830) | c2_1(a830) | c3_1(a830) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)))),
% 0.47/0.69 inference(transitivity,[status(thm)],[580, 578])).
% 0.47/0.69 tff(582,plain,
% 0.47/0.69 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a830) | c0_1(a830) | c3_1(a830))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(583,plain,
% 0.47/0.69 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a830) | c2_1(a830) | c3_1(a830) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.47/0.69 tff(584,plain,
% 0.47/0.69 (hskp5),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[583, 151, 577, 542, 541, 550, 552, 569, 559])).
% 0.47/0.69 tff(585,plain,
% 0.47/0.69 (((~hskp5) | (~c0_1(a825))) <=> ((~hskp5) | (~c0_1(a825)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(586,plain,
% 0.47/0.69 (((~c0_1(a825)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a825)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(587,axiom,((~c0_1(a825)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.47/0.69 tff(588,plain,
% 0.47/0.69 ((~hskp5) | (~c0_1(a825))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.47/0.69 tff(589,plain,
% 0.47/0.69 ((~hskp5) | (~c0_1(a825))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[588, 585])).
% 0.47/0.69 tff(590,plain,
% 0.47/0.69 (~c0_1(a825)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[589, 584])).
% 0.47/0.69 tff(591,plain,
% 0.47/0.69 (((~hskp5) | c3_1(a825)) <=> ((~hskp5) | c3_1(a825))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(592,axiom,((~hskp5) | c3_1(a825)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.47/0.69 tff(593,plain,
% 0.47/0.69 ((~hskp5) | c3_1(a825)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.47/0.69 tff(594,plain,
% 0.47/0.69 ((~hskp5) | c3_1(a825)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[593, 591])).
% 0.47/0.69 tff(595,plain,
% 0.47/0.69 ((~hskp5) | c3_1(a825)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[594, 591])).
% 0.47/0.69 tff(596,plain,
% 0.47/0.69 ((~hskp5) | c3_1(a825)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[595, 591])).
% 0.47/0.69 tff(597,plain,
% 0.47/0.69 ((~hskp5) | c3_1(a825)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[596, 591])).
% 0.47/0.69 tff(598,plain,
% 0.47/0.69 (c3_1(a825)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[597, 584])).
% 0.47/0.69 tff(599,plain,
% 0.47/0.69 (((~hskp5) | c1_1(a825)) <=> ((~hskp5) | c1_1(a825))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(600,axiom,((~hskp5) | c1_1(a825)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.47/0.69 tff(601,plain,
% 0.47/0.69 ((~hskp5) | c1_1(a825)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.47/0.69 tff(602,plain,
% 0.47/0.69 ((~hskp5) | c1_1(a825)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[601, 599])).
% 0.47/0.69 tff(603,plain,
% 0.47/0.69 ((~hskp5) | c1_1(a825)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[602, 599])).
% 0.47/0.69 tff(604,plain,
% 0.47/0.69 ((~hskp5) | c1_1(a825)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[603, 599])).
% 0.47/0.69 tff(605,plain,
% 0.47/0.69 ((~hskp5) | c1_1(a825)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[604, 599])).
% 0.47/0.69 tff(606,plain,
% 0.47/0.69 (c1_1(a825)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[605, 584])).
% 0.47/0.69 tff(607,plain,
% 0.47/0.69 (((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a825) | c0_1(a821) | c1_1(a821) | c3_1(a815) | (~ndr1_0) | (~c1_1(a815)) | (~c0_1(a815)) | (~c2_1(a821)) | (~c3_1(a825)) | (~c1_1(a825)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a825) | c0_1(a821) | c1_1(a821) | c3_1(a815) | (~ndr1_0) | (~c1_1(a815)) | (~c0_1(a815)) | (~c2_1(a821)) | (~c3_1(a825)) | (~c1_1(a825)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(608,plain,
% 0.47/0.69 (((~ndr1_0) | c3_1(a815) | (~c1_1(a815)) | (~c0_1(a815)) | c0_1(a825) | (~c3_1(a825)) | (~c1_1(a825)) | c1_1(a821) | c0_1(a821) | (~c2_1(a821))) <=> (c0_1(a825) | c0_1(a821) | c1_1(a821) | c3_1(a815) | (~ndr1_0) | (~c1_1(a815)) | (~c0_1(a815)) | (~c2_1(a821)) | (~c3_1(a825)) | (~c1_1(a825)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(609,plain,
% 0.47/0.69 (((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a815) | (~c1_1(a815)) | (~c0_1(a815)) | c0_1(a825) | (~c3_1(a825)) | (~c1_1(a825)) | c1_1(a821) | c0_1(a821) | (~c2_1(a821)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a825) | c0_1(a821) | c1_1(a821) | c3_1(a815) | (~ndr1_0) | (~c1_1(a815)) | (~c0_1(a815)) | (~c2_1(a821)) | (~c3_1(a825)) | (~c1_1(a825))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[608])).
% 0.47/0.69 tff(610,plain,
% 0.47/0.69 (((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a815) | (~c1_1(a815)) | (~c0_1(a815)) | c0_1(a825) | (~c3_1(a825)) | (~c1_1(a825)) | c1_1(a821) | c0_1(a821) | (~c2_1(a821)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a825) | c0_1(a821) | c1_1(a821) | c3_1(a815) | (~ndr1_0) | (~c1_1(a815)) | (~c0_1(a815)) | (~c2_1(a821)) | (~c3_1(a825)) | (~c1_1(a825)))),
% 0.47/0.69 inference(transitivity,[status(thm)],[609, 607])).
% 0.47/0.69 tff(611,plain,
% 0.47/0.69 ((~![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)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a815) | (~c1_1(a815)) | (~c0_1(a815)) | c0_1(a825) | (~c3_1(a825)) | (~c1_1(a825)) | c1_1(a821) | c0_1(a821) | (~c2_1(a821)))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(612,plain,
% 0.47/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a825) | c0_1(a821) | c1_1(a821) | c3_1(a815) | (~ndr1_0) | (~c1_1(a815)) | (~c0_1(a815)) | (~c2_1(a821)) | (~c3_1(a825)) | (~c1_1(a825))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[611, 610])).
% 0.47/0.69 tff(613,plain,
% 0.47/0.69 ($false),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[612, 151, 606, 598, 558, 577, 557, 590, 555, 554, 552, 34])).
% 0.47/0.69 tff(614,plain,(hskp24 | hskp7 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.47/0.69 tff(615,plain,
% 0.47/0.69 (hskp24),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[614, 13, 12])).
% 0.47/0.69 tff(616,plain,
% 0.47/0.69 (((~hskp24) | (~c3_1(a878))) <=> ((~hskp24) | (~c3_1(a878)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(617,plain,
% 0.47/0.69 (((~c3_1(a878)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a878)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(618,axiom,((~c3_1(a878)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.47/0.69 tff(619,plain,
% 0.47/0.69 ((~hskp24) | (~c3_1(a878))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.47/0.69 tff(620,plain,
% 0.47/0.69 ((~hskp24) | (~c3_1(a878))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[619, 616])).
% 0.47/0.69 tff(621,plain,
% 0.47/0.69 (~c3_1(a878)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[620, 615])).
% 0.47/0.69 tff(622,plain,
% 0.47/0.69 (((~hskp24) | c1_1(a878)) <=> ((~hskp24) | c1_1(a878))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(623,axiom,((~hskp24) | c1_1(a878)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.47/0.69 tff(624,plain,
% 0.47/0.69 ((~hskp24) | c1_1(a878)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[623, 622])).
% 0.47/0.69 tff(625,plain,
% 0.47/0.69 ((~hskp24) | c1_1(a878)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[624, 622])).
% 0.47/0.70 tff(626,plain,
% 0.47/0.70 ((~hskp24) | c1_1(a878)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[625, 622])).
% 0.47/0.70 tff(627,plain,
% 0.47/0.70 ((~hskp24) | c1_1(a878)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[626, 622])).
% 0.47/0.70 tff(628,plain,
% 0.47/0.70 ((~hskp24) | c1_1(a878)),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[627, 622])).
% 0.47/0.70 tff(629,plain,
% 0.47/0.70 (c1_1(a878)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[628, 615])).
% 0.47/0.70 tff(630,plain,
% 0.47/0.70 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | c3_1(a878) | (~ndr1_0) | c2_1(a878) | (~c1_1(a878)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c3_1(a878) | (~ndr1_0) | c2_1(a878) | (~c1_1(a878)))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(631,plain,
% 0.47/0.70 ((hskp22 | hskp1 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | (~c1_1(a878))) <=> (hskp22 | hskp1 | c3_1(a878) | (~ndr1_0) | c2_1(a878) | (~c1_1(a878)))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(632,plain,
% 0.47/0.70 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | (~c1_1(a878)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | c3_1(a878) | (~ndr1_0) | c2_1(a878) | (~c1_1(a878))))),
% 0.47/0.70 inference(monotonicity,[status(thm)],[631])).
% 0.47/0.70 tff(633,plain,
% 0.47/0.70 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | (~c1_1(a878)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c3_1(a878) | (~ndr1_0) | c2_1(a878) | (~c1_1(a878)))),
% 0.47/0.70 inference(transitivity,[status(thm)],[632, 630])).
% 0.47/0.70 tff(634,plain,
% 0.47/0.70 ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | (~c1_1(a878)))),
% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
% 0.47/0.70 tff(635,plain,
% 0.47/0.70 ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c3_1(a878) | (~ndr1_0) | c2_1(a878) | (~c1_1(a878))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[634, 633])).
% 0.47/0.70 tff(636,plain,
% 0.47/0.70 (hskp1 | c2_1(a878)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[635, 151, 13, 629, 621, 23])).
% 0.47/0.70 tff(637,plain,
% 0.47/0.70 (c2_1(a878)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[636, 24])).
% 0.47/0.70 tff(638,plain,
% 0.47/0.70 (^[U: $i] : refl((hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.47/0.70 inference(bind,[status(th)],[])).
% 0.47/0.70 tff(639,plain,
% 0.47/0.70 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.47/0.70 inference(quant_intro,[status(thm)],[638])).
% 0.47/0.70 tff(640,plain,
% 0.47/0.70 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(641,plain,
% 0.47/0.70 (^[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)) | 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)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp7) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp7))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp7) <=> (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp7) <=> (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.47/0.70 inference(bind,[status(th)],[])).
% 0.47/0.70 tff(642,plain,
% 0.47/0.70 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp7) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.47/0.70 inference(quant_intro,[status(thm)],[641])).
% 0.47/0.70 tff(643,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.47/0.70 tff(644,plain,
% 0.47/0.70 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[643, 642])).
% 0.47/0.70 tff(645,plain,
% 0.47/0.70 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[644, 640])).
% 0.47/0.70 tff(646,plain,(
% 0.47/0.70 ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.47/0.70 inference(skolemize,[status(sab)],[645])).
% 0.47/0.70 tff(647,plain,
% 0.47/0.70 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[646, 639])).
% 0.47/0.70 tff(648,plain,
% 0.47/0.70 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c3_1(a878) | (~ndr1_0) | (~c1_1(a878)) | (~c2_1(a878)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c3_1(a878) | (~ndr1_0) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(649,plain,
% 0.47/0.70 ((hskp14 | hskp7 | (~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878))) <=> (hskp14 | hskp7 | c3_1(a878) | (~ndr1_0) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(650,plain,
% 0.47/0.70 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c3_1(a878) | (~ndr1_0) | (~c1_1(a878)) | (~c2_1(a878))))),
% 0.47/0.70 inference(monotonicity,[status(thm)],[649])).
% 0.47/0.70 tff(651,plain,
% 0.47/0.70 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c3_1(a878) | (~ndr1_0) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.47/0.70 inference(transitivity,[status(thm)],[650, 648])).
% 0.47/0.70 tff(652,plain,
% 0.47/0.70 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)))),
% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
% 0.47/0.70 tff(653,plain,
% 0.47/0.70 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c3_1(a878) | (~ndr1_0) | (~c1_1(a878)) | (~c2_1(a878))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.47/0.70 tff(654,plain,
% 0.47/0.70 (hskp14 | (~c2_1(a878))),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[653, 151, 12, 629, 621, 647])).
% 0.47/0.70 tff(655,plain,
% 0.47/0.70 (hskp14),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[654, 637])).
% 0.47/0.70 tff(656,plain,
% 0.47/0.70 (~c2_1(a842)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[54, 655])).
% 0.47/0.70 tff(657,plain,
% 0.47/0.70 (c1_1(a842)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[62, 655])).
% 0.47/0.70 tff(658,plain,
% 0.47/0.70 (c3_1(a842)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[294, 151, 13, 24, 657, 656, 23])).
% 0.47/0.70 tff(659,plain,
% 0.47/0.70 (c0_1(a842)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[70, 655])).
% 0.47/0.70 tff(660,plain,
% 0.47/0.70 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(661,plain,
% 0.47/0.70 ((hskp29 | (~ndr1_0) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842))) <=> (hskp29 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(662,plain,
% 0.47/0.70 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842))))),
% 0.47/0.70 inference(monotonicity,[status(thm)],[661])).
% 0.47/0.70 tff(663,plain,
% 0.47/0.70 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.47/0.70 inference(transitivity,[status(thm)],[662, 660])).
% 0.47/0.70 tff(664,plain,
% 0.47/0.70 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)))),
% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
% 0.47/0.70 tff(665,plain,
% 0.47/0.70 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[664, 663])).
% 0.47/0.70 tff(666,plain,
% 0.47/0.70 (hskp29),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[665, 151, 659, 657, 656, 326, 658])).
% 0.47/0.70 tff(667,plain,
% 0.47/0.70 (c3_1(a865)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[344, 666])).
% 0.47/0.70 tff(668,plain,
% 0.47/0.70 (c2_1(a865)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[352, 666])).
% 0.47/0.70 tff(669,plain,
% 0.47/0.70 (c1_1(a865)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[360, 666])).
% 0.47/0.70 tff(670,plain,
% 0.47/0.70 (hskp8),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[367, 151, 669, 668, 667, 659, 657, 316, 658])).
% 0.47/0.70 tff(671,plain,
% 0.47/0.70 (~c2_1(a830)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[373, 670])).
% 0.47/0.70 tff(672,plain,
% 0.47/0.70 (~c0_1(a830)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[379, 670])).
% 0.47/0.70 tff(673,plain,
% 0.47/0.70 (~c1_1(a830)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[386, 151, 659, 657, 656, 672, 671, 306, 658])).
% 0.47/0.70 tff(674,plain,
% 0.47/0.70 (~c3_1(a830)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[402, 670])).
% 0.47/0.70 tff(675,plain,
% 0.47/0.70 (((~hskp24) | (~c0_1(a878))) <=> ((~hskp24) | (~c0_1(a878)))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(676,plain,
% 0.47/0.70 (((~c0_1(a878)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a878)))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(677,axiom,((~c0_1(a878)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.47/0.70 tff(678,plain,
% 0.47/0.70 ((~hskp24) | (~c0_1(a878))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[677, 676])).
% 0.47/0.70 tff(679,plain,
% 0.47/0.70 ((~hskp24) | (~c0_1(a878))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[678, 675])).
% 0.47/0.70 tff(680,plain,
% 0.47/0.70 (~c0_1(a878)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[679, 615])).
% 0.47/0.70 tff(681,plain,
% 0.47/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c0_1(a878) | c3_1(a878) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830) | (~c1_1(a878)) | (~c2_1(a878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c0_1(a878) | c3_1(a878) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(682,plain,
% 0.54/0.70 (((~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)) | c0_1(a878) | c3_1(a878) | (~c2_1(a878)) | c3_1(a830) | c2_1(a830) | c1_1(a830)) <=> (c0_1(a878) | c3_1(a878) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(683,plain,
% 0.54/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)) | c0_1(a878) | c3_1(a878) | (~c2_1(a878)) | c3_1(a830) | c2_1(a830) | c1_1(a830))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c0_1(a878) | c3_1(a878) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830) | (~c1_1(a878)) | (~c2_1(a878))))),
% 0.54/0.70 inference(monotonicity,[status(thm)],[682])).
