%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN477-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:39:16 AM UTC 2025
% Result : Unsatisfiable 0.69s 0.86s
% Output : Proof 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN477-1 : TPTP v9.0.0. Released v2.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 12:36:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.69/0.86 % SZS status Unsatisfiable
% 0.69/0.86 % SZS output start Proof
% 0.69/0.86 tff(c2_1_type, type, (
% 0.69/0.86 c2_1: $i > $o)).
% 0.69/0.86 tff(a1204_type, type, (
% 0.69/0.86 a1204: $i)).
% 0.69/0.86 tff(hskp25_type, type, (
% 0.69/0.86 hskp25: $o)).
% 0.69/0.86 tff(c3_1_type, type, (
% 0.69/0.86 c3_1: $i > $o)).
% 0.69/0.86 tff(a1208_type, type, (
% 0.69/0.86 a1208: $i)).
% 0.69/0.86 tff(c0_1_type, type, (
% 0.69/0.86 c0_1: $i > $o)).
% 0.69/0.86 tff(c1_1_type, type, (
% 0.69/0.86 c1_1: $i > $o)).
% 0.69/0.86 tff(ndr1_0_type, type, (
% 0.69/0.86 ndr1_0: $o)).
% 0.69/0.86 tff(a1212_type, type, (
% 0.69/0.86 a1212: $i)).
% 0.69/0.86 tff(hskp5_type, type, (
% 0.69/0.86 hskp5: $o)).
% 0.69/0.86 tff(a1257_type, type, (
% 0.69/0.86 a1257: $i)).
% 0.69/0.86 tff(hskp21_type, type, (
% 0.69/0.86 hskp21: $o)).
% 0.69/0.86 tff(a1233_type, type, (
% 0.69/0.86 a1233: $i)).
% 0.69/0.86 tff(hskp15_type, type, (
% 0.69/0.86 hskp15: $o)).
% 0.69/0.86 tff(hskp6_type, type, (
% 0.69/0.86 hskp6: $o)).
% 0.69/0.86 tff(hskp0_type, type, (
% 0.69/0.86 hskp0: $o)).
% 0.69/0.86 tff(a1205_type, type, (
% 0.69/0.86 a1205: $i)).
% 0.69/0.86 tff(a1216_type, type, (
% 0.69/0.86 a1216: $i)).
% 0.69/0.86 tff(a1215_type, type, (
% 0.69/0.86 a1215: $i)).
% 0.69/0.86 tff(a1224_type, type, (
% 0.69/0.86 a1224: $i)).
% 0.69/0.86 tff(hskp11_type, type, (
% 0.69/0.86 hskp11: $o)).
% 0.69/0.86 tff(a1219_type, type, (
% 0.69/0.86 a1219: $i)).
% 0.69/0.86 tff(hskp9_type, type, (
% 0.69/0.86 hskp9: $o)).
% 0.69/0.86 tff(a1229_type, type, (
% 0.69/0.86 a1229: $i)).
% 0.69/0.86 tff(hskp13_type, type, (
% 0.69/0.86 hskp13: $o)).
% 0.69/0.86 tff(a1223_type, type, (
% 0.69/0.86 a1223: $i)).
% 0.69/0.86 tff(hskp10_type, type, (
% 0.69/0.86 hskp10: $o)).
% 0.69/0.86 tff(hskp7_type, type, (
% 0.69/0.86 hskp7: $o)).
% 0.69/0.86 tff(hskp2_type, type, (
% 0.69/0.86 hskp2: $o)).
% 0.69/0.86 tff(hskp24_type, type, (
% 0.69/0.86 hskp24: $o)).
% 0.69/0.86 tff(hskp28_type, type, (
% 0.69/0.86 hskp28: $o)).
% 0.69/0.86 tff(hskp26_type, type, (
% 0.69/0.86 hskp26: $o)).
% 0.69/0.86 tff(a1214_type, type, (
% 0.69/0.86 a1214: $i)).
% 0.69/0.86 tff(a1261_type, type, (
% 0.69/0.86 a1261: $i)).
% 0.69/0.86 tff(hskp23_type, type, (
% 0.69/0.86 hskp23: $o)).
% 0.69/0.86 tff(a1232_type, type, (
% 0.69/0.86 a1232: $i)).
% 0.69/0.86 tff(a1217_type, type, (
% 0.69/0.86 a1217: $i)).
% 0.69/0.86 tff(hskp8_type, type, (
% 0.69/0.86 hskp8: $o)).
% 0.69/0.86 tff(hskp19_type, type, (
% 0.69/0.86 hskp19: $o)).
% 0.69/0.86 tff(hskp14_type, type, (
% 0.69/0.86 hskp14: $o)).
% 0.69/0.86 tff(hskp4_type, type, (
% 0.69/0.86 hskp4: $o)).
% 0.69/0.86 tff(a1211_type, type, (
% 0.69/0.86 a1211: $i)).
% 0.69/0.86 tff(a1267_type, type, (
% 0.69/0.86 a1267: $i)).
% 0.69/0.86 tff(a1247_type, type, (
% 0.69/0.86 a1247: $i)).
% 0.69/0.86 tff(hskp1_type, type, (
% 0.69/0.86 hskp1: $o)).
% 0.69/0.86 tff(a1206_type, type, (
% 0.69/0.86 a1206: $i)).
% 0.69/0.86 tff(a1207_type, type, (
% 0.69/0.86 a1207: $i)).
% 0.69/0.86 tff(a1237_type, type, (
% 0.69/0.86 a1237: $i)).
% 0.69/0.86 tff(hskp17_type, type, (
% 0.69/0.86 hskp17: $o)).
% 0.69/0.86 tff(a1213_type, type, (
% 0.69/0.86 a1213: $i)).
% 0.69/0.86 tff(hskp27_type, type, (
% 0.69/0.86 hskp27: $o)).
% 0.69/0.86 tff(a1246_type, type, (
% 0.69/0.86 a1246: $i)).
% 0.69/0.86 tff(hskp18_type, type, (
% 0.69/0.86 hskp18: $o)).
% 0.69/0.86 tff(a1210_type, type, (
% 0.69/0.86 a1210: $i)).
% 0.69/0.86 tff(hskp3_type, type, (
% 0.69/0.86 hskp3: $o)).
% 0.69/0.86 tff(1,plain,
% 0.69/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(2,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[1])).
% 0.69/0.86 tff(3,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(4,plain,
% 0.69/0.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~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)) | (~c1_1(U)) | (~c3_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))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(5,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[4])).
% 0.69/0.86 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 0.69/0.86 tff(7,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.69/0.86 tff(8,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.69/0.86 tff(9,plain,(
% 0.69/0.86 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.69/0.86 inference(skolemize,[status(sab)],[8])).
% 0.69/0.86 tff(10,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.69/0.86 tff(11,plain,
% 0.69/0.86 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(12,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[11])).
% 0.69/0.86 tff(13,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(14,plain,
% 0.69/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(15,plain,
% 0.69/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[14])).
% 0.69/0.86 tff(16,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 0.69/0.86 tff(17,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.69/0.86 tff(18,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.69/0.86 tff(19,plain,(
% 0.69/0.86 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(skolemize,[status(sab)],[18])).
% 0.69/0.86 tff(20,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.69/0.86 tff(21,assumption,(~hskp5), introduced(assumption)).
% 0.69/0.86 tff(22,assumption,(~c0_1(a1205)), introduced(assumption)).
% 0.69/0.86 tff(23,assumption,(~c1_1(a1205)), introduced(assumption)).
% 0.69/0.86 tff(24,assumption,(~hskp6), introduced(assumption)).
% 0.69/0.86 tff(25,plain,
% 0.69/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(26,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[25])).
% 0.69/0.86 tff(27,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(28,plain,
% 0.69/0.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~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(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(29,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[28])).
% 0.69/0.86 tff(30,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 0.69/0.86 tff(31,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.69/0.86 tff(32,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.69/0.87 tff(33,plain,(
% 0.69/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.87 inference(skolemize,[status(sab)],[32])).
% 0.69/0.87 tff(34,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.69/0.87 tff(35,plain,
% 0.69/0.87 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(36,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[35])).
% 0.69/0.87 tff(37,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(38,plain,
% 0.69/0.87 (^[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(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(39,plain,
% 0.69/0.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[38])).
% 0.69/0.87 tff(40,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 0.69/0.87 tff(41,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.69/0.87 tff(42,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.69/0.87 tff(43,plain,(
% 0.69/0.87 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(skolemize,[status(sab)],[42])).
% 0.69/0.87 tff(44,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.69/0.87 tff(45,plain,
% 0.69/0.87 (^[U: $i] : refl((hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(46,plain,
% 0.69/0.87 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[45])).
% 0.69/0.87 tff(47,plain,
% 0.69/0.87 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(48,plain,
% 0.69/0.87 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) | hskp6) <=> ((hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp6))), rewrite(((hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp6) <=> (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) | hskp6) <=> (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(49,plain,
% 0.69/0.87 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) | hskp6) <=> ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[48])).
% 0.69/0.87 tff(50,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 0.69/0.87 tff(51,plain,
% 0.69/0.87 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.69/0.87 tff(52,plain,
% 0.69/0.87 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.69/0.87 tff(53,plain,(
% 0.69/0.87 ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.69/0.87 inference(skolemize,[status(sab)],[52])).
% 0.69/0.87 tff(54,plain,
% 0.69/0.87 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.69/0.87 tff(55,plain,
% 0.69/0.87 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(56,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[55])).
% 0.69/0.87 tff(57,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(58,plain,
% 0.69/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(59,plain,
% 0.69/0.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[58])).
% 0.69/0.87 tff(60,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.69/0.87 tff(61,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.69/0.87 tff(62,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.69/0.87 tff(63,plain,(
% 0.69/0.87 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(skolemize,[status(sab)],[62])).
% 0.69/0.87 tff(64,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.69/0.87 tff(65,plain,
% 0.69/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(66,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[65])).
% 0.69/0.87 tff(67,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(68,plain,
% 0.69/0.87 (^[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))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(69,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[68])).
% 0.69/0.87 tff(70,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 0.69/0.87 tff(71,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.69/0.87 tff(72,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.69/0.87 tff(73,plain,(
% 0.69/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.69/0.87 inference(skolemize,[status(sab)],[72])).
% 0.69/0.87 tff(74,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.69/0.87 tff(75,assumption,(~hskp15), introduced(assumption)).
% 0.69/0.87 tff(76,plain,
% 0.69/0.87 ((hskp15 | hskp6 | hskp5) <=> (hskp15 | hskp6 | hskp5)),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(77,plain,
% 0.69/0.87 (((hskp15 | hskp6) | hskp5) <=> (hskp15 | hskp6 | hskp5)),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(78,axiom,((hskp15 | hskp6) | hskp5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 0.69/0.87 tff(79,plain,
% 0.69/0.87 (hskp15 | hskp6 | hskp5),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.69/0.87 tff(80,plain,
% 0.69/0.87 (hskp15 | hskp6 | hskp5),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.69/0.87 tff(81,plain,
% 0.69/0.87 (hskp15 | hskp6 | hskp5),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.69/0.87 tff(82,plain,
% 0.69/0.87 (hskp15 | hskp6 | hskp5),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[81, 76])).
% 0.69/0.87 tff(83,plain,
% 0.69/0.87 (hskp15 | hskp6 | hskp5),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[82, 76])).
% 0.69/0.87 tff(84,plain,
% 0.69/0.87 (hskp6),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[83, 75, 21])).
% 0.69/0.87 tff(85,plain,
% 0.69/0.87 (((~hskp6) | (~c3_1(a1215))) <=> ((~hskp6) | (~c3_1(a1215)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(86,plain,
% 0.69/0.87 (((~c3_1(a1215)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a1215)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(87,axiom,((~c3_1(a1215)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.69/0.87 tff(88,plain,
% 0.69/0.87 ((~hskp6) | (~c3_1(a1215))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.69/0.87 tff(89,plain,
% 0.69/0.87 ((~hskp6) | (~c3_1(a1215))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.69/0.87 tff(90,plain,
% 0.69/0.87 (~c3_1(a1215)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[89, 84])).
% 0.69/0.87 tff(91,plain,
% 0.69/0.87 (((~hskp6) | c1_1(a1215)) <=> ((~hskp6) | c1_1(a1215))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(92,axiom,((~hskp6) | c1_1(a1215)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.69/0.87 tff(93,plain,
% 0.69/0.87 ((~hskp6) | c1_1(a1215)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.69/0.87 tff(94,plain,
% 0.69/0.87 ((~hskp6) | c1_1(a1215)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[93, 91])).
% 0.69/0.87 tff(95,plain,
% 0.69/0.87 ((~hskp6) | c1_1(a1215)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[94, 91])).
% 0.69/0.87 tff(96,plain,
% 0.69/0.87 ((~hskp6) | c1_1(a1215)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.69/0.87 tff(97,plain,
% 0.69/0.87 ((~hskp6) | c1_1(a1215)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[96, 91])).
% 0.69/0.87 tff(98,plain,
% 0.69/0.87 (c1_1(a1215)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[97, 84])).
% 0.69/0.87 tff(99,plain,
% 0.69/0.87 (((~hskp6) | c2_1(a1215)) <=> ((~hskp6) | c2_1(a1215))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(100,axiom,((~hskp6) | c2_1(a1215)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.69/0.87 tff(101,plain,
% 0.69/0.87 ((~hskp6) | c2_1(a1215)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.69/0.87 tff(102,plain,
% 0.69/0.87 ((~hskp6) | c2_1(a1215)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[101, 99])).
% 0.69/0.87 tff(103,plain,
% 0.69/0.87 ((~hskp6) | c2_1(a1215)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.69/0.87 tff(104,plain,
% 0.69/0.87 ((~hskp6) | c2_1(a1215)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.69/0.87 tff(105,plain,
% 0.69/0.87 ((~hskp6) | c2_1(a1215)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[104, 99])).
% 0.69/0.87 tff(106,plain,
% 0.69/0.87 (c2_1(a1215)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[105, 84])).
% 0.69/0.87 tff(107,assumption,(~c2_1(a1205)), introduced(assumption)).
% 0.69/0.87 tff(108,plain,
% 0.69/0.87 (((~hskp0) | c2_1(a1205)) <=> ((~hskp0) | c2_1(a1205))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(109,axiom,((~hskp0) | c2_1(a1205)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.69/0.87 tff(110,plain,
% 0.69/0.87 ((~hskp0) | c2_1(a1205)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.69/0.87 tff(111,plain,
% 0.69/0.87 ((~hskp0) | c2_1(a1205)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[110, 108])).
% 0.69/0.87 tff(112,plain,
% 0.69/0.87 ((~hskp0) | c2_1(a1205)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[111, 108])).
% 0.69/0.87 tff(113,plain,
% 0.69/0.87 ((~hskp0) | c2_1(a1205)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.69/0.87 tff(114,plain,
% 0.69/0.87 ((~hskp0) | c2_1(a1205)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[113, 108])).
% 0.69/0.87 tff(115,plain,
% 0.69/0.87 (~hskp0),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[114, 107])).
% 0.69/0.87 tff(116,plain,
% 0.69/0.87 (^[U: $i] : refl((hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(117,plain,
% 0.69/0.87 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[116])).
% 0.69/0.87 tff(118,plain,
% 0.69/0.87 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(119,plain,
% 0.69/0.87 (^[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)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp21) <=> ((hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp21))), rewrite(((hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp21) <=> (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp21) <=> (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(120,plain,
% 0.69/0.87 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp21) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[119])).
% 0.69/0.87 tff(121,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 0.69/0.87 tff(122,plain,
% 0.69/0.87 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.69/0.87 tff(123,plain,
% 0.69/0.87 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.69/0.87 tff(124,plain,(
% 0.69/0.87 ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.69/0.87 inference(skolemize,[status(sab)],[123])).
% 0.69/0.87 tff(125,plain,
% 0.69/0.87 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.69/0.87 tff(126,assumption,(~c3_1(a1215)), introduced(assumption)).
% 0.69/0.87 tff(127,assumption,(c2_1(a1215)), introduced(assumption)).
% 0.69/0.87 tff(128,assumption,(c1_1(a1215)), introduced(assumption)).
% 0.69/0.87 tff(129,assumption,(~ndr1_0), introduced(assumption)).
% 0.69/0.87 tff(130,plain,
% 0.69/0.87 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(131,plain,
% 0.69/0.87 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(132,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause6')).
% 0.69/0.87 tff(133,plain,
% 0.69/0.87 (ndr1_0 | (~hskp24)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.69/0.87 tff(134,plain,
% 0.69/0.87 (ndr1_0 | (~hskp24)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[133, 130])).
% 0.69/0.87 tff(135,plain,
% 0.69/0.87 (~hskp24),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[134, 129])).
% 0.69/0.87 tff(136,plain,
% 0.69/0.87 (((~hskp28) | ndr1_0) <=> ((~hskp28) | ndr1_0)),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(137,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 0.69/0.87 tff(138,plain,
% 0.69/0.87 ((~hskp28) | ndr1_0),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.69/0.87 tff(139,plain,
% 0.69/0.87 ((~hskp28) | ndr1_0),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[138, 136])).
% 0.69/0.87 tff(140,plain,
% 0.69/0.87 ((~hskp28) | ndr1_0),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[139, 136])).
% 0.69/0.87 tff(141,plain,
% 0.69/0.87 ((~hskp28) | ndr1_0),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.69/0.87 tff(142,plain,
% 0.69/0.87 ((~hskp28) | ndr1_0),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[141, 136])).
% 0.69/0.87 tff(143,plain,
% 0.69/0.87 (~hskp28),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[142, 129])).
% 0.69/0.87 tff(144,plain,
% 0.69/0.87 ((ndr1_0 | (~hskp26)) <=> (ndr1_0 | (~hskp26))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(145,plain,
% 0.69/0.87 (((~hskp26) | ndr1_0) <=> (ndr1_0 | (~hskp26))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(146,axiom,((~hskp26) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause4')).
% 0.69/0.87 tff(147,plain,
% 0.69/0.87 (ndr1_0 | (~hskp26)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.69/0.87 tff(148,plain,
% 0.69/0.87 (ndr1_0 | (~hskp26)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[147, 144])).
% 0.69/0.87 tff(149,plain,
% 0.69/0.87 (~hskp26),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[148, 129])).
% 0.69/0.87 tff(150,plain,
% 0.69/0.87 ((hskp28 | hskp26 | hskp24) <=> (hskp28 | hskp26 | hskp24)),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(151,plain,
% 0.69/0.87 (((hskp26 | hskp28) | hskp24) <=> (hskp28 | hskp26 | hskp24)),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(152,axiom,((hskp26 | hskp28) | hskp24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause31')).
% 0.69/0.87 tff(153,plain,
% 0.69/0.87 (hskp28 | hskp26 | hskp24),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.69/0.87 tff(154,plain,
% 0.69/0.87 (hskp28 | hskp26 | hskp24),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[153, 150])).
% 0.69/0.87 tff(155,plain,
% 0.69/0.87 (hskp28 | hskp26 | hskp24),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.69/0.87 tff(156,plain,
% 0.69/0.87 (hskp28 | hskp26 | hskp24),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[155, 150])).
% 0.69/0.87 tff(157,plain,
% 0.69/0.87 (hskp28 | hskp26 | hskp24),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[156, 150])).
% 0.69/0.87 tff(158,plain,
% 0.69/0.87 ($false),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[157, 149, 143, 135])).
% 0.69/0.87 tff(159,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.69/0.87 tff(160,plain,
% 0.69/0.87 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp21 | hskp0 | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp21 | hskp0 | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(161,plain,
% 0.69/0.87 ((hskp21 | hskp0 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215))) <=> (hskp21 | hskp0 | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(162,plain,
% 0.69/0.87 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp21 | hskp0 | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[161])).
% 0.69/0.87 tff(163,plain,
% 0.69/0.87 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp21 | hskp0 | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[162, 160])).
% 0.69/0.87 tff(164,plain,
% 0.69/0.87 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(165,plain,
% 0.69/0.87 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp21 | hskp0 | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.69/0.87 tff(166,plain,
% 0.69/0.87 (hskp21 | hskp0),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[165, 159, 128, 127, 126, 125])).
% 0.69/0.87 tff(167,plain,
% 0.69/0.87 (hskp21),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[166, 115])).
% 0.69/0.87 tff(168,plain,
% 0.69/0.87 (((~hskp21) | (~c1_1(a1257))) <=> ((~hskp21) | (~c1_1(a1257)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(169,plain,
% 0.69/0.87 (((~c1_1(a1257)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a1257)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(170,axiom,((~c1_1(a1257)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 0.69/0.87 tff(171,plain,
% 0.69/0.87 ((~hskp21) | (~c1_1(a1257))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.69/0.87 tff(172,plain,
% 0.69/0.87 ((~hskp21) | (~c1_1(a1257))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[171, 168])).
% 0.69/0.87 tff(173,plain,
% 0.69/0.87 (~c1_1(a1257)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[172, 167])).
% 0.69/0.87 tff(174,plain,
% 0.69/0.87 (((~hskp21) | (~c0_1(a1257))) <=> ((~hskp21) | (~c0_1(a1257)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(175,plain,
% 0.69/0.87 (((~c0_1(a1257)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a1257)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(176,axiom,((~c0_1(a1257)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.69/0.87 tff(177,plain,
% 0.69/0.87 ((~hskp21) | (~c0_1(a1257))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.69/0.87 tff(178,plain,
% 0.69/0.87 ((~hskp21) | (~c0_1(a1257))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[177, 174])).
% 0.69/0.87 tff(179,plain,
% 0.69/0.87 (~c0_1(a1257)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[178, 167])).
% 0.69/0.87 tff(180,plain,
% 0.69/0.87 (((~hskp21) | c3_1(a1257)) <=> ((~hskp21) | c3_1(a1257))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(181,axiom,((~hskp21) | c3_1(a1257)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.69/0.87 tff(182,plain,
% 0.69/0.87 ((~hskp21) | c3_1(a1257)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.69/0.87 tff(183,plain,
% 0.69/0.87 ((~hskp21) | c3_1(a1257)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[182, 180])).
% 0.69/0.87 tff(184,plain,
% 0.69/0.87 ((~hskp21) | c3_1(a1257)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[183, 180])).
% 0.69/0.87 tff(185,plain,
% 0.69/0.87 ((~hskp21) | c3_1(a1257)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.69/0.87 tff(186,plain,
% 0.69/0.87 ((~hskp21) | c3_1(a1257)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[185, 180])).
% 0.69/0.87 tff(187,plain,
% 0.69/0.87 (c3_1(a1257)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[186, 167])).
% 0.69/0.87 tff(188,plain,
% 0.69/0.87 (^[U: $i] : refl((hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(189,plain,
% 0.69/0.87 (![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[188])).
% 0.69/0.87 tff(190,plain,
% 0.69/0.87 (![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(191,plain,
% 0.69/0.87 (^[U: $i] : 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)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(192,plain,
% 0.69/0.87 (![U: $i] : (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[191])).
% 0.69/0.87 tff(193,axiom,(![U: $i] : (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.69/0.87 tff(194,plain,
% 0.69/0.87 (![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.69/0.87 tff(195,plain,
% 0.69/0.87 (![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.69/0.87 tff(196,plain,(
% 0.69/0.87 ![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.69/0.87 inference(skolemize,[status(sab)],[195])).
% 0.69/0.87 tff(197,plain,
% 0.69/0.87 (![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[196, 189])).
% 0.69/0.87 tff(198,assumption,(~hskp28), introduced(assumption)).
% 0.69/0.87 tff(199,plain,
% 0.69/0.87 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c2_1(a1205) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c2_1(a1205) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(200,plain,
% 0.69/0.87 ((hskp28 | (~ndr1_0) | c3_1(a1205) | c2_1(a1205) | c0_1(a1205)) <=> (hskp28 | c2_1(a1205) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(201,plain,
% 0.69/0.87 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1205) | c2_1(a1205) | c0_1(a1205))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c2_1(a1205) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205)))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[200])).
% 0.69/0.87 tff(202,plain,
% 0.69/0.87 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1205) | c2_1(a1205) | c0_1(a1205))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c2_1(a1205) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205))),
% 0.69/0.87 inference(transitivity,[status(thm)],[201, 199])).
% 0.69/0.87 tff(203,plain,
% 0.69/0.87 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1205) | c2_1(a1205) | c0_1(a1205))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(204,plain,
% 0.69/0.87 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c2_1(a1205) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.69/0.87 tff(205,plain,
% 0.69/0.87 (hskp28 | c2_1(a1205) | c3_1(a1205)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[204, 159, 22, 197])).
% 0.69/0.87 tff(206,plain,
% 0.69/0.87 (c3_1(a1205)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[205, 198, 107])).
% 0.69/0.87 tff(207,plain,
% 0.69/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(208,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_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) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[207])).
% 0.69/0.87 tff(209,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_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) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(210,plain,
% 0.69/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(211,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[210])).
% 0.69/0.88 tff(212,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 0.69/0.88 tff(213,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.69/0.88 tff(214,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.69/0.88 tff(215,plain,(
% 0.69/0.88 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.88 inference(skolemize,[status(sab)],[214])).
% 0.69/0.88 tff(216,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.69/0.88 tff(217,plain,
% 0.69/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(218,plain,
% 0.69/0.88 (((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1205) | c2_1(a1205) | (~c3_1(a1205)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205)) <=> (c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(219,plain,
% 0.69/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1205) | c2_1(a1205) | (~c3_1(a1205)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | c0_1(a1215) | (~c1_1(a1215))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[218])).
% 0.69/0.88 tff(220,plain,
% 0.69/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1205) | c2_1(a1205) | (~c3_1(a1205)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[219, 217])).
% 0.69/0.88 tff(221,plain,
% 0.69/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1205) | c2_1(a1205) | (~c3_1(a1205)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(222,plain,
% 0.69/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | c0_1(a1215) | (~c1_1(a1215))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.69/0.88 tff(223,plain,
% 0.69/0.88 ((~c3_1(a1205)) | c0_1(a1215)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[222, 159, 128, 107, 126, 22, 23, 216])).
% 0.69/0.88 tff(224,plain,
% 0.69/0.88 (c0_1(a1215)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[223, 206])).
% 0.69/0.88 tff(225,plain,
% 0.69/0.88 (^[U: $i] : refl((hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(226,plain,
% 0.69/0.88 (![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[225])).
% 0.69/0.88 tff(227,plain,
% 0.69/0.88 (![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(228,plain,
% 0.69/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp23) <=> ((hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp23) <=> (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(229,plain,
% 0.69/0.88 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp23) <=> ![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[228])).
% 0.69/0.88 tff(230,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 0.69/0.88 tff(231,plain,
% 0.69/0.88 (![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.69/0.88 tff(232,plain,
% 0.69/0.88 (![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.69/0.88 tff(233,plain,(
% 0.69/0.88 ![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.88 inference(skolemize,[status(sab)],[232])).
% 0.69/0.88 tff(234,plain,
% 0.69/0.88 (![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.69/0.88 tff(235,plain,
% 0.69/0.88 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(236,plain,
% 0.69/0.88 ((hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215))) <=> (hskp23 | hskp0 | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(237,plain,
% 0.69/0.88 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[236])).
% 0.69/0.88 tff(238,plain,
% 0.69/0.88 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[237, 235])).
% 0.69/0.88 tff(239,plain,
% 0.69/0.88 ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(240,plain,
% 0.69/0.88 ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.69/0.88 tff(241,plain,
% 0.69/0.88 (hskp23 | hskp0 | (~c0_1(a1215))),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[240, 159, 128, 127, 234])).
% 0.69/0.88 tff(242,plain,
% 0.69/0.88 (hskp23),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[241, 224, 115])).
% 0.69/0.88 tff(243,plain,
% 0.69/0.88 (((~hskp23) | (~c3_1(a1261))) <=> ((~hskp23) | (~c3_1(a1261)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(244,plain,
% 0.69/0.88 (((~c3_1(a1261)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1261)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(245,axiom,((~c3_1(a1261)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.69/0.88 tff(246,plain,
% 0.69/0.88 ((~hskp23) | (~c3_1(a1261))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.69/0.88 tff(247,plain,
% 0.69/0.88 ((~hskp23) | (~c3_1(a1261))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[246, 243])).
% 0.69/0.88 tff(248,plain,
% 0.69/0.88 (~c3_1(a1261)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[247, 242])).
% 0.69/0.88 tff(249,plain,
% 0.69/0.88 (((~hskp23) | (~c2_1(a1261))) <=> ((~hskp23) | (~c2_1(a1261)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(250,plain,
% 0.69/0.88 (((~c2_1(a1261)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a1261)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(251,axiom,((~c2_1(a1261)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 0.69/0.88 tff(252,plain,
% 0.69/0.88 ((~hskp23) | (~c2_1(a1261))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.69/0.88 tff(253,plain,
% 0.69/0.88 ((~hskp23) | (~c2_1(a1261))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[252, 249])).
% 0.69/0.88 tff(254,plain,
% 0.69/0.88 (~c2_1(a1261)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[253, 242])).
% 0.69/0.88 tff(255,plain,
% 0.69/0.88 (((~hskp23) | (~c0_1(a1261))) <=> ((~hskp23) | (~c0_1(a1261)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(256,plain,
% 0.69/0.88 (((~c0_1(a1261)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a1261)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(257,axiom,((~c0_1(a1261)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 0.69/0.88 tff(258,plain,
% 0.69/0.88 ((~hskp23) | (~c0_1(a1261))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.69/0.88 tff(259,plain,
% 0.69/0.88 ((~hskp23) | (~c0_1(a1261))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[258, 255])).
% 0.69/0.88 tff(260,plain,
% 0.69/0.88 (~c0_1(a1261)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[259, 242])).
% 0.69/0.88 tff(261,plain,
% 0.69/0.88 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c0_1(a1261) | c2_1(a1261) | c3_1(a1261) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1261) | c2_1(a1261) | c3_1(a1261) | (~ndr1_0))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(262,plain,
% 0.69/0.88 ((hskp28 | (~ndr1_0) | c3_1(a1261) | c2_1(a1261) | c0_1(a1261)) <=> (hskp28 | c0_1(a1261) | c2_1(a1261) | c3_1(a1261) | (~ndr1_0))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(263,plain,
% 0.69/0.88 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1261) | c2_1(a1261) | c0_1(a1261))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c0_1(a1261) | c2_1(a1261) | c3_1(a1261) | (~ndr1_0)))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[262])).
% 0.69/0.88 tff(264,plain,
% 0.69/0.88 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1261) | c2_1(a1261) | c0_1(a1261))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1261) | c2_1(a1261) | c3_1(a1261) | (~ndr1_0))),
% 0.69/0.88 inference(transitivity,[status(thm)],[263, 261])).
% 0.69/0.88 tff(265,plain,
% 0.69/0.88 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1261) | c2_1(a1261) | c0_1(a1261))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(266,plain,
% 0.69/0.88 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1261) | c2_1(a1261) | c3_1(a1261) | (~ndr1_0)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.69/0.88 tff(267,plain,
% 0.69/0.88 ($false),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[266, 198, 159, 260, 254, 248, 197])).
% 0.69/0.88 tff(268,plain,(hskp28 | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.88 tff(269,plain,
% 0.69/0.88 (hskp28),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[268, 107, 127, 128, 126, 22, 23])).
% 0.69/0.88 tff(270,plain,
% 0.69/0.88 (((~hskp28) | c3_1(a1214)) <=> ((~hskp28) | c3_1(a1214))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(271,axiom,((~hskp28) | c3_1(a1214)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 0.69/0.88 tff(272,plain,
% 0.69/0.88 ((~hskp28) | c3_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.69/0.88 tff(273,plain,
% 0.69/0.88 ((~hskp28) | c3_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[272, 270])).
% 0.69/0.88 tff(274,plain,
% 0.69/0.88 ((~hskp28) | c3_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[273, 270])).
% 0.69/0.88 tff(275,plain,
% 0.69/0.88 ((~hskp28) | c3_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.69/0.88 tff(276,plain,
% 0.69/0.88 ((~hskp28) | c3_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[275, 270])).
% 0.69/0.88 tff(277,plain,
% 0.69/0.88 (c3_1(a1214)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[276, 269])).
% 0.69/0.88 tff(278,plain,
% 0.69/0.88 (((~hskp28) | c1_1(a1214)) <=> ((~hskp28) | c1_1(a1214))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(279,axiom,((~hskp28) | c1_1(a1214)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.69/0.88 tff(280,plain,
% 0.69/0.88 ((~hskp28) | c1_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.69/0.88 tff(281,plain,
% 0.69/0.88 ((~hskp28) | c1_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[280, 278])).
% 0.69/0.88 tff(282,plain,
% 0.69/0.88 ((~hskp28) | c1_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[281, 278])).
% 0.69/0.88 tff(283,plain,
% 0.69/0.88 ((~hskp28) | c1_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[282, 278])).
% 0.69/0.88 tff(284,plain,
% 0.69/0.88 ((~hskp28) | c1_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[283, 278])).
% 0.69/0.88 tff(285,plain,
% 0.69/0.88 (c1_1(a1214)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[284, 269])).
% 0.69/0.88 tff(286,plain,
% 0.69/0.88 (((~hskp28) | c0_1(a1214)) <=> ((~hskp28) | c0_1(a1214))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(287,axiom,((~hskp28) | c0_1(a1214)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.69/0.88 tff(288,plain,
% 0.69/0.88 ((~hskp28) | c0_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.69/0.88 tff(289,plain,
% 0.69/0.88 ((~hskp28) | c0_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[288, 286])).
% 0.69/0.88 tff(290,plain,
% 0.69/0.88 ((~hskp28) | c0_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[289, 286])).
% 0.69/0.88 tff(291,plain,
% 0.69/0.88 ((~hskp28) | c0_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[290, 286])).
% 0.69/0.88 tff(292,plain,
% 0.69/0.88 ((~hskp28) | c0_1(a1214)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[291, 286])).
% 0.69/0.88 tff(293,plain,
% 0.69/0.88 (c0_1(a1214)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[292, 269])).
% 0.69/0.88 tff(294,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(295,plain,
% 0.69/0.88 ((hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257))) <=> (hskp5 | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(296,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[295])).
% 0.69/0.88 tff(297,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[296, 294])).
% 0.69/0.88 tff(298,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(299,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.69/0.88 tff(300,plain,
% 0.69/0.88 ($false),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[299, 159, 21, 293, 285, 277, 187, 179, 173, 20])).
% 0.69/0.88 tff(301,plain,(c2_1(a1205) | hskp5 | (~c2_1(a1215)) | (~c1_1(a1215)) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.88 tff(302,plain,
% 0.69/0.88 (c2_1(a1205)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[301, 106, 21, 98, 90, 22, 23])).
% 0.69/0.88 tff(303,assumption,(~hskp11), introduced(assumption)).
% 0.69/0.88 tff(304,plain,
% 0.69/0.88 (^[U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(305,plain,
% 0.69/0.88 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[304])).
% 0.69/0.88 tff(306,plain,
% 0.69/0.88 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(307,plain,
% 0.69/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(308,plain,
% 0.69/0.88 (![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) <=> ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[307])).
% 0.69/0.88 tff(309,axiom,(![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.69/0.88 tff(310,plain,
% 0.69/0.88 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.69/0.88 tff(311,plain,
% 0.69/0.88 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[310, 306])).
% 0.69/0.88 tff(312,plain,(
% 0.69/0.88 ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.69/0.88 inference(skolemize,[status(sab)],[311])).
% 0.69/0.88 tff(313,plain,
% 0.69/0.88 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[312, 305])).
% 0.69/0.88 tff(314,plain,
% 0.69/0.88 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c2_1(a1215)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c2_1(a1215)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(315,plain,
% 0.69/0.88 ((hskp11 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c2_1(a1215))) <=> (hskp11 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c2_1(a1215)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(316,plain,
% 0.69/0.88 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c2_1(a1215)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c2_1(a1215))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[315])).
% 0.69/0.88 tff(317,plain,
% 0.69/0.88 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c2_1(a1215)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c2_1(a1215)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[316, 314])).
% 0.69/0.88 tff(318,plain,
% 0.69/0.88 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c2_1(a1215)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(319,plain,
% 0.69/0.88 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c2_1(a1215))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.69/0.88 tff(320,plain,
% 0.69/0.88 (hskp11 | c0_1(a1215)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[319, 159, 127, 126, 313])).
% 0.69/0.88 tff(321,plain,
% 0.69/0.88 (c0_1(a1215)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[320, 303])).
% 0.69/0.88 tff(322,assumption,(hskp4), introduced(assumption)).
% 0.69/0.88 tff(323,plain,
% 0.69/0.88 (((~hskp4) | (~c2_1(a1211))) <=> ((~hskp4) | (~c2_1(a1211)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(324,plain,
% 0.69/0.88 (((~c2_1(a1211)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a1211)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(325,axiom,((~c2_1(a1211)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 0.69/0.88 tff(326,plain,
% 0.69/0.88 ((~hskp4) | (~c2_1(a1211))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.69/0.88 tff(327,plain,
% 0.69/0.88 ((~hskp4) | (~c2_1(a1211))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[326, 323])).
% 0.69/0.88 tff(328,plain,
% 0.69/0.88 (~c2_1(a1211)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[327, 322])).
% 0.69/0.88 tff(329,plain,
% 0.69/0.88 (((~hskp4) | (~c0_1(a1211))) <=> ((~hskp4) | (~c0_1(a1211)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(330,plain,
% 0.69/0.88 (((~c0_1(a1211)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a1211)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(331,axiom,((~c0_1(a1211)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.69/0.88 tff(332,plain,
% 0.69/0.88 ((~hskp4) | (~c0_1(a1211))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.69/0.88 tff(333,plain,
% 0.69/0.88 ((~hskp4) | (~c0_1(a1211))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[332, 329])).
% 0.69/0.88 tff(334,plain,
% 0.69/0.88 (~c0_1(a1211)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[333, 322])).
% 0.69/0.88 tff(335,plain,
% 0.69/0.88 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | c3_1(a1211))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | c3_1(a1211))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(336,plain,
% 0.69/0.88 ((hskp28 | (~ndr1_0) | c3_1(a1211) | c2_1(a1211) | c0_1(a1211)) <=> (hskp28 | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | c3_1(a1211))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(337,plain,
% 0.69/0.88 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1211) | c2_1(a1211) | c0_1(a1211))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | c3_1(a1211)))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[336])).
% 0.69/0.88 tff(338,plain,
% 0.69/0.88 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1211) | c2_1(a1211) | c0_1(a1211))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | c3_1(a1211))),
% 0.69/0.88 inference(transitivity,[status(thm)],[337, 335])).
% 0.69/0.88 tff(339,plain,
% 0.69/0.88 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1211) | c2_1(a1211) | c0_1(a1211))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(340,plain,
% 0.69/0.88 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | c3_1(a1211)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.69/0.88 tff(341,plain,
% 0.69/0.88 (c3_1(a1211)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[340, 198, 159, 334, 328, 197])).
% 0.69/0.88 tff(342,assumption,(c0_1(a1215)), introduced(assumption)).
% 0.69/0.88 tff(343,plain,
% 0.69/0.88 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.69/0.88 inference(bind,[status(th)],[])).
% 0.69/0.88 tff(344,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.88 inference(quant_intro,[status(thm)],[343])).
% 0.69/0.88 tff(345,plain,
% 0.69/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(346,plain,
% 0.69/0.88 (^[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))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(347,plain,
% 0.69/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[346])).
% 0.69/0.89 tff(348,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 0.69/0.89 tff(349,plain,
% 0.69/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.69/0.89 tff(350,plain,
% 0.69/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[349, 345])).
% 0.69/0.89 tff(351,plain,(
% 0.69/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(skolemize,[status(sab)],[350])).
% 0.69/0.89 tff(352,plain,
% 0.69/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[351, 344])).
% 0.69/0.89 tff(353,plain,
% 0.69/0.89 (((~hskp4) | c1_1(a1211)) <=> ((~hskp4) | c1_1(a1211))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(354,axiom,((~hskp4) | c1_1(a1211)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.69/0.89 tff(355,plain,
% 0.69/0.89 ((~hskp4) | c1_1(a1211)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.69/0.89 tff(356,plain,
% 0.69/0.89 ((~hskp4) | c1_1(a1211)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[355, 353])).
% 0.69/0.89 tff(357,plain,
% 0.69/0.89 ((~hskp4) | c1_1(a1211)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[356, 353])).
% 0.69/0.89 tff(358,plain,
% 0.69/0.89 ((~hskp4) | c1_1(a1211)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[357, 353])).
% 0.69/0.89 tff(359,plain,
% 0.69/0.89 ((~hskp4) | c1_1(a1211)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[358, 353])).
% 0.69/0.89 tff(360,plain,
% 0.69/0.89 (c1_1(a1211)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[359, 322])).
% 0.69/0.89 tff(361,plain,
% 0.69/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c3_1(a1211)) | (~c1_1(a1211)) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c3_1(a1211)) | (~c1_1(a1211)) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(362,plain,
% 0.69/0.89 (((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1211) | (~c3_1(a1211)) | (~c1_1(a1211)) | c2_1(a1211) | c0_1(a1211) | (~c3_1(a1211))) <=> (c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c3_1(a1211)) | (~c1_1(a1211)) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(363,plain,
% 0.69/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1211) | (~c3_1(a1211)) | (~c1_1(a1211)) | c2_1(a1211) | c0_1(a1211) | (~c3_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c3_1(a1211)) | (~c1_1(a1211)) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215))))),
% 0.69/0.89 inference(monotonicity,[status(thm)],[362])).
% 0.69/0.89 tff(364,plain,
% 0.69/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1211) | (~c3_1(a1211)) | (~c1_1(a1211)) | c2_1(a1211) | c0_1(a1211) | (~c3_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c3_1(a1211)) | (~c1_1(a1211)) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 0.69/0.89 inference(transitivity,[status(thm)],[363, 361])).
% 0.69/0.89 tff(365,plain,
% 0.69/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1211) | (~c3_1(a1211)) | (~c1_1(a1211)) | c2_1(a1211) | c0_1(a1211) | (~c3_1(a1211)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(366,plain,
% 0.69/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c3_1(a1211)) | (~c1_1(a1211)) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.69/0.89 tff(367,plain,
% 0.69/0.89 ($false),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[366, 159, 128, 127, 360, 334, 328, 352, 342, 341])).
% 0.69/0.89 tff(368,plain,((~hskp4) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1215)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.69/0.89 tff(369,plain,
% 0.69/0.89 (~hskp4),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[368, 321, 127, 128, 198])).
% 0.69/0.89 tff(370,plain,
% 0.69/0.89 (^[U: $i] : refl((hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(371,plain,
% 0.69/0.89 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[370])).
% 0.69/0.89 tff(372,plain,
% 0.69/0.89 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(373,plain,
% 0.69/0.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp15) | hskp4) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp4))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp4) <=> (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp15) | hskp4) <=> (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(374,plain,
% 0.69/0.89 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp15) | hskp4) <=> ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[373])).
% 0.69/0.89 tff(375,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp15) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.69/0.89 tff(376,plain,
% 0.69/0.89 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.69/0.89 tff(377,plain,
% 0.69/0.89 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[376, 372])).
% 0.69/0.89 tff(378,plain,(
% 0.69/0.89 ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.69/0.89 inference(skolemize,[status(sab)],[377])).
% 0.69/0.89 tff(379,plain,
% 0.69/0.89 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[378, 371])).
% 0.69/0.89 tff(380,assumption,(hskp14), introduced(assumption)).
% 0.69/0.89 tff(381,plain,
% 0.69/0.89 (((~hskp14) | (~c2_1(a1232))) <=> ((~hskp14) | (~c2_1(a1232)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(382,plain,
% 0.69/0.89 (((~c2_1(a1232)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a1232)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(383,axiom,((~c2_1(a1232)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.69/0.89 tff(384,plain,
% 0.69/0.89 ((~hskp14) | (~c2_1(a1232))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.69/0.89 tff(385,plain,
% 0.69/0.89 ((~hskp14) | (~c2_1(a1232))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[384, 381])).
% 0.69/0.89 tff(386,plain,
% 0.69/0.89 (~c2_1(a1232)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[385, 380])).
% 0.69/0.89 tff(387,plain,
% 0.69/0.89 (((~hskp14) | c3_1(a1232)) <=> ((~hskp14) | c3_1(a1232))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(388,axiom,((~hskp14) | c3_1(a1232)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 0.69/0.89 tff(389,plain,
% 0.69/0.89 ((~hskp14) | c3_1(a1232)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.69/0.89 tff(390,plain,
% 0.69/0.89 ((~hskp14) | c3_1(a1232)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[389, 387])).
% 0.69/0.89 tff(391,plain,
% 0.69/0.89 ((~hskp14) | c3_1(a1232)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[390, 387])).
% 0.69/0.89 tff(392,plain,
% 0.69/0.89 ((~hskp14) | c3_1(a1232)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[391, 387])).
% 0.69/0.89 tff(393,plain,
% 0.69/0.89 ((~hskp14) | c3_1(a1232)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[392, 387])).
% 0.69/0.89 tff(394,plain,
% 0.69/0.89 (c3_1(a1232)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[393, 380])).
% 0.69/0.89 tff(395,assumption,(~hskp4), introduced(assumption)).
% 0.69/0.89 tff(396,plain,
% 0.69/0.89 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | c2_1(a1232) | (~ndr1_0) | c1_1(a1232) | (~c3_1(a1232)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp15 | hskp4 | c2_1(a1232) | (~ndr1_0) | c1_1(a1232) | (~c3_1(a1232)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(397,plain,
% 0.69/0.89 ((hskp15 | hskp4 | (~ndr1_0) | c2_1(a1232) | c1_1(a1232) | (~c3_1(a1232))) <=> (hskp15 | hskp4 | c2_1(a1232) | (~ndr1_0) | c1_1(a1232) | (~c3_1(a1232)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(398,plain,
% 0.69/0.89 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c2_1(a1232) | c1_1(a1232) | (~c3_1(a1232)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | c2_1(a1232) | (~ndr1_0) | c1_1(a1232) | (~c3_1(a1232))))),
% 0.69/0.89 inference(monotonicity,[status(thm)],[397])).
% 0.69/0.89 tff(399,plain,
% 0.69/0.89 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c2_1(a1232) | c1_1(a1232) | (~c3_1(a1232)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp15 | hskp4 | c2_1(a1232) | (~ndr1_0) | c1_1(a1232) | (~c3_1(a1232)))),
% 0.69/0.89 inference(transitivity,[status(thm)],[398, 396])).
% 0.69/0.89 tff(400,plain,
% 0.69/0.89 ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c2_1(a1232) | c1_1(a1232) | (~c3_1(a1232)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(401,plain,
% 0.69/0.89 ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp15 | hskp4 | c2_1(a1232) | (~ndr1_0) | c1_1(a1232) | (~c3_1(a1232))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.69/0.89 tff(402,plain,
% 0.69/0.89 (c1_1(a1232)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[401, 159, 75, 395, 394, 386, 379])).
% 0.69/0.89 tff(403,plain,
% 0.69/0.89 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(404,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[403])).
% 0.69/0.89 tff(405,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(406,plain,
% 0.69/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(407,plain,
% 0.69/0.89 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[406])).
% 0.69/0.89 tff(408,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 0.69/0.89 tff(409,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.69/0.89 tff(410,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[409, 405])).
% 0.69/0.89 tff(411,plain,(
% 0.69/0.89 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.69/0.89 inference(skolemize,[status(sab)],[410])).
% 0.69/0.89 tff(412,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[411, 404])).
% 0.69/0.89 tff(413,plain,
% 0.69/0.89 (((~hskp14) | (~c0_1(a1232))) <=> ((~hskp14) | (~c0_1(a1232)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(414,plain,
% 0.69/0.89 (((~c0_1(a1232)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a1232)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(415,axiom,((~c0_1(a1232)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.69/0.89 tff(416,plain,
% 0.69/0.89 ((~hskp14) | (~c0_1(a1232))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.69/0.89 tff(417,plain,
% 0.69/0.89 ((~hskp14) | (~c0_1(a1232))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[416, 413])).
% 0.69/0.89 tff(418,plain,
% 0.69/0.89 (~c0_1(a1232)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[417, 380])).
% 0.69/0.89 tff(419,plain,
% 0.69/0.89 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c0_1(a1232) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c0_1(a1232) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(420,plain,
% 0.69/0.89 ((hskp11 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232))) <=> (hskp11 | c0_1(a1232) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(421,plain,
% 0.69/0.89 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c0_1(a1232) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1232)) | (~c1_1(a1232))))),
% 0.69/0.89 inference(monotonicity,[status(thm)],[420])).
% 0.69/0.89 tff(422,plain,
% 0.69/0.89 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c0_1(a1232) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.69/0.89 inference(transitivity,[status(thm)],[421, 419])).
% 0.69/0.89 tff(423,plain,
% 0.69/0.89 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.69/0.89 inference(quant_inst,[status(thm)],[])).
% 0.69/0.89 tff(424,plain,
% 0.69/0.89 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c0_1(a1232) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1232)) | (~c1_1(a1232))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.69/0.89 tff(425,plain,
% 0.69/0.89 ($false),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[424, 159, 303, 394, 128, 127, 418, 126, 412, 402])).
% 0.69/0.89 tff(426,plain,((~hskp14) | hskp11 | (~c1_1(a1215)) | (~c2_1(a1215)) | c3_1(a1215) | hskp15 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.69/0.89 tff(427,plain,
% 0.69/0.89 (~hskp14),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[426, 369, 128, 127, 126, 75, 303])).
% 0.69/0.89 tff(428,plain,
% 0.69/0.89 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(429,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[428])).
% 0.69/0.89 tff(430,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(431,plain,
% 0.69/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.69/0.89 inference(bind,[status(th)],[])).
% 0.69/0.89 tff(432,plain,
% 0.69/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(quant_intro,[status(thm)],[431])).
% 0.69/0.89 tff(433,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.69/0.89 tff(434,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.69/0.89 tff(435,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[434, 430])).
% 0.69/0.89 tff(436,plain,(
% 0.69/0.89 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(skolemize,[status(sab)],[435])).
% 0.69/0.89 tff(437,plain,
% 0.69/0.89 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[436, 429])).
% 0.69/0.89 tff(438,assumption,(hskp24), introduced(assumption)).
% 0.69/0.89 tff(439,plain,
% 0.69/0.89 (((~hskp24) | (~c2_1(a1267))) <=> ((~hskp24) | (~c2_1(a1267)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(440,plain,
% 0.69/0.89 (((~c2_1(a1267)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a1267)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(441,axiom,((~c2_1(a1267)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 0.69/0.89 tff(442,plain,
% 0.69/0.89 ((~hskp24) | (~c2_1(a1267))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.69/0.89 tff(443,plain,
% 0.69/0.89 ((~hskp24) | (~c2_1(a1267))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[442, 439])).
% 0.69/0.89 tff(444,plain,
% 0.69/0.89 (~c2_1(a1267)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[443, 438])).
% 0.69/0.89 tff(445,plain,
% 0.69/0.89 (((~hskp24) | (~c1_1(a1267))) <=> ((~hskp24) | (~c1_1(a1267)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(446,plain,
% 0.69/0.89 (((~c1_1(a1267)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a1267)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(447,axiom,((~c1_1(a1267)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.69/0.89 tff(448,plain,
% 0.69/0.89 ((~hskp24) | (~c1_1(a1267))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.69/0.89 tff(449,plain,
% 0.69/0.89 ((~hskp24) | (~c1_1(a1267))),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[448, 445])).
% 0.69/0.89 tff(450,plain,
% 0.69/0.89 (~c1_1(a1267)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[449, 438])).
% 0.69/0.89 tff(451,plain,
% 0.69/0.89 (((~hskp24) | c0_1(a1267)) <=> ((~hskp24) | c0_1(a1267))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(452,axiom,((~hskp24) | c0_1(a1267)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.69/0.89 tff(453,plain,
% 0.69/0.89 ((~hskp24) | c0_1(a1267)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.69/0.89 tff(454,plain,
% 0.69/0.89 ((~hskp24) | c0_1(a1267)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[453, 451])).
% 0.69/0.89 tff(455,plain,
% 0.69/0.89 ((~hskp24) | c0_1(a1267)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[454, 451])).
% 0.69/0.89 tff(456,plain,
% 0.69/0.89 ((~hskp24) | c0_1(a1267)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[455, 451])).
% 0.69/0.89 tff(457,plain,
% 0.69/0.89 ((~hskp24) | c0_1(a1267)),
% 0.69/0.89 inference(modus_ponens,[status(thm)],[456, 451])).
% 0.69/0.89 tff(458,plain,
% 0.69/0.89 (c0_1(a1267)),
% 0.69/0.89 inference(unit_resolution,[status(thm)],[457, 438])).
% 0.69/0.89 tff(459,assumption,(~hskp14), introduced(assumption)).
% 0.69/0.89 tff(460,plain,
% 0.69/0.89 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(461,plain,
% 0.69/0.89 ((hskp14 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267))) <=> (hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)))),
% 0.69/0.89 inference(rewrite,[status(thm)],[])).
% 0.69/0.89 tff(462,plain,
% 0.69/0.89 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267))))),
% 0.69/0.89 inference(monotonicity,[status(thm)],[461])).
% 0.69/0.89 tff(463,plain,
% 0.69/0.89 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)))),
% 0.69/0.89 inference(transitivity,[status(thm)],[462, 460])).
% 0.69/0.90 tff(464,plain,
% 0.69/0.90 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(465,plain,
% 0.69/0.90 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.69/0.90 tff(466,plain,
% 0.69/0.90 ($false),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[465, 159, 459, 458, 127, 450, 444, 126, 437, 342])).
% 0.69/0.90 tff(467,plain,((~hskp24) | hskp14 | (~c2_1(a1215)) | c3_1(a1215) | (~c0_1(a1215))), inference(lemma,lemma(discharge,[]))).
% 0.69/0.90 tff(468,plain,
% 0.69/0.90 (~hskp24),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[467, 427, 127, 126, 321])).
% 0.69/0.90 tff(469,plain,
% 0.69/0.90 ((hskp24 | hskp19 | hskp14) <=> (hskp24 | hskp19 | hskp14)),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(470,plain,
% 0.69/0.90 (((hskp24 | hskp19) | hskp14) <=> (hskp24 | hskp19 | hskp14)),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(471,plain,
% 0.69/0.90 ((hskp24 | hskp19) <=> (hskp24 | hskp19)),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(472,plain,
% 0.69/0.90 (((hskp24 | hskp19) | hskp14) <=> ((hskp24 | hskp19) | hskp14)),
% 0.69/0.90 inference(monotonicity,[status(thm)],[471])).
% 0.69/0.90 tff(473,plain,
% 0.69/0.90 (((hskp24 | hskp19) | hskp14) <=> (hskp24 | hskp19 | hskp14)),
% 0.69/0.90 inference(transitivity,[status(thm)],[472, 470])).
% 0.69/0.90 tff(474,axiom,((hskp24 | hskp19) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 0.69/0.90 tff(475,plain,
% 0.69/0.90 (hskp24 | hskp19 | hskp14),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.69/0.90 tff(476,plain,
% 0.69/0.90 (hskp24 | hskp19 | hskp14),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[475, 469])).
% 0.69/0.90 tff(477,plain,
% 0.69/0.90 (hskp24 | hskp19 | hskp14),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[476, 469])).
% 0.69/0.90 tff(478,plain,
% 0.69/0.90 (hskp24 | hskp19 | hskp14),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[477, 469])).
% 0.69/0.90 tff(479,plain,
% 0.69/0.90 (hskp24 | hskp19 | hskp14),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[478, 469])).
% 0.69/0.90 tff(480,plain,
% 0.69/0.90 (hskp19),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[479, 468, 427])).
% 0.69/0.90 tff(481,plain,
% 0.69/0.90 (^[U: $i] : refl((hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.69/0.90 inference(bind,[status(th)],[])).
% 0.69/0.90 tff(482,plain,
% 0.69/0.90 (![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.90 inference(quant_intro,[status(thm)],[481])).
% 0.69/0.90 tff(483,plain,
% 0.69/0.90 (![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(484,plain,
% 0.69/0.90 (^[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)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) | hskp8) <=> ((hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8))), rewrite(((hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) | hskp8) <=> (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.69/0.90 inference(bind,[status(th)],[])).
% 0.69/0.90 tff(485,plain,
% 0.69/0.90 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) | hskp8) <=> ![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.90 inference(quant_intro,[status(thm)],[484])).
% 0.69/0.90 tff(486,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 0.69/0.90 tff(487,plain,
% 0.69/0.90 (![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.69/0.90 tff(488,plain,
% 0.69/0.90 (![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[487, 483])).
% 0.69/0.90 tff(489,plain,(
% 0.69/0.90 ![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.90 inference(skolemize,[status(sab)],[488])).
% 0.69/0.90 tff(490,plain,
% 0.69/0.90 (![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[489, 482])).
% 0.69/0.90 tff(491,assumption,(hskp19), introduced(assumption)).
% 0.69/0.90 tff(492,plain,
% 0.69/0.90 (((~hskp19) | (~c2_1(a1247))) <=> ((~hskp19) | (~c2_1(a1247)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(493,plain,
% 0.69/0.90 (((~c2_1(a1247)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a1247)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(494,axiom,((~c2_1(a1247)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.69/0.90 tff(495,plain,
% 0.69/0.90 ((~hskp19) | (~c2_1(a1247))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.69/0.90 tff(496,plain,
% 0.69/0.90 ((~hskp19) | (~c2_1(a1247))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[495, 492])).
% 0.69/0.90 tff(497,plain,
% 0.69/0.90 (~c2_1(a1247)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[496, 491])).
% 0.69/0.90 tff(498,plain,
% 0.69/0.90 (((~hskp19) | c1_1(a1247)) <=> ((~hskp19) | c1_1(a1247))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(499,axiom,((~hskp19) | c1_1(a1247)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.69/0.90 tff(500,plain,
% 0.69/0.90 ((~hskp19) | c1_1(a1247)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.69/0.90 tff(501,plain,
% 0.69/0.90 ((~hskp19) | c1_1(a1247)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[500, 498])).
% 0.69/0.90 tff(502,plain,
% 0.69/0.90 ((~hskp19) | c1_1(a1247)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[501, 498])).
% 0.69/0.90 tff(503,plain,
% 0.69/0.90 ((~hskp19) | c1_1(a1247)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[502, 498])).