% 0.54/0.70 tff(684,plain,
% 0.54/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)) | c0_1(a878) | c3_1(a878) | (~c2_1(a878)) | c3_1(a830) | c2_1(a830) | c1_1(a830))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c0_1(a878) | c3_1(a878) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.54/0.70 inference(transitivity,[status(thm)],[683, 681])).
% 0.54/0.70 tff(685,plain,
% 0.54/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)) | c0_1(a878) | c3_1(a878) | (~c2_1(a878)) | c3_1(a830) | c2_1(a830) | c1_1(a830))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(686,plain,
% 0.54/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c0_1(a878) | c3_1(a878) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830) | (~c1_1(a878)) | (~c2_1(a878))),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[685, 684])).
% 0.54/0.70 tff(687,plain,
% 0.54/0.70 ($false),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[686, 151, 629, 680, 621, 671, 674, 477, 637, 673])).
% 0.54/0.70 tff(688,plain,(hskp1 | hskp22 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.54/0.70 tff(689,plain,
% 0.54/0.70 (hskp1),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[688, 13, 12])).
% 0.54/0.70 tff(690,plain,
% 0.54/0.70 (c0_1(a816)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[515, 689])).
% 0.54/0.70 tff(691,plain,
% 0.54/0.70 (~c2_1(a816)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[499, 689])).
% 0.54/0.70 tff(692,plain,
% 0.54/0.70 (^[U: $i] : refl((hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.54/0.70 inference(bind,[status(th)],[])).
% 0.54/0.70 tff(693,plain,
% 0.54/0.70 (![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.54/0.70 inference(quant_intro,[status(thm)],[692])).
% 0.54/0.70 tff(694,plain,
% 0.54/0.70 (![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(695,plain,
% 0.54/0.70 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp14))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp22) <=> ((hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp22))), rewrite(((hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp22) <=> (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp22) <=> (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.54/0.70 inference(bind,[status(th)],[])).
% 0.54/0.70 tff(696,plain,
% 0.54/0.70 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp22) <=> ![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.54/0.70 inference(quant_intro,[status(thm)],[695])).
% 0.54/0.70 tff(697,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.54/0.70 tff(698,plain,
% 0.54/0.70 (![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[697, 696])).
% 0.54/0.70 tff(699,plain,
% 0.54/0.70 (![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[698, 694])).
% 0.54/0.70 tff(700,plain,(
% 0.54/0.70 ![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.54/0.70 inference(skolemize,[status(sab)],[699])).
% 0.54/0.70 tff(701,plain,
% 0.54/0.70 (![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[700, 693])).
% 0.54/0.70 tff(702,assumption,(~hskp14), introduced(assumption)).
% 0.54/0.70 tff(703,plain,
% 0.54/0.70 (~c2_1(a878)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[654, 702])).
% 0.54/0.70 tff(704,plain,
% 0.54/0.70 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | c0_1(a878) | c3_1(a878) | (~ndr1_0) | c2_1(a878))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a878) | c3_1(a878) | (~ndr1_0) | c2_1(a878))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(705,plain,
% 0.54/0.70 ((hskp7 | hskp4 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | c0_1(a878)) <=> (hskp7 | hskp4 | c0_1(a878) | c3_1(a878) | (~ndr1_0) | c2_1(a878))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(706,plain,
% 0.54/0.70 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | c0_1(a878))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | c0_1(a878) | c3_1(a878) | (~ndr1_0) | c2_1(a878)))),
% 0.54/0.70 inference(monotonicity,[status(thm)],[705])).
% 0.54/0.70 tff(707,plain,
% 0.54/0.70 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | c0_1(a878))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a878) | c3_1(a878) | (~ndr1_0) | c2_1(a878))),
% 0.54/0.70 inference(transitivity,[status(thm)],[706, 704])).
% 0.54/0.70 tff(708,plain,
% 0.54/0.70 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | c0_1(a878))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(709,plain,
% 0.54/0.70 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a878) | c3_1(a878) | (~ndr1_0) | c2_1(a878)),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.54/0.70 tff(710,plain,
% 0.54/0.70 (hskp4 | c2_1(a878)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[709, 151, 12, 680, 621, 441])).
% 0.54/0.70 tff(711,plain,
% 0.54/0.70 (hskp4),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[710, 703])).
% 0.54/0.70 tff(712,plain,
% 0.54/0.70 (~c1_1(a821)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[453, 711])).
% 0.54/0.70 tff(713,plain,
% 0.54/0.70 (c2_1(a821)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[484, 711])).
% 0.54/0.70 tff(714,plain,
% 0.54/0.70 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c2_1(a821)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c2_1(a821)))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(715,plain,
% 0.54/0.70 ((hskp14 | hskp22 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821))) <=> (hskp14 | hskp22 | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c2_1(a821)))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(716,plain,
% 0.54/0.70 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c2_1(a821))))),
% 0.54/0.70 inference(monotonicity,[status(thm)],[715])).
% 0.54/0.70 tff(717,plain,
% 0.54/0.70 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c2_1(a821)))),
% 0.54/0.70 inference(transitivity,[status(thm)],[716, 714])).
% 0.54/0.70 tff(718,plain,
% 0.54/0.70 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(719,plain,
% 0.54/0.70 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c2_1(a821))),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[718, 717])).
% 0.54/0.70 tff(720,plain,
% 0.54/0.70 (~c3_1(a821)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[719, 702, 151, 13, 713, 712, 701])).
% 0.54/0.70 tff(721,plain,
% 0.54/0.70 (~c0_1(a821)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[459, 711])).
% 0.54/0.70 tff(722,plain,
% 0.54/0.70 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.54/0.70 inference(bind,[status(th)],[])).
% 0.54/0.70 tff(723,plain,
% 0.54/0.70 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.54/0.70 inference(quant_intro,[status(thm)],[722])).
% 0.54/0.70 tff(724,plain,
% 0.54/0.70 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(725,plain,
% 0.54/0.70 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_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))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_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))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.54/0.71 inference(bind,[status(th)],[])).
% 0.54/0.71 tff(726,plain,
% 0.54/0.71 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.54/0.71 inference(quant_intro,[status(thm)],[725])).
% 0.54/0.71 tff(727,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 0.54/0.71 tff(728,plain,
% 0.54/0.71 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[727, 726])).
% 0.54/0.71 tff(729,plain,
% 0.54/0.71 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[728, 724])).
% 0.54/0.71 tff(730,plain,(
% 0.54/0.71 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.54/0.71 inference(skolemize,[status(sab)],[729])).
% 0.54/0.71 tff(731,plain,
% 0.54/0.71 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[730, 723])).
% 0.54/0.71 tff(732,plain,
% 0.54/0.71 (c3_1(a816)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[507, 689])).
% 0.54/0.71 tff(733,plain,
% 0.54/0.71 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(734,plain,
% 0.54/0.71 ((hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878))) <=> (hskp9 | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(735,plain,
% 0.54/0.71 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878))))),
% 0.54/0.71 inference(monotonicity,[status(thm)],[734])).
% 0.54/0.71 tff(736,plain,
% 0.54/0.71 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))),
% 0.54/0.71 inference(transitivity,[status(thm)],[735, 733])).
% 0.54/0.71 tff(737,plain,
% 0.54/0.71 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878)))),
% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(738,plain,
% 0.54/0.71 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.54/0.71 tff(739,plain,
% 0.54/0.71 (hskp9),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[738, 151, 629, 690, 732, 680, 691, 731, 703])).
% 0.54/0.71 tff(740,plain,
% 0.54/0.71 (~c1_1(a831)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[228, 739])).
% 0.54/0.71 tff(741,plain,
% 0.54/0.71 (~c0_1(a831)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[234, 739])).
% 0.54/0.71 tff(742,plain,
% 0.54/0.71 (c3_1(a831)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[242, 739])).
% 0.54/0.71 tff(743,plain,
% 0.54/0.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a831) | c1_1(a831) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | c3_1(a821) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a831) | c1_1(a831) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | c3_1(a821) | (~c3_1(a831)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(744,plain,
% 0.54/0.71 (((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a821) | c0_1(a821) | c3_1(a821)) <=> (c0_1(a831) | c1_1(a831) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | c3_1(a821) | (~c3_1(a831)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(745,plain,
% 0.54/0.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a821) | c0_1(a821) | c3_1(a821))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a831) | c1_1(a831) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | c3_1(a821) | (~c3_1(a831))))),
% 0.54/0.71 inference(monotonicity,[status(thm)],[744])).
% 0.54/0.71 tff(746,plain,
% 0.54/0.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a821) | c0_1(a821) | c3_1(a821))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a831) | c1_1(a831) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | c3_1(a821) | (~c3_1(a831)))),
% 0.54/0.71 inference(transitivity,[status(thm)],[745, 743])).
% 0.54/0.71 tff(747,plain,
% 0.54/0.71 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a821) | c0_1(a821) | c3_1(a821))),
% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(748,plain,
% 0.54/0.71 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a831) | c1_1(a831) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | c3_1(a821) | (~c3_1(a831))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[747, 746])).
% 0.54/0.71 tff(749,plain,
% 0.54/0.71 ($false),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[748, 151, 742, 741, 740, 721, 712, 190, 720])).
% 0.54/0.71 tff(750,plain,(hskp14 | hskp22 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.54/0.71 tff(751,plain,
% 0.54/0.71 (hskp14),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[750, 13, 12])).
% 0.54/0.71 tff(752,plain,
% 0.54/0.71 (~c2_1(a842)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[54, 751])).
% 0.54/0.71 tff(753,plain,
% 0.54/0.71 (c1_1(a842)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[62, 751])).
% 0.54/0.71 tff(754,plain,
% 0.54/0.71 (c0_1(a842)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[70, 751])).
% 0.54/0.71 tff(755,assumption,(~hskp8), introduced(assumption)).
% 0.54/0.71 tff(756,assumption,(~c2_1(a816)), introduced(assumption)).
% 0.54/0.71 tff(757,assumption,(c3_1(a816)), introduced(assumption)).
% 0.54/0.71 tff(758,assumption,(c0_1(a816)), introduced(assumption)).
% 0.54/0.71 tff(759,assumption,(~hskp29), introduced(assumption)).
% 0.54/0.71 tff(760,plain,
% 0.54/0.71 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(761,plain,
% 0.54/0.71 ((hskp29 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816))) <=> (hskp29 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(762,plain,
% 0.54/0.71 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816))))),
% 0.54/0.71 inference(monotonicity,[status(thm)],[761])).
% 0.54/0.71 tff(763,plain,
% 0.54/0.71 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))),
% 0.54/0.71 inference(transitivity,[status(thm)],[762, 760])).
% 0.54/0.71 tff(764,plain,
% 0.54/0.71 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))),
% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(765,plain,
% 0.54/0.71 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[764, 763])).
% 0.54/0.71 tff(766,plain,
% 0.54/0.71 (hskp29 | (~c1_1(a816))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[765, 151, 758, 757, 756, 326])).
% 0.54/0.71 tff(767,plain,
% 0.54/0.71 (~c1_1(a816)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[766, 759])).
% 0.54/0.71 tff(768,plain,
% 0.54/0.71 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(769,plain,
% 0.54/0.71 ((hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816))) <=> (hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(770,plain,
% 0.54/0.71 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816))))),
% 0.54/0.71 inference(monotonicity,[status(thm)],[769])).
% 0.54/0.71 tff(771,plain,
% 0.54/0.71 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))),
% 0.54/0.71 inference(transitivity,[status(thm)],[770, 768])).
% 0.54/0.71 tff(772,plain,
% 0.54/0.71 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816)))),
% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(773,plain,
% 0.54/0.71 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[772, 771])).
% 0.54/0.71 tff(774,plain,
% 0.54/0.71 (hskp9 | c1_1(a816)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[773, 151, 758, 757, 756, 215])).
% 0.54/0.71 tff(775,plain,
% 0.54/0.71 (hskp9),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[774, 767])).
% 0.54/0.71 tff(776,plain,
% 0.54/0.71 (~c1_1(a831)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[228, 775])).
% 0.54/0.71 tff(777,plain,
% 0.54/0.71 (~c0_1(a831)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[234, 775])).
% 0.54/0.71 tff(778,plain,
% 0.54/0.71 (^[U: $i] : refl((hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.54/0.71 inference(bind,[status(th)],[])).
% 0.54/0.71 tff(779,plain,
% 0.54/0.71 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.54/0.71 inference(quant_intro,[status(thm)],[778])).
% 0.54/0.71 tff(780,plain,
% 0.54/0.71 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(781,plain,
% 0.54/0.71 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp19) <=> ((hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite(((hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp19) <=> (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.54/0.71 inference(bind,[status(th)],[])).
% 0.54/0.71 tff(782,plain,
% 0.54/0.71 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp19) <=> ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.54/0.71 inference(quant_intro,[status(thm)],[781])).
% 0.54/0.71 tff(783,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 0.54/0.71 tff(784,plain,
% 0.54/0.71 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[783, 782])).
% 0.54/0.71 tff(785,plain,
% 0.54/0.71 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[784, 780])).
% 0.54/0.71 tff(786,plain,(
% 0.54/0.71 ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.54/0.71 inference(skolemize,[status(sab)],[785])).
% 0.54/0.71 tff(787,plain,
% 0.54/0.71 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[786, 779])).
% 0.54/0.71 tff(788,plain,
% 0.54/0.71 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(789,plain,
% 0.54/0.71 ((hskp29 | hskp19 | (~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842))) <=> (hskp29 | hskp19 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(790,plain,
% 0.54/0.71 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842))))),
% 0.54/0.71 inference(monotonicity,[status(thm)],[789])).
% 0.54/0.71 tff(791,plain,
% 0.54/0.71 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.54/0.71 inference(transitivity,[status(thm)],[790, 788])).
% 0.54/0.71 tff(792,plain,
% 0.54/0.71 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(793,plain,
% 0.54/0.71 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[792, 791])).
% 0.54/0.71 tff(794,plain,
% 0.54/0.71 (hskp29 | hskp19),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[793, 151, 101, 100, 92, 787])).
% 0.54/0.71 tff(795,plain,
% 0.54/0.71 (hskp19),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[794, 759])).
% 0.54/0.71 tff(796,plain,
% 0.54/0.71 (((~hskp19) | (~c3_1(a855))) <=> ((~hskp19) | (~c3_1(a855)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(797,plain,
% 0.54/0.71 (((~c3_1(a855)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a855)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(798,axiom,((~c3_1(a855)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.54/0.71 tff(799,plain,
% 0.54/0.71 ((~hskp19) | (~c3_1(a855))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[798, 797])).
% 0.54/0.71 tff(800,plain,
% 0.54/0.71 ((~hskp19) | (~c3_1(a855))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[799, 796])).
% 0.54/0.71 tff(801,plain,
% 0.54/0.71 (~c3_1(a855)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[800, 795])).
% 0.54/0.71 tff(802,plain,
% 0.54/0.71 (((~hskp19) | (~c1_1(a855))) <=> ((~hskp19) | (~c1_1(a855)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(803,plain,
% 0.54/0.71 (((~c1_1(a855)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a855)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(804,axiom,((~c1_1(a855)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.54/0.71 tff(805,plain,
% 0.54/0.71 ((~hskp19) | (~c1_1(a855))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[804, 803])).
% 0.54/0.71 tff(806,plain,
% 0.54/0.71 ((~hskp19) | (~c1_1(a855))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[805, 802])).
% 0.54/0.71 tff(807,plain,
% 0.54/0.71 (~c1_1(a855)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[806, 795])).
% 0.54/0.71 tff(808,plain,
% 0.54/0.71 (((~hskp19) | (~c0_1(a855))) <=> ((~hskp19) | (~c0_1(a855)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(809,plain,
% 0.54/0.71 (((~c0_1(a855)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a855)))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(810,axiom,((~c0_1(a855)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.54/0.71 tff(811,plain,
% 0.54/0.72 ((~hskp19) | (~c0_1(a855))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[810, 809])).