% 0.69/0.90 tff(504,plain,
% 0.69/0.90 ((~hskp19) | c1_1(a1247)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[503, 498])).
% 0.69/0.90 tff(505,plain,
% 0.69/0.90 (c1_1(a1247)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[504, 491])).
% 0.69/0.90 tff(506,assumption,(~hskp8), introduced(assumption)).
% 0.69/0.90 tff(507,plain,
% 0.69/0.90 (((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | c2_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)))) <=> ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp8 | c2_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(508,plain,
% 0.69/0.90 ((hskp11 | hskp8 | (~ndr1_0) | c2_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247))) <=> (hskp11 | hskp8 | c2_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(509,plain,
% 0.69/0.90 (((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | (~ndr1_0) | c2_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)))) <=> ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | c2_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247))))),
% 0.69/0.90 inference(monotonicity,[status(thm)],[508])).
% 0.69/0.90 tff(510,plain,
% 0.69/0.90 (((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | (~ndr1_0) | c2_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)))) <=> ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp8 | c2_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 0.69/0.90 inference(transitivity,[status(thm)],[509, 507])).
% 0.69/0.90 tff(511,plain,
% 0.69/0.90 ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | (~ndr1_0) | c2_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(512,plain,
% 0.69/0.90 ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp8 | c2_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.69/0.90 tff(513,plain,
% 0.69/0.90 (~c0_1(a1247)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[512, 159, 303, 506, 505, 497, 490])).
% 0.69/0.90 tff(514,plain,
% 0.69/0.90 (((~hskp19) | (~c3_1(a1247))) <=> ((~hskp19) | (~c3_1(a1247)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(515,plain,
% 0.69/0.90 (((~c3_1(a1247)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a1247)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(516,axiom,((~c3_1(a1247)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.69/0.90 tff(517,plain,
% 0.69/0.90 ((~hskp19) | (~c3_1(a1247))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.69/0.90 tff(518,plain,
% 0.69/0.90 ((~hskp19) | (~c3_1(a1247))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[517, 514])).
% 0.69/0.90 tff(519,plain,
% 0.69/0.90 (~c3_1(a1247)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[518, 491])).
% 0.69/0.90 tff(520,plain,
% 0.69/0.90 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c0_1(a1247))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c0_1(a1247))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(521,plain,
% 0.69/0.90 ((hskp28 | (~ndr1_0) | c3_1(a1247) | c2_1(a1247) | c0_1(a1247)) <=> (hskp28 | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c0_1(a1247))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(522,plain,
% 0.69/0.90 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1247) | c2_1(a1247) | c0_1(a1247))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c0_1(a1247)))),
% 0.69/0.90 inference(monotonicity,[status(thm)],[521])).
% 0.69/0.90 tff(523,plain,
% 0.69/0.90 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1247) | c2_1(a1247) | c0_1(a1247))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c0_1(a1247))),
% 0.69/0.90 inference(transitivity,[status(thm)],[522, 520])).
% 0.69/0.90 tff(524,plain,
% 0.69/0.90 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1247) | c2_1(a1247) | c0_1(a1247))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(525,plain,
% 0.69/0.90 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c0_1(a1247)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.69/0.90 tff(526,plain,
% 0.69/0.90 ($false),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[525, 198, 159, 497, 519, 197, 513])).
% 0.69/0.90 tff(527,plain,((~hskp19) | hskp28 | hskp11 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.69/0.90 tff(528,plain,
% 0.69/0.90 (hskp8),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[527, 480, 303, 198])).
% 0.69/0.90 tff(529,plain,
% 0.69/0.90 (((~hskp8) | (~c0_1(a1217))) <=> ((~hskp8) | (~c0_1(a1217)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(530,plain,
% 0.69/0.90 (((~c0_1(a1217)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a1217)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(531,axiom,((~c0_1(a1217)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 0.69/0.90 tff(532,plain,
% 0.69/0.90 ((~hskp8) | (~c0_1(a1217))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.69/0.90 tff(533,plain,
% 0.69/0.90 ((~hskp8) | (~c0_1(a1217))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[532, 529])).
% 0.69/0.90 tff(534,plain,
% 0.69/0.90 (~c0_1(a1217)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[533, 528])).
% 0.69/0.90 tff(535,plain,
% 0.69/0.90 (((~hskp8) | (~c3_1(a1217))) <=> ((~hskp8) | (~c3_1(a1217)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(536,plain,
% 0.69/0.90 (((~c3_1(a1217)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a1217)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(537,axiom,((~c3_1(a1217)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.69/0.90 tff(538,plain,
% 0.69/0.90 ((~hskp8) | (~c3_1(a1217))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.69/0.90 tff(539,plain,
% 0.69/0.90 ((~hskp8) | (~c3_1(a1217))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[538, 535])).
% 0.69/0.90 tff(540,plain,
% 0.69/0.90 (~c3_1(a1217)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[539, 528])).
% 0.69/0.90 tff(541,assumption,(~c0_1(a1217)), introduced(assumption)).
% 0.69/0.90 tff(542,assumption,(~c3_1(a1217)), introduced(assumption)).
% 0.69/0.90 tff(543,plain,
% 0.69/0.90 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(544,plain,
% 0.69/0.90 ((hskp11 | (~ndr1_0) | c3_1(a1217) | c0_1(a1217) | (~c2_1(a1217))) <=> (hskp11 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(545,plain,
% 0.69/0.90 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1217) | c0_1(a1217) | (~c2_1(a1217)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217))))),
% 0.69/0.90 inference(monotonicity,[status(thm)],[544])).
% 0.69/0.90 tff(546,plain,
% 0.69/0.90 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1217) | c0_1(a1217) | (~c2_1(a1217)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)))),
% 0.69/0.90 inference(transitivity,[status(thm)],[545, 543])).
% 0.69/0.90 tff(547,plain,
% 0.69/0.90 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1217) | c0_1(a1217) | (~c2_1(a1217)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(548,plain,
% 0.69/0.90 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.69/0.90 tff(549,plain,
% 0.69/0.90 (c0_1(a1217) | (~c2_1(a1217))),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[548, 159, 303, 542, 313])).
% 0.69/0.90 tff(550,plain,
% 0.69/0.90 (~c2_1(a1217)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[549, 541])).
% 0.69/0.90 tff(551,plain,
% 0.69/0.90 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | c2_1(a1217))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | c2_1(a1217))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(552,plain,
% 0.69/0.90 ((hskp28 | (~ndr1_0) | c3_1(a1217) | c2_1(a1217) | c0_1(a1217)) <=> (hskp28 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | c2_1(a1217))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(553,plain,
% 0.69/0.90 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1217) | c2_1(a1217) | c0_1(a1217))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | c2_1(a1217)))),
% 0.69/0.90 inference(monotonicity,[status(thm)],[552])).
% 0.69/0.90 tff(554,plain,
% 0.69/0.90 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1217) | c2_1(a1217) | c0_1(a1217))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | c2_1(a1217))),
% 0.69/0.90 inference(transitivity,[status(thm)],[553, 551])).
% 0.69/0.90 tff(555,plain,
% 0.69/0.90 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1217) | c2_1(a1217) | c0_1(a1217))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(556,plain,
% 0.69/0.90 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | c2_1(a1217)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.69/0.90 tff(557,plain,
% 0.69/0.90 (c0_1(a1217) | c2_1(a1217)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[556, 198, 159, 542, 197])).
% 0.69/0.90 tff(558,plain,
% 0.69/0.90 ($false),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[557, 550, 541])).
% 0.69/0.90 tff(559,plain,(c0_1(a1217) | hskp28 | c3_1(a1217) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.69/0.90 tff(560,plain,
% 0.69/0.90 ($false),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[559, 540, 534, 198, 303])).
% 0.69/0.90 tff(561,plain,(hskp11 | hskp28 | (~c2_1(a1215)) | c3_1(a1215) | (~c1_1(a1215)) | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.69/0.90 tff(562,plain,
% 0.69/0.90 (hskp11),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[561, 198, 106, 90, 98, 75])).
% 0.69/0.90 tff(563,plain,
% 0.69/0.90 (((~hskp11) | (~c2_1(a1224))) <=> ((~hskp11) | (~c2_1(a1224)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(564,plain,
% 0.69/0.90 (((~c2_1(a1224)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a1224)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(565,axiom,((~c2_1(a1224)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.69/0.90 tff(566,plain,
% 0.69/0.90 ((~hskp11) | (~c2_1(a1224))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.69/0.90 tff(567,plain,
% 0.69/0.90 ((~hskp11) | (~c2_1(a1224))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[566, 563])).
% 0.69/0.90 tff(568,plain,
% 0.69/0.90 (~c2_1(a1224)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[567, 562])).
% 0.69/0.90 tff(569,plain,
% 0.69/0.90 (((~hskp11) | c3_1(a1224)) <=> ((~hskp11) | c3_1(a1224))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(570,axiom,((~hskp11) | c3_1(a1224)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.69/0.90 tff(571,plain,
% 0.69/0.90 ((~hskp11) | c3_1(a1224)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.69/0.90 tff(572,plain,
% 0.69/0.90 ((~hskp11) | c3_1(a1224)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[571, 569])).
% 0.69/0.90 tff(573,plain,
% 0.69/0.90 ((~hskp11) | c3_1(a1224)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[572, 569])).
% 0.69/0.90 tff(574,plain,
% 0.69/0.90 ((~hskp11) | c3_1(a1224)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[573, 569])).
% 0.69/0.90 tff(575,plain,
% 0.69/0.90 ((~hskp11) | c3_1(a1224)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[574, 569])).
% 0.69/0.90 tff(576,plain,
% 0.69/0.90 (c3_1(a1224)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[575, 562])).
% 0.69/0.90 tff(577,plain,
% 0.69/0.90 (((~hskp11) | c1_1(a1224)) <=> ((~hskp11) | c1_1(a1224))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(578,axiom,((~hskp11) | c1_1(a1224)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.69/0.90 tff(579,plain,
% 0.69/0.90 ((~hskp11) | c1_1(a1224)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.69/0.90 tff(580,plain,
% 0.69/0.90 ((~hskp11) | c1_1(a1224)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[579, 577])).
% 0.69/0.90 tff(581,plain,
% 0.69/0.90 ((~hskp11) | c1_1(a1224)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[580, 577])).
% 0.69/0.90 tff(582,plain,
% 0.69/0.90 ((~hskp11) | c1_1(a1224)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[581, 577])).
% 0.69/0.90 tff(583,plain,
% 0.69/0.90 ((~hskp11) | c1_1(a1224)),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[582, 577])).
% 0.69/0.90 tff(584,plain,
% 0.69/0.90 (c1_1(a1224)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[583, 562])).
% 0.69/0.90 tff(585,assumption,(~c2_1(a1224)), introduced(assumption)).
% 0.69/0.90 tff(586,assumption,(c3_1(a1224)), introduced(assumption)).
% 0.69/0.90 tff(587,assumption,(c1_1(a1224)), introduced(assumption)).
% 0.69/0.90 tff(588,plain,
% 0.69/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(589,plain,
% 0.69/0.90 (((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224))) <=> (c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(590,plain,
% 0.69/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 0.69/0.90 inference(monotonicity,[status(thm)],[589])).
% 0.69/0.90 tff(591,plain,
% 0.69/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.69/0.90 inference(transitivity,[status(thm)],[590, 588])).
% 0.69/0.90 tff(592,plain,
% 0.69/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(593,plain,
% 0.69/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.69/0.90 tff(594,plain,
% 0.69/0.90 ((~c0_1(a1215)) | c0_1(a1224)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[593, 159, 587, 586, 128, 127, 585, 352])).
% 0.69/0.90 tff(595,plain,
% 0.69/0.90 (c0_1(a1224)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[594, 342])).
% 0.69/0.90 tff(596,plain,
% 0.69/0.90 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(597,plain,
% 0.69/0.90 ((hskp5 | (~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205))) <=> (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(598,plain,
% 0.69/0.90 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 0.69/0.90 inference(monotonicity,[status(thm)],[597])).
% 0.69/0.90 tff(599,plain,
% 0.69/0.90 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.69/0.90 inference(transitivity,[status(thm)],[598, 596])).
% 0.69/0.90 tff(600,plain,
% 0.69/0.90 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(601,plain,
% 0.69/0.90 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.69/0.90 tff(602,plain,
% 0.69/0.90 ((~c3_1(a1205)) | (~c0_1(a1224))),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[601, 159, 21, 587, 586, 22, 23, 20])).
% 0.69/0.90 tff(603,plain,
% 0.69/0.90 (~c3_1(a1205)),
% 0.69/0.90 inference(unit_resolution,[status(thm)],[602, 595])).
% 0.69/0.90 tff(604,plain,
% 0.69/0.90 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.69/0.90 inference(bind,[status(th)],[])).
% 0.69/0.90 tff(605,plain,
% 0.69/0.90 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.69/0.90 inference(quant_intro,[status(thm)],[604])).
% 0.69/0.90 tff(606,plain,
% 0.69/0.90 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(607,plain,
% 0.69/0.90 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.69/0.90 inference(bind,[status(th)],[])).
% 0.69/0.90 tff(608,plain,
% 0.69/0.90 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.69/0.90 inference(quant_intro,[status(thm)],[607])).
% 0.69/0.90 tff(609,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 0.69/0.90 tff(610,plain,
% 0.69/0.90 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[609, 608])).
% 0.69/0.90 tff(611,plain,
% 0.69/0.90 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[610, 606])).
% 0.69/0.90 tff(612,plain,(
% 0.69/0.90 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.69/0.90 inference(skolemize,[status(sab)],[611])).
% 0.69/0.90 tff(613,plain,
% 0.69/0.90 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.69/0.90 inference(modus_ponens,[status(thm)],[612, 605])).
% 0.69/0.90 tff(614,assumption,(c2_1(a1205)), introduced(assumption)).
% 0.69/0.90 tff(615,plain,
% 0.69/0.90 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(616,plain,
% 0.69/0.90 ((hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205))) <=> (hskp14 | c2_1(a1224) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.69/0.90 inference(rewrite,[status(thm)],[])).
% 0.69/0.90 tff(617,plain,
% 0.69/0.90 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 0.69/0.90 inference(monotonicity,[status(thm)],[616])).
% 0.69/0.90 tff(618,plain,
% 0.69/0.90 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.69/0.90 inference(transitivity,[status(thm)],[617, 615])).
% 0.69/0.90 tff(619,plain,
% 0.69/0.90 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205)))),
% 0.69/0.90 inference(quant_inst,[status(thm)],[])).
% 0.69/0.90 tff(620,plain,
% 0.69/0.90 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.69/0.91 tff(621,plain,
% 0.69/0.91 (hskp14),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[620, 159, 587, 586, 614, 585, 23, 613, 603])).
% 0.69/0.91 tff(622,plain,
% 0.69/0.91 (~c2_1(a1232)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[385, 621])).
% 0.69/0.91 tff(623,plain,
% 0.69/0.91 (~c0_1(a1232)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[417, 621])).
% 0.69/0.91 tff(624,plain,
% 0.69/0.91 (c3_1(a1232)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[393, 621])).
% 0.69/0.91 tff(625,plain,
% 0.69/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(626,plain,
% 0.69/0.91 (((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(627,plain,
% 0.69/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232))))),
% 0.69/0.91 inference(monotonicity,[status(thm)],[626])).
% 0.69/0.91 tff(628,plain,
% 0.69/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 0.69/0.91 inference(transitivity,[status(thm)],[627, 625])).
% 0.69/0.91 tff(629,plain,
% 0.69/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(630,plain,
% 0.69/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.69/0.91 tff(631,plain,
% 0.69/0.91 ($false),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[630, 159, 624, 587, 586, 128, 127, 623, 622, 585, 352, 342])).
% 0.69/0.91 tff(632,plain,((~c0_1(a1215)) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1224) | (~c2_1(a1205)) | c1_1(a1205) | hskp5 | c0_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.91 tff(633,plain,
% 0.69/0.91 (~c0_1(a1215)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[632, 584, 576, 98, 106, 568, 302, 23, 21, 22])).
% 0.69/0.91 tff(634,assumption,(hskp26), introduced(assumption)).
% 0.69/0.91 tff(635,plain,
% 0.69/0.91 (((~hskp26) | c2_1(a1208)) <=> ((~hskp26) | c2_1(a1208))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(636,axiom,((~hskp26) | c2_1(a1208)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 0.69/0.91 tff(637,plain,
% 0.69/0.91 ((~hskp26) | c2_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[636, 635])).
% 0.69/0.91 tff(638,plain,
% 0.69/0.91 ((~hskp26) | c2_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[637, 635])).
% 0.69/0.91 tff(639,plain,
% 0.69/0.91 ((~hskp26) | c2_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[638, 635])).
% 0.69/0.91 tff(640,plain,
% 0.69/0.91 ((~hskp26) | c2_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[639, 635])).
% 0.69/0.91 tff(641,plain,
% 0.69/0.91 ((~hskp26) | c2_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[640, 635])).
% 0.69/0.91 tff(642,plain,
% 0.69/0.91 (c2_1(a1208)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[641, 634])).
% 0.69/0.91 tff(643,plain,
% 0.69/0.91 (((~hskp26) | c1_1(a1208)) <=> ((~hskp26) | c1_1(a1208))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(644,axiom,((~hskp26) | c1_1(a1208)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.69/0.91 tff(645,plain,
% 0.69/0.91 ((~hskp26) | c1_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[644, 643])).
% 0.69/0.91 tff(646,plain,
% 0.69/0.91 ((~hskp26) | c1_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[645, 643])).
% 0.69/0.91 tff(647,plain,
% 0.69/0.91 ((~hskp26) | c1_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[646, 643])).
% 0.69/0.91 tff(648,plain,
% 0.69/0.91 ((~hskp26) | c1_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[647, 643])).
% 0.69/0.91 tff(649,plain,
% 0.69/0.91 ((~hskp26) | c1_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[648, 643])).
% 0.69/0.91 tff(650,plain,
% 0.69/0.91 (c1_1(a1208)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[649, 634])).
% 0.69/0.91 tff(651,plain,
% 0.69/0.91 (((~hskp26) | c0_1(a1208)) <=> ((~hskp26) | c0_1(a1208))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(652,axiom,((~hskp26) | c0_1(a1208)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.69/0.91 tff(653,plain,
% 0.69/0.91 ((~hskp26) | c0_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.69/0.91 tff(654,plain,
% 0.69/0.91 ((~hskp26) | c0_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[653, 651])).
% 0.69/0.91 tff(655,plain,
% 0.69/0.91 ((~hskp26) | c0_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[654, 651])).
% 0.69/0.91 tff(656,plain,
% 0.69/0.91 ((~hskp26) | c0_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[655, 651])).
% 0.69/0.91 tff(657,plain,
% 0.69/0.91 ((~hskp26) | c0_1(a1208)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[656, 651])).
% 0.69/0.91 tff(658,plain,
% 0.69/0.91 (c0_1(a1208)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[657, 634])).
% 0.69/0.91 tff(659,plain,
% 0.69/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(660,plain,
% 0.69/0.91 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224))) <=> (c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(661,plain,
% 0.69/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 0.69/0.91 inference(monotonicity,[status(thm)],[660])).
% 0.69/0.91 tff(662,plain,
% 0.69/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.69/0.91 inference(transitivity,[status(thm)],[661, 659])).
% 0.69/0.91 tff(663,plain,
% 0.69/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(664,plain,
% 0.69/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[663, 662])).
% 0.69/0.91 tff(665,plain,
% 0.69/0.91 (c0_1(a1224)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[664, 159, 658, 650, 642, 587, 586, 585, 352])).
% 0.69/0.91 tff(666,plain,
% 0.69/0.91 (~c3_1(a1205)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[602, 665])).
% 0.69/0.91 tff(667,plain,
% 0.69/0.91 (hskp14),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[620, 159, 587, 586, 614, 585, 23, 613, 666])).
% 0.69/0.91 tff(668,plain,
% 0.69/0.91 (~c2_1(a1232)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[385, 667])).
% 0.69/0.91 tff(669,plain,
% 0.69/0.91 (~c0_1(a1232)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[417, 667])).
% 0.69/0.91 tff(670,plain,
% 0.69/0.91 (c3_1(a1232)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[393, 667])).
% 0.69/0.91 tff(671,plain,
% 0.69/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(672,plain,
% 0.69/0.91 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(673,plain,
% 0.69/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232))))),
% 0.69/0.91 inference(monotonicity,[status(thm)],[672])).
% 0.69/0.91 tff(674,plain,
% 0.69/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 0.69/0.91 inference(transitivity,[status(thm)],[673, 671])).
% 0.69/0.91 tff(675,plain,
% 0.69/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(676,plain,
% 0.69/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.69/0.91 tff(677,plain,
% 0.69/0.91 ($false),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[676, 159, 658, 650, 642, 670, 587, 586, 669, 668, 585, 352])).
% 0.69/0.91 tff(678,plain,((~hskp26) | (~c1_1(a1224)) | (~c3_1(a1224)) | c2_1(a1224) | (~c2_1(a1205)) | c1_1(a1205) | hskp5 | c0_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.91 tff(679,plain,
% 0.69/0.91 (~hskp26),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[678, 584, 576, 568, 302, 23, 21, 22])).
% 0.69/0.91 tff(680,plain,
% 0.69/0.91 (hskp24),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[157, 679, 198])).
% 0.69/0.91 tff(681,plain,
% 0.69/0.91 (~c2_1(a1267)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[443, 680])).
% 0.69/0.91 tff(682,plain,
% 0.69/0.91 (~c1_1(a1267)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[449, 680])).
% 0.69/0.91 tff(683,plain,
% 0.69/0.91 (c0_1(a1267)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[457, 680])).
% 0.69/0.91 tff(684,assumption,(hskp25), introduced(assumption)).
% 0.69/0.91 tff(685,plain,
% 0.69/0.91 (((~hskp25) | c0_1(a1204)) <=> ((~hskp25) | c0_1(a1204))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(686,axiom,((~hskp25) | c0_1(a1204)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.69/0.91 tff(687,plain,
% 0.69/0.91 ((~hskp25) | c0_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[686, 685])).
% 0.69/0.91 tff(688,plain,
% 0.69/0.91 ((~hskp25) | c0_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[687, 685])).
% 0.69/0.91 tff(689,plain,
% 0.69/0.91 ((~hskp25) | c0_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[688, 685])).
% 0.69/0.91 tff(690,plain,
% 0.69/0.91 ((~hskp25) | c0_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[689, 685])).
% 0.69/0.91 tff(691,plain,
% 0.69/0.91 ((~hskp25) | c0_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[690, 685])).
% 0.69/0.91 tff(692,plain,
% 0.69/0.91 (c0_1(a1204)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[691, 684])).
% 0.69/0.91 tff(693,assumption,(~c0_1(a1215)), introduced(assumption)).
% 0.69/0.91 tff(694,plain,
% 0.69/0.91 (((~hskp25) | c2_1(a1204)) <=> ((~hskp25) | c2_1(a1204))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(695,axiom,((~hskp25) | c2_1(a1204)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.69/0.91 tff(696,plain,
% 0.69/0.91 ((~hskp25) | c2_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.69/0.91 tff(697,plain,
% 0.69/0.91 ((~hskp25) | c2_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[696, 694])).
% 0.69/0.91 tff(698,plain,
% 0.69/0.91 ((~hskp25) | c2_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[697, 694])).
% 0.69/0.91 tff(699,plain,
% 0.69/0.91 ((~hskp25) | c2_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[698, 694])).
% 0.69/0.91 tff(700,plain,
% 0.69/0.91 ((~hskp25) | c2_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[699, 694])).
% 0.69/0.91 tff(701,plain,
% 0.69/0.91 (c2_1(a1204)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[700, 684])).
% 0.69/0.91 tff(702,plain,
% 0.69/0.91 (((~hskp25) | c3_1(a1204)) <=> ((~hskp25) | c3_1(a1204))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(703,axiom,((~hskp25) | c3_1(a1204)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.69/0.91 tff(704,plain,
% 0.69/0.91 ((~hskp25) | c3_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[703, 702])).
% 0.69/0.91 tff(705,plain,
% 0.69/0.91 ((~hskp25) | c3_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[704, 702])).
% 0.69/0.91 tff(706,plain,
% 0.69/0.91 ((~hskp25) | c3_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[705, 702])).
% 0.69/0.91 tff(707,plain,
% 0.69/0.91 ((~hskp25) | c3_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[706, 702])).
% 0.69/0.91 tff(708,plain,
% 0.69/0.91 ((~hskp25) | c3_1(a1204)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[707, 702])).
% 0.69/0.91 tff(709,plain,
% 0.69/0.91 (c3_1(a1204)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[708, 684])).
% 0.69/0.91 tff(710,plain,
% 0.69/0.91 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.69/0.91 inference(bind,[status(th)],[])).
% 0.69/0.91 tff(711,plain,
% 0.69/0.91 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(quant_intro,[status(thm)],[710])).
% 0.69/0.91 tff(712,plain,
% 0.69/0.91 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(713,plain,
% 0.69/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.69/0.91 inference(bind,[status(th)],[])).
% 0.69/0.91 tff(714,plain,
% 0.69/0.91 (![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(quant_intro,[status(thm)],[713])).
% 0.69/0.91 tff(715,axiom,(![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 0.69/0.91 tff(716,plain,
% 0.69/0.91 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[715, 714])).
% 0.69/0.91 tff(717,plain,
% 0.69/0.91 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[716, 712])).
% 0.69/0.91 tff(718,plain,(
% 0.69/0.91 ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(skolemize,[status(sab)],[717])).
% 0.69/0.91 tff(719,plain,
% 0.69/0.91 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[718, 711])).
% 0.69/0.91 tff(720,plain,
% 0.69/0.91 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.69/0.91 inference(bind,[status(th)],[])).
% 0.69/0.91 tff(721,plain,
% 0.69/0.91 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(quant_intro,[status(thm)],[720])).
% 0.69/0.91 tff(722,plain,
% 0.69/0.91 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(723,plain,
% 0.69/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.69/0.91 inference(bind,[status(th)],[])).
% 0.69/0.91 tff(724,plain,
% 0.69/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(quant_intro,[status(thm)],[723])).
% 0.69/0.91 tff(725,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 0.69/0.91 tff(726,plain,
% 0.69/0.91 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[725, 724])).
% 0.69/0.91 tff(727,plain,
% 0.69/0.91 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[726, 722])).
% 0.69/0.91 tff(728,plain,(
% 0.69/0.91 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(skolemize,[status(sab)],[727])).
% 0.69/0.91 tff(729,plain,
% 0.69/0.91 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[728, 721])).
% 0.69/0.91 tff(730,assumption,(c3_1(a1204)), introduced(assumption)).
% 0.69/0.91 tff(731,assumption,(c2_1(a1204)), introduced(assumption)).
% 0.69/0.91 tff(732,assumption,(c0_1(a1204)), introduced(assumption)).
% 0.69/0.91 tff(733,plain,
% 0.69/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(734,plain,
% 0.69/0.91 ((hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215))) <=> (hskp9 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(735,plain,
% 0.69/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 0.69/0.91 inference(monotonicity,[status(thm)],[734])).
% 0.69/0.91 tff(736,plain,
% 0.69/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.69/0.91 inference(transitivity,[status(thm)],[735, 733])).
% 0.69/0.91 tff(737,plain,
% 0.69/0.91 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(738,plain,
% 0.69/0.91 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.69/0.91 tff(739,plain,
% 0.69/0.91 (hskp9 | c0_1(a1215)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[738, 159, 732, 731, 730, 128, 126, 729])).
% 0.69/0.91 tff(740,plain,
% 0.69/0.91 (hskp9),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[739, 693])).
% 0.69/0.91 tff(741,plain,
% 0.69/0.91 (((~hskp9) | c2_1(a1219)) <=> ((~hskp9) | c2_1(a1219))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(742,axiom,((~hskp9) | c2_1(a1219)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.69/0.91 tff(743,plain,
% 0.69/0.91 ((~hskp9) | c2_1(a1219)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[742, 741])).
% 0.69/0.91 tff(744,plain,
% 0.69/0.91 ((~hskp9) | c2_1(a1219)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[743, 741])).
% 0.69/0.91 tff(745,plain,
% 0.69/0.91 ((~hskp9) | c2_1(a1219)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[744, 741])).
% 0.69/0.91 tff(746,plain,
% 0.69/0.91 ((~hskp9) | c2_1(a1219)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[745, 741])).
% 0.69/0.91 tff(747,plain,
% 0.69/0.91 ((~hskp9) | c2_1(a1219)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[746, 741])).
% 0.69/0.91 tff(748,plain,
% 0.69/0.91 (c2_1(a1219)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[747, 740])).
% 0.69/0.91 tff(749,plain,
% 0.69/0.91 (((~hskp9) | c1_1(a1219)) <=> ((~hskp9) | c1_1(a1219))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(750,axiom,((~hskp9) | c1_1(a1219)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.69/0.91 tff(751,plain,
% 0.69/0.91 ((~hskp9) | c1_1(a1219)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[750, 749])).
% 0.69/0.91 tff(752,plain,
% 0.69/0.91 ((~hskp9) | c1_1(a1219)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[751, 749])).
% 0.69/0.91 tff(753,plain,
% 0.69/0.91 ((~hskp9) | c1_1(a1219)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[752, 749])).
% 0.69/0.91 tff(754,plain,
% 0.69/0.91 ((~hskp9) | c1_1(a1219)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[753, 749])).