% 0.54/0.72 tff(812,plain,
% 0.54/0.72 ((~hskp19) | (~c0_1(a855))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[811, 808])).
% 0.54/0.72 tff(813,plain,
% 0.54/0.72 (~c0_1(a855)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[812, 795])).
% 0.54/0.72 tff(814,plain,
% 0.54/0.72 (c3_1(a831)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[242, 775])).
% 0.54/0.72 tff(815,plain,
% 0.54/0.72 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a855) | c1_1(a855) | c3_1(a855) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a855) | c1_1(a855) | c3_1(a855) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(816,plain,
% 0.54/0.72 (((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a855) | c0_1(a855) | c3_1(a855)) <=> (c0_1(a855) | c1_1(a855) | c3_1(a855) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(817,plain,
% 0.54/0.72 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a855) | c0_1(a855) | c3_1(a855))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a855) | c1_1(a855) | c3_1(a855) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[816])).
% 0.54/0.72 tff(818,plain,
% 0.54/0.72 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a855) | c0_1(a855) | c3_1(a855))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a855) | c1_1(a855) | c3_1(a855) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)))),
% 0.54/0.72 inference(transitivity,[status(thm)],[817, 815])).
% 0.54/0.72 tff(819,plain,
% 0.54/0.72 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a855) | c0_1(a855) | c3_1(a855))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(820,plain,
% 0.54/0.72 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a855) | c1_1(a855) | c3_1(a855) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[819, 818])).
% 0.54/0.72 tff(821,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[820, 151, 814, 813, 807, 801, 777, 776, 190])).
% 0.54/0.72 tff(822,plain,(hskp29 | (~c0_1(a816)) | (~c3_1(a816)) | c2_1(a816) | (~c0_1(a842)) | (~c1_1(a842)) | c2_1(a842)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(823,plain,
% 0.54/0.72 (hskp29),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[822, 758, 757, 756, 101, 100, 92])).
% 0.54/0.72 tff(824,plain,
% 0.54/0.72 (c3_1(a865)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[344, 823])).
% 0.54/0.72 tff(825,plain,
% 0.54/0.72 (c2_1(a865)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[352, 823])).
% 0.54/0.72 tff(826,plain,
% 0.54/0.72 (c1_1(a865)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[360, 823])).
% 0.54/0.72 tff(827,plain,
% 0.54/0.72 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c0_1(a865)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c0_1(a865)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(828,plain,
% 0.54/0.72 ((hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865))) <=> (hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c0_1(a865)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(829,plain,
% 0.54/0.72 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c0_1(a865))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[828])).
% 0.54/0.72 tff(830,plain,
% 0.54/0.72 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c0_1(a865)))),
% 0.54/0.72 inference(transitivity,[status(thm)],[829, 827])).
% 0.54/0.72 tff(831,plain,
% 0.54/0.72 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(832,plain,
% 0.54/0.72 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c0_1(a865))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[831, 830])).
% 0.54/0.72 tff(833,plain,
% 0.54/0.72 (hskp8 | (~c0_1(a865))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[832, 151, 826, 825, 824, 316])).
% 0.54/0.72 tff(834,plain,
% 0.54/0.72 (~c0_1(a865)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[833, 755])).
% 0.54/0.72 tff(835,plain,
% 0.54/0.72 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(836,plain,
% 0.54/0.72 ((hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816))) <=> (hskp8 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(837,plain,
% 0.54/0.72 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[836])).
% 0.54/0.72 tff(838,plain,
% 0.54/0.72 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))),
% 0.54/0.72 inference(transitivity,[status(thm)],[837, 835])).
% 0.54/0.72 tff(839,plain,
% 0.54/0.72 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(840,plain,
% 0.54/0.72 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[839, 838])).
% 0.54/0.72 tff(841,plain,
% 0.54/0.72 (hskp8 | (~c1_1(a816))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[840, 151, 826, 825, 824, 758, 757, 316])).
% 0.54/0.72 tff(842,plain,
% 0.54/0.72 (~c1_1(a816)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[841, 755])).
% 0.54/0.72 tff(843,plain,
% 0.54/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(844,plain,
% 0.54/0.72 (((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865))) <=> (c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(845,plain,
% 0.54/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[844])).
% 0.54/0.72 tff(846,plain,
% 0.54/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.54/0.72 inference(transitivity,[status(thm)],[845, 843])).
% 0.54/0.72 tff(847,plain,
% 0.54/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(848,plain,
% 0.54/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[847, 846])).
% 0.54/0.72 tff(849,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[848, 151, 826, 825, 101, 100, 757, 92, 756, 81, 842, 834])).
% 0.54/0.72 tff(850,plain,(hskp8 | (~c0_1(a842)) | (~c1_1(a842)) | (~c3_1(a816)) | c2_1(a842) | c2_1(a816) | (~c0_1(a816))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(851,plain,
% 0.54/0.72 (hskp8),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[850, 754, 753, 732, 752, 691, 690])).
% 0.54/0.72 tff(852,plain,
% 0.54/0.72 (~c0_1(a830)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[379, 851])).
% 0.54/0.72 tff(853,plain,
% 0.54/0.72 (~c3_1(a830)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[402, 851])).
% 0.54/0.72 tff(854,plain,
% 0.54/0.72 (~c2_1(a830)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[373, 851])).
% 0.54/0.72 tff(855,assumption,(c1_1(a816)), introduced(assumption)).
% 0.54/0.72 tff(856,assumption,(~c2_1(a830)), introduced(assumption)).
% 0.54/0.72 tff(857,assumption,(~c0_1(a830)), introduced(assumption)).
% 0.54/0.72 tff(858,plain,
% 0.54/0.72 ((~c1_1(a816)) | (~c1_1(a830))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[548, 151, 758, 757, 857, 856, 756, 306])).
% 0.54/0.72 tff(859,plain,
% 0.54/0.72 (~c1_1(a830)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[858, 855])).
% 0.54/0.72 tff(860,assumption,(~c3_1(a830)), introduced(assumption)).
% 0.54/0.72 tff(861,assumption,(~c3_1(a878)), introduced(assumption)).
% 0.54/0.72 tff(862,assumption,(~c0_1(a878)), introduced(assumption)).
% 0.54/0.72 tff(863,assumption,(c1_1(a878)), introduced(assumption)).
% 0.54/0.72 tff(864,plain,
% 0.54/0.72 (c1_1(a830) | (~c2_1(a878))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[686, 151, 863, 862, 861, 856, 860, 477])).
% 0.54/0.72 tff(865,plain,
% 0.54/0.72 (~c2_1(a878)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[864, 859])).
% 0.54/0.72 tff(866,plain,
% 0.54/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(867,plain,
% 0.54/0.72 (((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878))) <=> (c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(868,plain,
% 0.54/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[867])).
% 0.54/0.72 tff(869,plain,
% 0.54/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))),
% 0.54/0.72 inference(transitivity,[status(thm)],[868, 866])).
% 0.54/0.72 tff(870,plain,
% 0.54/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(871,plain,
% 0.54/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[870, 869])).
% 0.54/0.72 tff(872,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[871, 151, 863, 758, 757, 862, 756, 306, 865, 855])).
% 0.54/0.72 tff(873,plain,((~c1_1(a816)) | (~c1_1(a878)) | (~c0_1(a816)) | (~c3_1(a816)) | c0_1(a878) | c2_1(a816) | c3_1(a878) | c2_1(a830) | c3_1(a830) | c0_1(a830)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(874,plain,
% 0.54/0.72 (~c1_1(a816)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[873, 629, 690, 732, 680, 691, 621, 854, 853, 852])).
% 0.54/0.72 tff(875,plain,
% 0.54/0.72 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.54/0.72 inference(bind,[status(th)],[])).
% 0.54/0.72 tff(876,plain,
% 0.54/0.72 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.54/0.72 inference(quant_intro,[status(thm)],[875])).
% 0.54/0.72 tff(877,plain,
% 0.54/0.72 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(878,plain,
% 0.54/0.72 (^[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)) | (~c3_1(V)) | (~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)) | (~c3_1(V)) | (~c0_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)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_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)) | (~c3_1(V)) | (~c0_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)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_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) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.54/0.72 inference(bind,[status(th)],[])).
% 0.54/0.72 tff(879,plain,
% 0.54/0.72 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.54/0.72 inference(quant_intro,[status(thm)],[878])).
% 0.54/0.72 tff(880,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)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.54/0.72 tff(881,plain,
% 0.54/0.72 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[880, 879])).
% 0.54/0.72 tff(882,plain,
% 0.54/0.72 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[881, 877])).
% 0.54/0.72 tff(883,plain,(
% 0.54/0.72 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.54/0.72 inference(skolemize,[status(sab)],[882])).
% 0.54/0.72 tff(884,plain,
% 0.54/0.72 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[883, 876])).
% 0.54/0.72 tff(885,assumption,(~hskp4), introduced(assumption)).
% 0.54/0.72 tff(886,plain,
% 0.54/0.72 (hskp4 | c2_1(a878)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[709, 151, 12, 862, 861, 441])).
% 0.54/0.72 tff(887,plain,
% 0.54/0.72 (c2_1(a878)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[886, 885])).
% 0.54/0.72 tff(888,plain,
% 0.54/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a878) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c1_1(a842)) | (~c0_1(a842)) | (~c1_1(a878)) | (~c2_1(a878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a878) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c1_1(a842)) | (~c0_1(a842)) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(889,plain,
% 0.54/0.72 (((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a878) | (~c2_1(a878)) | (~c1_1(a878))) <=> (c0_1(a878) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c1_1(a842)) | (~c0_1(a842)) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(890,plain,
% 0.54/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a878) | (~c2_1(a878)) | (~c1_1(a878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a878) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c1_1(a842)) | (~c0_1(a842)) | (~c1_1(a878)) | (~c2_1(a878))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[889])).
% 0.54/0.72 tff(891,plain,
% 0.54/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a878) | (~c2_1(a878)) | (~c1_1(a878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a878) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c1_1(a842)) | (~c0_1(a842)) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.54/0.72 inference(transitivity,[status(thm)],[890, 888])).
% 0.54/0.72 tff(892,plain,
% 0.54/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a878) | (~c2_1(a878)) | (~c1_1(a878)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(893,plain,
% 0.54/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a878) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c1_1(a842)) | (~c0_1(a842)) | (~c1_1(a878)) | (~c2_1(a878))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[892, 891])).
% 0.54/0.73 tff(894,plain,
% 0.54/0.73 (c1_1(a816) | (~c2_1(a878))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[893, 151, 863, 101, 100, 757, 862, 92, 756, 81])).
% 0.54/0.73 tff(895,plain,
% 0.54/0.73 (c1_1(a816)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[894, 887])).
% 0.54/0.73 tff(896,plain,
% 0.54/0.73 (hskp29),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[766, 895])).
% 0.54/0.73 tff(897,plain,
% 0.54/0.73 (c3_1(a865)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[344, 896])).
% 0.54/0.73 tff(898,plain,
% 0.54/0.73 (c2_1(a865)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[352, 896])).
% 0.54/0.73 tff(899,plain,
% 0.54/0.73 (c1_1(a865)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[360, 896])).
% 0.54/0.73 tff(900,plain,
% 0.54/0.73 (hskp8),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[840, 151, 899, 898, 897, 758, 757, 316, 895])).
% 0.54/0.73 tff(901,plain,
% 0.54/0.73 (~c3_1(a830)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[402, 900])).
% 0.54/0.73 tff(902,plain,
% 0.54/0.73 (~c2_1(a830)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[373, 900])).
% 0.54/0.73 tff(903,plain,
% 0.54/0.73 (~c0_1(a830)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[379, 900])).
% 0.54/0.73 tff(904,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[447, 151, 12, 885, 903, 902, 901, 441])).
% 0.54/0.73 tff(905,plain,(hskp4 | hskp7 | (~c0_1(a816)) | (~c3_1(a816)) | c2_1(a816) | (~c1_1(a878)) | (~c0_1(a842)) | (~c1_1(a842)) | c0_1(a878) | c2_1(a842) | c3_1(a878)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(906,plain,
% 0.54/0.73 (hskp4),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[905, 690, 12, 732, 691, 629, 754, 753, 680, 752, 621])).
% 0.54/0.73 tff(907,plain,
% 0.54/0.73 (~c1_1(a821)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[453, 906])).
% 0.54/0.73 tff(908,plain,
% 0.54/0.73 (c2_1(a821)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[484, 906])).
% 0.54/0.73 tff(909,plain,
% 0.54/0.73 (~hskp20),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[262, 754, 753, 752])).
% 0.54/0.73 tff(910,plain,
% 0.54/0.73 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a821) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)) | (~c3_1(a821)) | (~c2_1(a821)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a821) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)) | (~c3_1(a821)) | (~c2_1(a821)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(911,plain,
% 0.54/0.73 ((hskp20 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816))) <=> (hskp20 | c1_1(a821) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)) | (~c3_1(a821)) | (~c2_1(a821)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(912,plain,
% 0.54/0.73 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a821) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)) | (~c3_1(a821)) | (~c2_1(a821))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[911])).
% 0.54/0.73 tff(913,plain,
% 0.54/0.73 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a821) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)) | (~c3_1(a821)) | (~c2_1(a821)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[912, 910])).
% 0.54/0.73 tff(914,plain,
% 0.54/0.73 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(915,plain,
% 0.54/0.73 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a821) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)) | (~c3_1(a821)) | (~c2_1(a821))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[914, 913])).
% 0.54/0.73 tff(916,plain,
% 0.54/0.73 (~c3_1(a821)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[915, 151, 909, 908, 690, 732, 907, 884, 874])).
% 0.54/0.73 tff(917,plain,
% 0.54/0.73 (~c0_1(a821)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[459, 906])).
% 0.54/0.73 tff(918,plain,
% 0.54/0.73 (hskp9 | c1_1(a816)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[773, 151, 690, 732, 691, 215])).
% 0.54/0.73 tff(919,plain,
% 0.54/0.73 (hskp9),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[918, 874])).
% 0.54/0.73 tff(920,plain,
% 0.54/0.73 (~c1_1(a831)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[228, 919])).
% 0.54/0.73 tff(921,plain,
% 0.54/0.73 (~c0_1(a831)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[234, 919])).
% 0.54/0.73 tff(922,plain,
% 0.54/0.73 (c3_1(a831)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[242, 919])).
% 0.54/0.73 tff(923,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[748, 151, 922, 921, 920, 917, 907, 190, 916])).
% 0.54/0.73 tff(924,plain,(hskp22 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(925,plain,
% 0.54/0.73 (hskp22),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[924, 12])).
% 0.54/0.73 tff(926,plain,
% 0.54/0.73 (((~hskp22) | (~c1_1(a860))) <=> ((~hskp22) | (~c1_1(a860)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(927,plain,
% 0.54/0.73 (((~c1_1(a860)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a860)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(928,axiom,((~c1_1(a860)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.54/0.73 tff(929,plain,
% 0.54/0.73 ((~hskp22) | (~c1_1(a860))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[928, 927])).
% 0.54/0.73 tff(930,plain,
% 0.54/0.73 ((~hskp22) | (~c1_1(a860))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[929, 926])).
% 0.54/0.73 tff(931,plain,
% 0.54/0.73 (~c1_1(a860)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[930, 925])).
% 0.54/0.73 tff(932,plain,
% 0.54/0.73 (((~hskp22) | (~c2_1(a860))) <=> ((~hskp22) | (~c2_1(a860)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(933,plain,
% 0.54/0.73 (((~c2_1(a860)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a860)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(934,axiom,((~c2_1(a860)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.54/0.73 tff(935,plain,
% 0.54/0.73 ((~hskp22) | (~c2_1(a860))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[934, 933])).
% 0.54/0.73 tff(936,plain,
% 0.54/0.73 ((~hskp22) | (~c2_1(a860))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[935, 932])).
% 0.54/0.73 tff(937,plain,
% 0.54/0.73 (~c2_1(a860)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[936, 925])).
% 0.54/0.73 tff(938,plain,
% 0.54/0.73 (((~hskp22) | (~c0_1(a860))) <=> ((~hskp22) | (~c0_1(a860)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(939,plain,
% 0.54/0.73 (((~c0_1(a860)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a860)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(940,axiom,((~c0_1(a860)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.54/0.73 tff(941,plain,
% 0.54/0.73 ((~hskp22) | (~c0_1(a860))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[940, 939])).
% 0.54/0.73 tff(942,plain,
% 0.54/0.73 ((~hskp22) | (~c0_1(a860))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[941, 938])).
% 0.54/0.73 tff(943,plain,
% 0.54/0.73 (~c0_1(a860)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[942, 925])).
% 0.54/0.73 tff(944,assumption,(c3_1(a860)), introduced(assumption)).
% 0.54/0.73 tff(945,plain,
% 0.54/0.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | (~c3_1(a860)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | (~c3_1(a860)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(946,plain,
% 0.54/0.73 ((hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a860) | c0_1(a860) | (~c3_1(a860))) <=> (hskp2 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | (~c3_1(a860)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(947,plain,
% 0.54/0.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | (~c3_1(a860))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[946])).
% 0.54/0.73 tff(948,plain,
% 0.54/0.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | (~c3_1(a860)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[947, 945])).
% 0.54/0.73 tff(949,plain,
% 0.54/0.73 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(950,plain,
% 0.54/0.73 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | (~c3_1(a860))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[949, 948])).
% 0.54/0.73 tff(951,plain,
% 0.54/0.73 (hskp2 | (~c3_1(a860))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[950, 151, 943, 931, 937, 91])).
% 0.54/0.73 tff(952,plain,
% 0.54/0.73 (hskp2),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[951, 944])).
% 0.54/0.73 tff(953,plain,
% 0.54/0.73 (~c3_1(a817)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[195, 952])).
% 0.54/0.73 tff(954,plain,
% 0.54/0.73 (~c0_1(a817)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[164, 952])).
% 0.54/0.73 tff(955,assumption,(~c1_1(a817)), introduced(assumption)).
% 0.54/0.73 tff(956,assumption,(~c3_1(a817)), introduced(assumption)).
% 0.54/0.73 tff(957,assumption,(~c0_1(a817)), introduced(assumption)).
% 0.54/0.73 tff(958,assumption,(~c1_1(a860)), introduced(assumption)).
% 0.54/0.73 tff(959,assumption,(~c0_1(a860)), introduced(assumption)).
% 0.54/0.73 tff(960,plain,
% 0.54/0.73 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a860)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a860)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(961,plain,
% 0.54/0.73 (((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a817) | c0_1(a817) | c3_1(a817)) <=> (c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a860)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(962,plain,
% 0.54/0.73 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a817) | c0_1(a817) | c3_1(a817))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a860))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[961])).
% 0.54/0.73 tff(963,plain,
% 0.54/0.73 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a817) | c0_1(a817) | c3_1(a817))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a860)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[962, 960])).
% 0.54/0.73 tff(964,plain,
% 0.54/0.73 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a817) | c0_1(a817) | c3_1(a817))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(965,plain,
% 0.54/0.73 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a860))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[964, 963])).
% 0.54/0.73 tff(966,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[965, 151, 959, 958, 957, 956, 190, 944, 955])).
% 0.54/0.73 tff(967,plain,(c1_1(a817) | c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~c3_1(a860))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(968,plain,
% 0.54/0.73 (c1_1(a817)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[967, 954, 931, 943, 953, 944])).
% 0.54/0.73 tff(969,plain,
% 0.54/0.73 (c2_1(a817)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[172, 952])).
% 0.54/0.73 tff(970,plain,
% 0.54/0.73 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(971,plain,
% 0.54/0.73 ((hskp14 | hskp7 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817))) <=> (hskp14 | hskp7 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(972,plain,
% 0.54/0.73 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[971])).
% 0.54/0.73 tff(973,plain,
% 0.54/0.73 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[972, 970])).
% 0.54/0.73 tff(974,plain,
% 0.54/0.73 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(975,plain,
% 0.54/0.73 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[974, 973])).
% 0.54/0.73 tff(976,plain,
% 0.54/0.73 (hskp14 | (~c1_1(a817))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[975, 151, 12, 969, 953, 647])).
% 0.54/0.73 tff(977,plain,
% 0.54/0.73 (hskp14),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[976, 968])).
% 0.54/0.73 tff(978,plain,
% 0.54/0.73 (~c2_1(a842)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[54, 977])).
% 0.54/0.73 tff(979,plain,
% 0.54/0.73 (c1_1(a842)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[62, 977])).
% 0.54/0.73 tff(980,plain,
% 0.54/0.73 (c0_1(a842)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[70, 977])).
% 0.54/0.73 tff(981,plain,
% 0.54/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a860) | c2_1(a860) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a860)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a860) | c2_1(a860) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a860)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(982,plain,
% 0.54/0.73 (((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817))) <=> (c1_1(a860) | c2_1(a860) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a860)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(983,plain,
% 0.54/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a860) | c2_1(a860) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a860))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[982])).
% 0.54/0.73 tff(984,plain,
% 0.54/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a860) | c2_1(a860) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a860)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[983, 981])).
% 0.54/0.73 tff(985,plain,
% 0.54/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(986,plain,
% 0.54/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a860) | c2_1(a860) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a860))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[985, 984])).
% 0.54/0.73 tff(987,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[986, 151, 980, 979, 969, 931, 937, 978, 954, 81, 944, 968])).
% 0.54/0.73 tff(988,plain,((~c3_1(a860)) | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(989,plain,
% 0.54/0.73 (~c3_1(a860)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[988, 12])).
% 0.54/0.73 tff(990,plain,
% 0.54/0.73 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | c0_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(991,plain,
% 0.54/0.73 ((hskp7 | hskp4 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c0_1(a860)) <=> (hskp7 | hskp4 | c0_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(992,plain,
% 0.54/0.73 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c0_1(a860))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | c0_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860)))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[991])).
% 0.54/0.73 tff(993,plain,
% 0.54/0.73 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c0_1(a860))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))),
% 0.54/0.73 inference(transitivity,[status(thm)],[992, 990])).
% 0.54/0.73 tff(994,plain,
% 0.54/0.73 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c0_1(a860))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(995,plain,
% 0.54/0.73 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[994, 993])).
% 0.54/0.73 tff(996,plain,
% 0.54/0.73 (hskp4 | c3_1(a860)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[995, 151, 12, 943, 937, 441])).
% 0.54/0.73 tff(997,plain,
% 0.54/0.73 (hskp4),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[996, 989])).
% 0.54/0.73 tff(998,plain,
% 0.54/0.73 (~c1_1(a821)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[453, 997])).
% 0.54/0.74 tff(999,plain,
% 0.54/0.74 (c2_1(a821)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[484, 997])).
% 0.54/0.74 tff(1000,plain,
% 0.54/0.74 (~c0_1(a821)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[459, 997])).
% 0.54/0.74 tff(1001,assumption,(~c2_1(a860)), introduced(assumption)).
% 0.54/0.74 tff(1002,assumption,(~c3_1(a860)), introduced(assumption)).
% 0.54/0.74 tff(1003,assumption,(~hskp0), introduced(assumption)).
% 0.54/0.74 tff(1004,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1005,plain,
% 0.54/0.74 ((hskp0 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a860) | c0_1(a860)) <=> (hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1006,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a860) | c0_1(a860))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860)))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[1005])).
% 0.54/0.74 tff(1007,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a860) | c0_1(a860))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))),
% 0.54/0.74 inference(transitivity,[status(thm)],[1006, 1004])).
% 0.54/0.74 tff(1008,plain,
% 0.54/0.74 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a860) | c0_1(a860))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(1009,plain,
% 0.54/0.74 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 0.54/0.74 tff(1010,plain,
% 0.54/0.74 ($false),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1009, 151, 1003, 959, 958, 1001, 397, 1002])).
% 0.54/0.74 tff(1011,plain,(c3_1(a860) | hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.74 tff(1012,plain,
% 0.54/0.74 (hskp0),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1011, 1002, 959, 958, 1001])).
% 0.54/0.74 tff(1013,plain,
% 0.54/0.74 (~c3_1(a815)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[415, 1012])).
% 0.54/0.74 tff(1014,assumption,(~c1_1(a821)), introduced(assumption)).
% 0.54/0.74 tff(1015,assumption,(~c0_1(a821)), introduced(assumption)).
% 0.54/0.74 tff(1016,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c3_1(a860))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c3_1(a860))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1017,plain,
% 0.54/0.74 (((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a860) | c0_1(a860) | c3_1(a860)) <=> (c0_1(a860) | c1_1(a860) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c3_1(a860))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1018,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a860) | c0_1(a860) | c3_1(a860))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c3_1(a860)))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[1017])).
% 0.54/0.74 tff(1019,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a860) | c0_1(a860) | c3_1(a860))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c3_1(a860))),
% 0.54/0.74 inference(transitivity,[status(thm)],[1018, 1016])).
% 0.54/0.74 tff(1020,plain,
% 0.54/0.74 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a860) | c0_1(a860) | c3_1(a860))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(1021,plain,
% 0.54/0.74 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c3_1(a860)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 0.54/0.74 tff(1022,plain,
% 0.54/0.74 ((~c3_1(a821)) | c3_1(a860)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1021, 151, 959, 958, 1015, 1014, 190])).
% 0.54/0.74 tff(1023,plain,
% 0.54/0.74 (~c3_1(a821)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1022, 1002])).
% 0.54/0.74 tff(1024,plain,
% 0.54/0.74 (c1_1(a815)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[423, 1012])).
% 0.54/0.74 tff(1025,assumption,(c2_1(a821)), introduced(assumption)).
% 0.54/0.74 tff(1026,plain,
% 0.54/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a860) | c2_1(a860) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a860) | c2_1(a860) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1027,plain,
% 0.54/0.74 (((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860) | c2_1(a860) | c1_1(a860)) <=> (c1_1(a860) | c2_1(a860) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1028,plain,
% 0.54/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860) | c2_1(a860) | c1_1(a860))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a860) | c2_1(a860) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860)))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[1027])).
% 0.54/0.74 tff(1029,plain,
% 0.54/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860) | c2_1(a860) | c1_1(a860))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a860) | c2_1(a860) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860))),
% 0.54/0.74 inference(transitivity,[status(thm)],[1028, 1026])).
% 0.54/0.74 tff(1030,plain,
% 0.54/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860) | c2_1(a860) | c1_1(a860))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(1031,plain,
% 0.54/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a860) | c2_1(a860) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 0.54/0.74 tff(1032,plain,
% 0.54/0.74 (~c2_1(a815)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1031, 151, 1025, 1024, 958, 1001, 1015, 1013, 477, 1002, 1023])).
% 0.54/0.74 tff(1033,plain,
% 0.54/0.74 (c0_1(a815)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[576, 1012])).
% 0.54/0.74 tff(1034,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a860) | c2_1(a860) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)) | c3_1(a860))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a860) | c2_1(a860) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)) | c3_1(a860))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1035,plain,
% 0.54/0.74 ((hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a860) | c0_1(a860) | c3_1(a860)) <=> (hskp5 | c0_1(a860) | c2_1(a860) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)) | c3_1(a860))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1036,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a860) | c0_1(a860) | c3_1(a860))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a860) | c2_1(a860) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)) | c3_1(a860)))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[1035])).
% 0.54/0.74 tff(1037,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a860) | c0_1(a860) | c3_1(a860))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a860) | c2_1(a860) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)) | c3_1(a860))),
% 0.54/0.74 inference(transitivity,[status(thm)],[1036, 1034])).
% 0.54/0.74 tff(1038,plain,
% 0.54/0.74 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a860) | c0_1(a860) | c3_1(a860))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(1039,plain,
% 0.54/0.74 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a860) | c2_1(a860) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)) | c3_1(a860)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.54/0.74 tff(1040,plain,
% 0.54/0.74 (hskp5),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1039, 151, 1033, 959, 1001, 1013, 569, 1002, 1032])).
% 0.54/0.74 tff(1041,plain,
% 0.54/0.74 (~c0_1(a825)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[589, 1040])).
% 0.54/0.74 tff(1042,plain,
% 0.54/0.74 (c3_1(a825)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[597, 1040])).
% 0.54/0.74 tff(1043,plain,
% 0.54/0.74 (c1_1(a825)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[605, 1040])).
% 0.54/0.74 tff(1044,plain,
% 0.54/0.74 ($false),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[612, 151, 1043, 1042, 1025, 1033, 1024, 1041, 1015, 1014, 1013, 34])).
% 0.54/0.74 tff(1045,plain,(c3_1(a860) | (~c2_1(a821)) | c0_1(a821) | c1_1(a821) | c0_1(a860) | c2_1(a860) | c1_1(a860)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.74 tff(1046,plain,
% 0.54/0.74 ($false),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1045, 1000, 999, 989, 998, 943, 937, 931])).
% 0.54/0.74 tff(1047,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 0.54/0.74 tff(1048,plain,
% 0.54/0.74 (((~hskp7) | (~c2_1(a828))) <=> ((~hskp7) | (~c2_1(a828)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1049,plain,
% 0.54/0.74 (((~c2_1(a828)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a828)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1050,axiom,((~c2_1(a828)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.54/0.74 tff(1051,plain,
% 0.54/0.74 ((~hskp7) | (~c2_1(a828))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 0.54/0.74 tff(1052,plain,
% 0.54/0.74 ((~hskp7) | (~c2_1(a828))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1051, 1048])).
% 0.54/0.74 tff(1053,plain,
% 0.54/0.74 (~c2_1(a828)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1052, 1047])).
% 0.54/0.74 tff(1054,plain,
% 0.54/0.74 (((~hskp7) | (~c1_1(a828))) <=> ((~hskp7) | (~c1_1(a828)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1055,plain,
% 0.54/0.74 (((~c1_1(a828)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a828)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1056,axiom,((~c1_1(a828)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.54/0.74 tff(1057,plain,
% 0.54/0.74 ((~hskp7) | (~c1_1(a828))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 0.54/0.74 tff(1058,plain,
% 0.54/0.74 ((~hskp7) | (~c1_1(a828))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1057, 1054])).
% 0.54/0.74 tff(1059,plain,
% 0.54/0.74 (~c1_1(a828)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1058, 1047])).
% 0.54/0.74 tff(1060,plain,
% 0.54/0.74 (((~hskp7) | c0_1(a828)) <=> ((~hskp7) | c0_1(a828))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1061,axiom,((~hskp7) | c0_1(a828)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.54/0.74 tff(1062,plain,
% 0.54/0.74 ((~hskp7) | c0_1(a828)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 0.54/0.74 tff(1063,plain,
% 0.54/0.74 ((~hskp7) | c0_1(a828)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1062, 1060])).
% 0.54/0.74 tff(1064,plain,
% 0.54/0.74 ((~hskp7) | c0_1(a828)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1063, 1060])).
% 0.54/0.74 tff(1065,plain,
% 0.54/0.74 ((~hskp7) | c0_1(a828)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1064, 1060])).
% 0.54/0.74 tff(1066,plain,
% 0.54/0.74 ((~hskp7) | c0_1(a828)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1065, 1060])).
% 0.54/0.74 tff(1067,plain,
% 0.54/0.74 (c0_1(a828)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1066, 1047])).
% 0.54/0.74 tff(1068,plain,
% 0.54/0.74 (^[U: $i] : refl((hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(1069,plain,
% 0.54/0.74 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[1068])).
% 0.54/0.74 tff(1070,plain,
% 0.54/0.74 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1071,plain,
% 0.54/0.74 (^[U: $i] : 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)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(1072,plain,
% 0.54/0.74 (![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[1071])).