% 0.69/0.91 tff(755,plain,
% 0.69/0.91 ((~hskp9) | c1_1(a1219)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[754, 749])).
% 0.69/0.91 tff(756,plain,
% 0.69/0.91 (c1_1(a1219)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[755, 740])).
% 0.69/0.91 tff(757,plain,
% 0.69/0.91 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(758,plain,
% 0.69/0.91 (((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215))) <=> (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(759,plain,
% 0.69/0.91 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219))))),
% 0.69/0.91 inference(monotonicity,[status(thm)],[758])).
% 0.69/0.91 tff(760,plain,
% 0.69/0.91 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)))),
% 0.69/0.91 inference(transitivity,[status(thm)],[759, 757])).
% 0.69/0.91 tff(761,plain,
% 0.69/0.91 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(762,plain,
% 0.69/0.91 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[761, 760])).
% 0.69/0.92 tff(763,plain,
% 0.69/0.92 (~c3_1(a1219)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[762, 159, 756, 748, 128, 126, 719, 693])).
% 0.69/0.92 tff(764,plain,
% 0.69/0.92 (((~hskp9) | (~c0_1(a1219))) <=> ((~hskp9) | (~c0_1(a1219)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(765,plain,
% 0.69/0.92 (((~c0_1(a1219)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a1219)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(766,axiom,((~c0_1(a1219)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 0.69/0.92 tff(767,plain,
% 0.69/0.92 ((~hskp9) | (~c0_1(a1219))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[766, 765])).
% 0.69/0.92 tff(768,plain,
% 0.69/0.92 ((~hskp9) | (~c0_1(a1219))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[767, 764])).
% 0.69/0.92 tff(769,plain,
% 0.69/0.92 (~c0_1(a1219)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[768, 740])).
% 0.69/0.92 tff(770,plain,
% 0.69/0.92 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(771,plain,
% 0.69/0.92 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215))) <=> (c3_1(a1215) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(772,plain,
% 0.69/0.92 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | c0_1(a1215) | (~c1_1(a1215))))),
% 0.69/0.92 inference(monotonicity,[status(thm)],[771])).
% 0.69/0.92 tff(773,plain,
% 0.69/0.92 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.69/0.92 inference(transitivity,[status(thm)],[772, 770])).
% 0.69/0.92 tff(774,plain,
% 0.69/0.92 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(775,plain,
% 0.69/0.92 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | c0_1(a1215) | (~c1_1(a1215))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[774, 773])).
% 0.69/0.92 tff(776,plain,
% 0.69/0.92 (~c3_1(a1208)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[775, 159, 650, 642, 128, 126, 719, 693])).
% 0.69/0.92 tff(777,plain,
% 0.69/0.92 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(778,plain,
% 0.69/0.92 (((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215))) <=> (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(779,plain,
% 0.69/0.92 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204))))),
% 0.69/0.92 inference(monotonicity,[status(thm)],[778])).
% 0.69/0.92 tff(780,plain,
% 0.69/0.92 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)))),
% 0.69/0.92 inference(transitivity,[status(thm)],[779, 777])).
% 0.69/0.92 tff(781,plain,
% 0.69/0.92 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(782,plain,
% 0.69/0.92 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[781, 780])).
% 0.69/0.92 tff(783,plain,
% 0.69/0.92 (c0_1(a1215) | (~c1_1(a1204))),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[782, 159, 731, 730, 128, 126, 719])).
% 0.69/0.92 tff(784,plain,
% 0.69/0.92 (~c1_1(a1204)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[783, 693])).
% 0.69/0.92 tff(785,plain,
% 0.69/0.92 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(786,plain,
% 0.69/0.92 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[785])).
% 0.69/0.92 tff(787,plain,
% 0.69/0.92 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(788,plain,
% 0.69/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | 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(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(789,plain,
% 0.69/0.92 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[788])).
% 0.69/0.92 tff(790,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.69/0.92 tff(791,plain,
% 0.69/0.92 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[790, 789])).
% 0.69/0.92 tff(792,plain,
% 0.69/0.92 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[791, 787])).
% 0.69/0.92 tff(793,plain,(
% 0.69/0.92 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.69/0.92 inference(skolemize,[status(sab)],[792])).
% 0.69/0.92 tff(794,plain,
% 0.69/0.92 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[793, 786])).
% 0.69/0.92 tff(795,plain,
% 0.69/0.92 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1224)) | (~c1_1(a1224)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1224)) | (~c1_1(a1224)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(796,plain,
% 0.69/0.92 ((hskp19 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204))) <=> (hskp19 | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1224)) | (~c1_1(a1224)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(797,plain,
% 0.69/0.92 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1224)) | (~c1_1(a1224)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204))))),
% 0.69/0.92 inference(monotonicity,[status(thm)],[796])).
% 0.69/0.92 tff(798,plain,
% 0.69/0.92 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1224)) | (~c1_1(a1224)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 0.69/0.92 inference(transitivity,[status(thm)],[797, 795])).
% 0.69/0.92 tff(799,plain,
% 0.69/0.92 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(800,plain,
% 0.69/0.92 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1224)) | (~c1_1(a1224)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.69/0.92 tff(801,plain,
% 0.69/0.92 (hskp19 | (~c0_1(a1224))),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[800, 159, 731, 730, 587, 585, 794, 784])).
% 0.69/0.92 tff(802,plain,
% 0.69/0.92 (hskp19),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[801, 665])).
% 0.69/0.92 tff(803,plain,
% 0.69/0.92 (~c3_1(a1247)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[518, 802])).
% 0.69/0.92 tff(804,plain,
% 0.69/0.92 (~c2_1(a1247)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[496, 802])).
% 0.69/0.92 tff(805,plain,
% 0.69/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)) | c0_1(a1247))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)) | c0_1(a1247))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(806,plain,
% 0.69/0.92 (((~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c3_1(a1208) | (~c1_1(a1208)) | (~c2_1(a1208)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247)) <=> (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)) | c0_1(a1247))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(807,plain,
% 0.69/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c3_1(a1208) | (~c1_1(a1208)) | (~c2_1(a1208)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)) | c0_1(a1247)))),
% 0.69/0.92 inference(monotonicity,[status(thm)],[806])).
% 0.69/0.92 tff(808,plain,
% 0.69/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c3_1(a1208) | (~c1_1(a1208)) | (~c2_1(a1208)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)) | c0_1(a1247))),
% 0.69/0.92 inference(transitivity,[status(thm)],[807, 805])).
% 0.69/0.92 tff(809,plain,
% 0.69/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c3_1(a1208) | (~c1_1(a1208)) | (~c2_1(a1208)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(810,plain,
% 0.69/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)) | c0_1(a1247)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[809, 808])).
% 0.69/0.92 tff(811,plain,
% 0.69/0.92 (c0_1(a1247)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[810, 159, 650, 642, 587, 586, 804, 803, 74, 665, 776])).
% 0.69/0.92 tff(812,plain,
% 0.69/0.92 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(813,plain,
% 0.69/0.92 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[812])).
% 0.69/0.92 tff(814,plain,
% 0.69/0.92 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(815,plain,
% 0.69/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(816,plain,
% 0.69/0.92 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[815])).
% 0.69/0.92 tff(817,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 0.69/0.92 tff(818,plain,
% 0.69/0.92 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[817, 816])).
% 0.69/0.92 tff(819,plain,
% 0.69/0.92 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[818, 814])).
% 0.69/0.92 tff(820,plain,(
% 0.69/0.92 ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.92 inference(skolemize,[status(sab)],[819])).
% 0.69/0.92 tff(821,plain,
% 0.69/0.92 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[820, 813])).
% 0.69/0.92 tff(822,plain,
% 0.69/0.92 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1247)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1247)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(823,plain,
% 0.69/0.92 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1247) | c2_1(a1247) | (~c0_1(a1247))) <=> (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1247)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(824,plain,
% 0.69/0.92 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1247) | c2_1(a1247) | (~c0_1(a1247)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1247))))),
% 0.69/0.92 inference(monotonicity,[status(thm)],[823])).
% 0.69/0.92 tff(825,plain,
% 0.69/0.92 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1247) | c2_1(a1247) | (~c0_1(a1247)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1247)))),
% 0.69/0.92 inference(transitivity,[status(thm)],[824, 822])).
% 0.69/0.92 tff(826,plain,
% 0.69/0.92 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1247) | c2_1(a1247) | (~c0_1(a1247)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(827,plain,
% 0.69/0.92 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1247))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[826, 825])).
% 0.69/0.92 tff(828,plain,
% 0.69/0.92 ($false),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[827, 159, 658, 650, 642, 804, 803, 821, 811])).
% 0.69/0.92 tff(829,plain,((~hskp26) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c2_1(a1204)) | (~c3_1(a1204)) | c2_1(a1224) | (~c1_1(a1215)) | c3_1(a1215) | c0_1(a1215)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.92 tff(830,plain,
% 0.69/0.92 (~hskp26),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[829, 693, 586, 731, 730, 585, 128, 126, 587])).
% 0.69/0.92 tff(831,plain,
% 0.69/0.92 (hskp24),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[157, 830, 198])).
% 0.69/0.92 tff(832,plain,
% 0.69/0.92 (~c2_1(a1267)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[443, 831])).
% 0.69/0.92 tff(833,plain,
% 0.69/0.92 (~c1_1(a1267)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[449, 831])).
% 0.69/0.92 tff(834,plain,
% 0.69/0.92 (c0_1(a1267)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[457, 831])).
% 0.69/0.92 tff(835,assumption,(~c3_1(a1267)), introduced(assumption)).
% 0.69/0.92 tff(836,assumption,(~c3_1(a1219)), introduced(assumption)).
% 0.69/0.92 tff(837,plain,
% 0.69/0.92 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(838,plain,
% 0.69/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[837])).
% 0.69/0.92 tff(839,plain,
% 0.69/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(840,plain,
% 0.69/0.92 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(841,plain,
% 0.69/0.92 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[840])).
% 0.69/0.92 tff(842,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 0.69/0.92 tff(843,plain,
% 0.69/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[842, 841])).
% 0.69/0.92 tff(844,plain,
% 0.69/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[843, 839])).
% 0.69/0.92 tff(845,plain,(
% 0.69/0.92 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.69/0.92 inference(skolemize,[status(sab)],[844])).
% 0.69/0.92 tff(846,plain,
% 0.69/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[845, 838])).
% 0.69/0.92 tff(847,assumption,(~c0_1(a1219)), introduced(assumption)).
% 0.69/0.92 tff(848,assumption,(~c2_1(a1267)), introduced(assumption)).
% 0.69/0.92 tff(849,assumption,(~c1_1(a1267)), introduced(assumption)).
% 0.69/0.92 tff(850,assumption,(c1_1(a1219)), introduced(assumption)).
% 0.69/0.92 tff(851,assumption,(c0_1(a1267)), introduced(assumption)).
% 0.69/0.92 tff(852,plain,
% 0.69/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1267)) | c3_1(a1267))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1267)) | c3_1(a1267))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(853,plain,
% 0.69/0.92 (((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219))) <=> (c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1267)) | c3_1(a1267))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(854,plain,
% 0.69/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1267)) | c3_1(a1267)))),
% 0.69/0.92 inference(monotonicity,[status(thm)],[853])).
% 0.69/0.92 tff(855,plain,
% 0.69/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1267)) | c3_1(a1267))),
% 0.69/0.92 inference(transitivity,[status(thm)],[854, 852])).
% 0.69/0.92 tff(856,plain,
% 0.69/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(857,plain,
% 0.69/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1267)) | c3_1(a1267)),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[856, 855])).
% 0.69/0.93 tff(858,plain,
% 0.69/0.93 ($false),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[857, 159, 851, 850, 849, 848, 847, 846, 836, 835])).
% 0.69/0.93 tff(859,plain,(c3_1(a1267) | (~c0_1(a1267)) | (~c1_1(a1219)) | c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | c3_1(a1219)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.93 tff(860,plain,
% 0.69/0.93 (c3_1(a1267)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[859, 834, 756, 833, 832, 769, 763])).
% 0.69/0.93 tff(861,plain,
% 0.69/0.93 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.69/0.93 inference(bind,[status(th)],[])).
% 0.69/0.93 tff(862,plain,
% 0.69/0.93 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.69/0.93 inference(quant_intro,[status(thm)],[861])).
% 0.69/0.93 tff(863,plain,
% 0.69/0.93 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(864,plain,
% 0.69/0.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.69/0.93 inference(bind,[status(th)],[])).
% 0.69/0.93 tff(865,plain,
% 0.69/0.93 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.69/0.93 inference(quant_intro,[status(thm)],[864])).
% 0.69/0.93 tff(866,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 0.69/0.93 tff(867,plain,
% 0.69/0.93 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[866, 865])).
% 0.69/0.93 tff(868,plain,
% 0.69/0.93 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[867, 863])).
% 0.69/0.93 tff(869,plain,(
% 0.69/0.93 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.69/0.93 inference(skolemize,[status(sab)],[868])).
% 0.69/0.93 tff(870,plain,
% 0.69/0.93 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[869, 862])).
% 0.69/0.93 tff(871,plain,
% 0.69/0.93 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.69/0.93 inference(bind,[status(th)],[])).
% 0.69/0.93 tff(872,plain,
% 0.69/0.93 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.93 inference(quant_intro,[status(thm)],[871])).
% 0.69/0.93 tff(873,plain,
% 0.69/0.93 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(874,plain,
% 0.69/0.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.69/0.93 inference(bind,[status(th)],[])).
% 0.69/0.93 tff(875,plain,
% 0.69/0.93 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.93 inference(quant_intro,[status(thm)],[874])).
% 0.69/0.93 tff(876,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.69/0.93 tff(877,plain,
% 0.69/0.93 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[876, 875])).
% 0.69/0.93 tff(878,plain,
% 0.69/0.93 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[877, 873])).
% 0.69/0.93 tff(879,plain,(
% 0.69/0.93 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.93 inference(skolemize,[status(sab)],[878])).
% 0.69/0.93 tff(880,plain,
% 0.69/0.93 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[879, 872])).
% 0.69/0.93 tff(881,plain,
% 0.69/0.93 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | c1_1(a1267) | c2_1(a1267) | (~ndr1_0) | (~c3_1(a1267)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp15 | hskp4 | c1_1(a1267) | c2_1(a1267) | (~ndr1_0) | (~c3_1(a1267)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(882,plain,
% 0.69/0.93 ((hskp15 | hskp4 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267))) <=> (hskp15 | hskp4 | c1_1(a1267) | c2_1(a1267) | (~ndr1_0) | (~c3_1(a1267)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(883,plain,
% 0.69/0.93 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | c1_1(a1267) | c2_1(a1267) | (~ndr1_0) | (~c3_1(a1267))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[882])).
% 0.77/0.93 tff(884,plain,
% 0.77/0.93 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp15 | hskp4 | c1_1(a1267) | c2_1(a1267) | (~ndr1_0) | (~c3_1(a1267)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[883, 881])).
% 0.77/0.93 tff(885,plain,
% 0.77/0.93 ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(886,plain,
% 0.77/0.93 ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp15 | hskp4 | c1_1(a1267) | c2_1(a1267) | (~ndr1_0) | (~c3_1(a1267))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[885, 884])).
% 0.77/0.93 tff(887,plain,
% 0.77/0.93 (hskp4 | (~c3_1(a1267))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[886, 159, 75, 833, 832, 379])).
% 0.77/0.93 tff(888,plain,
% 0.77/0.93 (hskp4),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[887, 860])).
% 0.77/0.93 tff(889,plain,
% 0.77/0.93 (~c2_1(a1211)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[327, 888])).
% 0.77/0.93 tff(890,plain,
% 0.77/0.93 (~c0_1(a1211)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[333, 888])).
% 0.77/0.93 tff(891,plain,
% 0.77/0.93 (c1_1(a1211)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[359, 888])).
% 0.77/0.93 tff(892,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c3_1(a1215) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c1_1(a1211)) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c3_1(a1215) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c1_1(a1211)) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(893,plain,
% 0.77/0.93 ((hskp8 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1211) | c2_1(a1211) | (~c1_1(a1211))) <=> (hskp8 | c3_1(a1215) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c1_1(a1211)) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(894,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1211) | c2_1(a1211) | (~c1_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c3_1(a1215) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c1_1(a1211)) | c0_1(a1215) | (~c1_1(a1215))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[893])).
% 0.77/0.93 tff(895,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1211) | c2_1(a1211) | (~c1_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c3_1(a1215) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c1_1(a1211)) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[894, 892])).
% 0.77/0.93 tff(896,plain,
% 0.77/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1211) | c2_1(a1211) | (~c1_1(a1211)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(897,plain,
% 0.77/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c3_1(a1215) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c1_1(a1211)) | c0_1(a1215) | (~c1_1(a1215))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[896, 895])).
% 0.77/0.93 tff(898,plain,
% 0.77/0.93 (hskp8),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[897, 159, 128, 891, 126, 890, 889, 880, 693])).
% 0.77/0.93 tff(899,plain,
% 0.77/0.93 (~c3_1(a1217)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[539, 898])).
% 0.77/0.93 tff(900,plain,
% 0.77/0.93 (((~hskp8) | (~c1_1(a1217))) <=> ((~hskp8) | (~c1_1(a1217)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(901,plain,
% 0.77/0.93 (((~c1_1(a1217)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a1217)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(902,axiom,((~c1_1(a1217)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.77/0.93 tff(903,plain,
% 0.77/0.93 ((~hskp8) | (~c1_1(a1217))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[902, 901])).
% 0.77/0.93 tff(904,plain,
% 0.77/0.93 ((~hskp8) | (~c1_1(a1217))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[903, 900])).
% 0.77/0.93 tff(905,plain,
% 0.77/0.93 (~c1_1(a1217)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[904, 898])).
% 0.77/0.93 tff(906,plain,
% 0.77/0.93 (~c0_1(a1217)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[533, 898])).
% 0.77/0.93 tff(907,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1217) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c3_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1217) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c3_1(a1267)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(908,plain,
% 0.77/0.93 ((hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1217) | c1_1(a1217) | c0_1(a1217)) <=> (hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1217) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c3_1(a1267)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(909,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1217) | c1_1(a1217) | c0_1(a1217))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1217) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c3_1(a1267))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[908])).
% 0.77/0.93 tff(910,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1217) | c1_1(a1217) | c0_1(a1217))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1217) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c3_1(a1267)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[909, 907])).
% 0.77/0.93 tff(911,plain,
% 0.77/0.93 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1217) | c1_1(a1217) | c0_1(a1217))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(912,plain,
% 0.77/0.93 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1217) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c3_1(a1267))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[911, 910])).
% 0.77/0.93 tff(913,plain,
% 0.77/0.93 ($false),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[912, 159, 830, 833, 832, 906, 905, 899, 870, 860])).
% 0.77/0.93 tff(914,plain,(c0_1(a1215) | (~c1_1(a1215)) | c3_1(a1215) | hskp15 | hskp28 | (~c3_1(a1224)) | (~c2_1(a1204)) | (~c3_1(a1204)) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1204))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.93 tff(915,plain,
% 0.77/0.93 ($false),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[914, 709, 701, 126, 75, 198, 586, 128, 693, 585, 587, 692])).
% 0.77/0.93 tff(916,plain,((~hskp25) | c3_1(a1215) | hskp15 | hskp28 | (~c3_1(a1224)) | (~c1_1(a1215)) | c0_1(a1215) | c2_1(a1224) | (~c1_1(a1224))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.93 tff(917,plain,
% 0.77/0.93 (~hskp25),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[916, 198, 75, 90, 576, 98, 633, 568, 584])).
% 0.77/0.93 tff(918,plain,
% 0.77/0.93 ((hskp25 | hskp26 | hskp1) <=> (hskp25 | hskp26 | hskp1)),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(919,plain,
% 0.77/0.93 (((hskp25 | hskp26) | hskp1) <=> (hskp25 | hskp26 | hskp1)),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(920,plain,
% 0.77/0.93 ((hskp26 | hskp25) <=> (hskp25 | hskp26)),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(921,plain,
% 0.77/0.93 (((hskp26 | hskp25) | hskp1) <=> ((hskp25 | hskp26) | hskp1)),
% 0.77/0.93 inference(monotonicity,[status(thm)],[920])).
% 0.77/0.93 tff(922,plain,
% 0.77/0.93 (((hskp26 | hskp25) | hskp1) <=> (hskp25 | hskp26 | hskp1)),
% 0.77/0.93 inference(transitivity,[status(thm)],[921, 919])).
% 0.77/0.93 tff(923,axiom,((hskp26 | hskp25) | hskp1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 0.77/0.93 tff(924,plain,
% 0.77/0.93 (hskp25 | hskp26 | hskp1),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[923, 922])).
% 0.77/0.93 tff(925,plain,
% 0.77/0.93 (hskp25 | hskp26 | hskp1),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[924, 918])).
% 0.77/0.93 tff(926,plain,
% 0.77/0.93 (hskp25 | hskp26 | hskp1),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[925, 918])).
% 0.77/0.93 tff(927,plain,
% 0.77/0.93 (hskp25 | hskp26 | hskp1),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[926, 918])).
% 0.77/0.93 tff(928,plain,
% 0.77/0.93 (hskp25 | hskp26 | hskp1),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[927, 918])).
% 0.77/0.93 tff(929,plain,
% 0.77/0.93 (hskp1),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[928, 917, 679])).
% 0.77/0.93 tff(930,assumption,(hskp1), introduced(assumption)).
% 0.77/0.93 tff(931,plain,
% 0.77/0.93 (((~hskp1) | (~c3_1(a1206))) <=> ((~hskp1) | (~c3_1(a1206)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(932,plain,
% 0.77/0.93 (((~c3_1(a1206)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a1206)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(933,axiom,((~c3_1(a1206)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.77/0.93 tff(934,plain,
% 0.77/0.93 ((~hskp1) | (~c3_1(a1206))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[933, 932])).
% 0.77/0.93 tff(935,plain,
% 0.77/0.93 ((~hskp1) | (~c3_1(a1206))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[934, 931])).
% 0.77/0.93 tff(936,plain,
% 0.77/0.93 (~c3_1(a1206)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[935, 930])).
% 0.77/0.93 tff(937,plain,
% 0.77/0.93 (((~hskp1) | c2_1(a1206)) <=> ((~hskp1) | c2_1(a1206))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(938,axiom,((~hskp1) | c2_1(a1206)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.77/0.93 tff(939,plain,
% 0.77/0.93 ((~hskp1) | c2_1(a1206)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[938, 937])).
% 0.77/0.93 tff(940,plain,
% 0.77/0.93 ((~hskp1) | c2_1(a1206)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[939, 937])).
% 0.77/0.93 tff(941,plain,
% 0.77/0.93 ((~hskp1) | c2_1(a1206)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[940, 937])).
% 0.77/0.93 tff(942,plain,
% 0.77/0.93 ((~hskp1) | c2_1(a1206)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[941, 937])).
% 0.77/0.93 tff(943,plain,
% 0.77/0.93 ((~hskp1) | c2_1(a1206)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[942, 937])).
% 0.77/0.93 tff(944,plain,
% 0.77/0.93 (c2_1(a1206)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[943, 930])).
% 0.77/0.93 tff(945,plain,
% 0.77/0.93 (((~hskp1) | c0_1(a1206)) <=> ((~hskp1) | c0_1(a1206))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(946,axiom,((~hskp1) | c0_1(a1206)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.77/0.93 tff(947,plain,
% 0.77/0.93 ((~hskp1) | c0_1(a1206)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[946, 945])).
% 0.77/0.93 tff(948,plain,
% 0.77/0.93 ((~hskp1) | c0_1(a1206)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[947, 945])).
% 0.77/0.93 tff(949,plain,
% 0.77/0.93 ((~hskp1) | c0_1(a1206)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[948, 945])).
% 0.77/0.93 tff(950,plain,
% 0.77/0.93 ((~hskp1) | c0_1(a1206)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[949, 945])).
% 0.77/0.93 tff(951,plain,
% 0.77/0.93 ((~hskp1) | c0_1(a1206)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[950, 945])).
% 0.77/0.93 tff(952,plain,
% 0.77/0.93 (c0_1(a1206)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[951, 930])).
% 0.77/0.93 tff(953,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1267)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(954,plain,
% 0.77/0.93 ((hskp14 | (~ndr1_0) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267))) <=> (hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1267)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(955,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1267))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[954])).
% 0.77/0.93 tff(956,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1267)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[955, 953])).
% 0.77/0.93 tff(957,plain,
% 0.77/0.93 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(958,plain,
% 0.77/0.93 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1267))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[957, 956])).
% 0.77/0.93 tff(959,plain,
% 0.77/0.93 ($false),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[958, 159, 459, 851, 952, 944, 849, 848, 936, 437])).
% 0.77/0.93 tff(960,plain,((~hskp1) | hskp14 | (~c0_1(a1267)) | c1_1(a1267) | c2_1(a1267)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.93 tff(961,plain,
% 0.77/0.93 (hskp14),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[960, 929, 683, 682, 681])).
% 0.77/0.93 tff(962,plain,
% 0.77/0.93 (~c2_1(a1232)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[385, 961])).
% 0.77/0.93 tff(963,plain,
% 0.77/0.93 (~c0_1(a1232)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[417, 961])).
% 0.77/0.93 tff(964,plain,
% 0.77/0.93 (c3_1(a1232)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[393, 961])).
% 0.77/0.93 tff(965,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1232) | c2_1(a1232) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | c1_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1232) | c2_1(a1232) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | c1_1(a1232) | (~c3_1(a1232)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(966,plain,
% 0.77/0.93 (((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1232) | c2_1(a1232) | (~c3_1(a1232)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232)) <=> (c0_1(a1232) | c2_1(a1232) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | c1_1(a1232) | (~c3_1(a1232)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(967,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1232) | c2_1(a1232) | (~c3_1(a1232)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1232) | c2_1(a1232) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | c1_1(a1232) | (~c3_1(a1232))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[966])).
% 0.77/0.93 tff(968,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1232) | c2_1(a1232) | (~c3_1(a1232)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1232) | c2_1(a1232) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | c1_1(a1232) | (~c3_1(a1232)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[967, 965])).
% 0.77/0.93 tff(969,plain,
% 0.77/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1232) | c2_1(a1232) | (~c3_1(a1232)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(970,plain,
% 0.77/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1232) | c2_1(a1232) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | c1_1(a1232) | (~c3_1(a1232))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[969, 968])).
% 0.77/0.93 tff(971,plain,
% 0.77/0.93 (c1_1(a1232)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[970, 159, 964, 98, 963, 962, 90, 216, 633])).
% 0.77/0.93 tff(972,plain,
% 0.77/0.93 (c2_1(a1206)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[943, 929])).
% 0.77/0.93 tff(973,plain,
% 0.77/0.93 (c0_1(a1206)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[951, 929])).
% 0.77/0.93 tff(974,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(975,plain,
% 0.77/0.93 (((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(976,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1232)) | (~c1_1(a1232))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[975])).
% 0.77/0.93 tff(977,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[976, 974])).
% 0.77/0.93 tff(978,plain,
% 0.77/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(979,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1232)) | (~c1_1(a1232))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[978, 977])).
% 0.77/0.94 tff(980,plain,
% 0.77/0.94 (~c1_1(a1206)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[979, 159, 964, 973, 972, 963, 962, 352, 971])).
% 0.77/0.94 tff(981,plain,
% 0.77/0.94 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(982,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[981])).
% 0.77/0.94 tff(983,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(984,plain,
% 0.77/0.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp25) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp25))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(985,plain,
% 0.77/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[984])).
% 0.77/0.94 tff(986,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 0.77/0.94 tff(987,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[986, 985])).
% 0.77/0.94 tff(988,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[987, 983])).
% 0.77/0.94 tff(989,plain,(
% 0.77/0.94 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(skolemize,[status(sab)],[988])).
% 0.77/0.94 tff(990,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[989, 982])).
% 0.77/0.94 tff(991,plain,
% 0.77/0.94 (~c3_1(a1206)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[935, 929])).
% 0.77/0.94 tff(992,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | c0_1(a1232) | c2_1(a1232) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c0_1(a1232) | c2_1(a1232) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | (~c1_1(a1232)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(993,plain,
% 0.77/0.94 ((hskp25 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1232) | c2_1(a1232) | (~c1_1(a1232))) <=> (hskp25 | c0_1(a1232) | c2_1(a1232) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | (~c1_1(a1232)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(994,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1232) | c2_1(a1232) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | c0_1(a1232) | c2_1(a1232) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | (~c1_1(a1232))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[993])).
% 0.77/0.94 tff(995,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1232) | c2_1(a1232) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c0_1(a1232) | c2_1(a1232) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | (~c1_1(a1232)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[994, 992])).
% 0.77/0.94 tff(996,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1232) | c2_1(a1232) | (~c1_1(a1232)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(997,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c0_1(a1232) | c2_1(a1232) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | (~c1_1(a1232))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[996, 995])).
% 0.77/0.94 tff(998,plain,
% 0.77/0.94 (c1_1(a1206) | (~c1_1(a1232))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[997, 917, 159, 973, 963, 962, 991, 990])).
% 0.77/0.94 tff(999,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[998, 980, 971])).
% 0.77/0.94 tff(1000,plain,(hskp28 | hskp15 | c1_1(a1205) | hskp5 | c0_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(1001,plain,
% 0.77/0.94 (hskp28),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1000, 75, 23, 21, 22])).