% 0.54/0.74 tff(1073,axiom,(![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.54/0.74 tff(1074,plain,
% 0.54/0.74 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1073, 1072])).
% 0.54/0.74 tff(1075,plain,
% 0.54/0.74 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1074, 1070])).
% 0.54/0.74 tff(1076,plain,(
% 0.54/0.74 ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.54/0.74 inference(skolemize,[status(sab)],[1075])).
% 0.54/0.74 tff(1077,plain,
% 0.54/0.74 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1076, 1069])).
% 0.54/0.74 tff(1078,plain,
% 0.54/0.74 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c3_1(a828))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c3_1(a828))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1079,plain,
% 0.54/0.74 ((hskp27 | (~ndr1_0) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (hskp27 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c3_1(a828))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1080,plain,
% 0.54/0.74 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c3_1(a828)))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[1079])).
% 0.54/0.74 tff(1081,plain,
% 0.54/0.74 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c3_1(a828))),
% 0.54/0.74 inference(transitivity,[status(thm)],[1080, 1078])).
% 0.54/0.74 tff(1082,plain,
% 0.54/0.74 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(1083,plain,
% 0.54/0.74 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c3_1(a828)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 0.54/0.74 tff(1084,plain,
% 0.54/0.74 (hskp27 | c3_1(a828)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1083, 151, 1059, 1053, 1077])).
% 0.54/0.74 tff(1085,plain,
% 0.54/0.74 (hskp27),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1084, 1])).
% 0.54/0.74 tff(1086,plain,
% 0.54/0.74 (((~hskp27) | c3_1(a826)) <=> ((~hskp27) | c3_1(a826))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1087,axiom,((~hskp27) | c3_1(a826)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.54/0.74 tff(1088,plain,
% 0.54/0.74 ((~hskp27) | c3_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 0.54/0.74 tff(1089,plain,
% 0.54/0.74 ((~hskp27) | c3_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1088, 1086])).
% 0.54/0.74 tff(1090,plain,
% 0.54/0.74 ((~hskp27) | c3_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1089, 1086])).
% 0.54/0.74 tff(1091,plain,
% 0.54/0.74 ((~hskp27) | c3_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1090, 1086])).
% 0.54/0.74 tff(1092,plain,
% 0.54/0.74 ((~hskp27) | c3_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1091, 1086])).
% 0.54/0.74 tff(1093,plain,
% 0.54/0.74 (c3_1(a826)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1092, 1085])).
% 0.54/0.74 tff(1094,plain,
% 0.54/0.74 (((~hskp27) | c2_1(a826)) <=> ((~hskp27) | c2_1(a826))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1095,axiom,((~hskp27) | c2_1(a826)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.54/0.74 tff(1096,plain,
% 0.54/0.74 ((~hskp27) | c2_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1095, 1094])).
% 0.54/0.74 tff(1097,plain,
% 0.54/0.74 ((~hskp27) | c2_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1096, 1094])).
% 0.54/0.74 tff(1098,plain,
% 0.54/0.74 ((~hskp27) | c2_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1097, 1094])).
% 0.54/0.74 tff(1099,plain,
% 0.54/0.74 ((~hskp27) | c2_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1098, 1094])).
% 0.54/0.74 tff(1100,plain,
% 0.54/0.74 ((~hskp27) | c2_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1099, 1094])).
% 0.54/0.74 tff(1101,plain,
% 0.54/0.74 (c2_1(a826)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1100, 1085])).
% 0.54/0.74 tff(1102,plain,
% 0.54/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | (~c0_1(a828)) | c3_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | (~c0_1(a828)) | c3_1(a828))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1103,plain,
% 0.54/0.74 (((~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | (~c0_1(a828)) | c3_1(a828))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1104,plain,
% 0.54/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | (~c0_1(a828)) | c3_1(a828)))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[1103])).
% 0.54/0.74 tff(1105,plain,
% 0.54/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | (~c0_1(a828)) | c3_1(a828))),
% 0.54/0.74 inference(transitivity,[status(thm)],[1104, 1102])).
% 0.54/0.74 tff(1106,plain,
% 0.54/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(1107,plain,
% 0.54/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | (~c0_1(a828)) | c3_1(a828)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 0.54/0.74 tff(1108,plain,
% 0.54/0.74 (~c1_1(a826)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1107, 151, 1101, 1093, 1067, 1059, 1053, 11, 1])).
% 0.54/0.74 tff(1109,plain,
% 0.54/0.74 (((~hskp27) | c0_1(a826)) <=> ((~hskp27) | c0_1(a826))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1110,axiom,((~hskp27) | c0_1(a826)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.54/0.74 tff(1111,plain,
% 0.54/0.74 ((~hskp27) | c0_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 0.54/0.74 tff(1112,plain,
% 0.54/0.74 ((~hskp27) | c0_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1111, 1109])).
% 0.54/0.74 tff(1113,plain,
% 0.54/0.74 ((~hskp27) | c0_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1112, 1109])).
% 0.54/0.74 tff(1114,plain,
% 0.54/0.74 ((~hskp27) | c0_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1113, 1109])).
% 0.54/0.74 tff(1115,plain,
% 0.54/0.74 ((~hskp27) | c0_1(a826)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[1114, 1109])).
% 0.54/0.74 tff(1116,plain,
% 0.54/0.74 (c0_1(a826)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1115, 1085])).
% 0.54/0.74 tff(1117,plain,
% 0.54/0.74 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1118,plain,
% 0.54/0.74 ((hskp14 | hskp22 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826))) <=> (hskp14 | hskp22 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1119,plain,
% 0.54/0.75 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826)))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[1118])).
% 0.54/0.75 tff(1120,plain,
% 0.54/0.75 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826))),
% 0.54/0.75 inference(transitivity,[status(thm)],[1119, 1117])).
% 0.54/0.75 tff(1121,plain,
% 0.54/0.75 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1122,plain,
% 0.54/0.75 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 0.54/0.75 tff(1123,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1122, 702, 151, 13, 1101, 1093, 701, 1108])).
% 0.54/0.75 tff(1124,plain,(c3_1(a828) | hskp14 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(1125,plain,
% 0.54/0.75 (c3_1(a828)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1124, 13, 702])).
% 0.54/0.75 tff(1126,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1127,plain,
% 0.54/0.75 ((hskp9 | (~ndr1_0) | c2_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828))) <=> (hskp9 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1128,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[1127])).
% 0.54/0.75 tff(1129,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[1128, 1126])).
% 0.54/0.75 tff(1130,plain,
% 0.54/0.75 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1131,plain,
% 0.54/0.75 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 0.54/0.75 tff(1132,plain,
% 0.54/0.75 (hskp9 | (~c3_1(a828))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1131, 151, 1067, 1059, 1053, 215])).
% 0.54/0.75 tff(1133,plain,
% 0.54/0.75 (hskp9),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1132, 1125])).
% 0.54/0.75 tff(1134,plain,
% 0.54/0.75 (~c1_1(a831)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[228, 1133])).
% 0.54/0.75 tff(1135,plain,
% 0.54/0.75 (c3_1(a831)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[242, 1133])).
% 0.54/0.75 tff(1136,plain,
% 0.54/0.75 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | c1_1(a831) | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a831) | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1137,plain,
% 0.54/0.75 ((hskp14 | hskp22 | (~ndr1_0) | c1_1(a831) | (~c2_1(a831)) | (~c3_1(a831))) <=> (hskp14 | hskp22 | c1_1(a831) | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1138,plain,
% 0.54/0.75 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a831) | (~c2_1(a831)) | (~c3_1(a831)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | c1_1(a831) | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[1137])).
% 0.54/0.75 tff(1139,plain,
% 0.54/0.75 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a831) | (~c2_1(a831)) | (~c3_1(a831)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a831) | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[1138, 1136])).
% 0.54/0.75 tff(1140,plain,
% 0.54/0.75 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a831) | (~c2_1(a831)) | (~c3_1(a831)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1141,plain,
% 0.54/0.75 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a831) | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 0.54/0.75 tff(1142,plain,
% 0.54/0.75 (~c2_1(a831)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1141, 702, 151, 13, 1135, 1134, 701])).
% 0.54/0.75 tff(1143,plain,
% 0.54/0.75 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(1144,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[1143])).
% 0.54/0.75 tff(1145,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1146,plain,
% 0.54/0.75 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | 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)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(1147,plain,
% 0.54/0.75 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[1146])).
% 0.54/0.75 tff(1148,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.54/0.75 tff(1149,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 0.54/0.75 tff(1150,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1149, 1145])).
% 0.54/0.75 tff(1151,plain,(
% 0.54/0.75 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.75 inference(skolemize,[status(sab)],[1150])).
% 0.54/0.75 tff(1152,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1151, 1144])).
% 0.54/0.75 tff(1153,plain,
% 0.54/0.75 (~c0_1(a831)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[234, 1133])).
% 0.54/0.75 tff(1154,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a831) | c1_1(a831) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | c2_1(a831))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a831) | c1_1(a831) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | c2_1(a831))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1155,plain,
% 0.54/0.75 ((hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a831) | c1_1(a831) | c0_1(a831)) <=> (hskp1 | c0_1(a831) | c1_1(a831) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | c2_1(a831))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1156,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a831) | c1_1(a831) | c0_1(a831))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a831) | c1_1(a831) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | c2_1(a831)))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[1155])).
% 0.54/0.75 tff(1157,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a831) | c1_1(a831) | c0_1(a831))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a831) | c1_1(a831) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | c2_1(a831))),
% 0.54/0.75 inference(transitivity,[status(thm)],[1156, 1154])).
% 0.54/0.75 tff(1158,plain,
% 0.54/0.75 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a831) | c1_1(a831) | c0_1(a831))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1159,plain,
% 0.54/0.75 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a831) | c1_1(a831) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | c2_1(a831)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1158, 1157])).
% 0.54/0.75 tff(1160,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1159, 151, 24, 1067, 1153, 1134, 1059, 1053, 1152, 1142])).
% 0.54/0.75 tff(1161,plain,(hskp22 | hskp1 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(1162,plain,
% 0.54/0.75 (hskp22),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1161, 24, 702])).
% 0.54/0.75 tff(1163,plain,
% 0.54/0.75 (~c1_1(a860)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[930, 1162])).
% 0.54/0.75 tff(1164,plain,
% 0.54/0.75 (~c0_1(a860)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[942, 1162])).
% 0.54/0.75 tff(1165,plain,
% 0.54/0.75 (~c2_1(a860)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[936, 1162])).
% 0.54/0.75 tff(1166,assumption,(hskp7), introduced(assumption)).
% 0.54/0.75 tff(1167,plain,
% 0.54/0.75 ((ndr1_0 | (~hskp7)) <=> (ndr1_0 | (~hskp7))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1168,plain,
% 0.54/0.75 (((~hskp7) | ndr1_0) <=> (ndr1_0 | (~hskp7))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1169,axiom,((~hskp7) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause24')).
% 0.54/0.75 tff(1170,plain,
% 0.54/0.75 (ndr1_0 | (~hskp7)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 0.54/0.75 tff(1171,plain,
% 0.54/0.75 (ndr1_0 | (~hskp7)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1170, 1167])).
% 0.54/0.75 tff(1172,plain,
% 0.54/0.75 (ndr1_0),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1171, 1166])).
% 0.54/0.75 tff(1173,plain,
% 0.54/0.75 (c0_1(a828)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1066, 1166])).
% 0.54/0.75 tff(1174,assumption,(~c2_1(a828)), introduced(assumption)).
% 0.54/0.75 tff(1175,assumption,(~c1_1(a828)), introduced(assumption)).
% 0.54/0.75 tff(1176,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1177,plain,
% 0.54/0.75 ((hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a860) | c1_1(a860) | c0_1(a860)) <=> (hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1178,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a860) | c1_1(a860) | c0_1(a860))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[1177])).
% 0.54/0.75 tff(1179,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a860) | c1_1(a860) | c0_1(a860))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[1178, 1176])).
% 0.54/0.75 tff(1180,plain,
% 0.54/0.75 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a860) | c1_1(a860) | c0_1(a860))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1181,plain,
% 0.54/0.75 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 0.54/0.75 tff(1182,plain,
% 0.54/0.75 (hskp1 | c0_1(a860) | c1_1(a860) | (~ndr1_0) | (~c0_1(a828))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1181, 1001, 1175, 1174, 1152])).
% 0.54/0.75 tff(1183,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1182, 1173, 1172, 24, 959, 958])).
% 0.54/0.75 tff(1184,plain,((~hskp7) | hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(1185,plain,
% 0.54/0.75 (hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1184, 1047, 1059, 1053])).
% 0.54/0.75 tff(1186,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1185, 1165, 1164, 24, 1163])).
% 0.54/0.75 tff(1187,plain,(hskp1 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(1188,plain,
% 0.54/0.75 (hskp1),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1187, 702])).
% 0.54/0.75 tff(1189,plain,
% 0.54/0.75 (~c2_1(a816)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[499, 1188])).
% 0.54/0.75 tff(1190,plain,
% 0.54/0.75 (c3_1(a816)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[507, 1188])).
% 0.54/0.75 tff(1191,plain,
% 0.54/0.75 (c0_1(a816)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[515, 1188])).
% 0.54/0.75 tff(1192,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a828) | c2_1(a828) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a828) | c2_1(a828) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c0_1(a828)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1193,plain,
% 0.54/0.75 ((hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828))) <=> (hskp9 | c1_1(a828) | c2_1(a828) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c0_1(a828)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1194,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a828) | c2_1(a828) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c0_1(a828))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[1193])).
% 0.54/0.75 tff(1195,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a828) | c2_1(a828) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c0_1(a828)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[1194, 1192])).
% 0.54/0.75 tff(1196,plain,
% 0.54/0.75 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1197,plain,
% 0.54/0.75 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a828) | c2_1(a828) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c0_1(a828))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 0.54/0.75 tff(1198,plain,
% 0.54/0.75 (hskp9),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1197, 151, 1067, 1191, 1190, 1059, 1053, 1189, 215])).
% 0.54/0.75 tff(1199,plain,
% 0.54/0.75 (~c1_1(a831)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[228, 1198])).
% 0.54/0.75 tff(1200,plain,
% 0.54/0.75 (~c0_1(a831)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[234, 1198])).
% 0.54/0.75 tff(1201,plain,
% 0.54/0.75 (c3_1(a831)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[242, 1198])).
% 0.54/0.75 tff(1202,plain,
% 0.54/0.75 (hskp22 | (~c2_1(a831))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1141, 702, 151, 1201, 1199, 701])).
% 0.54/0.75 tff(1203,plain,
% 0.54/0.75 (~c2_1(a831)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1202, 13])).
% 0.54/0.75 tff(1204,plain,
% 0.54/0.75 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(1205,plain,
% 0.54/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_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)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[1204])).
% 0.54/0.75 tff(1206,plain,
% 0.54/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_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)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1207,plain,
% 0.54/0.75 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.54/0.76 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(1208,plain,
% 0.54/0.76 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_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)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[1207])).
% 0.54/0.76 tff(1209,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 0.54/0.76 tff(1210,plain,
% 0.54/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 0.54/0.76 tff(1211,plain,
% 0.54/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1210, 1206])).
% 0.54/0.76 tff(1212,plain,(
% 0.54/0.76 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.54/0.76 inference(skolemize,[status(sab)],[1211])).
% 0.54/0.76 tff(1213,plain,
% 0.54/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1212, 1205])).
% 0.54/0.76 tff(1214,assumption,(~c1_1(a831)), introduced(assumption)).
% 0.54/0.76 tff(1215,assumption,(~c0_1(a831)), introduced(assumption)).
% 0.54/0.76 tff(1216,assumption,(hskp19), introduced(assumption)).
% 0.54/0.76 tff(1217,plain,
% 0.54/0.76 (~c3_1(a855)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[800, 1216])).
% 0.54/0.76 tff(1218,plain,
% 0.54/0.76 (~c1_1(a855)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[806, 1216])).
% 0.54/0.76 tff(1219,plain,
% 0.54/0.76 (~c0_1(a855)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[812, 1216])).