% 0.77/0.94 tff(1002,plain,
% 0.77/0.94 (c3_1(a1214)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[276, 1001])).
% 0.77/0.94 tff(1003,plain,
% 0.77/0.94 (c1_1(a1214)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[284, 1001])).
% 0.77/0.94 tff(1004,plain,
% 0.77/0.94 (c0_1(a1214)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[292, 1001])).
% 0.77/0.94 tff(1005,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1006,plain,
% 0.77/0.94 ((hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205))) <=> (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1007,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1006])).
% 0.77/0.94 tff(1008,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1007, 1005])).
% 0.77/0.94 tff(1009,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1010,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 0.77/0.94 tff(1011,plain,
% 0.77/0.94 (~c3_1(a1205)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1010, 159, 21, 1004, 1003, 1002, 22, 23, 20])).
% 0.77/0.94 tff(1012,plain,
% 0.77/0.94 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1013,plain,
% 0.77/0.94 ((hskp11 | (~ndr1_0) | c3_1(a1205) | c0_1(a1205) | (~c2_1(a1205))) <=> (hskp11 | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1014,plain,
% 0.77/0.94 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1205) | c0_1(a1205) | (~c2_1(a1205)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1013])).
% 0.77/0.94 tff(1015,plain,
% 0.77/0.94 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1205) | c0_1(a1205) | (~c2_1(a1205)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1014, 1012])).
% 0.77/0.94 tff(1016,plain,
% 0.77/0.94 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1205) | c0_1(a1205) | (~c2_1(a1205)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1017,plain,
% 0.77/0.94 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 0.77/0.94 tff(1018,plain,
% 0.77/0.94 (hskp11 | c3_1(a1205) | (~c2_1(a1205))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1017, 159, 22, 313])).
% 0.77/0.94 tff(1019,plain,
% 0.77/0.94 (hskp11),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1018, 1011, 302])).
% 0.77/0.94 tff(1020,plain,
% 0.77/0.94 (~c2_1(a1224)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[567, 1019])).
% 0.77/0.94 tff(1021,plain,
% 0.77/0.94 (c3_1(a1224)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[575, 1019])).
% 0.77/0.94 tff(1022,plain,
% 0.77/0.94 (c1_1(a1224)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[583, 1019])).
% 0.77/0.94 tff(1023,plain,
% 0.77/0.94 (~c0_1(a1215)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[632, 1022, 1021, 98, 106, 1020, 302, 23, 21, 22])).
% 0.77/0.94 tff(1024,assumption,(hskp2), introduced(assumption)).
% 0.77/0.94 tff(1025,plain,
% 0.77/0.94 (((~hskp2) | (~c2_1(a1207))) <=> ((~hskp2) | (~c2_1(a1207)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1026,plain,
% 0.77/0.94 (((~c2_1(a1207)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a1207)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1027,axiom,((~c2_1(a1207)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.77/0.94 tff(1028,plain,
% 0.77/0.94 ((~hskp2) | (~c2_1(a1207))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1027, 1026])).
% 0.77/0.94 tff(1029,plain,
% 0.77/0.94 ((~hskp2) | (~c2_1(a1207))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1028, 1025])).
% 0.77/0.94 tff(1030,plain,
% 0.77/0.94 (~c2_1(a1207)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1029, 1024])).
% 0.77/0.94 tff(1031,plain,
% 0.77/0.94 (((~hskp2) | (~c1_1(a1207))) <=> ((~hskp2) | (~c1_1(a1207)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1032,plain,
% 0.77/0.94 (((~c1_1(a1207)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a1207)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1033,axiom,((~c1_1(a1207)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.77/0.94 tff(1034,plain,
% 0.77/0.94 ((~hskp2) | (~c1_1(a1207))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1033, 1032])).
% 0.77/0.94 tff(1035,plain,
% 0.77/0.94 ((~hskp2) | (~c1_1(a1207))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1034, 1031])).
% 0.77/0.94 tff(1036,plain,
% 0.77/0.94 (~c1_1(a1207)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1035, 1024])).
% 0.77/0.94 tff(1037,plain,
% 0.77/0.94 (((~hskp2) | (~c0_1(a1207))) <=> ((~hskp2) | (~c0_1(a1207)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1038,plain,
% 0.77/0.94 (((~c0_1(a1207)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a1207)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1039,axiom,((~c0_1(a1207)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.77/0.94 tff(1040,plain,
% 0.77/0.94 ((~hskp2) | (~c0_1(a1207))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1039, 1038])).
% 0.77/0.94 tff(1041,plain,
% 0.77/0.94 ((~hskp2) | (~c0_1(a1207))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1040, 1037])).
% 0.77/0.94 tff(1042,plain,
% 0.77/0.94 (~c0_1(a1207)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1041, 1024])).
% 0.77/0.94 tff(1043,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1215) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1215) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1044,plain,
% 0.77/0.94 (((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207)) <=> (c3_1(a1215) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1045,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1215) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1215) | (~c1_1(a1215))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1044])).
% 0.77/0.94 tff(1046,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1215) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1045, 1043])).
% 0.77/0.94 tff(1047,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1048,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1215) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1215) | (~c1_1(a1215))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 0.77/0.94 tff(1049,plain,
% 0.77/0.94 (~c3_1(a1207)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1048, 159, 128, 126, 1042, 1036, 1030, 216, 693])).
% 0.77/0.94 tff(1050,assumption,(c3_1(a1214)), introduced(assumption)).
% 0.77/0.94 tff(1051,assumption,(c1_1(a1214)), introduced(assumption)).
% 0.77/0.94 tff(1052,assumption,(c0_1(a1214)), introduced(assumption)).
% 0.77/0.94 tff(1053,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1215) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1215) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1054,plain,
% 0.77/0.94 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207)) <=> (c3_1(a1215) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1055,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1215) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1054])).
% 0.77/0.94 tff(1056,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1215) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1055, 1053])).
% 0.77/0.94 tff(1057,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1058,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1215) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 0.77/0.94 tff(1059,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1058, 159, 1052, 1051, 1050, 128, 127, 126, 1042, 1030, 74, 1049])).
% 0.77/0.94 tff(1060,plain,((~hskp2) | (~c0_1(a1214)) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c3_1(a1215) | c0_1(a1215)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(1061,plain,
% 0.77/0.94 (~hskp2),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1060, 1004, 1003, 1002, 98, 106, 90, 1023])).
% 0.77/0.94 tff(1062,plain,
% 0.77/0.94 (^[U: $i] : refl((hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(1063,plain,
% 0.77/0.94 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[1062])).
% 0.77/0.94 tff(1064,plain,
% 0.77/0.94 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1065,plain,
% 0.77/0.94 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp2))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp7) <=> ((hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp7))), rewrite(((hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(1066,plain,
% 0.77/0.94 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp7) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[1065])).
% 0.77/0.94 tff(1067,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 0.77/0.94 tff(1068,plain,
% 0.77/0.94 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 0.77/0.94 tff(1069,plain,
% 0.77/0.94 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1068, 1064])).
% 0.77/0.94 tff(1070,plain,(
% 0.77/0.94 ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.94 inference(skolemize,[status(sab)],[1069])).
% 0.77/0.94 tff(1071,plain,
% 0.77/0.94 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1070, 1063])).
% 0.77/0.94 tff(1072,plain,
% 0.77/0.94 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1073,plain,
% 0.77/0.94 ((hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214))) <=> (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1074,plain,
% 0.77/0.94 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1073])).
% 0.77/0.94 tff(1075,plain,
% 0.77/0.94 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1074, 1072])).
% 0.77/0.94 tff(1076,plain,
% 0.77/0.94 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1077,plain,
% 0.77/0.94 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 0.77/0.94 tff(1078,plain,
% 0.77/0.94 (hskp7 | hskp2),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1077, 159, 1004, 1003, 1002, 1071])).
% 0.77/0.94 tff(1079,plain,
% 0.77/0.94 (hskp7),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1078, 1061])).
% 0.77/0.94 tff(1080,plain,
% 0.77/0.94 (((~hskp7) | (~c3_1(a1216))) <=> ((~hskp7) | (~c3_1(a1216)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1081,plain,
% 0.77/0.94 (((~c3_1(a1216)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a1216)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1082,axiom,((~c3_1(a1216)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.77/0.94 tff(1083,plain,
% 0.77/0.94 ((~hskp7) | (~c3_1(a1216))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 0.77/0.94 tff(1084,plain,
% 0.77/0.94 ((~hskp7) | (~c3_1(a1216))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1083, 1080])).
% 0.77/0.94 tff(1085,plain,
% 0.77/0.94 (~c3_1(a1216)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1084, 1079])).
% 0.77/0.94 tff(1086,plain,
% 0.77/0.94 (((~hskp7) | (~c2_1(a1216))) <=> ((~hskp7) | (~c2_1(a1216)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1087,plain,
% 0.77/0.94 (((~c2_1(a1216)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a1216)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1088,axiom,((~c2_1(a1216)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.77/0.95 tff(1089,plain,
% 0.77/0.95 ((~hskp7) | (~c2_1(a1216))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 0.77/0.95 tff(1090,plain,
% 0.77/0.95 ((~hskp7) | (~c2_1(a1216))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1089, 1086])).
% 0.77/0.95 tff(1091,plain,
% 0.77/0.95 (~c2_1(a1216)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1090, 1079])).
% 0.77/0.95 tff(1092,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1216) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1216) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1093,plain,
% 0.77/0.95 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216)) <=> (c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1216) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1094,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1216) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1093])).
% 0.77/0.95 tff(1095,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1216) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1094, 1092])).
% 0.77/0.95 tff(1096,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1097,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1216) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 0.77/0.95 tff(1098,plain,
% 0.77/0.95 (c0_1(a1216)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1097, 159, 1004, 1003, 1002, 98, 106, 1091, 1085, 90, 74])).
% 0.77/0.95 tff(1099,plain,
% 0.77/0.95 (~hskp26),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[678, 1022, 1021, 1020, 302, 23, 21, 22])).
% 0.77/0.95 tff(1100,plain,
% 0.77/0.95 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(1101,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[1100])).
% 0.77/0.95 tff(1102,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1103,plain,
% 0.77/0.95 (^[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))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(1104,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[1103])).
% 0.77/0.95 tff(1105,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 0.77/0.95 tff(1106,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 0.77/0.95 tff(1107,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1106, 1102])).
% 0.77/0.95 tff(1108,plain,(
% 0.77/0.95 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(skolemize,[status(sab)],[1107])).
% 0.77/0.95 tff(1109,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1108, 1101])).
% 0.77/0.95 tff(1110,assumption,(~hskp26), introduced(assumption)).
% 0.77/0.95 tff(1111,assumption,(~hskp25), introduced(assumption)).
% 0.77/0.95 tff(1112,plain,
% 0.77/0.95 (hskp1),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[928, 1111, 1110])).
% 0.77/0.95 tff(1113,plain,
% 0.77/0.95 (~c3_1(a1206)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[935, 1112])).
% 0.77/0.95 tff(1114,plain,
% 0.77/0.95 ((hskp25 | hskp21) <=> (hskp25 | hskp21)),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1115,axiom,(hskp25 | hskp21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.77/0.95 tff(1116,plain,
% 0.77/0.95 (hskp25 | hskp21),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 0.77/0.95 tff(1117,plain,
% 0.77/0.95 (hskp25 | hskp21),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1116, 1114])).
% 0.77/0.95 tff(1118,plain,
% 0.77/0.95 (hskp25 | hskp21),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1117, 1114])).
% 0.77/0.95 tff(1119,plain,
% 0.77/0.95 (hskp25 | hskp21),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1118, 1114])).
% 0.77/0.95 tff(1120,plain,
% 0.77/0.95 (hskp25 | hskp21),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1119, 1114])).
% 0.77/0.95 tff(1121,plain,
% 0.77/0.95 (hskp21),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1120, 1111])).
% 0.77/0.95 tff(1122,plain,
% 0.77/0.95 (~c1_1(a1257)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[172, 1121])).
% 0.77/0.95 tff(1123,plain,
% 0.77/0.95 (~c0_1(a1257)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[178, 1121])).
% 0.77/0.95 tff(1124,plain,
% 0.77/0.95 (c2_1(a1206)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[943, 1112])).
% 0.77/0.95 tff(1125,plain,
% 0.77/0.95 (c0_1(a1206)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[951, 1112])).
% 0.77/0.95 tff(1126,plain,
% 0.77/0.95 (c3_1(a1257)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[186, 1121])).
% 0.77/0.95 tff(1127,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1128,plain,
% 0.77/0.95 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257))) <=> (c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1129,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1128])).
% 0.77/0.95 tff(1130,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1129, 1127])).
% 0.77/0.95 tff(1131,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1132,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 0.77/0.95 tff(1133,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1132, 159, 1052, 1051, 1050, 1126, 1125, 1124, 1123, 1122, 1113, 1109])).
% 0.77/0.95 tff(1134,plain,(hskp25 | (~c0_1(a1214)) | (~c1_1(a1214)) | (~c3_1(a1214)) | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(1135,plain,
% 0.77/0.95 (hskp25),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1134, 1004, 1003, 1002, 1099])).
% 0.77/0.95 tff(1136,plain,
% 0.77/0.95 (c3_1(a1204)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[708, 1135])).
% 0.77/0.95 tff(1137,plain,
% 0.77/0.95 (c2_1(a1204)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[700, 1135])).
% 0.77/0.95 tff(1138,plain,
% 0.77/0.95 (c0_1(a1204)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[691, 1135])).
% 0.77/0.95 tff(1139,plain,
% 0.77/0.95 (hskp9),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[738, 159, 1138, 1137, 1136, 98, 90, 729, 1023])).
% 0.77/0.95 tff(1140,plain,
% 0.77/0.95 (c2_1(a1219)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[747, 1139])).
% 0.77/0.95 tff(1141,plain,
% 0.77/0.95 (c1_1(a1219)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[755, 1139])).
% 0.77/0.95 tff(1142,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1143,plain,
% 0.77/0.95 (((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1205) | c3_1(a1205) | (~c2_1(a1205))) <=> (c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1144,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1205) | c3_1(a1205) | (~c2_1(a1205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1143])).
% 0.77/0.95 tff(1145,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1205) | c3_1(a1205) | (~c2_1(a1205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1144, 1142])).
% 0.77/0.95 tff(1146,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1205) | c3_1(a1205) | (~c2_1(a1205)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1147,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 0.77/0.95 tff(1148,plain,
% 0.77/0.95 (~c3_1(a1219)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1147, 159, 1004, 1003, 1002, 1141, 1140, 302, 22, 10, 1011])).
% 0.77/0.95 tff(1149,plain,
% 0.77/0.95 (((~hskp7) | (~c1_1(a1216))) <=> ((~hskp7) | (~c1_1(a1216)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1150,plain,
% 0.77/0.95 (((~c1_1(a1216)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a1216)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1151,axiom,((~c1_1(a1216)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 0.77/0.95 tff(1152,plain,
% 0.77/0.95 ((~hskp7) | (~c1_1(a1216))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 0.77/0.95 tff(1153,plain,
% 0.77/0.95 ((~hskp7) | (~c1_1(a1216))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1152, 1149])).
% 0.77/0.95 tff(1154,plain,
% 0.77/0.95 (~c1_1(a1216)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1153, 1079])).
% 0.77/0.95 tff(1155,plain,
% 0.77/0.95 (~c0_1(a1219)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[768, 1139])).
% 0.77/0.95 tff(1156,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a1219) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1219) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | c3_1(a1219) | (~c1_1(a1219)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1157,plain,
% 0.77/0.95 (((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219))) <=> (c0_1(a1219) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | c3_1(a1219) | (~c1_1(a1219)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1158,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a1219) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | c3_1(a1219) | (~c1_1(a1219))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1157])).
% 0.77/0.95 tff(1159,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1219) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | c3_1(a1219) | (~c1_1(a1219)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1158, 1156])).
% 0.77/0.95 tff(1160,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1161,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1219) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | c3_1(a1219) | (~c1_1(a1219))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 0.77/0.95 tff(1162,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1161, 159, 1141, 1155, 1154, 1091, 1085, 846, 1148, 1098])).
% 0.77/0.95 tff(1163,plain,(hskp15 | c0_1(a1205) | c1_1(a1205) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(1164,plain,
% 0.77/0.95 (hskp15),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1163, 23, 22, 21])).
% 0.77/0.95 tff(1165,plain,
% 0.77/0.95 (((~hskp15) | (~c2_1(a1233))) <=> ((~hskp15) | (~c2_1(a1233)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1166,plain,
% 0.77/0.95 (((~c2_1(a1233)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a1233)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1167,axiom,((~c2_1(a1233)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 0.77/0.95 tff(1168,plain,
% 0.77/0.95 ((~hskp15) | (~c2_1(a1233))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 0.77/0.95 tff(1169,plain,
% 0.77/0.95 ((~hskp15) | (~c2_1(a1233))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1168, 1165])).
% 0.77/0.95 tff(1170,plain,
% 0.77/0.95 (~c2_1(a1233)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1169, 1164])).
% 0.77/0.95 tff(1171,plain,
% 0.77/0.95 (((~hskp15) | c1_1(a1233)) <=> ((~hskp15) | c1_1(a1233))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1172,axiom,((~hskp15) | c1_1(a1233)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 0.77/0.95 tff(1173,plain,
% 0.77/0.95 ((~hskp15) | c1_1(a1233)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 0.77/0.95 tff(1174,plain,
% 0.77/0.95 ((~hskp15) | c1_1(a1233)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1173, 1171])).
% 0.77/0.95 tff(1175,plain,
% 0.77/0.95 ((~hskp15) | c1_1(a1233)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1174, 1171])).
% 0.77/0.95 tff(1176,plain,
% 0.77/0.95 ((~hskp15) | c1_1(a1233)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1175, 1171])).
% 0.77/0.95 tff(1177,plain,
% 0.77/0.95 ((~hskp15) | c1_1(a1233)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1176, 1171])).
% 0.77/0.95 tff(1178,plain,
% 0.77/0.95 (c1_1(a1233)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1177, 1164])).
% 0.77/0.95 tff(1179,plain,
% 0.77/0.95 (((~hskp15) | c0_1(a1233)) <=> ((~hskp15) | c0_1(a1233))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1180,axiom,((~hskp15) | c0_1(a1233)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 0.77/0.95 tff(1181,plain,
% 0.77/0.95 ((~hskp15) | c0_1(a1233)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 0.77/0.95 tff(1182,plain,
% 0.77/0.95 ((~hskp15) | c0_1(a1233)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1181, 1179])).
% 0.77/0.95 tff(1183,plain,
% 0.77/0.95 ((~hskp15) | c0_1(a1233)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1182, 1179])).
% 0.77/0.95 tff(1184,plain,
% 0.77/0.95 ((~hskp15) | c0_1(a1233)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1183, 1179])).
% 0.77/0.95 tff(1185,plain,
% 0.77/0.95 ((~hskp15) | c0_1(a1233)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1184, 1179])).
% 0.77/0.95 tff(1186,plain,
% 0.77/0.95 (c0_1(a1233)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1185, 1164])).
% 0.77/0.95 tff(1187,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1188,plain,
% 0.77/0.95 ((hskp10 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233))) <=> (hskp10 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1189,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1188])).
% 0.77/0.95 tff(1190,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1189, 1187])).
% 0.77/0.95 tff(1191,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(1192,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 0.77/0.95 tff(1193,plain,
% 0.77/0.95 (hskp10),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1192, 159, 692, 701, 709, 1186, 1178, 1170, 64])).
% 0.77/0.95 tff(1194,plain,
% 0.77/0.95 (((~hskp10) | (~c3_1(a1223))) <=> ((~hskp10) | (~c3_1(a1223)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1195,plain,
% 0.77/0.95 (((~c3_1(a1223)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a1223)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1196,axiom,((~c3_1(a1223)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.77/0.95 tff(1197,plain,
% 0.77/0.95 ((~hskp10) | (~c3_1(a1223))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 0.77/0.95 tff(1198,plain,
% 0.77/0.95 ((~hskp10) | (~c3_1(a1223))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1197, 1194])).
% 0.77/0.95 tff(1199,plain,
% 0.77/0.95 (~c3_1(a1223)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1198, 1193])).
% 0.77/0.95 tff(1200,plain,
% 0.77/0.95 (((~hskp10) | (~c1_1(a1223))) <=> ((~hskp10) | (~c1_1(a1223)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1201,plain,
% 0.77/0.95 (((~c1_1(a1223)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1223)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1202,axiom,((~c1_1(a1223)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 0.77/0.95 tff(1203,plain,
% 0.77/0.95 ((~hskp10) | (~c1_1(a1223))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 0.77/0.95 tff(1204,plain,
% 0.77/0.95 ((~hskp10) | (~c1_1(a1223))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1203, 1200])).
% 0.77/0.95 tff(1205,plain,
% 0.77/0.95 (~c1_1(a1223)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1204, 1193])).
% 0.77/0.95 tff(1206,plain,
% 0.77/0.95 (((~hskp10) | c2_1(a1223)) <=> ((~hskp10) | c2_1(a1223))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1207,axiom,((~hskp10) | c2_1(a1223)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.77/0.95 tff(1208,plain,
% 0.77/0.95 ((~hskp10) | c2_1(a1223)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 0.77/0.95 tff(1209,plain,
% 0.77/0.95 ((~hskp10) | c2_1(a1223)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1208, 1206])).
% 0.77/0.95 tff(1210,plain,
% 0.77/0.95 ((~hskp10) | c2_1(a1223)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1209, 1206])).
% 0.77/0.95 tff(1211,plain,
% 0.77/0.95 ((~hskp10) | c2_1(a1223)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1210, 1206])).
% 0.77/0.95 tff(1212,plain,
% 0.77/0.95 ((~hskp10) | c2_1(a1223)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[1211, 1206])).
% 0.77/0.95 tff(1213,plain,
% 0.77/0.95 (c2_1(a1223)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[1212, 1193])).
% 0.77/0.95 tff(1214,plain,
% 0.77/0.95 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp13 | hskp6 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1215,plain,
% 0.77/0.95 ((hskp13 | hskp6 | (~ndr1_0) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223))) <=> (hskp13 | hskp6 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(1216,plain,
% 0.77/0.95 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[1215])).
% 0.77/0.95 tff(1217,plain,
% 0.77/0.95 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp13 | hskp6 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[1216, 1214])).
% 0.77/0.95 tff(1218,plain,
% 0.77/0.95 ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1219,plain,
% 0.77/0.96 ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp13 | hskp6 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 0.77/0.96 tff(1220,plain,
% 0.77/0.96 (hskp13),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1219, 159, 24, 1213, 1205, 1199, 54])).
% 0.77/0.96 tff(1221,plain,
% 0.77/0.96 (((~hskp13) | (~c1_1(a1229))) <=> ((~hskp13) | (~c1_1(a1229)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1222,plain,
% 0.77/0.96 (((~c1_1(a1229)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1229)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1223,axiom,((~c1_1(a1229)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.77/0.96 tff(1224,plain,
% 0.77/0.96 ((~hskp13) | (~c1_1(a1229))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 0.77/0.96 tff(1225,plain,
% 0.77/0.96 ((~hskp13) | (~c1_1(a1229))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1224, 1221])).
% 0.77/0.96 tff(1226,plain,
% 0.77/0.96 (~c1_1(a1229)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1225, 1220])).
% 0.77/0.96 tff(1227,plain,
% 0.77/0.96 (((~hskp13) | c2_1(a1229)) <=> ((~hskp13) | c2_1(a1229))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1228,axiom,((~hskp13) | c2_1(a1229)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.77/0.96 tff(1229,plain,
% 0.77/0.96 ((~hskp13) | c2_1(a1229)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 0.77/0.96 tff(1230,plain,
% 0.77/0.96 ((~hskp13) | c2_1(a1229)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1229, 1227])).
% 0.77/0.96 tff(1231,plain,
% 0.77/0.96 ((~hskp13) | c2_1(a1229)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1230, 1227])).
% 0.77/0.96 tff(1232,plain,
% 0.77/0.96 ((~hskp13) | c2_1(a1229)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1231, 1227])).
% 0.77/0.96 tff(1233,plain,
% 0.77/0.96 ((~hskp13) | c2_1(a1229)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1232, 1227])).
% 0.77/0.96 tff(1234,plain,
% 0.77/0.96 (c2_1(a1229)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1233, 1220])).
% 0.77/0.96 tff(1235,plain,
% 0.77/0.96 (((~hskp13) | c0_1(a1229)) <=> ((~hskp13) | c0_1(a1229))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1236,axiom,((~hskp13) | c0_1(a1229)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.77/0.96 tff(1237,plain,
% 0.77/0.96 ((~hskp13) | c0_1(a1229)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 0.77/0.96 tff(1238,plain,
% 0.77/0.96 ((~hskp13) | c0_1(a1229)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1237, 1235])).
% 0.77/0.96 tff(1239,plain,
% 0.77/0.96 ((~hskp13) | c0_1(a1229)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1238, 1235])).
% 0.77/0.96 tff(1240,plain,
% 0.77/0.96 ((~hskp13) | c0_1(a1229)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1239, 1235])).
% 0.77/0.96 tff(1241,plain,
% 0.77/0.96 ((~hskp13) | c0_1(a1229)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1240, 1235])).
% 0.77/0.96 tff(1242,plain,
% 0.77/0.96 (c0_1(a1229)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1241, 1220])).
% 0.77/0.96 tff(1243,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c2_1(a1233) | c1_1(a1229) | (~ndr1_0) | (~c0_1(a1229)) | (~c2_1(a1229)) | (~c0_1(a1233)) | (~c3_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1233) | c1_1(a1229) | (~ndr1_0) | (~c0_1(a1229)) | (~c2_1(a1229)) | (~c0_1(a1233)) | (~c3_1(a1233)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1244,plain,
% 0.77/0.96 ((hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1229) | (~c2_1(a1229)) | (~c0_1(a1229))) <=> (hskp6 | c2_1(a1233) | c1_1(a1229) | (~ndr1_0) | (~c0_1(a1229)) | (~c2_1(a1229)) | (~c0_1(a1233)) | (~c3_1(a1233)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1245,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1229) | (~c2_1(a1229)) | (~c0_1(a1229)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c2_1(a1233) | c1_1(a1229) | (~ndr1_0) | (~c0_1(a1229)) | (~c2_1(a1229)) | (~c0_1(a1233)) | (~c3_1(a1233))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[1244])).
% 0.77/0.96 tff(1246,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1229) | (~c2_1(a1229)) | (~c0_1(a1229)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1233) | c1_1(a1229) | (~ndr1_0) | (~c0_1(a1229)) | (~c2_1(a1229)) | (~c0_1(a1233)) | (~c3_1(a1233)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[1245, 1243])).
% 0.77/0.96 tff(1247,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1229) | (~c2_1(a1229)) | (~c0_1(a1229)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1248,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1233) | c1_1(a1229) | (~ndr1_0) | (~c0_1(a1229)) | (~c2_1(a1229)) | (~c0_1(a1233)) | (~c3_1(a1233))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 0.77/0.96 tff(1249,plain,
% 0.77/0.96 (~c3_1(a1233)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1248, 159, 24, 1186, 1242, 1234, 1170, 1226, 44])).
% 0.77/0.96 tff(1250,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1251,plain,
% 0.77/0.96 (((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233))) <=> (c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1252,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[1251])).
% 0.77/0.96 tff(1253,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[1252, 1250])).
% 0.77/0.96 tff(1254,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1255,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 0.77/0.96 tff(1256,plain,
% 0.77/0.96 (~c1_1(a1204)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1255, 159, 692, 701, 1186, 1170, 821, 1249])).
% 0.77/0.96 tff(1257,plain,
% 0.77/0.96 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(1258,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[1257])).
% 0.77/0.96 tff(1259,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1260,plain,
% 0.77/0.96 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(1261,plain,
% 0.77/0.96 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[1260])).
% 0.77/0.96 tff(1262,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 0.77/0.96 tff(1263,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 0.77/0.96 tff(1264,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1263, 1259])).
% 0.77/0.96 tff(1265,plain,(
% 0.77/0.96 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.96 inference(skolemize,[status(sab)],[1264])).
% 0.77/0.96 tff(1266,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1265, 1258])).
% 0.77/0.96 tff(1267,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1268,plain,
% 0.77/0.96 ((hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223))) <=> (hskp9 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1269,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[1268])).
% 0.77/0.96 tff(1270,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[1269, 1267])).
% 0.77/0.96 tff(1271,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1272,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 0.77/0.96 tff(1273,plain,
% 0.77/0.96 (hskp9),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1272, 159, 692, 709, 1213, 1205, 1199, 1266, 1256])).
% 0.77/0.96 tff(1274,plain,
% 0.77/0.96 (~c0_1(a1219)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[768, 1273])).
% 0.77/0.96 tff(1275,plain,
% 0.77/0.96 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(1276,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[1275])).
% 0.77/0.96 tff(1277,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1278,plain,
% 0.77/0.96 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(1279,plain,
% 0.77/0.96 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[1278])).
% 0.77/0.96 tff(1280,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 0.77/0.96 tff(1281,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 0.77/0.96 tff(1282,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1281, 1277])).
% 0.77/0.96 tff(1283,plain,(
% 0.77/0.96 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.96 inference(skolemize,[status(sab)],[1282])).