% 0.54/0.76 tff(1220,assumption,(c3_1(a831)), introduced(assumption)).
% 0.54/0.76 tff(1221,plain,
% 0.54/0.76 ($false),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[820, 151, 1220, 1219, 1218, 1217, 1215, 1214, 190])).
% 0.54/0.76 tff(1222,plain,((~hskp19) | (~c3_1(a831)) | c0_1(a831) | c1_1(a831)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.76 tff(1223,plain,
% 0.54/0.76 (~hskp19),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1222, 1201, 1200, 1199])).
% 0.54/0.76 tff(1224,assumption,(hskp16), introduced(assumption)).
% 0.54/0.76 tff(1225,plain,
% 0.54/0.76 (((~hskp16) | (~c1_1(a848))) <=> ((~hskp16) | (~c1_1(a848)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1226,plain,
% 0.54/0.76 (((~c1_1(a848)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a848)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1227,axiom,((~c1_1(a848)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.54/0.76 tff(1228,plain,
% 0.54/0.76 ((~hskp16) | (~c1_1(a848))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 0.54/0.76 tff(1229,plain,
% 0.54/0.76 ((~hskp16) | (~c1_1(a848))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1228, 1225])).
% 0.54/0.76 tff(1230,plain,
% 0.54/0.76 (~c1_1(a848)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1229, 1224])).
% 0.54/0.76 tff(1231,plain,
% 0.54/0.76 (((~hskp16) | c3_1(a848)) <=> ((~hskp16) | c3_1(a848))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1232,axiom,((~hskp16) | c3_1(a848)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.54/0.76 tff(1233,plain,
% 0.54/0.76 ((~hskp16) | c3_1(a848)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 0.54/0.76 tff(1234,plain,
% 0.54/0.76 ((~hskp16) | c3_1(a848)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1233, 1231])).
% 0.54/0.76 tff(1235,plain,
% 0.54/0.76 ((~hskp16) | c3_1(a848)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1234, 1231])).
% 0.54/0.76 tff(1236,plain,
% 0.54/0.76 ((~hskp16) | c3_1(a848)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1235, 1231])).
% 0.54/0.76 tff(1237,plain,
% 0.54/0.76 ((~hskp16) | c3_1(a848)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1236, 1231])).
% 0.54/0.76 tff(1238,plain,
% 0.54/0.76 (c3_1(a848)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1237, 1224])).
% 0.54/0.76 tff(1239,plain,
% 0.54/0.76 (((~hskp16) | c2_1(a848)) <=> ((~hskp16) | c2_1(a848))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1240,axiom,((~hskp16) | c2_1(a848)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.54/0.76 tff(1241,plain,
% 0.54/0.76 ((~hskp16) | c2_1(a848)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 0.54/0.76 tff(1242,plain,
% 0.54/0.76 ((~hskp16) | c2_1(a848)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1241, 1239])).
% 0.54/0.76 tff(1243,plain,
% 0.54/0.76 ((~hskp16) | c2_1(a848)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1242, 1239])).
% 0.54/0.76 tff(1244,plain,
% 0.54/0.76 ((~hskp16) | c2_1(a848)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1243, 1239])).
% 0.54/0.76 tff(1245,plain,
% 0.54/0.76 ((~hskp16) | c2_1(a848)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1244, 1239])).
% 0.54/0.76 tff(1246,plain,
% 0.54/0.76 (c2_1(a848)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1245, 1224])).
% 0.54/0.76 tff(1247,plain,
% 0.54/0.76 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | c1_1(a848) | (~ndr1_0) | (~c2_1(a848)) | (~c3_1(a848)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a848) | (~ndr1_0) | (~c2_1(a848)) | (~c3_1(a848)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1248,plain,
% 0.54/0.76 ((hskp14 | hskp22 | (~ndr1_0) | c1_1(a848) | (~c2_1(a848)) | (~c3_1(a848))) <=> (hskp14 | hskp22 | c1_1(a848) | (~ndr1_0) | (~c2_1(a848)) | (~c3_1(a848)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1249,plain,
% 0.54/0.76 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a848) | (~c2_1(a848)) | (~c3_1(a848)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | c1_1(a848) | (~ndr1_0) | (~c2_1(a848)) | (~c3_1(a848))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[1248])).
% 0.54/0.76 tff(1250,plain,
% 0.54/0.76 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a848) | (~c2_1(a848)) | (~c3_1(a848)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a848) | (~ndr1_0) | (~c2_1(a848)) | (~c3_1(a848)))),
% 0.54/0.76 inference(transitivity,[status(thm)],[1249, 1247])).
% 0.54/0.76 tff(1251,plain,
% 0.54/0.76 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a848) | (~c2_1(a848)) | (~c3_1(a848)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(1252,plain,
% 0.54/0.76 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a848) | (~ndr1_0) | (~c2_1(a848)) | (~c3_1(a848))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1251, 1250])).
% 0.54/0.76 tff(1253,plain,
% 0.54/0.76 ($false),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1252, 702, 151, 13, 1246, 1238, 1230, 701])).
% 0.54/0.76 tff(1254,plain,((~hskp16) | hskp14 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.54/0.76 tff(1255,plain,
% 0.54/0.76 (~hskp16),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1254, 13, 702])).
% 0.54/0.76 tff(1256,plain,
% 0.54/0.76 ((hskp19 | hskp16 | hskp13) <=> (hskp19 | hskp16 | hskp13)),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1257,plain,
% 0.54/0.76 (((hskp13 | hskp16) | hskp19) <=> (hskp19 | hskp16 | hskp13)),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1258,axiom,((hskp13 | hskp16) | hskp19), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.54/0.76 tff(1259,plain,
% 0.54/0.76 (hskp19 | hskp16 | hskp13),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 0.54/0.76 tff(1260,plain,
% 0.54/0.76 (hskp19 | hskp16 | hskp13),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1259, 1256])).
% 0.54/0.76 tff(1261,plain,
% 0.54/0.76 (hskp19 | hskp16 | hskp13),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1260, 1256])).
% 0.54/0.76 tff(1262,plain,
% 0.54/0.76 (hskp19 | hskp16 | hskp13),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1261, 1256])).
% 0.54/0.76 tff(1263,plain,
% 0.54/0.76 (hskp19 | hskp16 | hskp13),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1262, 1256])).
% 0.54/0.76 tff(1264,plain,
% 0.54/0.76 (hskp13),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1263, 1255, 1223])).
% 0.54/0.76 tff(1265,plain,
% 0.54/0.76 (((~hskp13) | (~c2_1(a839))) <=> ((~hskp13) | (~c2_1(a839)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1266,plain,
% 0.54/0.76 (((~c2_1(a839)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a839)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1267,axiom,((~c2_1(a839)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.54/0.76 tff(1268,plain,
% 0.54/0.76 ((~hskp13) | (~c2_1(a839))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1267, 1266])).
% 0.54/0.76 tff(1269,plain,
% 0.54/0.76 ((~hskp13) | (~c2_1(a839))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1268, 1265])).
% 0.54/0.76 tff(1270,plain,
% 0.54/0.76 (~c2_1(a839)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1269, 1264])).
% 0.54/0.76 tff(1271,plain,
% 0.54/0.76 (((~hskp13) | c3_1(a839)) <=> ((~hskp13) | c3_1(a839))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1272,axiom,((~hskp13) | c3_1(a839)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.54/0.76 tff(1273,plain,
% 0.54/0.76 ((~hskp13) | c3_1(a839)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 0.54/0.76 tff(1274,plain,
% 0.54/0.76 ((~hskp13) | c3_1(a839)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1273, 1271])).
% 0.54/0.76 tff(1275,plain,
% 0.54/0.76 ((~hskp13) | c3_1(a839)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1274, 1271])).
% 0.54/0.76 tff(1276,plain,
% 0.54/0.76 ((~hskp13) | c3_1(a839)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1275, 1271])).
% 0.54/0.76 tff(1277,plain,
% 0.54/0.76 ((~hskp13) | c3_1(a839)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1276, 1271])).
% 0.54/0.76 tff(1278,plain,
% 0.54/0.76 (c3_1(a839)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1277, 1264])).
% 0.54/0.76 tff(1279,plain,
% 0.54/0.76 (((~hskp13) | c1_1(a839)) <=> ((~hskp13) | c1_1(a839))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1280,axiom,((~hskp13) | c1_1(a839)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.54/0.76 tff(1281,plain,
% 0.54/0.76 ((~hskp13) | c1_1(a839)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 0.54/0.76 tff(1282,plain,
% 0.54/0.76 ((~hskp13) | c1_1(a839)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1281, 1279])).
% 0.54/0.76 tff(1283,plain,
% 0.54/0.76 ((~hskp13) | c1_1(a839)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1282, 1279])).
% 0.54/0.76 tff(1284,plain,
% 0.54/0.76 ((~hskp13) | c1_1(a839)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1283, 1279])).
% 0.54/0.76 tff(1285,plain,
% 0.54/0.76 ((~hskp13) | c1_1(a839)),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1284, 1279])).
% 0.54/0.76 tff(1286,plain,
% 0.54/0.76 (c1_1(a839)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1285, 1264])).
% 0.54/0.76 tff(1287,plain,
% 0.54/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a839) | c0_1(a831) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | c2_1(a831) | (~c3_1(a831)) | (~c1_1(a839)) | (~c3_1(a839)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a839) | c0_1(a831) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | c2_1(a831) | (~c3_1(a831)) | (~c1_1(a839)) | (~c3_1(a839)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1288,plain,
% 0.54/0.76 (((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a831) | c0_1(a831) | (~c3_1(a831))) <=> (c2_1(a839) | c0_1(a831) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | c2_1(a831) | (~c3_1(a831)) | (~c1_1(a839)) | (~c3_1(a839)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1289,plain,
% 0.54/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a839) | c0_1(a831) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | c2_1(a831) | (~c3_1(a831)) | (~c1_1(a839)) | (~c3_1(a839))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[1288])).
% 0.54/0.76 tff(1290,plain,
% 0.54/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a839) | c0_1(a831) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | c2_1(a831) | (~c3_1(a831)) | (~c1_1(a839)) | (~c3_1(a839)))),
% 0.54/0.76 inference(transitivity,[status(thm)],[1289, 1287])).
% 0.54/0.76 tff(1291,plain,
% 0.54/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a831) | c0_1(a831) | (~c3_1(a831)))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(1292,plain,
% 0.54/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a839) | c0_1(a831) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | c2_1(a831) | (~c3_1(a831)) | (~c1_1(a839)) | (~c3_1(a839))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 0.54/0.76 tff(1293,plain,
% 0.54/0.76 ($false),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1292, 151, 1286, 1278, 1201, 1067, 1270, 1200, 1059, 1213, 1125, 1203])).
% 0.54/0.76 tff(1294,plain,(hskp22 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.54/0.76 tff(1295,plain,
% 0.54/0.76 (hskp22),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1294, 702])).
% 0.54/0.76 tff(1296,plain,
% 0.54/0.76 (~c1_1(a860)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[930, 1295])).
% 0.54/0.76 tff(1297,plain,
% 0.54/0.76 (~c0_1(a860)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[942, 1295])).
% 0.54/0.76 tff(1298,plain,
% 0.54/0.76 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | c3_1(a860))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | c3_1(a860))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1299,plain,
% 0.54/0.76 (((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a860) | c0_1(a860) | c3_1(a860)) <=> (c0_1(a860) | c1_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | c3_1(a860))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1300,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a860) | c0_1(a860) | c3_1(a860))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | c3_1(a860)))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[1299])).
% 0.60/0.76 tff(1301,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a860) | c0_1(a860) | c3_1(a860))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | c3_1(a860))),
% 0.60/0.76 inference(transitivity,[status(thm)],[1300, 1298])).
% 0.60/0.76 tff(1302,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a860) | c0_1(a860) | c3_1(a860))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1303,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | c3_1(a860)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 0.60/0.76 tff(1304,plain,
% 0.60/0.76 (c3_1(a860)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1303, 151, 1201, 1297, 1296, 1200, 1199, 190])).
% 0.60/0.76 tff(1305,plain,
% 0.60/0.76 (~c2_1(a860)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[936, 1295])).
% 0.60/0.76 tff(1306,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a860) | c2_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a860)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a860) | c2_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a860)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1307,plain,
% 0.60/0.76 ((hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831))) <=> (hskp2 | c1_1(a860) | c2_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a860)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1308,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a860) | c2_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a860))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[1307])).
% 0.60/0.76 tff(1309,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a860) | c2_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a860)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[1308, 1306])).
% 0.60/0.76 tff(1310,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1311,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a860) | c2_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a860))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 0.60/0.76 tff(1312,plain,
% 0.60/0.76 (hskp2),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1311, 151, 1201, 1296, 1305, 1200, 1199, 91, 1304])).
% 0.60/0.76 tff(1313,plain,
% 0.60/0.76 (~c3_1(a817)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[195, 1312])).
% 0.60/0.76 tff(1314,plain,
% 0.60/0.76 (~c0_1(a817)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[164, 1312])).
% 0.60/0.76 tff(1315,plain,
% 0.60/0.76 (c1_1(a817)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[967, 1314, 1296, 1304, 1313, 1297])).
% 0.60/0.76 tff(1316,plain,
% 0.60/0.76 (^[U: $i] : refl((hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(1317,plain,
% 0.60/0.76 (![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[1316])).
% 0.60/0.76 tff(1318,plain,
% 0.60/0.76 (![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1319,plain,
% 0.60/0.76 (^[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)) | 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)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp15) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp15) <=> (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(1320,plain,
% 0.60/0.76 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp15) <=> ![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[1319])).
% 0.60/0.76 tff(1321,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.60/0.76 tff(1322,plain,
% 0.60/0.76 (![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 0.60/0.76 tff(1323,plain,
% 0.60/0.76 (![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1322, 1318])).
% 0.60/0.76 tff(1324,plain,(
% 0.60/0.76 ![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.60/0.76 inference(skolemize,[status(sab)],[1323])).
% 0.60/0.76 tff(1325,plain,
% 0.60/0.76 (![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1324, 1317])).
% 0.60/0.76 tff(1326,plain,
% 0.60/0.76 (c2_1(a817)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[172, 1312])).
% 0.60/0.76 tff(1327,plain,
% 0.60/0.76 (((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp15 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp15 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1328,plain,
% 0.60/0.77 ((hskp14 | hskp15 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817))) <=> (hskp14 | hskp15 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1329,plain,
% 0.60/0.77 (((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp15 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp15 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1328])).
% 0.60/0.77 tff(1330,plain,
% 0.60/0.77 (((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp15 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp15 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1329, 1327])).
% 0.60/0.77 tff(1331,plain,
% 0.60/0.77 ((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp15 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1332,plain,
% 0.60/0.77 ((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp15 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 0.60/0.77 tff(1333,plain,
% 0.60/0.77 (hskp15),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1332, 702, 151, 1326, 1313, 1325, 1315])).
% 0.60/0.77 tff(1334,plain,
% 0.60/0.77 (((~hskp15) | (~c3_1(a844))) <=> ((~hskp15) | (~c3_1(a844)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1335,plain,
% 0.60/0.77 (((~c3_1(a844)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a844)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1336,axiom,((~c3_1(a844)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.60/0.77 tff(1337,plain,
% 0.60/0.77 ((~hskp15) | (~c3_1(a844))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 0.60/0.77 tff(1338,plain,
% 0.60/0.77 ((~hskp15) | (~c3_1(a844))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1337, 1334])).
% 0.60/0.77 tff(1339,plain,
% 0.60/0.77 (~c3_1(a844)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1338, 1333])).
% 0.60/0.77 tff(1340,plain,
% 0.60/0.77 (((~hskp15) | (~c1_1(a844))) <=> ((~hskp15) | (~c1_1(a844)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1341,plain,
% 0.60/0.77 (((~c1_1(a844)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a844)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1342,axiom,((~c1_1(a844)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.60/0.77 tff(1343,plain,
% 0.60/0.77 ((~hskp15) | (~c1_1(a844))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 0.60/0.77 tff(1344,plain,
% 0.60/0.77 ((~hskp15) | (~c1_1(a844))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1343, 1340])).
% 0.60/0.77 tff(1345,plain,
% 0.60/0.77 (~c1_1(a844)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1344, 1333])).
% 0.60/0.77 tff(1346,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c1_1(a844) | c3_1(a844) | (~ndr1_0) | c0_1(a844) | (~c3_1(a860)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c1_1(a844) | c3_1(a844) | (~ndr1_0) | c0_1(a844) | (~c3_1(a860)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1347,plain,
% 0.60/0.77 (((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a844) | c0_1(a844) | c3_1(a844)) <=> (c0_1(a860) | c1_1(a860) | c1_1(a844) | c3_1(a844) | (~ndr1_0) | c0_1(a844) | (~c3_1(a860)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1348,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a844) | c0_1(a844) | c3_1(a844))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c1_1(a844) | c3_1(a844) | (~ndr1_0) | c0_1(a844) | (~c3_1(a860))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1347])).
% 0.60/0.77 tff(1349,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a844) | c0_1(a844) | c3_1(a844))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c1_1(a844) | c3_1(a844) | (~ndr1_0) | c0_1(a844) | (~c3_1(a860)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1348, 1346])).
% 0.60/0.77 tff(1350,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a844) | c0_1(a844) | c3_1(a844))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1351,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c1_1(a844) | c3_1(a844) | (~ndr1_0) | c0_1(a844) | (~c3_1(a860))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 0.60/0.77 tff(1352,plain,
% 0.60/0.77 (c0_1(a844)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1351, 151, 1297, 1296, 1345, 1339, 190, 1304])).
% 0.60/0.77 tff(1353,plain,
% 0.60/0.77 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(1354,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[1353])).
% 0.60/0.77 tff(1355,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1356,plain,
% 0.60/0.77 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(1357,plain,
% 0.60/0.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[1356])).
% 0.60/0.77 tff(1358,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 0.60/0.77 tff(1359,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 0.60/0.77 tff(1360,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1359, 1355])).
% 0.60/0.77 tff(1361,plain,(
% 0.60/0.77 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.77 inference(skolemize,[status(sab)],[1360])).
% 0.60/0.77 tff(1362,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1361, 1354])).
% 0.60/0.77 tff(1363,plain,
% 0.60/0.77 (hskp24),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[48, 702])).
% 0.60/0.77 tff(1364,plain,
% 0.60/0.77 (~c3_1(a878)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[620, 1363])).
% 0.60/0.77 tff(1365,plain,
% 0.60/0.77 (~c0_1(a878)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[679, 1363])).
% 0.60/0.77 tff(1366,plain,
% 0.60/0.77 (((~hskp15) | c2_1(a844)) <=> ((~hskp15) | c2_1(a844))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1367,axiom,((~hskp15) | c2_1(a844)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.60/0.77 tff(1368,plain,
% 0.60/0.77 ((~hskp15) | c2_1(a844)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 0.60/0.77 tff(1369,plain,
% 0.60/0.77 ((~hskp15) | c2_1(a844)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1368, 1366])).
% 0.60/0.77 tff(1370,plain,
% 0.60/0.77 ((~hskp15) | c2_1(a844)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1369, 1366])).
% 0.60/0.77 tff(1371,plain,
% 0.60/0.77 ((~hskp15) | c2_1(a844)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1370, 1366])).
% 0.60/0.77 tff(1372,plain,
% 0.60/0.77 ((~hskp15) | c2_1(a844)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1371, 1366])).
% 0.60/0.77 tff(1373,plain,
% 0.60/0.77 (c2_1(a844)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1372, 1333])).
% 0.60/0.77 tff(1374,plain,
% 0.60/0.77 (c1_1(a878)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[628, 1363])).
% 0.60/0.77 tff(1375,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a878) | c3_1(a878) | c3_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c2_1(a844)) | (~c1_1(a878)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a878) | c3_1(a878) | c3_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c2_1(a844)) | (~c1_1(a878)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1376,plain,
% 0.60/0.77 ((hskp6 | (~ndr1_0) | c3_1(a844) | (~c2_1(a844)) | (~c0_1(a844)) | c0_1(a878) | c3_1(a878) | (~c1_1(a878))) <=> (hskp6 | c0_1(a878) | c3_1(a878) | c3_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c2_1(a844)) | (~c1_1(a878)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1377,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a844) | (~c2_1(a844)) | (~c0_1(a844)) | c0_1(a878) | c3_1(a878) | (~c1_1(a878)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a878) | c3_1(a878) | c3_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c2_1(a844)) | (~c1_1(a878))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1376])).
% 0.60/0.77 tff(1378,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a844) | (~c2_1(a844)) | (~c0_1(a844)) | c0_1(a878) | c3_1(a878) | (~c1_1(a878)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a878) | c3_1(a878) | c3_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c2_1(a844)) | (~c1_1(a878)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1377, 1375])).
% 0.60/0.77 tff(1379,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a844) | (~c2_1(a844)) | (~c0_1(a844)) | c0_1(a878) | c3_1(a878) | (~c1_1(a878)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1380,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a878) | c3_1(a878) | c3_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c2_1(a844)) | (~c1_1(a878))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1379, 1378])).
% 0.60/0.77 tff(1381,plain,
% 0.60/0.77 (hskp6),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1380, 151, 1374, 1373, 1365, 1364, 1339, 1362, 1352])).
% 0.60/0.77 tff(1382,plain,
% 0.60/0.77 (((~hskp6) | c1_1(a827)) <=> ((~hskp6) | c1_1(a827))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1383,axiom,((~hskp6) | c1_1(a827)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.60/0.77 tff(1384,plain,
% 0.60/0.77 ((~hskp6) | c1_1(a827)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 0.60/0.77 tff(1385,plain,
% 0.60/0.77 ((~hskp6) | c1_1(a827)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1384, 1382])).
% 0.60/0.77 tff(1386,plain,
% 0.60/0.77 ((~hskp6) | c1_1(a827)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1385, 1382])).
% 0.60/0.77 tff(1387,plain,
% 0.60/0.77 ((~hskp6) | c1_1(a827)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1386, 1382])).
% 0.60/0.77 tff(1388,plain,
% 0.60/0.77 ((~hskp6) | c1_1(a827)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1387, 1382])).
% 0.60/0.77 tff(1389,plain,
% 0.60/0.77 (c1_1(a827)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1388, 1381])).
% 0.60/0.77 tff(1390,plain,
% 0.60/0.77 (((~hskp6) | (~c0_1(a827))) <=> ((~hskp6) | (~c0_1(a827)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1391,plain,
% 0.60/0.77 (((~c0_1(a827)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a827)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1392,axiom,((~c0_1(a827)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.60/0.77 tff(1393,plain,
% 0.60/0.77 ((~hskp6) | (~c0_1(a827))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 0.60/0.77 tff(1394,plain,
% 0.60/0.77 ((~hskp6) | (~c0_1(a827))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1393, 1390])).
% 0.60/0.77 tff(1395,plain,
% 0.60/0.77 (~c0_1(a827)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1394, 1381])).
% 0.60/0.77 tff(1396,plain,
% 0.60/0.77 (((~hskp6) | c2_1(a827)) <=> ((~hskp6) | c2_1(a827))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1397,axiom,((~hskp6) | c2_1(a827)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.60/0.77 tff(1398,plain,
% 0.60/0.77 ((~hskp6) | c2_1(a827)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1397, 1396])).
% 0.60/0.77 tff(1399,plain,
% 0.60/0.77 ((~hskp6) | c2_1(a827)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1398, 1396])).
% 0.60/0.77 tff(1400,plain,
% 0.60/0.77 ((~hskp6) | c2_1(a827)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1399, 1396])).
% 0.60/0.77 tff(1401,plain,
% 0.60/0.77 ((~hskp6) | c2_1(a827)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1400, 1396])).
% 0.60/0.77 tff(1402,plain,
% 0.60/0.77 ((~hskp6) | c2_1(a827)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1401, 1396])).
% 0.60/0.77 tff(1403,plain,
% 0.60/0.77 (c2_1(a827)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1402, 1381])).
% 0.60/0.77 tff(1404,assumption,(c2_1(a827)), introduced(assumption)).
% 0.60/0.77 tff(1405,assumption,(c1_1(a827)), introduced(assumption)).
% 0.60/0.77 tff(1406,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | (~c0_1(a828)) | c3_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | (~c0_1(a828)) | c3_1(a828))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1407,plain,
% 0.60/0.77 (((~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | (~c0_1(a828)) | c3_1(a828))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1408,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | (~c0_1(a828)) | c3_1(a828)))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1407])).
% 0.60/0.77 tff(1409,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | (~c0_1(a828)) | c3_1(a828))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1408, 1406])).
% 0.60/0.77 tff(1410,plain,
% 0.60/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1411,plain,
% 0.60/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | (~c0_1(a828)) | c3_1(a828)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 0.60/0.77 tff(1412,plain,
% 0.60/0.77 (~c3_1(a827)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1411, 151, 1067, 1405, 1404, 1059, 1053, 11, 1])).
% 0.60/0.77 tff(1413,assumption,(c1_1(a817)), introduced(assumption)).
% 0.60/0.77 tff(1414,assumption,(~c0_1(a827)), introduced(assumption)).
% 0.60/0.77 tff(1415,assumption,(c2_1(a817)), introduced(assumption)).
% 0.60/0.77 tff(1416,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a828) | c2_1(a828) | c0_1(a827) | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c2_1(a827)) | c3_1(a827) | c3_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | c0_1(a827) | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c2_1(a827)) | c3_1(a827) | c3_1(a828))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1417,plain,
% 0.60/0.77 (((~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (c1_1(a828) | c2_1(a828) | c0_1(a827) | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c2_1(a827)) | c3_1(a827) | c3_1(a828))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1418,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a828) | c2_1(a828) | c0_1(a827) | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c2_1(a827)) | c3_1(a827) | c3_1(a828)))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1417])).
% 0.60/0.77 tff(1419,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | c0_1(a827) | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c2_1(a827)) | c3_1(a827) | c3_1(a828))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1418, 1416])).
% 0.60/0.77 tff(1420,plain,
% 0.60/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1421,plain,
% 0.60/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | c0_1(a827) | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c2_1(a827)) | c3_1(a827) | c3_1(a828)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 0.60/0.77 tff(1422,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1421, 151, 1404, 1415, 1059, 1053, 1414, 956, 477, 1413, 1, 1412])).
% 0.60/0.77 tff(1423,plain,(c3_1(a828) | (~c2_1(a827)) | (~c2_1(a817)) | c0_1(a827) | c3_1(a817) | (~c1_1(a817)) | (~c1_1(a827))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1424,plain,
% 0.60/0.77 (c3_1(a828)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1423, 1403, 1326, 1395, 1313, 1315, 1389])).
% 0.60/0.77 tff(1425,assumption,(~hskp13), introduced(assumption)).
% 0.60/0.77 tff(1426,plain,
% 0.60/0.77 (^[U: $i] : refl((hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(1427,plain,
% 0.60/0.77 (![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[1426])).
% 0.60/0.77 tff(1428,plain,
% 0.60/0.77 (![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1429,plain,
% 0.60/0.77 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp13) <=> ((hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp13))), rewrite(((hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp13) <=> (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(1430,plain,
% 0.60/0.78 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp13) <=> ![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[1429])).
% 0.60/0.78 tff(1431,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.60/0.78 tff(1432,plain,
% 0.60/0.78 (![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 0.60/0.78 tff(1433,plain,
% 0.60/0.78 (![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1432, 1428])).
% 0.60/0.78 tff(1434,plain,(
% 0.60/0.78 ![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[1433])).
% 0.60/0.78 tff(1435,plain,
% 0.60/0.78 (![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1434, 1427])).
% 0.60/0.78 tff(1436,plain,
% 0.60/0.78 (((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp13 | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))) <=> ((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp13 | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1437,plain,
% 0.60/0.78 ((hskp21 | hskp13 | (~ndr1_0) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828))) <=> (hskp21 | hskp13 | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1438,plain,
% 0.60/0.78 (((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp13 | (~ndr1_0) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)))) <=> ((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp13 | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1437])).
% 0.60/0.78 tff(1439,plain,
% 0.60/0.78 (((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp13 | (~ndr1_0) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)))) <=> ((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp13 | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1438, 1436])).
% 0.60/0.78 tff(1440,plain,
% 0.60/0.78 ((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp13 | (~ndr1_0) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1441,plain,
% 0.60/0.78 ((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp13 | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 0.60/0.78 tff(1442,plain,
% 0.60/0.78 (hskp21 | hskp13 | (~c3_1(a828))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1441, 151, 1067, 1059, 1435])).
% 0.60/0.78 tff(1443,plain,
% 0.60/0.78 (hskp21),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1442, 1425, 1424])).
% 0.60/0.78 tff(1444,plain,
% 0.60/0.78 (((~hskp21) | (~c2_1(a857))) <=> ((~hskp21) | (~c2_1(a857)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1445,plain,
% 0.60/0.78 (((~c2_1(a857)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a857)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1446,axiom,((~c2_1(a857)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.60/0.78 tff(1447,plain,
% 0.60/0.78 ((~hskp21) | (~c2_1(a857))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 0.60/0.78 tff(1448,plain,
% 0.60/0.78 ((~hskp21) | (~c2_1(a857))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1447, 1444])).
% 0.60/0.78 tff(1449,plain,
% 0.60/0.78 (~c2_1(a857)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1448, 1443])).
% 0.60/0.78 tff(1450,plain,
% 0.60/0.78 (((~hskp21) | c0_1(a857)) <=> ((~hskp21) | c0_1(a857))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1451,axiom,((~hskp21) | c0_1(a857)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.60/0.78 tff(1452,plain,
% 0.60/0.78 ((~hskp21) | c0_1(a857)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 0.60/0.78 tff(1453,plain,
% 0.60/0.78 ((~hskp21) | c0_1(a857)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1452, 1450])).
% 0.60/0.78 tff(1454,plain,
% 0.60/0.78 ((~hskp21) | c0_1(a857)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1453, 1450])).
% 0.60/0.78 tff(1455,plain,
% 0.60/0.78 ((~hskp21) | c0_1(a857)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1454, 1450])).
% 0.60/0.78 tff(1456,plain,
% 0.60/0.78 ((~hskp21) | c0_1(a857)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1455, 1450])).
% 0.60/0.78 tff(1457,plain,
% 0.60/0.78 (c0_1(a857)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1456, 1443])).
% 0.60/0.78 tff(1458,plain,
% 0.60/0.78 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | c2_1(a857) | (~ndr1_0) | (~c1_1(a857)) | (~c0_1(a857)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a857) | (~ndr1_0) | (~c1_1(a857)) | (~c0_1(a857)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1459,plain,
% 0.60/0.78 ((hskp29 | hskp19 | (~ndr1_0) | c2_1(a857) | (~c1_1(a857)) | (~c0_1(a857))) <=> (hskp29 | hskp19 | c2_1(a857) | (~ndr1_0) | (~c1_1(a857)) | (~c0_1(a857)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1460,plain,
% 0.60/0.78 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a857) | (~c1_1(a857)) | (~c0_1(a857)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | c2_1(a857) | (~ndr1_0) | (~c1_1(a857)) | (~c0_1(a857))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1459])).
% 0.60/0.78 tff(1461,plain,
% 0.60/0.78 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a857) | (~c1_1(a857)) | (~c0_1(a857)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a857) | (~ndr1_0) | (~c1_1(a857)) | (~c0_1(a857)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1460, 1458])).
% 0.60/0.78 tff(1462,plain,
% 0.60/0.78 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a857) | (~c1_1(a857)) | (~c0_1(a857)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1463,plain,
% 0.60/0.78 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a857) | (~ndr1_0) | (~c1_1(a857)) | (~c0_1(a857))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 0.60/0.78 tff(1464,plain,
% 0.60/0.78 (~c1_1(a857)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1463, 759, 151, 1223, 1457, 1449, 787])).