% 0.77/0.96 tff(1284,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1283, 1276])).
% 0.77/0.96 tff(1285,plain,
% 0.77/0.96 (c2_1(a1219)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[747, 1273])).
% 0.77/0.96 tff(1286,plain,
% 0.77/0.96 (c1_1(a1219)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[755, 1273])).
% 0.77/0.96 tff(1287,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | c2_1(a1233) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c0_1(a1233)) | (~c1_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp1 | c2_1(a1233) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1288,plain,
% 0.77/0.96 ((hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219))) <=> (hskp1 | c2_1(a1233) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1289,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | c2_1(a1233) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c0_1(a1233)) | (~c1_1(a1233))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[1288])).
% 0.77/0.96 tff(1290,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp1 | c2_1(a1233) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[1289, 1287])).
% 0.77/0.96 tff(1291,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1292,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp1 | c2_1(a1233) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c0_1(a1233)) | (~c1_1(a1233))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 0.77/0.96 tff(1293,plain,
% 0.77/0.96 (hskp1),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1292, 159, 1186, 1178, 1286, 1285, 1170, 1274, 1284])).
% 0.77/0.96 tff(1294,plain,
% 0.77/0.96 (c2_1(a1206)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[943, 1293])).
% 0.77/0.96 tff(1295,plain,
% 0.77/0.96 (c0_1(a1206)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[951, 1293])).
% 0.77/0.96 tff(1296,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1233) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | c3_1(a1233))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | c3_1(a1233))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1297,plain,
% 0.77/0.96 (((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233))) <=> (c2_1(a1233) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | c3_1(a1233))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1298,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1233) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | c3_1(a1233)))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[1297])).
% 0.77/0.96 tff(1299,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | c3_1(a1233))),
% 0.77/0.96 inference(transitivity,[status(thm)],[1298, 1296])).
% 0.77/0.96 tff(1300,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(1301,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | c3_1(a1233)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 0.77/0.96 tff(1302,plain,
% 0.77/0.96 (~c1_1(a1206)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[1301, 159, 1186, 1295, 1294, 1170, 821, 1249])).
% 0.77/0.96 tff(1303,plain,
% 0.77/0.96 (^[U: $i] : refl((hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(1304,plain,
% 0.77/0.96 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[1303])).
% 0.77/0.96 tff(1305,plain,
% 0.77/0.96 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(1306,plain,
% 0.77/0.96 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp17) | hskp5) <=> ((hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp5))), rewrite(((hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp5) <=> (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp17) | hskp5) <=> (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(1307,plain,
% 0.77/0.96 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp17) | hskp5) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[1306])).
% 0.77/0.96 tff(1308,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp17) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 0.77/0.96 tff(1309,plain,
% 0.77/0.96 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[1308, 1307])).
% 0.77/0.96 tff(1310,plain,
% 0.77/0.96 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1309, 1305])).
% 0.77/0.97 tff(1311,plain,(
% 0.77/0.97 ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.97 inference(skolemize,[status(sab)],[1310])).
% 0.77/0.97 tff(1312,plain,
% 0.77/0.97 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1311, 1304])).
% 0.77/0.97 tff(1313,plain,
% 0.77/0.97 (~c3_1(a1206)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[935, 1293])).
% 0.77/0.97 tff(1314,plain,
% 0.77/0.97 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp5 | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp5 | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1315,plain,
% 0.77/0.97 ((hskp17 | hskp5 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206))) <=> (hskp17 | hskp5 | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1316,plain,
% 0.77/0.97 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp5 | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1315])).
% 0.77/0.97 tff(1317,plain,
% 0.77/0.97 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp5 | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1316, 1314])).
% 0.77/0.97 tff(1318,plain,
% 0.77/0.97 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1319,plain,
% 0.77/0.97 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp5 | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 0.77/0.97 tff(1320,plain,
% 0.77/0.97 (hskp17 | c1_1(a1206)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1319, 159, 21, 1295, 1313, 1312])).
% 0.77/0.97 tff(1321,plain,
% 0.77/0.97 (hskp17),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1320, 1302])).
% 0.77/0.97 tff(1322,plain,
% 0.77/0.97 (((~hskp17) | (~c1_1(a1237))) <=> ((~hskp17) | (~c1_1(a1237)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1323,plain,
% 0.77/0.97 (((~c1_1(a1237)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1237)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1324,axiom,((~c1_1(a1237)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 0.77/0.97 tff(1325,plain,
% 0.77/0.97 ((~hskp17) | (~c1_1(a1237))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 0.77/0.97 tff(1326,plain,
% 0.77/0.97 ((~hskp17) | (~c1_1(a1237))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1325, 1322])).
% 0.77/0.97 tff(1327,plain,
% 0.77/0.97 (~c1_1(a1237)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1326, 1321])).
% 0.77/0.97 tff(1328,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a1233) | c0_1(a1219) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1233)) | c3_1(a1233))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a1233) | c0_1(a1219) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1233)) | c3_1(a1233))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1329,plain,
% 0.77/0.97 (((~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219))) <=> (c2_1(a1233) | c0_1(a1219) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1233)) | c3_1(a1233))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1330,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a1233) | c0_1(a1219) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1233)) | c3_1(a1233)))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1329])).
% 0.77/0.97 tff(1331,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a1233) | c0_1(a1219) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1233)) | c3_1(a1233))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1330, 1328])).
% 0.77/0.97 tff(1332,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1333,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a1233) | c0_1(a1219) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1233)) | c3_1(a1233)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 0.77/0.97 tff(1334,plain,
% 0.77/0.97 (c3_1(a1219)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1333, 159, 1186, 1286, 1295, 1170, 1274, 1313, 846, 1249, 1302])).
% 0.77/0.97 tff(1335,assumption,(c3_1(a1233)), introduced(assumption)).
% 0.77/0.97 tff(1336,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1337,plain,
% 0.77/0.97 ((hskp5 | (~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205))) <=> (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1338,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1337])).
% 0.77/0.97 tff(1339,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1338, 1336])).
% 0.77/0.97 tff(1340,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1341,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1340, 1339])).
% 0.77/0.97 tff(1342,plain,
% 0.77/0.97 ((~c3_1(a1205)) | (~c3_1(a1233))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1341, 159, 21, 1186, 1178, 22, 23, 20])).
% 0.77/0.97 tff(1343,plain,
% 0.77/0.97 (~c3_1(a1205)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1342, 1335])).
% 0.77/0.97 tff(1344,plain,
% 0.77/0.97 (c2_1(a1205)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[205, 1343, 198])).
% 0.77/0.97 tff(1345,plain,
% 0.77/0.97 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp13 | hskp6 | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1346,plain,
% 0.77/0.97 ((hskp13 | hskp6 | (~ndr1_0) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205))) <=> (hskp13 | hskp6 | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1347,plain,
% 0.77/0.97 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1346])).
% 0.77/0.97 tff(1348,plain,
% 0.77/0.97 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp13 | hskp6 | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1347, 1345])).
% 0.77/0.97 tff(1349,plain,
% 0.77/0.97 ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1350,plain,
% 0.77/0.97 ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp13 | hskp6 | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 0.77/0.97 tff(1351,plain,
% 0.77/0.97 (hskp13 | hskp6 | c3_1(a1205) | (~c2_1(a1205))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1350, 159, 23, 54])).
% 0.77/0.97 tff(1352,plain,
% 0.77/0.97 (hskp13),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1351, 1344, 24, 1343])).
% 0.77/0.97 tff(1353,plain,
% 0.77/0.97 (~c1_1(a1229)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1225, 1352])).
% 0.77/0.97 tff(1354,plain,
% 0.77/0.97 (c2_1(a1229)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1233, 1352])).
% 0.77/0.97 tff(1355,plain,
% 0.77/0.97 (c0_1(a1229)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1241, 1352])).
% 0.77/0.97 tff(1356,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1248, 159, 24, 1186, 1355, 1354, 1170, 1353, 44, 1335])).
% 0.77/0.97 tff(1357,plain,((~c3_1(a1233)) | hskp6 | c1_1(a1205) | hskp28 | c0_1(a1205) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(1358,plain,
% 0.77/0.97 (~c3_1(a1233)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1357, 198, 23, 24, 22, 21])).
% 0.77/0.97 tff(1359,assumption,(~c2_1(a1233)), introduced(assumption)).
% 0.77/0.97 tff(1360,assumption,(~c3_1(a1233)), introduced(assumption)).
% 0.77/0.97 tff(1361,assumption,(c1_1(a1233)), introduced(assumption)).
% 0.77/0.97 tff(1362,assumption,(c0_1(a1233)), introduced(assumption)).
% 0.77/0.97 tff(1363,plain,
% 0.77/0.97 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(1364,plain,
% 0.77/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_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)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[1363])).
% 0.77/0.97 tff(1365,plain,
% 0.77/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_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)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1366,plain,
% 0.77/0.97 (^[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))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_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)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_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)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(1367,plain,
% 0.77/0.97 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_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)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[1366])).
% 0.77/0.97 tff(1368,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 0.77/0.97 tff(1369,plain,
% 0.77/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 0.77/0.97 tff(1370,plain,
% 0.77/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1369, 1365])).
% 0.77/0.97 tff(1371,plain,(
% 0.77/0.97 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.97 inference(skolemize,[status(sab)],[1370])).
% 0.77/0.97 tff(1372,plain,
% 0.77/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1371, 1364])).
% 0.77/0.97 tff(1373,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1267)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1374,plain,
% 0.77/0.97 (((~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267))) <=> (c1_1(a1267) | c2_1(a1267) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1267)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1375,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1267))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1374])).
% 0.77/0.97 tff(1376,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1267)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1375, 1373])).
% 0.77/0.97 tff(1377,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1378,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1267))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1377, 1376])).
% 0.77/0.97 tff(1379,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1378, 159, 851, 1362, 1361, 849, 848, 1359, 1372, 1360])).
% 0.77/0.97 tff(1380,plain,(c3_1(a1233) | (~c0_1(a1267)) | (~c0_1(a1233)) | (~c1_1(a1233)) | c1_1(a1267) | c2_1(a1267) | c2_1(a1233)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(1381,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1380, 450, 458, 1362, 1361, 1360, 444, 1359])).
% 0.77/0.97 tff(1382,plain,((~hskp24) | (~c0_1(a1233)) | (~c1_1(a1233)) | c3_1(a1233) | c2_1(a1233)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(1383,plain,
% 0.77/0.97 (~hskp24),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1382, 1358, 1178, 1186, 1170])).
% 0.77/0.97 tff(1384,plain,
% 0.77/0.97 (hskp26),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[157, 1383, 198])).
% 0.77/0.97 tff(1385,plain,
% 0.77/0.97 (c2_1(a1208)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[641, 1384])).
% 0.77/0.97 tff(1386,plain,
% 0.77/0.97 (c1_1(a1208)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[649, 1384])).
% 0.77/0.97 tff(1387,plain,
% 0.77/0.97 (c0_1(a1208)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[657, 1384])).
% 0.77/0.97 tff(1388,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | c3_1(a1233))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | c3_1(a1233))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1389,plain,
% 0.77/0.97 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233))) <=> (c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | c3_1(a1233))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1390,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | c3_1(a1233)))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1389])).
% 0.77/0.97 tff(1391,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | c3_1(a1233))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1390, 1388])).
% 0.77/0.97 tff(1392,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1393,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | c3_1(a1233)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 0.77/0.97 tff(1394,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1393, 159, 1387, 1386, 1385, 1186, 1170, 821, 1358])).
% 0.77/0.97 tff(1395,plain,(hskp28 | c1_1(a1205) | hskp6 | c0_1(a1205) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(1396,plain,
% 0.77/0.97 (hskp28),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1395, 24, 23, 22, 21])).
% 0.77/0.97 tff(1397,plain,
% 0.77/0.97 (c3_1(a1214)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[276, 1396])).
% 0.77/0.97 tff(1398,plain,
% 0.77/0.97 (c1_1(a1214)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[284, 1396])).
% 0.77/0.97 tff(1399,plain,
% 0.77/0.97 (c0_1(a1214)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[292, 1396])).
% 0.77/0.97 tff(1400,plain,
% 0.77/0.97 (~c3_1(a1205)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1010, 159, 21, 1399, 1398, 1397, 22, 23, 20])).
% 0.77/0.97 tff(1401,plain,
% 0.77/0.97 ((~c2_1(a1205)) | (~c3_1(a1219))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1147, 159, 1399, 1398, 1397, 1286, 1285, 22, 10, 1400])).
% 0.77/0.97 tff(1402,plain,
% 0.77/0.97 (~c2_1(a1205)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1401, 1334])).
% 0.77/0.97 tff(1403,plain,
% 0.77/0.97 (((~hskp17) | c3_1(a1237)) <=> ((~hskp17) | c3_1(a1237))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1404,axiom,((~hskp17) | c3_1(a1237)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 0.77/0.97 tff(1405,plain,
% 0.77/0.97 ((~hskp17) | c3_1(a1237)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 0.77/0.97 tff(1406,plain,
% 0.77/0.97 ((~hskp17) | c3_1(a1237)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1405, 1403])).
% 0.77/0.97 tff(1407,plain,
% 0.77/0.97 ((~hskp17) | c3_1(a1237)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1406, 1403])).
% 0.77/0.97 tff(1408,plain,
% 0.77/0.97 ((~hskp17) | c3_1(a1237)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1407, 1403])).
% 0.77/0.97 tff(1409,plain,
% 0.77/0.97 ((~hskp17) | c3_1(a1237)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1408, 1403])).
% 0.77/0.97 tff(1410,plain,
% 0.77/0.97 (c3_1(a1237)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1409, 1321])).
% 0.77/0.97 tff(1411,plain,
% 0.77/0.97 (((~hskp17) | c0_1(a1237)) <=> ((~hskp17) | c0_1(a1237))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1412,axiom,((~hskp17) | c0_1(a1237)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.77/0.97 tff(1413,plain,
% 0.77/0.97 ((~hskp17) | c0_1(a1237)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1412, 1411])).
% 0.77/0.97 tff(1414,plain,
% 0.77/0.97 ((~hskp17) | c0_1(a1237)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1413, 1411])).
% 0.77/0.97 tff(1415,plain,
% 0.77/0.97 ((~hskp17) | c0_1(a1237)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1414, 1411])).
% 0.77/0.97 tff(1416,plain,
% 0.77/0.97 ((~hskp17) | c0_1(a1237)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1415, 1411])).
% 0.77/0.97 tff(1417,plain,
% 0.77/0.97 ((~hskp17) | c0_1(a1237)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1416, 1411])).
% 0.77/0.97 tff(1418,plain,
% 0.77/0.97 (c0_1(a1237)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1417, 1321])).
% 0.77/0.97 tff(1419,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1205) | c1_1(a1237) | c0_1(a1219) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1237)) | (~c0_1(a1237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1205) | c1_1(a1237) | c0_1(a1219) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1237)) | (~c0_1(a1237)))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(1420,plain,
% 0.81/0.97 (((~ndr1_0) | c1_1(a1237) | (~c3_1(a1237)) | (~c0_1(a1237)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205)) <=> (c2_1(a1205) | c1_1(a1237) | c0_1(a1219) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1237)) | (~c0_1(a1237)))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(1421,plain,
% 0.81/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1237) | (~c3_1(a1237)) | (~c0_1(a1237)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1205) | c1_1(a1237) | c0_1(a1219) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1237)) | (~c0_1(a1237))))),
% 0.81/0.97 inference(monotonicity,[status(thm)],[1420])).
% 0.81/0.97 tff(1422,plain,
% 0.81/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1237) | (~c3_1(a1237)) | (~c0_1(a1237)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1205) | c1_1(a1237) | c0_1(a1219) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1237)) | (~c0_1(a1237)))),
% 0.81/0.97 inference(transitivity,[status(thm)],[1421, 1419])).
% 0.81/0.97 tff(1423,plain,
% 0.81/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1237) | (~c3_1(a1237)) | (~c0_1(a1237)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205))),
% 0.81/0.97 inference(quant_inst,[status(thm)],[])).
% 0.81/0.97 tff(1424,plain,
% 0.81/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1205) | c1_1(a1237) | c0_1(a1219) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1237)) | (~c0_1(a1237))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 0.81/0.97 tff(1425,plain,
% 0.81/0.97 ($false),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[1424, 159, 1418, 1410, 1286, 1285, 1402, 1327, 1274, 22, 23, 34])).
% 0.81/0.97 tff(1426,plain,((~hskp25) | c0_1(a1205) | c1_1(a1205) | hskp5 | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.81/0.97 tff(1427,plain,
% 0.81/0.97 (~hskp25),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[1426, 24, 23, 21, 22])).
% 0.81/0.97 tff(1428,plain,
% 0.81/0.97 (hskp21),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[1120, 1427])).
% 0.81/0.97 tff(1429,plain,
% 0.81/0.97 (~c1_1(a1257)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[172, 1428])).
% 0.81/0.97 tff(1430,plain,
% 0.81/0.97 (~c0_1(a1257)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[178, 1428])).
% 0.81/0.97 tff(1431,plain,
% 0.81/0.97 (c3_1(a1257)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[186, 1428])).
% 0.81/0.97 tff(1432,plain,
% 0.81/0.97 ($false),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[299, 159, 21, 1399, 1398, 1397, 1431, 1430, 1429, 20])).
% 0.81/0.97 tff(1433,plain,(hskp6 | hskp5 | c1_1(a1205) | c0_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 0.81/0.97 tff(1434,plain,
% 0.81/0.97 (hskp6),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[1433, 23, 21, 22])).
% 0.81/0.97 tff(1435,plain,
% 0.81/0.97 (~c3_1(a1215)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[89, 1434])).
% 0.81/0.97 tff(1436,plain,
% 0.81/0.97 (c1_1(a1215)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[97, 1434])).
% 0.81/0.97 tff(1437,plain,
% 0.81/0.97 (c2_1(a1215)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[105, 1434])).
% 0.81/0.97 tff(1438,plain,
% 0.81/0.97 (c2_1(a1205)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[301, 1437, 21, 1436, 1435, 22, 23])).
% 0.81/0.97 tff(1439,plain,
% 0.81/0.97 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.81/0.98 inference(bind,[status(th)],[])).
% 0.81/0.98 tff(1440,plain,
% 0.81/0.98 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.81/0.98 inference(quant_intro,[status(thm)],[1439])).
% 0.81/0.98 tff(1441,plain,
% 0.81/0.98 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1442,plain,
% 0.81/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.81/0.98 inference(bind,[status(th)],[])).
% 0.81/0.98 tff(1443,plain,
% 0.81/0.98 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.81/0.98 inference(quant_intro,[status(thm)],[1442])).
% 0.81/0.98 tff(1444,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.81/0.98 tff(1445,plain,
% 0.81/0.98 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1444, 1443])).
% 0.81/0.98 tff(1446,plain,
% 0.81/0.98 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1445, 1441])).
% 0.81/0.98 tff(1447,plain,(
% 0.81/0.98 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.81/0.98 inference(skolemize,[status(sab)],[1446])).
% 0.81/0.98 tff(1448,plain,
% 0.81/0.98 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1447, 1440])).
% 0.81/0.98 tff(1449,plain,
% 0.81/0.98 (hskp24),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[157, 1110, 198])).
% 0.81/0.98 tff(1450,plain,
% 0.81/0.98 (c3_1(a1233)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1382, 1449, 1178, 1186, 1170])).
% 0.81/0.98 tff(1451,plain,
% 0.81/0.98 (~c3_1(a1205)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1342, 1450])).
% 0.81/0.98 tff(1452,plain,
% 0.81/0.98 (~c2_1(a1267)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[443, 1449])).
% 0.81/0.98 tff(1453,plain,
% 0.81/0.98 (~c1_1(a1267)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[449, 1449])).
% 0.81/0.98 tff(1454,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c3_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c3_1(a1267)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1455,plain,
% 0.81/0.98 ((hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1205) | c1_1(a1205) | c0_1(a1205)) <=> (hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c3_1(a1267)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1456,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1205) | c1_1(a1205) | c0_1(a1205))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c3_1(a1267))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1455])).
% 0.81/0.98 tff(1457,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1205) | c1_1(a1205) | c0_1(a1205))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c3_1(a1267)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1456, 1454])).
% 0.81/0.98 tff(1458,plain,
% 0.81/0.98 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1205) | c1_1(a1205) | c0_1(a1205))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1459,plain,
% 0.81/0.98 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c3_1(a1267))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1458, 1457])).
% 0.81/0.98 tff(1460,plain,
% 0.81/0.98 (~c3_1(a1267)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1459, 159, 1110, 1453, 1452, 22, 23, 870, 1451])).
% 0.81/0.98 tff(1461,plain,
% 0.81/0.98 (hskp11),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1018, 1451, 1438])).
% 0.81/0.98 tff(1462,plain,
% 0.81/0.98 (c1_1(a1224)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[583, 1461])).
% 0.81/0.98 tff(1463,plain,
% 0.81/0.98 (~c2_1(a1224)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[567, 1461])).
% 0.81/0.98 tff(1464,plain,
% 0.81/0.98 (c3_1(a1224)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[575, 1461])).
% 0.81/0.98 tff(1465,plain,
% 0.81/0.98 (~c0_1(a1215)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[632, 1464, 1436, 1438, 1437, 1463, 1462, 23, 21, 22])).
% 0.81/0.98 tff(1466,plain,
% 0.81/0.98 (c0_1(a1267)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[457, 1449])).
% 0.81/0.98 tff(1467,plain,
% 0.81/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1468,plain,
% 0.81/0.98 (((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215))) <=> (c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1469,plain,
% 0.81/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267)))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1468])).
% 0.81/0.98 tff(1470,plain,
% 0.81/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1469, 1467])).
% 0.81/0.98 tff(1471,plain,
% 0.81/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1472,plain,
% 0.81/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 0.81/0.98 tff(1473,plain,
% 0.81/0.98 ($false),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1472, 159, 1466, 1436, 1453, 1452, 1435, 846, 1465, 1460])).
% 0.81/0.98 tff(1474,plain,(hskp26 | c0_1(a1205) | c1_1(a1205) | hskp5 | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.81/0.98 tff(1475,plain,
% 0.81/0.98 (hskp26),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1474, 198, 23, 21, 22])).
% 0.81/0.98 tff(1476,plain,
% 0.81/0.98 (c2_1(a1208)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[641, 1475])).
% 0.81/0.98 tff(1477,plain,
% 0.81/0.98 (c1_1(a1208)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[649, 1475])).
% 0.81/0.98 tff(1478,plain,
% 0.81/0.98 (c0_1(a1208)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[657, 1475])).
% 0.81/0.98 tff(1479,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | (~c1_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1480,plain,
% 0.81/0.98 ((hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233))) <=> (hskp8 | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1481,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | (~c1_1(a1233))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1480])).
% 0.81/0.98 tff(1482,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1481, 1479])).
% 0.81/0.98 tff(1483,plain,
% 0.81/0.98 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1484,plain,
% 0.81/0.98 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | (~c1_1(a1233))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 0.81/0.98 tff(1485,plain,
% 0.81/0.98 (hskp8),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1484, 159, 1478, 1477, 1476, 1186, 1178, 1170, 1448])).
% 0.81/0.98 tff(1486,plain,
% 0.81/0.98 (~c0_1(a1217)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[533, 1485])).
% 0.81/0.98 tff(1487,plain,
% 0.81/0.98 (~c3_1(a1217)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[539, 1485])).
% 0.81/0.98 tff(1488,plain,
% 0.81/0.98 (hskp11),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[559, 1487, 198, 1486])).
% 0.81/0.98 tff(1489,plain,
% 0.81/0.98 (~c2_1(a1224)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[567, 1488])).
% 0.81/0.98 tff(1490,plain,
% 0.81/0.98 (c1_1(a1224)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[583, 1488])).
% 0.81/0.98 tff(1491,plain,
% 0.81/0.98 (c3_1(a1224)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[575, 1488])).
% 0.81/0.98 tff(1492,plain,
% 0.81/0.98 ($false),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[678, 1491, 1490, 1475, 1489, 1438, 23, 21, 22])).
% 0.81/0.98 tff(1493,plain,(hskp28 | c1_1(a1205) | hskp5 | c0_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 0.81/0.98 tff(1494,plain,
% 0.81/0.98 (hskp28),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1493, 23, 21, 22])).
% 0.81/0.98 tff(1495,plain,
% 0.81/0.98 (c3_1(a1214)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[276, 1494])).
% 0.81/0.98 tff(1496,plain,
% 0.81/0.98 (c1_1(a1214)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[284, 1494])).
% 0.81/0.98 tff(1497,plain,
% 0.81/0.98 (c0_1(a1214)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[292, 1494])).
% 0.81/0.98 tff(1498,plain,
% 0.81/0.98 (~c3_1(a1205)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1010, 159, 21, 1497, 1496, 1495, 22, 23, 20])).
% 0.81/0.98 tff(1499,plain,
% 0.81/0.98 (hskp11),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1018, 1498, 1438])).
% 0.81/0.98 tff(1500,plain,
% 0.81/0.98 (c1_1(a1224)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[583, 1499])).
% 0.81/0.98 tff(1501,plain,
% 0.81/0.98 (~c2_1(a1224)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[567, 1499])).
% 0.81/0.98 tff(1502,plain,
% 0.81/0.98 (c3_1(a1224)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[575, 1499])).
% 0.81/0.98 tff(1503,plain,
% 0.81/0.98 (~c0_1(a1215)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[632, 1502, 1436, 1438, 1437, 1501, 1500, 23, 21, 22])).
% 0.81/0.98 tff(1504,plain,
% 0.81/0.98 (~hskp2),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1060, 1503, 1496, 1495, 1436, 1437, 1435, 1497])).
% 0.81/0.98 tff(1505,plain,
% 0.81/0.98 (hskp7 | hskp2),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1077, 159, 1497, 1496, 1495, 1071])).
% 0.81/0.98 tff(1506,plain,
% 0.81/0.98 (hskp7),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1505, 1504])).
% 0.81/0.98 tff(1507,plain,
% 0.81/0.98 (~c3_1(a1216)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1084, 1506])).
% 0.81/0.98 tff(1508,plain,
% 0.81/0.98 (~c2_1(a1216)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1090, 1506])).
% 0.81/0.98 tff(1509,plain,
% 0.81/0.98 (~c1_1(a1216)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1153, 1506])).
% 0.81/0.98 tff(1510,plain,
% 0.81/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1216)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1511,plain,
% 0.81/0.98 (((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215))) <=> (c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1216)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1512,plain,
% 0.81/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1216))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1511])).
% 0.81/0.98 tff(1513,plain,
% 0.81/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1216)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1512, 1510])).
% 0.81/0.98 tff(1514,plain,
% 0.81/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1515,plain,
% 0.81/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1216))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1514, 1513])).
% 0.81/0.98 tff(1516,plain,
% 0.81/0.98 (~c0_1(a1216)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1515, 159, 1436, 1509, 1508, 1507, 1435, 846, 1503])).
% 0.81/0.98 tff(1517,plain,
% 0.81/0.98 ($false),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1097, 159, 1497, 1496, 1495, 1436, 1437, 1508, 1507, 1435, 74, 1516])).
% 0.81/0.98 tff(1518,plain,(c1_1(a1205) | hskp5 | c0_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 0.81/0.98 tff(1519,plain,
% 0.81/0.98 (c1_1(a1205)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1518, 22, 21])).
% 0.81/0.98 tff(1520,plain,
% 0.81/0.98 (((~hskp0) | (~c1_1(a1205))) <=> ((~hskp0) | (~c1_1(a1205)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1521,plain,
% 0.81/0.98 (((~c1_1(a1205)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a1205)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1522,axiom,((~c1_1(a1205)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.81/0.98 tff(1523,plain,
% 0.81/0.98 ((~hskp0) | (~c1_1(a1205))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 0.81/0.98 tff(1524,plain,
% 0.81/0.98 ((~hskp0) | (~c1_1(a1205))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1523, 1520])).
% 0.81/0.98 tff(1525,plain,
% 0.81/0.98 (~hskp0),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1524, 1519])).
% 0.81/0.98 tff(1526,assumption,(hskp6), introduced(assumption)).
% 0.81/0.98 tff(1527,plain,
% 0.81/0.98 (~c3_1(a1215)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[89, 1526])).
% 0.81/0.98 tff(1528,assumption,(~hskp0), introduced(assumption)).
% 0.81/0.98 tff(1529,plain,
% 0.81/0.98 (c1_1(a1215)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[97, 1526])).
% 0.81/0.98 tff(1530,plain,
% 0.81/0.98 (c2_1(a1215)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[105, 1526])).
% 0.81/0.98 tff(1531,plain,
% 0.81/0.98 (^[U: $i] : refl((hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.81/0.98 inference(bind,[status(th)],[])).
% 0.81/0.98 tff(1532,plain,
% 0.81/0.98 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.81/0.98 inference(quant_intro,[status(thm)],[1531])).
% 0.81/0.98 tff(1533,plain,
% 0.81/0.98 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1534,plain,
% 0.81/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp0))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp0) <=> (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.81/0.98 inference(bind,[status(th)],[])).
% 0.81/0.98 tff(1535,plain,
% 0.81/0.98 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.81/0.98 inference(quant_intro,[status(thm)],[1534])).
% 0.81/0.98 tff(1536,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 0.81/0.98 tff(1537,plain,
% 0.81/0.98 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1536, 1535])).
% 0.81/0.98 tff(1538,plain,
% 0.81/0.98 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1537, 1533])).
% 0.81/0.98 tff(1539,plain,(
% 0.81/0.98 ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.81/0.98 inference(skolemize,[status(sab)],[1538])).
% 0.81/0.98 tff(1540,plain,
% 0.81/0.98 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1539, 1532])).
% 0.81/0.98 tff(1541,plain,
% 0.81/0.98 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp0 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp0 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1542,plain,
% 0.81/0.98 ((hskp27 | hskp0 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215))) <=> (hskp27 | hskp0 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1543,plain,
% 0.81/0.98 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp0 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp0 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1542])).
% 0.81/0.98 tff(1544,plain,
% 0.81/0.98 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp0 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp0 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1543, 1541])).
% 0.81/0.98 tff(1545,plain,
% 0.81/0.98 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp0 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1546,plain,
% 0.81/0.98 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp0 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 0.81/0.98 tff(1547,plain,
% 0.81/0.98 (hskp27 | hskp0 | c0_1(a1215)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1546, 159, 128, 126, 1540])).
% 0.81/0.98 tff(1548,plain,
% 0.81/0.98 (hskp27),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1547, 693, 1528])).
% 0.81/0.98 tff(1549,plain,
% 0.81/0.98 (((~hskp27) | c3_1(a1213)) <=> ((~hskp27) | c3_1(a1213))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1550,axiom,((~hskp27) | c3_1(a1213)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 0.81/0.98 tff(1551,plain,
% 0.81/0.98 ((~hskp27) | c3_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 0.81/0.98 tff(1552,plain,
% 0.81/0.98 ((~hskp27) | c3_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1551, 1549])).
% 0.81/0.98 tff(1553,plain,
% 0.81/0.98 ((~hskp27) | c3_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1552, 1549])).
% 0.81/0.98 tff(1554,plain,
% 0.81/0.98 ((~hskp27) | c3_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1553, 1549])).
% 0.81/0.98 tff(1555,plain,
% 0.81/0.98 ((~hskp27) | c3_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1554, 1549])).
% 0.81/0.98 tff(1556,plain,
% 0.81/0.98 (c3_1(a1213)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1555, 1548])).
% 0.81/0.98 tff(1557,plain,
% 0.81/0.98 (((~hskp27) | c2_1(a1213)) <=> ((~hskp27) | c2_1(a1213))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1558,axiom,((~hskp27) | c2_1(a1213)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.81/0.98 tff(1559,plain,
% 0.81/0.98 ((~hskp27) | c2_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1558, 1557])).
% 0.81/0.98 tff(1560,plain,
% 0.81/0.98 ((~hskp27) | c2_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1559, 1557])).
% 0.81/0.98 tff(1561,plain,
% 0.81/0.98 ((~hskp27) | c2_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1560, 1557])).
% 0.81/0.98 tff(1562,plain,
% 0.81/0.98 ((~hskp27) | c2_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1561, 1557])).
% 0.81/0.98 tff(1563,plain,
% 0.81/0.98 ((~hskp27) | c2_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1562, 1557])).
% 0.81/0.98 tff(1564,plain,
% 0.81/0.98 (c2_1(a1213)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1563, 1548])).
% 0.81/0.98 tff(1565,plain,
% 0.81/0.98 (((~hskp27) | c1_1(a1213)) <=> ((~hskp27) | c1_1(a1213))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1566,axiom,((~hskp27) | c1_1(a1213)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.81/0.98 tff(1567,plain,
% 0.81/0.98 ((~hskp27) | c1_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 0.81/0.98 tff(1568,plain,
% 0.81/0.98 ((~hskp27) | c1_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1567, 1565])).
% 0.81/0.98 tff(1569,plain,
% 0.81/0.98 ((~hskp27) | c1_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1568, 1565])).
% 0.81/0.98 tff(1570,plain,
% 0.81/0.98 ((~hskp27) | c1_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1569, 1565])).
% 0.81/0.98 tff(1571,plain,
% 0.81/0.98 ((~hskp27) | c1_1(a1213)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1570, 1565])).
% 0.81/0.98 tff(1572,plain,
% 0.81/0.98 (c1_1(a1213)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1571, 1548])).
% 0.81/0.98 tff(1573,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1574,plain,
% 0.81/0.98 (((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215))) <=> (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1575,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1574])).
% 0.81/0.98 tff(1576,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1575, 1573])).
% 0.81/0.98 tff(1577,plain,
% 0.81/0.98 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1578,plain,
% 0.81/0.98 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1577, 1576])).
% 0.81/0.98 tff(1579,plain,
% 0.81/0.98 ($false),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1578, 159, 1572, 1564, 1556, 128, 126, 719, 693])).
% 0.81/0.98 tff(1580,plain,(c0_1(a1215) | (~c1_1(a1215)) | c3_1(a1215) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.81/0.98 tff(1581,plain,
% 0.81/0.98 (c0_1(a1215)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1580, 1528, 126, 128])).
% 0.81/0.98 tff(1582,plain,
% 0.81/0.98 (hskp21),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[166, 1528])).
% 0.81/0.98 tff(1583,plain,
% 0.81/0.98 (~c1_1(a1257)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[172, 1582])).
% 0.81/0.98 tff(1584,plain,
% 0.81/0.98 (~c0_1(a1257)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[178, 1582])).
% 0.81/0.98 tff(1585,plain,
% 0.81/0.98 (c3_1(a1257)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[186, 1582])).
% 0.81/0.98 tff(1586,plain,
% 0.81/0.98 (hskp23),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[241, 1581, 1528])).
% 0.81/0.98 tff(1587,plain,
% 0.81/0.98 (~c3_1(a1261)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[247, 1586])).
% 0.81/0.98 tff(1588,plain,
% 0.81/0.98 (~c2_1(a1261)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[253, 1586])).
% 0.81/0.98 tff(1589,plain,
% 0.81/0.98 (~c0_1(a1261)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[259, 1586])).
% 0.81/0.98 tff(1590,plain,
% 0.81/0.98 (hskp28),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[266, 159, 1589, 1588, 1587, 197])).
% 0.81/0.99 tff(1591,plain,
% 0.81/0.99 (c3_1(a1214)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[276, 1590])).
% 0.81/0.99 tff(1592,plain,
% 0.81/0.99 (c1_1(a1214)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[284, 1590])).
% 0.81/0.99 tff(1593,plain,
% 0.81/0.99 (c0_1(a1214)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[292, 1590])).
% 0.81/0.99 tff(1594,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1595,plain,
% 0.81/0.99 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257))) <=> (c0_1(a1257) | c1_1(a1257) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1596,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.81/0.99 inference(monotonicity,[status(thm)],[1595])).
% 0.81/0.99 tff(1597,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/0.99 inference(transitivity,[status(thm)],[1596, 1594])).
% 0.81/0.99 tff(1598,plain,
% 0.81/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1599,plain,
% 0.81/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 0.81/0.99 tff(1600,plain,
% 0.81/0.99 ($false),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1599, 159, 1593, 1592, 1591, 1585, 127, 1584, 1583, 126, 1109, 1581])).
% 0.81/0.99 tff(1601,plain,(hskp0 | (~c2_1(a1215)) | c3_1(a1215) | (~c1_1(a1215))), inference(lemma,lemma(discharge,[]))).
% 0.81/0.99 tff(1602,plain,
% 0.81/0.99 ($false),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1601, 1530, 1529, 1528, 1527])).
% 0.81/0.99 tff(1603,plain,((~hskp6) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.81/0.99 tff(1604,plain,
% 0.81/0.99 (~hskp6),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1603, 1525])).
% 0.81/0.99 tff(1605,plain,
% 0.81/0.99 (hskp15),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[83, 1604, 21])).
% 0.81/0.99 tff(1606,plain,
% 0.81/0.99 (~c2_1(a1233)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1169, 1605])).
% 0.81/0.99 tff(1607,plain,
% 0.81/0.99 (c1_1(a1233)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1177, 1605])).
% 0.81/0.99 tff(1608,plain,
% 0.81/0.99 (c0_1(a1233)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1185, 1605])).
% 0.81/0.99 tff(1609,assumption,(c1_1(a1205)), introduced(assumption)).
% 0.81/0.99 tff(1610,plain,
% 0.81/0.99 (~hskp0),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1524, 1609])).
% 0.81/0.99 tff(1611,plain,
% 0.81/0.99 (~hskp6),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1603, 1610])).
% 0.81/0.99 tff(1612,plain,
% 0.81/0.99 (c3_1(a1205)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[205, 107, 198])).
% 0.81/0.99 tff(1613,plain,
% 0.81/0.99 (c3_1(a1233)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1382, 1449, 1361, 1359, 1362])).
% 0.81/0.99 tff(1614,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1257)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1615,plain,
% 0.81/0.99 (((~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257))) <=> (c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1257)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1616,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1257))))),
% 0.81/0.99 inference(monotonicity,[status(thm)],[1615])).
% 0.81/0.99 tff(1617,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1257)))),
% 0.81/0.99 inference(transitivity,[status(thm)],[1616, 1614])).
% 0.81/0.99 tff(1618,plain,
% 0.81/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1619,plain,
% 0.81/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1257))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1618, 1617])).
% 0.81/0.99 tff(1620,plain,
% 0.81/0.99 ($false),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1619, 159, 1126, 1362, 1361, 1125, 1124, 1123, 1122, 1113, 1109, 1335])).
% 0.81/0.99 tff(1621,plain,(hskp25 | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1233)) | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.81/0.99 tff(1622,plain,
% 0.81/0.99 (hskp25),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1621, 1613, 1361, 1362, 1110])).
% 0.81/0.99 tff(1623,plain,
% 0.81/0.99 (c2_1(a1204)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[700, 1622])).
% 0.81/0.99 tff(1624,plain,
% 0.81/0.99 (c0_1(a1204)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[691, 1622])).
% 0.81/0.99 tff(1625,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1626,plain,
% 0.81/0.99 (((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205))) <=> (c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1627,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))))),
% 0.81/0.99 inference(monotonicity,[status(thm)],[1626])).
% 0.81/0.99 tff(1628,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 0.81/0.99 inference(transitivity,[status(thm)],[1627, 1625])).
% 0.81/0.99 tff(1629,plain,
% 0.81/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1630,plain,
% 0.81/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1629, 1628])).
% 0.81/0.99 tff(1631,plain,
% 0.81/0.99 (~c1_1(a1204)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1630, 159, 1624, 1623, 107, 22, 1609, 352, 1612])).
% 0.81/0.99 tff(1632,plain,
% 0.81/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1633,plain,
% 0.81/0.99 ((hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204))) <=> (hskp6 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1634,plain,
% 0.81/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204))))),
% 0.81/0.99 inference(monotonicity,[status(thm)],[1633])).
% 0.81/0.99 tff(1635,plain,
% 0.81/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))),
% 0.81/0.99 inference(transitivity,[status(thm)],[1634, 1632])).
% 0.81/0.99 tff(1636,plain,
% 0.81/0.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204)))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1637,plain,
% 0.81/0.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1636, 1635])).
% 0.81/0.99 tff(1638,plain,
% 0.81/0.99 ($false),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1637, 159, 24, 1624, 1623, 1362, 1359, 44, 1631, 1613])).
% 0.81/0.99 tff(1639,plain,(hskp26 | hskp6 | (~c0_1(a1233)) | c2_1(a1233) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~c1_1(a1233)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.81/0.99 tff(1640,plain,
% 0.81/0.99 (hskp26),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1639, 107, 1362, 1359, 24, 22, 1609, 1361, 198])).
% 0.81/0.99 tff(1641,plain,
% 0.81/0.99 (c2_1(a1208)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[641, 1640])).
% 0.81/0.99 tff(1642,plain,
% 0.81/0.99 (c1_1(a1208)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[649, 1640])).
% 0.81/0.99 tff(1643,plain,
% 0.81/0.99 (c0_1(a1208)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[657, 1640])).
% 0.81/0.99 tff(1644,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1645,plain,
% 0.81/0.99 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205))) <=> (c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1646,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208))))),
% 0.81/0.99 inference(monotonicity,[status(thm)],[1645])).
% 0.81/0.99 tff(1647,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))),
% 0.81/0.99 inference(transitivity,[status(thm)],[1646, 1644])).
% 0.81/0.99 tff(1648,plain,
% 0.81/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1649,plain,
% 0.81/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1648, 1647])).
% 0.81/0.99 tff(1650,plain,
% 0.81/0.99 ($false),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1649, 159, 1643, 1642, 1641, 107, 22, 1609, 352, 1612])).
% 0.81/0.99 tff(1651,plain,(c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~c0_1(a1233)) | c2_1(a1233) | hskp6 | (~c1_1(a1233)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.81/0.99 tff(1652,plain,
% 0.81/0.99 (c2_1(a1205)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1651, 198, 1609, 22, 1359, 1611, 1361, 1362])).
% 0.81/0.99 tff(1653,plain,
% 0.81/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | c2_1(a1233) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c2_1(a1205)) | (~c0_1(a1233)) | (~c1_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp1 | c2_1(a1233) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c2_1(a1205)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1654,plain,
% 0.81/0.99 ((hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1205) | (~c1_1(a1205)) | (~c2_1(a1205))) <=> (hskp1 | c2_1(a1233) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c2_1(a1205)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1655,plain,
% 0.81/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1205) | (~c1_1(a1205)) | (~c2_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | c2_1(a1233) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c2_1(a1205)) | (~c0_1(a1233)) | (~c1_1(a1233))))),
% 0.81/0.99 inference(monotonicity,[status(thm)],[1654])).
% 0.81/0.99 tff(1656,plain,
% 0.81/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1205) | (~c1_1(a1205)) | (~c2_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp1 | c2_1(a1233) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c2_1(a1205)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 0.81/0.99 inference(transitivity,[status(thm)],[1655, 1653])).
% 0.81/0.99 tff(1657,plain,
% 0.81/0.99 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1205) | (~c1_1(a1205)) | (~c2_1(a1205)))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1658,plain,
% 0.81/0.99 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp1 | c2_1(a1233) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c2_1(a1205)) | (~c0_1(a1233)) | (~c1_1(a1233))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 0.81/0.99 tff(1659,plain,
% 0.81/0.99 (hskp1 | (~c2_1(a1205))),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1658, 159, 1362, 1361, 1359, 22, 1609, 1284])).
% 0.81/0.99 tff(1660,plain,
% 0.81/0.99 (hskp1),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1659, 1652])).
% 0.81/0.99 tff(1661,plain,
% 0.81/0.99 (hskp14),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[960, 1466, 930, 1453, 1452])).
% 0.81/0.99 tff(1662,plain,
% 0.81/0.99 (~c2_1(a1232)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[385, 1661])).
% 0.81/0.99 tff(1663,plain,
% 0.81/0.99 (~c0_1(a1232)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[417, 1661])).
% 0.81/0.99 tff(1664,plain,
% 0.81/0.99 (c3_1(a1232)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[393, 1661])).
% 0.81/0.99 tff(1665,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1233) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1233) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1666,plain,
% 0.81/0.99 (((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c3_1(a1233)) | (~c1_1(a1233)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c2_1(a1233) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1667,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c3_1(a1233)) | (~c1_1(a1233)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1233) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))))),
% 0.81/0.99 inference(monotonicity,[status(thm)],[1666])).
% 0.81/0.99 tff(1668,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c3_1(a1233)) | (~c1_1(a1233)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1233) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 0.81/0.99 inference(transitivity,[status(thm)],[1667, 1665])).
% 0.81/0.99 tff(1669,plain,
% 0.81/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c3_1(a1233)) | (~c1_1(a1233)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1670,plain,
% 0.81/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1233) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1669, 1668])).
% 0.81/0.99 tff(1671,plain,
% 0.81/0.99 (~c1_1(a1204)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1670, 159, 1624, 1623, 1361, 1664, 1359, 1663, 1662, 352, 1613])).
% 0.81/0.99 tff(1672,plain,
% 0.81/0.99 ($false),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1637, 159, 24, 1624, 1623, 1362, 1359, 44, 1671, 1613])).
% 0.81/0.99 tff(1673,plain,(hskp26 | hskp6 | (~c0_1(a1233)) | c2_1(a1233) | (~c1_1(a1233)) | (~hskp1) | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.81/0.99 tff(1674,plain,
% 0.81/0.99 (hskp26),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1673, 1660, 1611, 1359, 1361, 1362, 198])).
% 0.81/0.99 tff(1675,plain,
% 0.81/0.99 (c2_1(a1208)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[641, 1674])).
% 0.81/0.99 tff(1676,plain,
% 0.81/0.99 (c1_1(a1208)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[649, 1674])).
% 0.81/0.99 tff(1677,plain,
% 0.81/0.99 (c0_1(a1208)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[657, 1674])).
% 0.81/0.99 tff(1678,assumption,(hskp23), introduced(assumption)).
% 0.81/0.99 tff(1679,plain,
% 0.81/0.99 (~c3_1(a1261)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[247, 1678])).
% 0.81/0.99 tff(1680,plain,
% 0.81/0.99 (~c2_1(a1261)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[253, 1678])).
% 0.81/0.99 tff(1681,plain,
% 0.81/0.99 (~c0_1(a1261)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[259, 1678])).
% 0.81/0.99 tff(1682,plain,
% 0.81/0.99 ($false),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[266, 198, 159, 1681, 1680, 1679, 197])).
% 0.81/0.99 tff(1683,plain,((~hskp23) | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.81/0.99 tff(1684,plain,
% 0.81/0.99 (~hskp23),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1683, 198])).
% 0.81/0.99 tff(1685,plain,
% 0.81/0.99 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1686,plain,
% 0.81/0.99 ((hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208))) <=> (hskp23 | hskp0 | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1687,plain,
% 0.81/0.99 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208))))),
% 0.81/0.99 inference(monotonicity,[status(thm)],[1686])).
% 0.81/0.99 tff(1688,plain,
% 0.81/0.99 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))),
% 0.81/0.99 inference(transitivity,[status(thm)],[1687, 1685])).
% 0.81/0.99 tff(1689,plain,
% 0.81/0.99 ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1690,plain,
% 0.81/0.99 ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 0.81/0.99 tff(1691,plain,
% 0.81/0.99 ($false),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1690, 159, 1684, 1610, 1677, 1676, 1675, 234])).
% 0.81/0.99 tff(1692,plain,(hskp28 | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1205) | (~c1_1(a1205))), inference(lemma,lemma(discharge,[]))).
% 0.81/0.99 tff(1693,plain,
% 0.81/0.99 (hskp28),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1692, 1606, 1607, 1608, 22, 1519])).
% 0.81/1.00 tff(1694,plain,
% 0.81/1.00 (c3_1(a1214)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[276, 1693])).
% 0.81/1.00 tff(1695,plain,
% 0.81/1.00 (c1_1(a1214)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[284, 1693])).
% 0.81/1.00 tff(1696,plain,
% 0.81/1.00 (c0_1(a1214)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[292, 1693])).
% 0.81/1.00 tff(1697,plain,
% 0.81/1.00 (hskp10),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1192, 159, 692, 701, 709, 1362, 1361, 1359, 64])).
% 0.81/1.00 tff(1698,plain,
% 0.81/1.00 (~c3_1(a1223)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1198, 1697])).
% 0.81/1.00 tff(1699,plain,
% 0.81/1.00 (~c1_1(a1223)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1204, 1697])).
% 0.81/1.00 tff(1700,plain,
% 0.81/1.00 (c2_1(a1223)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1212, 1697])).
% 0.81/1.00 tff(1701,plain,
% 0.81/1.00 (hskp13),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1219, 159, 24, 1700, 1699, 1698, 54])).
% 0.81/1.00 tff(1702,plain,
% 0.81/1.00 (~c1_1(a1229)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1225, 1701])).
% 0.81/1.00 tff(1703,plain,
% 0.81/1.00 (c2_1(a1229)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1233, 1701])).
% 0.81/1.00 tff(1704,plain,
% 0.81/1.00 (c0_1(a1229)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1241, 1701])).
% 0.81/1.00 tff(1705,plain,
% 0.81/1.00 (~c3_1(a1233)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1248, 159, 24, 1362, 1704, 1703, 1359, 1702, 44])).
% 0.81/1.00 tff(1706,plain,
% 0.81/1.00 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.81/1.00 inference(bind,[status(th)],[])).
% 0.81/1.00 tff(1707,plain,
% 0.81/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.81/1.00 inference(quant_intro,[status(thm)],[1706])).
% 0.81/1.00 tff(1708,plain,
% 0.81/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1709,plain,
% 0.81/1.00 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.81/1.00 inference(bind,[status(th)],[])).
% 0.81/1.00 tff(1710,plain,
% 0.81/1.00 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.81/1.00 inference(quant_intro,[status(thm)],[1709])).
% 0.81/1.00 tff(1711,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 0.81/1.00 tff(1712,plain,
% 0.81/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 0.81/1.00 tff(1713,plain,
% 0.81/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1712, 1708])).
% 0.81/1.00 tff(1714,plain,(
% 0.81/1.00 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.81/1.00 inference(skolemize,[status(sab)],[1713])).
% 0.81/1.00 tff(1715,plain,
% 0.81/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1714, 1707])).
% 0.81/1.00 tff(1716,plain,
% 0.81/1.00 (~c1_1(a1204)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1255, 159, 692, 701, 1362, 1359, 821, 1705])).
% 0.81/1.00 tff(1717,plain,
% 0.81/1.00 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.81/1.00 inference(bind,[status(th)],[])).
% 0.81/1.00 tff(1718,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/1.00 inference(quant_intro,[status(thm)],[1717])).
% 0.81/1.00 tff(1719,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1720,plain,
% 0.81/1.00 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.81/1.00 inference(bind,[status(th)],[])).
% 0.81/1.00 tff(1721,plain,
% 0.81/1.00 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/1.00 inference(quant_intro,[status(thm)],[1720])).
% 0.81/1.00 tff(1722,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 0.81/1.00 tff(1723,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1722, 1721])).
% 0.81/1.00 tff(1724,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1723, 1719])).
% 0.81/1.00 tff(1725,plain,(
% 0.81/1.00 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/1.00 inference(skolemize,[status(sab)],[1724])).
% 0.81/1.00 tff(1726,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1725, 1718])).
% 0.81/1.00 tff(1727,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | c2_1(a1233) | (~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp18 | c2_1(a1233) | (~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1728,plain,
% 0.81/1.00 ((hskp18 | (~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204))) <=> (hskp18 | c2_1(a1233) | (~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1729,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | c2_1(a1233) | (~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204))))),
% 0.81/1.00 inference(monotonicity,[status(thm)],[1728])).
% 0.81/1.00 tff(1730,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp18 | c2_1(a1233) | (~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 0.81/1.00 inference(transitivity,[status(thm)],[1729, 1727])).
% 0.81/1.00 tff(1731,plain,
% 0.81/1.00 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))),
% 0.81/1.00 inference(quant_inst,[status(thm)],[])).
% 0.81/1.00 tff(1732,plain,
% 0.81/1.00 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp18 | c2_1(a1233) | (~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1731, 1730])).
% 0.81/1.00 tff(1733,plain,
% 0.81/1.00 (hskp18),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1732, 159, 701, 709, 1361, 1359, 1726, 1716, 1705])).
% 0.81/1.00 tff(1734,plain,
% 0.81/1.00 (((~hskp18) | (~c1_1(a1246))) <=> ((~hskp18) | (~c1_1(a1246)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1735,plain,
% 0.81/1.00 (((~c1_1(a1246)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a1246)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1736,axiom,((~c1_1(a1246)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.81/1.00 tff(1737,plain,
% 0.81/1.00 ((~hskp18) | (~c1_1(a1246))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 0.81/1.00 tff(1738,plain,
% 0.81/1.00 ((~hskp18) | (~c1_1(a1246))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1737, 1734])).
% 0.81/1.00 tff(1739,plain,
% 0.81/1.00 (~c1_1(a1246)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1738, 1733])).
% 0.81/1.00 tff(1740,plain,
% 0.81/1.00 (((~hskp18) | c3_1(a1246)) <=> ((~hskp18) | c3_1(a1246))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1741,axiom,((~hskp18) | c3_1(a1246)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.81/1.00 tff(1742,plain,
% 0.81/1.00 ((~hskp18) | c3_1(a1246)),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 0.81/1.00 tff(1743,plain,
% 0.81/1.00 ((~hskp18) | c3_1(a1246)),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1742, 1740])).
% 0.81/1.00 tff(1744,plain,
% 0.81/1.00 ((~hskp18) | c3_1(a1246)),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1743, 1740])).
% 0.81/1.00 tff(1745,plain,
% 0.81/1.00 ((~hskp18) | c3_1(a1246)),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1744, 1740])).
% 0.81/1.00 tff(1746,plain,
% 0.81/1.00 ((~hskp18) | c3_1(a1246)),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1745, 1740])).
% 0.81/1.00 tff(1747,plain,
% 0.81/1.00 (c3_1(a1246)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1746, 1733])).
% 0.81/1.00 tff(1748,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a1246) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c3_1(a1246)) | c0_1(a1246) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a1246) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c3_1(a1246)) | c0_1(a1246) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1749,plain,
% 0.81/1.00 (((~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c1_1(a1246) | c0_1(a1246) | (~c3_1(a1246))) <=> (c1_1(a1246) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c3_1(a1246)) | c0_1(a1246) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1750,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c1_1(a1246) | c0_1(a1246) | (~c3_1(a1246)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a1246) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c3_1(a1246)) | c0_1(a1246) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 0.81/1.00 inference(monotonicity,[status(thm)],[1749])).
% 0.81/1.00 tff(1751,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c1_1(a1246) | c0_1(a1246) | (~c3_1(a1246)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a1246) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c3_1(a1246)) | c0_1(a1246) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.81/1.00 inference(transitivity,[status(thm)],[1750, 1748])).
% 0.81/1.00 tff(1752,plain,
% 0.81/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c1_1(a1246) | c0_1(a1246) | (~c3_1(a1246)))),
% 0.81/1.00 inference(quant_inst,[status(thm)],[])).
% 0.81/1.00 tff(1753,plain,
% 0.81/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a1246) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c3_1(a1246)) | c0_1(a1246) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 0.81/1.00 tff(1754,plain,
% 0.81/1.00 (c0_1(a1246)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1753, 159, 692, 701, 709, 1747, 1362, 1739, 1359, 1715, 1705])).
% 0.81/1.00 tff(1755,plain,
% 0.81/1.00 (hskp9),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1272, 159, 692, 709, 1700, 1699, 1698, 1266, 1716])).
% 0.81/1.00 tff(1756,plain,
% 0.81/1.00 (~c0_1(a1219)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[768, 1755])).
% 0.81/1.00 tff(1757,plain,
% 0.81/1.00 (c2_1(a1219)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[747, 1755])).
% 0.81/1.00 tff(1758,plain,
% 0.81/1.00 (c1_1(a1219)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[755, 1755])).
% 0.81/1.00 tff(1759,plain,
% 0.81/1.00 (hskp1),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1292, 159, 1362, 1361, 1758, 1757, 1359, 1756, 1284])).
% 0.81/1.00 tff(1760,plain,
% 0.81/1.00 (c2_1(a1206)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[943, 1759])).
% 0.81/1.00 tff(1761,plain,
% 0.81/1.00 (c0_1(a1206)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[951, 1759])).
% 0.81/1.00 tff(1762,plain,
% 0.81/1.00 (~c1_1(a1206)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1301, 159, 1362, 1761, 1760, 1359, 821, 1705])).
% 0.81/1.00 tff(1763,plain,
% 0.81/1.00 (~c3_1(a1206)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[935, 1759])).
% 0.81/1.00 tff(1764,plain,
% 0.81/1.00 (c3_1(a1219)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1333, 159, 1362, 1758, 1761, 1359, 1756, 1763, 846, 1705, 1762])).
% 0.81/1.00 tff(1765,assumption,(c0_1(a1246)), introduced(assumption)).
% 0.81/1.00 tff(1766,assumption,(c3_1(a1219)), introduced(assumption)).
% 0.81/1.00 tff(1767,assumption,(hskp8), introduced(assumption)).
% 0.81/1.00 tff(1768,plain,
% 0.81/1.00 (~c3_1(a1217)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[539, 1767])).
% 0.81/1.00 tff(1769,plain,
% 0.81/1.00 (~c0_1(a1217)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[533, 1767])).
% 0.81/1.00 tff(1770,assumption,(c2_1(a1219)), introduced(assumption)).
% 0.81/1.00 tff(1771,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1772,plain,
% 0.81/1.00 (((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1217) | c3_1(a1217) | (~c2_1(a1217))) <=> (c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1773,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1217) | c3_1(a1217) | (~c2_1(a1217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.81/1.00 inference(monotonicity,[status(thm)],[1772])).
% 0.81/1.00 tff(1774,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1217) | c3_1(a1217) | (~c2_1(a1217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.00 inference(transitivity,[status(thm)],[1773, 1771])).
% 0.81/1.00 tff(1775,plain,
% 0.81/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1217) | c3_1(a1217) | (~c2_1(a1217)))),
% 0.81/1.00 inference(quant_inst,[status(thm)],[])).
% 0.81/1.00 tff(1776,plain,
% 0.81/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 0.81/1.00 tff(1777,plain,
% 0.81/1.00 (~c2_1(a1217)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1776, 159, 1052, 1051, 1050, 850, 1770, 1769, 1768, 10, 1766])).