% 0.60/0.78 tff(1465,plain,
% 0.60/0.78 (^[U: $i] : refl((hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(1466,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[1465])).
% 0.60/0.78 tff(1467,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1468,plain,
% 0.60/0.78 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp13) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp13) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(1469,plain,
% 0.60/0.78 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp13) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[1468])).
% 0.60/0.78 tff(1470,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.60/0.78 tff(1471,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1470, 1469])).
% 0.60/0.78 tff(1472,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1471, 1467])).
% 0.60/0.78 tff(1473,plain,(
% 0.60/0.78 ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[1472])).
% 0.60/0.78 tff(1474,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1473, 1466])).
% 0.60/0.78 tff(1475,plain,
% 0.60/0.78 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | c0_1(a827) | (~ndr1_0) | (~c3_1(a827)) | (~c1_1(a827)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp13 | c0_1(a827) | (~ndr1_0) | (~c3_1(a827)) | (~c1_1(a827)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1476,plain,
% 0.60/0.78 ((hskp14 | hskp13 | (~ndr1_0) | c0_1(a827) | (~c3_1(a827)) | (~c1_1(a827))) <=> (hskp14 | hskp13 | c0_1(a827) | (~ndr1_0) | (~c3_1(a827)) | (~c1_1(a827)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1477,plain,
% 0.60/0.78 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a827) | (~c3_1(a827)) | (~c1_1(a827)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | c0_1(a827) | (~ndr1_0) | (~c3_1(a827)) | (~c1_1(a827))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1476])).
% 0.60/0.78 tff(1478,plain,
% 0.60/0.78 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a827) | (~c3_1(a827)) | (~c1_1(a827)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp13 | c0_1(a827) | (~ndr1_0) | (~c3_1(a827)) | (~c1_1(a827)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1477, 1475])).
% 0.60/0.78 tff(1479,plain,
% 0.60/0.78 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a827) | (~c3_1(a827)) | (~c1_1(a827)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1480,plain,
% 0.60/0.78 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp13 | c0_1(a827) | (~ndr1_0) | (~c3_1(a827)) | (~c1_1(a827))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1479, 1478])).
% 0.60/0.78 tff(1481,plain,
% 0.60/0.78 (hskp13 | (~c3_1(a827))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1480, 702, 151, 1389, 1395, 1474])).
% 0.60/0.78 tff(1482,plain,
% 0.60/0.78 (~c3_1(a827)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1481, 1425])).
% 0.60/0.78 tff(1483,plain,
% 0.60/0.78 (((~hskp21) | (~c3_1(a857))) <=> ((~hskp21) | (~c3_1(a857)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1484,plain,
% 0.60/0.78 (((~c3_1(a857)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a857)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1485,axiom,((~c3_1(a857)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.60/0.78 tff(1486,plain,
% 0.60/0.78 ((~hskp21) | (~c3_1(a857))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 0.60/0.78 tff(1487,plain,
% 0.60/0.78 ((~hskp21) | (~c3_1(a857))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1486, 1483])).
% 0.60/0.78 tff(1488,plain,
% 0.60/0.78 (~c3_1(a857)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1487, 1443])).
% 0.60/0.78 tff(1489,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a857) | c3_1(a857) | c0_1(a827) | (~ndr1_0) | (~c2_1(a827)) | c3_1(a827) | (~c1_1(a827)) | c1_1(a857))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a857) | c3_1(a857) | c0_1(a827) | (~ndr1_0) | (~c2_1(a827)) | c3_1(a827) | (~c1_1(a827)) | c1_1(a857))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1490,plain,
% 0.60/0.78 (((~ndr1_0) | c3_1(a827) | (~c2_1(a827)) | (~c1_1(a827)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a857) | c2_1(a857) | c1_1(a857)) <=> (c2_1(a857) | c3_1(a857) | c0_1(a827) | (~ndr1_0) | (~c2_1(a827)) | c3_1(a827) | (~c1_1(a827)) | c1_1(a857))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1491,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a827) | (~c2_1(a827)) | (~c1_1(a827)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a857) | c2_1(a857) | c1_1(a857))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a857) | c3_1(a857) | c0_1(a827) | (~ndr1_0) | (~c2_1(a827)) | c3_1(a827) | (~c1_1(a827)) | c1_1(a857)))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1490])).
% 0.60/0.78 tff(1492,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a827) | (~c2_1(a827)) | (~c1_1(a827)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a857) | c2_1(a857) | c1_1(a857))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a857) | c3_1(a857) | c0_1(a827) | (~ndr1_0) | (~c2_1(a827)) | c3_1(a827) | (~c1_1(a827)) | c1_1(a857))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1491, 1489])).
% 0.60/0.78 tff(1493,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a827) | (~c2_1(a827)) | (~c1_1(a827)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a857) | c2_1(a857) | c1_1(a857))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1494,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a857) | c3_1(a857) | c0_1(a827) | (~ndr1_0) | (~c2_1(a827)) | c3_1(a827) | (~c1_1(a827)) | c1_1(a857)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 0.60/0.78 tff(1495,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1494, 151, 1389, 1403, 1449, 1488, 1395, 477, 1482, 1464])).
% 0.60/0.78 tff(1496,plain,(hskp13 | hskp29 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1497,plain,
% 0.60/0.78 (hskp13),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1496, 759, 702])).
% 0.60/0.78 tff(1498,plain,
% 0.60/0.78 (~c2_1(a839)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1269, 1497])).
% 0.60/0.78 tff(1499,plain,
% 0.60/0.78 (c1_1(a839)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1285, 1497])).
% 0.60/0.78 tff(1500,plain,
% 0.60/0.78 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | c2_1(a839) | (~ndr1_0) | (~c1_1(a839)) | (~c0_1(a839)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a839) | (~ndr1_0) | (~c1_1(a839)) | (~c0_1(a839)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1501,plain,
% 0.60/0.78 ((hskp29 | hskp19 | (~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839))) <=> (hskp29 | hskp19 | c2_1(a839) | (~ndr1_0) | (~c1_1(a839)) | (~c0_1(a839)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1502,plain,
% 0.60/0.78 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | c2_1(a839) | (~ndr1_0) | (~c1_1(a839)) | (~c0_1(a839))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1501])).
% 0.60/0.78 tff(1503,plain,
% 0.60/0.78 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a839) | (~ndr1_0) | (~c1_1(a839)) | (~c0_1(a839)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1502, 1500])).
% 0.60/0.78 tff(1504,plain,
% 0.60/0.78 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1505,plain,
% 0.60/0.78 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a839) | (~ndr1_0) | (~c1_1(a839)) | (~c0_1(a839))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 0.60/0.78 tff(1506,plain,
% 0.60/0.78 (~c0_1(a839)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1505, 759, 151, 1223, 1499, 1498, 787])).
% 0.60/0.78 tff(1507,plain,
% 0.60/0.78 (c3_1(a839)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1277, 1497])).
% 0.60/0.78 tff(1508,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a839) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | (~c1_1(a839)) | c0_1(a839) | (~c3_1(a839)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a839) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | (~c1_1(a839)) | c0_1(a839) | (~c3_1(a839)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1509,plain,
% 0.60/0.78 (((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a839) | c0_1(a839) | (~c3_1(a839))) <=> (c2_1(a839) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | (~c1_1(a839)) | c0_1(a839) | (~c3_1(a839)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1510,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a839) | c0_1(a839) | (~c3_1(a839)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a839) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | (~c1_1(a839)) | c0_1(a839) | (~c3_1(a839))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1509])).
% 0.60/0.78 tff(1511,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a839) | c0_1(a839) | (~c3_1(a839)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a839) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | (~c1_1(a839)) | c0_1(a839) | (~c3_1(a839)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1510, 1508])).
% 0.60/0.78 tff(1512,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a839) | c0_1(a839) | (~c3_1(a839)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1513,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a839) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | (~c1_1(a839)) | c0_1(a839) | (~c3_1(a839))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 0.60/0.78 tff(1514,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1513, 151, 1499, 1507, 1067, 1498, 1059, 1213, 1424, 1506])).
% 0.60/0.78 tff(1515,plain,(hskp29 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1516,plain,
% 0.60/0.78 (hskp29),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1515, 702])).
% 0.60/0.78 tff(1517,plain,
% 0.60/0.78 (c3_1(a865)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[344, 1516])).
% 0.60/0.78 tff(1518,plain,
% 0.60/0.78 (c1_1(a865)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[360, 1516])).
% 0.60/0.78 tff(1519,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a860)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a860)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1520,plain,
% 0.60/0.79 (((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828))) <=> (c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a860)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1521,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a860))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1520])).
% 0.60/0.79 tff(1522,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a860)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1521, 1519])).
% 0.60/0.79 tff(1523,plain,
% 0.60/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1524,plain,
% 0.60/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a860))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 0.60/0.79 tff(1525,plain,
% 0.60/0.79 (~c0_1(a865)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1524, 151, 1518, 1517, 1067, 1296, 1305, 1059, 1053, 44, 1304])).
% 0.60/0.79 tff(1526,plain,
% 0.60/0.79 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a865) | (~c3_1(a865)) | (~c1_1(a865)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp13 | (~ndr1_0) | c0_1(a865) | (~c3_1(a865)) | (~c1_1(a865)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1527,plain,
% 0.60/0.79 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a865) | (~c3_1(a865)) | (~c1_1(a865)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1528,plain,
% 0.60/0.79 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp13 | (~ndr1_0) | c0_1(a865) | (~c3_1(a865)) | (~c1_1(a865))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 0.60/0.79 tff(1529,plain,
% 0.60/0.79 (hskp13 | c0_1(a865)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1528, 702, 151, 1518, 1517, 1474])).
% 0.60/0.79 tff(1530,plain,
% 0.60/0.79 (hskp13),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1529, 1525])).
% 0.60/0.79 tff(1531,plain,
% 0.60/0.79 (~c2_1(a839)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1269, 1530])).
% 0.60/0.79 tff(1532,plain,
% 0.60/0.79 (c1_1(a839)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1285, 1530])).
% 0.60/0.79 tff(1533,plain,
% 0.60/0.79 (c2_1(a865)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[352, 1516])).
% 0.60/0.79 tff(1534,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a860) | c2_1(a860) | c2_1(a839) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a839)) | (~c0_1(a839)) | (~c3_1(a860)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a860) | c2_1(a860) | c2_1(a839) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a839)) | (~c0_1(a839)) | (~c3_1(a860)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1535,plain,
% 0.60/0.79 (((~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865))) <=> (c1_1(a860) | c2_1(a860) | c2_1(a839) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a839)) | (~c0_1(a839)) | (~c3_1(a860)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1536,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a860) | c2_1(a860) | c2_1(a839) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a839)) | (~c0_1(a839)) | (~c3_1(a860))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1535])).
% 0.60/0.79 tff(1537,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a860) | c2_1(a860) | c2_1(a839) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a839)) | (~c0_1(a839)) | (~c3_1(a860)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1536, 1534])).
% 0.60/0.79 tff(1538,plain,
% 0.60/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1539,plain,
% 0.60/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a860) | c2_1(a860) | c2_1(a839) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a839)) | (~c0_1(a839)) | (~c3_1(a860))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 0.60/0.79 tff(1540,plain,
% 0.60/0.79 (~c0_1(a839)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1539, 151, 1518, 1533, 1532, 1296, 1305, 1531, 81, 1304, 1525])).
% 0.60/0.79 tff(1541,plain,
% 0.60/0.79 (c3_1(a839)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1277, 1530])).
% 0.60/0.79 tff(1542,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1513, 151, 1532, 1541, 1067, 1531, 1059, 1213, 1424, 1540])).
% 0.60/0.79 tff(1543,plain,(hskp14), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1544,plain,
% 0.60/0.79 (~c2_1(a842)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[54, 1543])).
% 0.60/0.79 tff(1545,plain,
% 0.60/0.79 (c1_1(a842)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[62, 1543])).
% 0.60/0.79 tff(1546,plain,
% 0.60/0.79 (c0_1(a842)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[70, 1543])).
% 0.60/0.79 tff(1547,plain,
% 0.60/0.79 (~hskp20),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[262, 1546, 1545, 1544])).
% 0.60/0.79 tff(1548,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c0_1(a826)) | c1_1(a826))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c0_1(a826)) | c1_1(a826))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1549,plain,
% 0.60/0.79 ((hskp20 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826) | (~c3_1(a826)) | (~c0_1(a826))) <=> (hskp20 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c0_1(a826)) | c1_1(a826))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1550,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826) | (~c3_1(a826)) | (~c0_1(a826)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c0_1(a826)) | c1_1(a826)))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1549])).
% 0.60/0.79 tff(1551,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826) | (~c3_1(a826)) | (~c0_1(a826)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c0_1(a826)) | c1_1(a826))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1550, 1548])).
% 0.60/0.79 tff(1552,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826) | (~c3_1(a826)) | (~c0_1(a826)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1553,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c0_1(a826)) | c1_1(a826)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1552, 1551])).
% 0.60/0.79 tff(1554,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1553, 151, 1547, 1116, 1101, 1093, 884, 1108])).
% 0.60/0.79 tff(1555,plain,(c3_1(a828)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1556,plain,
% 0.60/0.79 (hskp9),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1132, 1555])).
% 0.60/0.79 tff(1557,plain,
% 0.60/0.79 (~c1_1(a831)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[228, 1556])).
% 0.60/0.79 tff(1558,plain,
% 0.60/0.79 (~c0_1(a831)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[234, 1556])).
% 0.60/0.79 tff(1559,plain,
% 0.60/0.79 (c3_1(a831)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[242, 1556])).
% 0.60/0.79 tff(1560,plain,
% 0.60/0.79 (~hskp19),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1222, 1559, 1558, 1557])).
% 0.60/0.79 tff(1561,plain,
% 0.60/0.79 (hskp29 | hskp19),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[793, 151, 1546, 1545, 1544, 787])).
% 0.60/0.79 tff(1562,plain,
% 0.60/0.79 (hskp29),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1561, 1560])).
% 0.60/0.79 tff(1563,plain,
% 0.60/0.79 (c3_1(a865)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[344, 1562])).
% 0.60/0.79 tff(1564,plain,
% 0.60/0.79 (c1_1(a865)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[360, 1562])).
% 0.60/0.79 tff(1565,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1566,plain,
% 0.60/0.79 (((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828))) <=> (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1567,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a828))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1566])).
% 0.60/0.79 tff(1568,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1567, 1565])).
% 0.60/0.79 tff(1569,plain,
% 0.60/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1570,plain,
% 0.60/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a828))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1569, 1568])).
% 0.60/0.79 tff(1571,plain,
% 0.60/0.79 (~c0_1(a865)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1570, 151, 1564, 1563, 1067, 1059, 1053, 44, 1555])).
% 0.60/0.79 tff(1572,plain,
% 0.60/0.79 (c2_1(a865)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[352, 1562])).
% 0.60/0.79 tff(1573,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a842) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c3_1(a828)) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a842) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c3_1(a828)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1574,plain,
% 0.60/0.80 (((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865))) <=> (c2_1(a842) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c3_1(a828)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1575,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a842) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c3_1(a828)) | (~c1_1(a842)) | (~c0_1(a842))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1574])).
% 0.60/0.80 tff(1576,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a842) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c3_1(a828)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1575, 1573])).
% 0.60/0.80 tff(1577,plain,
% 0.60/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1578,plain,
% 0.60/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a842) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c3_1(a828)) | (~c1_1(a842)) | (~c0_1(a842))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1577, 1576])).
% 0.60/0.80 tff(1579,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1578, 151, 1564, 1572, 1546, 1545, 1544, 1059, 1053, 81, 1555, 1571])).
% 0.60/0.80 % SZS output end Proof
% 0.60/0.80 % E exiting
%------------------------------------------------------------------------------