% 0.81/1.00 tff(1778,plain,
% 0.81/1.00 (~c1_1(a1217)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[904, 1767])).
% 0.81/1.00 tff(1779,assumption,(~c1_1(a1246)), introduced(assumption)).
% 0.81/1.00 tff(1780,assumption,(c3_1(a1246)), introduced(assumption)).
% 0.81/1.00 tff(1781,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1246) | c0_1(a1219) | c0_1(a1217) | c1_1(a1217) | (~ndr1_0) | c2_1(a1217) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1246)) | (~c0_1(a1246)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1246) | c0_1(a1219) | c0_1(a1217) | c1_1(a1217) | (~ndr1_0) | c2_1(a1217) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1246)) | (~c0_1(a1246)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1782,plain,
% 0.81/1.00 (((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1217) | c1_1(a1217) | c0_1(a1217)) <=> (c1_1(a1246) | c0_1(a1219) | c0_1(a1217) | c1_1(a1217) | (~ndr1_0) | c2_1(a1217) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1246)) | (~c0_1(a1246)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1783,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1217) | c1_1(a1217) | c0_1(a1217))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1246) | c0_1(a1219) | c0_1(a1217) | c1_1(a1217) | (~ndr1_0) | c2_1(a1217) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1246)) | (~c0_1(a1246))))),
% 0.81/1.00 inference(monotonicity,[status(thm)],[1782])).
% 0.81/1.00 tff(1784,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1217) | c1_1(a1217) | c0_1(a1217))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1246) | c0_1(a1219) | c0_1(a1217) | c1_1(a1217) | (~ndr1_0) | c2_1(a1217) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1246)) | (~c0_1(a1246)))),
% 0.81/1.00 inference(transitivity,[status(thm)],[1783, 1781])).
% 0.81/1.00 tff(1785,plain,
% 0.81/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1217) | c1_1(a1217) | c0_1(a1217))),
% 0.81/1.00 inference(quant_inst,[status(thm)],[])).
% 0.81/1.00 tff(1786,plain,
% 0.81/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1246) | c0_1(a1219) | c0_1(a1217) | c1_1(a1217) | (~ndr1_0) | c2_1(a1217) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1246)) | (~c0_1(a1246))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1785, 1784])).
% 0.81/1.00 tff(1787,plain,
% 0.81/1.00 ($false),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1786, 159, 1780, 850, 1770, 1779, 847, 1769, 1778, 34, 1777, 1765])).
% 0.81/1.00 tff(1788,plain,((~hskp8) | (~c3_1(a1246)) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1246) | c0_1(a1219) | (~c0_1(a1246)) | (~c0_1(a1214)) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1219))), inference(lemma,lemma(discharge,[]))).
% 0.81/1.00 tff(1789,plain,
% 0.81/1.00 (~hskp8),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1788, 1747, 1758, 1757, 1739, 1756, 1754, 1052, 1051, 1050, 1764])).
% 0.81/1.00 tff(1790,plain,
% 0.81/1.00 (((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)))) <=> ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1791,plain,
% 0.81/1.00 ((hskp11 | hskp8 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233))) <=> (hskp11 | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1792,plain,
% 0.81/1.00 (((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))) <=> ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233))))),
% 0.81/1.00 inference(monotonicity,[status(thm)],[1791])).
% 0.81/1.00 tff(1793,plain,
% 0.81/1.00 (((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))) <=> ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 0.81/1.00 inference(transitivity,[status(thm)],[1792, 1790])).
% 0.81/1.00 tff(1794,plain,
% 0.81/1.00 ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))),
% 0.81/1.00 inference(quant_inst,[status(thm)],[])).
% 0.81/1.00 tff(1795,plain,
% 0.81/1.00 ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 0.81/1.00 tff(1796,plain,
% 0.81/1.00 (hskp11 | hskp8),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1795, 159, 1362, 1361, 1359, 490])).
% 0.81/1.00 tff(1797,plain,
% 0.81/1.00 (hskp11),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1796, 1789])).
% 0.81/1.00 tff(1798,plain,
% 0.81/1.00 (~c2_1(a1224)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[567, 1797])).
% 0.81/1.00 tff(1799,plain,
% 0.81/1.00 (c3_1(a1224)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[575, 1797])).
% 0.81/1.00 tff(1800,plain,
% 0.81/1.00 (c1_1(a1224)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[583, 1797])).
% 0.81/1.00 tff(1801,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1802,plain,
% 0.81/1.00 ((hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223))) <=> (hskp14 | c2_1(a1224) | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1803,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1802])).
% 0.81/1.01 tff(1804,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1803, 1801])).
% 0.81/1.01 tff(1805,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1806,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 0.81/1.01 tff(1807,plain,
% 0.81/1.01 (hskp14),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1806, 159, 1800, 1799, 1700, 1798, 1699, 1698, 613])).
% 0.81/1.01 tff(1808,plain,
% 0.81/1.01 (~c2_1(a1232)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[385, 1807])).
% 0.81/1.01 tff(1809,plain,
% 0.81/1.01 (~c0_1(a1232)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[417, 1807])).
% 0.81/1.01 tff(1810,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1246) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | (~c3_1(a1246)) | (~c0_1(a1246)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1246) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | (~c3_1(a1246)) | (~c0_1(a1246)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1811,plain,
% 0.81/1.01 (((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232)) <=> (c1_1(a1246) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | (~c3_1(a1246)) | (~c0_1(a1246)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1812,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1246) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | (~c3_1(a1246)) | (~c0_1(a1246))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1811])).
% 0.81/1.01 tff(1813,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1246) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | (~c3_1(a1246)) | (~c0_1(a1246)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1812, 1810])).
% 0.81/1.01 tff(1814,plain,
% 0.81/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1815,plain,
% 0.81/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1246) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | (~c3_1(a1246)) | (~c0_1(a1246))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 0.81/1.01 tff(1816,plain,
% 0.81/1.01 (c1_1(a1232)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1815, 159, 1747, 1758, 1757, 1739, 1809, 1808, 1756, 34, 1754])).
% 0.81/1.01 tff(1817,plain,
% 0.81/1.01 (((~hskp18) | c2_1(a1246)) <=> ((~hskp18) | c2_1(a1246))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1818,axiom,((~hskp18) | c2_1(a1246)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 0.81/1.01 tff(1819,plain,
% 0.81/1.01 ((~hskp18) | c2_1(a1246)),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 0.81/1.01 tff(1820,plain,
% 0.81/1.01 ((~hskp18) | c2_1(a1246)),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1819, 1817])).
% 0.81/1.01 tff(1821,plain,
% 0.81/1.01 ((~hskp18) | c2_1(a1246)),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1820, 1817])).
% 0.81/1.01 tff(1822,plain,
% 0.81/1.01 ((~hskp18) | c2_1(a1246)),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1821, 1817])).
% 0.81/1.01 tff(1823,plain,
% 0.81/1.01 ((~hskp18) | c2_1(a1246)),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1822, 1817])).
% 0.81/1.01 tff(1824,plain,
% 0.81/1.01 (c2_1(a1246)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1823, 1733])).
% 0.81/1.01 tff(1825,assumption,(~c2_1(a1214)), introduced(assumption)).
% 0.81/1.01 tff(1826,assumption,(c2_1(a1246)), introduced(assumption)).
% 0.81/1.01 tff(1827,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1246) | (~ndr1_0) | (~c0_1(a1246)) | (~c2_1(a1246)) | c2_1(a1214) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1246) | (~ndr1_0) | (~c0_1(a1246)) | (~c2_1(a1246)) | c2_1(a1214) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1828,plain,
% 0.81/1.01 ((hskp6 | (~ndr1_0) | c2_1(a1214) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1246) | (~c2_1(a1246)) | (~c0_1(a1246))) <=> (hskp6 | c1_1(a1246) | (~ndr1_0) | (~c0_1(a1246)) | (~c2_1(a1246)) | c2_1(a1214) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1829,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1214) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1246) | (~c2_1(a1246)) | (~c0_1(a1246)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1246) | (~ndr1_0) | (~c0_1(a1246)) | (~c2_1(a1246)) | c2_1(a1214) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1828])).
% 0.81/1.01 tff(1830,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1214) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1246) | (~c2_1(a1246)) | (~c0_1(a1246)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1246) | (~ndr1_0) | (~c0_1(a1246)) | (~c2_1(a1246)) | c2_1(a1214) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1829, 1827])).
% 0.81/1.01 tff(1831,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1214) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1246) | (~c2_1(a1246)) | (~c0_1(a1246)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1832,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1246) | (~ndr1_0) | (~c0_1(a1246)) | (~c2_1(a1246)) | c2_1(a1214) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1831, 1830])).
% 0.81/1.01 tff(1833,plain,
% 0.81/1.01 ($false),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1832, 159, 24, 1052, 1050, 1826, 1779, 44, 1825, 1765])).
% 0.81/1.01 tff(1834,plain,(c2_1(a1214) | hskp6 | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c2_1(a1246)) | c1_1(a1246) | (~c0_1(a1246))), inference(lemma,lemma(discharge,[]))).
% 0.81/1.01 tff(1835,plain,
% 0.81/1.01 (c2_1(a1214)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1834, 1824, 1052, 1050, 24, 1739, 1754])).
% 0.81/1.01 tff(1836,plain,
% 0.81/1.01 (c3_1(a1232)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[393, 1807])).
% 0.81/1.01 tff(1837,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c1_1(a1232)) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c1_1(a1232)) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1838,plain,
% 0.81/1.01 (((~ndr1_0) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c1_1(a1232)) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1839,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c1_1(a1232)) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1838])).
% 0.81/1.01 tff(1840,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c1_1(a1232)) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1839, 1837])).
% 0.81/1.01 tff(1841,plain,
% 0.81/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1842,plain,
% 0.81/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c1_1(a1232)) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1841, 1840])).
% 0.81/1.01 tff(1843,plain,
% 0.81/1.01 ($false),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1842, 159, 1052, 1051, 1836, 1809, 1808, 352, 1835, 1816])).
% 0.81/1.01 tff(1844,plain,((~hskp25) | (~c0_1(a1214)) | (~c1_1(a1214)) | (~c3_1(a1214)) | hskp6 | (~c0_1(a1233)) | (~c1_1(a1233)) | c2_1(a1233)), inference(lemma,lemma(discharge,[]))).
% 0.81/1.01 tff(1845,plain,
% 0.81/1.01 (~hskp25),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1844, 1696, 1695, 1694, 1604, 1608, 1607, 1606])).
% 0.81/1.01 tff(1846,plain,
% 0.81/1.01 (hskp21),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1120, 1845])).
% 0.81/1.01 tff(1847,plain,
% 0.81/1.01 (~c1_1(a1257)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[172, 1846])).
% 0.81/1.01 tff(1848,plain,
% 0.81/1.01 (~c0_1(a1257)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[178, 1846])).
% 0.81/1.01 tff(1849,plain,
% 0.81/1.01 (c3_1(a1257)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[186, 1846])).
% 0.81/1.01 tff(1850,plain,
% 0.81/1.01 ($false),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[299, 159, 21, 1696, 1695, 1694, 1849, 1848, 1847, 20])).
% 0.81/1.01 tff(1851,plain,(c0_1(a1205) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.81/1.01 tff(1852,plain,
% 0.81/1.01 (c0_1(a1205)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1851, 21])).
% 0.81/1.01 tff(1853,plain,
% 0.81/1.01 (((~hskp0) | (~c0_1(a1205))) <=> ((~hskp0) | (~c0_1(a1205)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1854,plain,
% 0.81/1.01 (((~c0_1(a1205)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a1205)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1855,axiom,((~c0_1(a1205)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.81/1.01 tff(1856,plain,
% 0.81/1.01 ((~hskp0) | (~c0_1(a1205))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1855, 1854])).
% 0.81/1.01 tff(1857,plain,
% 0.81/1.01 ((~hskp0) | (~c0_1(a1205))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1856, 1853])).
% 0.81/1.01 tff(1858,plain,
% 0.81/1.01 (~hskp0),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1857, 1852])).
% 0.81/1.01 tff(1859,plain,
% 0.81/1.01 (~hskp6),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1603, 1858])).
% 0.81/1.01 tff(1860,plain,
% 0.81/1.01 (hskp15),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[83, 1859, 21])).
% 0.81/1.01 tff(1861,plain,
% 0.81/1.01 (~c2_1(a1233)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1169, 1860])).
% 0.81/1.01 tff(1862,plain,
% 0.81/1.01 (c1_1(a1233)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1177, 1860])).
% 0.81/1.01 tff(1863,plain,
% 0.81/1.01 (c0_1(a1233)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1185, 1860])).
% 0.81/1.01 tff(1864,plain,
% 0.81/1.01 (~hskp6),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1603, 1528])).
% 0.81/1.01 tff(1865,plain,
% 0.81/1.01 (~hskp1),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1673, 1110, 1864, 1359, 1361, 1362, 198])).
% 0.81/1.01 tff(1866,plain,
% 0.81/1.01 (hskp25),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[928, 1865, 1110])).
% 0.81/1.01 tff(1867,plain,
% 0.81/1.01 (c2_1(a1204)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[700, 1866])).
% 0.81/1.01 tff(1868,plain,
% 0.81/1.01 (c0_1(a1204)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[691, 1866])).
% 0.81/1.01 tff(1869,plain,
% 0.81/1.01 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1870,plain,
% 0.81/1.01 ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1871,plain,
% 0.81/1.01 ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1870, 1869])).
% 0.81/1.01 tff(1872,plain,
% 0.81/1.01 (~c1_1(a1204)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1871, 159, 1684, 1528, 1868, 1867, 234])).
% 0.81/1.01 tff(1873,plain,
% 0.81/1.01 ($false),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1637, 159, 1864, 1868, 1867, 1362, 1359, 44, 1872, 1613])).
% 0.81/1.01 tff(1874,plain,(hskp26 | (~c0_1(a1233)) | c2_1(a1233) | hskp0 | (~c1_1(a1233)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.81/1.01 tff(1875,plain,
% 0.81/1.01 (hskp26),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1874, 198, 1359, 1528, 1361, 1362])).
% 0.81/1.01 tff(1876,plain,
% 0.81/1.01 (c2_1(a1208)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[641, 1875])).
% 0.81/1.01 tff(1877,plain,
% 0.81/1.01 (c1_1(a1208)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[649, 1875])).
% 0.81/1.01 tff(1878,plain,
% 0.81/1.01 (c0_1(a1208)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[657, 1875])).
% 0.81/1.01 tff(1879,plain,
% 0.81/1.01 ($false),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1690, 159, 1684, 1528, 1878, 1877, 1876, 234])).
% 0.81/1.01 tff(1880,plain,(hskp28 | hskp0 | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233))), inference(lemma,lemma(discharge,[]))).
% 0.81/1.01 tff(1881,plain,
% 0.81/1.01 (hskp28),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1880, 1858, 1861, 1862, 1863])).
% 0.81/1.01 tff(1882,plain,
% 0.81/1.01 (c3_1(a1214)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[276, 1881])).
% 0.81/1.01 tff(1883,plain,
% 0.81/1.01 (c1_1(a1214)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[284, 1881])).
% 0.81/1.01 tff(1884,plain,
% 0.81/1.01 (c0_1(a1214)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[292, 1881])).
% 0.81/1.01 tff(1885,plain,
% 0.81/1.01 (~hskp25),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1844, 1884, 1883, 1882, 1859, 1863, 1862, 1861])).
% 0.81/1.01 tff(1886,plain,
% 0.81/1.01 (hskp21),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1120, 1885])).
% 0.81/1.01 tff(1887,plain,
% 0.81/1.01 (~c1_1(a1257)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[172, 1886])).
% 0.81/1.01 tff(1888,plain,
% 0.81/1.01 (~c0_1(a1257)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[178, 1886])).
% 0.81/1.01 tff(1889,plain,
% 0.81/1.01 (c3_1(a1257)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[186, 1886])).
% 0.81/1.01 tff(1890,plain,
% 0.81/1.01 ($false),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[299, 159, 21, 1884, 1883, 1882, 1889, 1888, 1887, 20])).
% 0.81/1.01 tff(1891,plain,(hskp5), inference(lemma,lemma(discharge,[]))).
% 0.81/1.01 tff(1892,plain,
% 0.81/1.01 (((~hskp5) | (~c3_1(a1212))) <=> ((~hskp5) | (~c3_1(a1212)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1893,plain,
% 0.81/1.01 (((~c3_1(a1212)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a1212)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1894,axiom,((~c3_1(a1212)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.81/1.01 tff(1895,plain,
% 0.81/1.01 ((~hskp5) | (~c3_1(a1212))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1894, 1893])).
% 0.81/1.01 tff(1896,plain,
% 0.81/1.01 ((~hskp5) | (~c3_1(a1212))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1895, 1892])).
% 0.81/1.01 tff(1897,plain,
% 0.81/1.01 (~c3_1(a1212)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1896, 1891])).
% 0.81/1.01 tff(1898,plain,
% 0.81/1.01 (((~hskp5) | (~c0_1(a1212))) <=> ((~hskp5) | (~c0_1(a1212)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1899,plain,
% 0.81/1.01 (((~c0_1(a1212)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a1212)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1900,axiom,((~c0_1(a1212)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.81/1.01 tff(1901,plain,
% 0.81/1.01 ((~hskp5) | (~c0_1(a1212))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1900, 1899])).
% 0.81/1.01 tff(1902,plain,
% 0.81/1.01 ((~hskp5) | (~c0_1(a1212))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1901, 1898])).
% 0.81/1.01 tff(1903,plain,
% 0.81/1.01 (~c0_1(a1212)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1902, 1891])).
% 0.81/1.01 tff(1904,plain,
% 0.81/1.01 (((~hskp5) | c2_1(a1212)) <=> ((~hskp5) | c2_1(a1212))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1905,axiom,((~hskp5) | c2_1(a1212)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.81/1.01 tff(1906,plain,
% 0.81/1.01 ((~hskp5) | c2_1(a1212)),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 0.81/1.01 tff(1907,plain,
% 0.81/1.01 ((~hskp5) | c2_1(a1212)),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1906, 1904])).
% 0.81/1.01 tff(1908,plain,
% 0.81/1.01 ((~hskp5) | c2_1(a1212)),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1907, 1904])).
% 0.81/1.01 tff(1909,plain,
% 0.81/1.01 ((~hskp5) | c2_1(a1212)),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1908, 1904])).
% 0.81/1.01 tff(1910,plain,
% 0.81/1.01 ((~hskp5) | c2_1(a1212)),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1909, 1904])).
% 0.81/1.01 tff(1911,plain,
% 0.81/1.01 (c2_1(a1212)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1910, 1891])).
% 0.81/1.01 tff(1912,plain,
% 0.81/1.01 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1913,plain,
% 0.81/1.01 ((hskp11 | (~ndr1_0) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212))) <=> (hskp11 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1914,plain,
% 0.81/1.01 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1913])).
% 0.81/1.01 tff(1915,plain,
% 0.81/1.01 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1914, 1912])).
% 0.81/1.01 tff(1916,plain,
% 0.81/1.01 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1917,plain,
% 0.81/1.01 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1916, 1915])).
% 0.81/1.01 tff(1918,plain,
% 0.81/1.01 (hskp11),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1917, 159, 1911, 1903, 1897, 313])).
% 0.81/1.01 tff(1919,plain,
% 0.81/1.01 (~c2_1(a1224)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[567, 1918])).
% 0.81/1.01 tff(1920,plain,
% 0.81/1.01 (c3_1(a1224)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[575, 1918])).
% 0.81/1.01 tff(1921,plain,
% 0.81/1.01 (c1_1(a1224)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[583, 1918])).
% 0.81/1.01 tff(1922,plain,
% 0.81/1.01 (c0_1(a1224)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[664, 159, 658, 650, 642, 1921, 1920, 1919, 352])).
% 0.81/1.01 tff(1923,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c1_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c1_1(a1224)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1924,plain,
% 0.81/1.01 ((hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224))) <=> (hskp8 | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c1_1(a1224)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1925,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c1_1(a1224))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1924])).
% 0.81/1.01 tff(1926,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c1_1(a1224)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1925, 1923])).
% 0.81/1.01 tff(1927,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1928,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c1_1(a1224))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 0.81/1.01 tff(1929,plain,
% 0.81/1.01 (hskp8),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1928, 159, 658, 650, 642, 1921, 1919, 1448, 1922])).
% 0.81/1.01 tff(1930,plain,
% 0.81/1.01 (~c3_1(a1217)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[539, 1929])).
% 0.81/1.01 tff(1931,plain,
% 0.81/1.01 (~c0_1(a1217)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[533, 1929])).
% 0.81/1.01 tff(1932,plain,
% 0.81/1.01 (c2_1(a1217)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[556, 198, 159, 1931, 1930, 197])).
% 0.81/1.01 tff(1933,plain,
% 0.81/1.01 (~c1_1(a1217)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[904, 1929])).
% 0.81/1.01 tff(1934,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1935,plain,
% 0.81/1.01 ((hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1217) | c1_1(a1217) | (~c2_1(a1217))) <=> (hskp14 | c2_1(a1224) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1936,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1217) | c1_1(a1217) | (~c2_1(a1217)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1935])).
% 0.81/1.01 tff(1937,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1217) | c1_1(a1217) | (~c2_1(a1217)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1936, 1934])).
% 0.81/1.01 tff(1938,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1217) | c1_1(a1217) | (~c2_1(a1217)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1939,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1938, 1937])).
% 0.81/1.01 tff(1940,plain,
% 0.81/1.01 (hskp14),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1939, 159, 1921, 1920, 1919, 1933, 1930, 613, 1932])).
% 0.81/1.01 tff(1941,plain,
% 0.81/1.01 (~c2_1(a1232)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[385, 1940])).
% 0.81/1.01 tff(1942,plain,
% 0.81/1.01 (~c0_1(a1232)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[417, 1940])).
% 0.81/1.01 tff(1943,plain,
% 0.81/1.01 (c3_1(a1232)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[393, 1940])).
% 0.81/1.01 tff(1944,plain,
% 0.81/1.01 ($false),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[676, 159, 658, 650, 642, 1943, 1921, 1920, 1942, 1941, 1919, 352])).
% 0.81/1.01 tff(1945,plain,((~hskp26) | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.81/1.01 tff(1946,plain,
% 0.81/1.01 (~hskp26),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1945, 198])).
% 0.81/1.01 tff(1947,plain,
% 0.81/1.01 (hskp24),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[157, 1946, 198])).
% 0.81/1.02 tff(1948,plain,
% 0.81/1.02 (~c2_1(a1267)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[443, 1947])).
% 0.81/1.02 tff(1949,plain,
% 0.81/1.02 (~c1_1(a1267)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[449, 1947])).
% 0.81/1.02 tff(1950,plain,
% 0.81/1.02 (c0_1(a1267)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[457, 1947])).
% 0.81/1.02 tff(1951,plain,
% 0.81/1.02 (hskp14),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[960, 1112, 851, 849, 848])).
% 0.81/1.02 tff(1952,plain,
% 0.81/1.02 (~c2_1(a1232)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[385, 1951])).
% 0.81/1.02 tff(1953,plain,
% 0.81/1.02 (~c0_1(a1232)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[417, 1951])).
% 0.81/1.02 tff(1954,plain,
% 0.81/1.02 (c3_1(a1232)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[393, 1951])).
% 0.81/1.02 tff(1955,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1956,plain,
% 0.81/1.02 (((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1957,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232))))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[1956])).
% 0.81/1.02 tff(1958,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 0.81/1.02 inference(transitivity,[status(thm)],[1957, 1955])).
% 0.81/1.02 tff(1959,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(1960,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1959, 1958])).
% 0.81/1.02 tff(1961,plain,
% 0.81/1.02 (~c1_1(a1206)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1960, 159, 1954, 1921, 1920, 1125, 1124, 1953, 1952, 1919, 352])).
% 0.81/1.02 tff(1962,plain,
% 0.81/1.02 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.81/1.02 inference(bind,[status(th)],[])).
% 0.81/1.02 tff(1963,plain,
% 0.81/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.81/1.02 inference(quant_intro,[status(thm)],[1962])).
% 0.81/1.02 tff(1964,plain,
% 0.81/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1965,plain,
% 0.81/1.02 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.81/1.02 inference(bind,[status(th)],[])).
% 0.81/1.02 tff(1966,plain,
% 0.81/1.02 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.81/1.02 inference(quant_intro,[status(thm)],[1965])).
% 0.81/1.02 tff(1967,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 0.81/1.02 tff(1968,plain,
% 0.81/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 0.81/1.02 tff(1969,plain,
% 0.81/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1968, 1964])).
% 0.81/1.02 tff(1970,plain,(
% 0.81/1.02 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.81/1.02 inference(skolemize,[status(sab)],[1969])).
% 0.81/1.02 tff(1971,plain,
% 0.81/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1970, 1963])).
% 0.81/1.02 tff(1972,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1267) | c2_1(a1267) | c0_1(a1232) | c2_1(a1232) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | c1_1(a1232) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1232) | c2_1(a1232) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | c1_1(a1232) | (~c0_1(a1267)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1973,plain,
% 0.81/1.02 (((~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232)) <=> (c1_1(a1267) | c2_1(a1267) | c0_1(a1232) | c2_1(a1232) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | c1_1(a1232) | (~c0_1(a1267)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1974,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1267) | c2_1(a1267) | c0_1(a1232) | c2_1(a1232) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | c1_1(a1232) | (~c0_1(a1267))))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[1973])).
% 0.81/1.02 tff(1975,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1232) | c2_1(a1232) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | c1_1(a1232) | (~c0_1(a1267)))),
% 0.81/1.02 inference(transitivity,[status(thm)],[1974, 1972])).
% 0.81/1.02 tff(1976,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(1977,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1232) | c2_1(a1232) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | c1_1(a1232) | (~c0_1(a1267))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1976, 1975])).
% 0.81/1.02 tff(1978,plain,
% 0.81/1.02 (c1_1(a1232)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1977, 159, 851, 1911, 849, 848, 1953, 1952, 1903, 1897, 1971])).
% 0.81/1.02 tff(1979,plain,
% 0.81/1.02 (c1_1(a1206) | (~c1_1(a1232))),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[997, 1111, 159, 1125, 1953, 1952, 1113, 990])).
% 0.81/1.02 tff(1980,plain,
% 0.81/1.02 ($false),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1979, 1978, 1961])).
% 0.81/1.02 tff(1981,plain,(hskp25 | (~c0_1(a1267)) | c1_1(a1267) | c2_1(a1267) | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.81/1.02 tff(1982,plain,
% 0.81/1.02 (hskp25),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1981, 1950, 1949, 1948, 1946])).
% 0.81/1.02 tff(1983,plain,
% 0.81/1.02 (c3_1(a1204)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[708, 1982])).
% 0.81/1.02 tff(1984,plain,
% 0.81/1.02 (c2_1(a1204)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[700, 1982])).
% 0.81/1.02 tff(1985,plain,
% 0.81/1.02 (c0_1(a1204)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[691, 1982])).
% 0.81/1.02 tff(1986,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1987,plain,
% 0.81/1.02 (((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212))) <=> (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1988,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[1987])).
% 0.81/1.02 tff(1989,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.81/1.02 inference(transitivity,[status(thm)],[1988, 1986])).
% 0.81/1.02 tff(1990,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(1991,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1990, 1989])).
% 0.81/1.02 tff(1992,plain,
% 0.81/1.02 (~c1_1(a1204)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1991, 159, 1985, 1984, 1983, 1911, 1903, 1897, 10])).
% 0.81/1.02 tff(1993,plain,
% 0.81/1.02 (hskp25),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1981, 1466, 1453, 1452, 1110])).
% 0.81/1.02 tff(1994,plain,
% 0.81/1.02 (c3_1(a1204)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[708, 1993])).
% 0.81/1.02 tff(1995,plain,
% 0.81/1.02 (c2_1(a1204)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[700, 1993])).
% 0.81/1.02 tff(1996,plain,
% 0.81/1.02 (c0_1(a1204)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[691, 1993])).
% 0.81/1.02 tff(1997,plain,
% 0.81/1.02 (~c1_1(a1204)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1991, 159, 1996, 1995, 1994, 1911, 1903, 1897, 10])).
% 0.81/1.02 tff(1998,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1267)) | (~c3_1(a1267)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1267)) | (~c3_1(a1267)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1999,plain,
% 0.81/1.02 ((hskp6 | (~ndr1_0) | c2_1(a1267) | (~c3_1(a1267)) | (~c0_1(a1267)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204))) <=> (hskp6 | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1267)) | (~c3_1(a1267)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(2000,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1267) | (~c3_1(a1267)) | (~c0_1(a1267)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1267)) | (~c3_1(a1267)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204))))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[1999])).
% 0.81/1.02 tff(2001,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1267) | (~c3_1(a1267)) | (~c0_1(a1267)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1267)) | (~c3_1(a1267)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))),
% 0.81/1.02 inference(transitivity,[status(thm)],[2000, 1998])).
% 0.81/1.02 tff(2002,plain,
% 0.81/1.02 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1267) | (~c3_1(a1267)) | (~c0_1(a1267)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204)))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(2003,plain,
% 0.81/1.02 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1267)) | (~c3_1(a1267)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[2002, 2001])).
% 0.81/1.02 tff(2004,plain,
% 0.81/1.02 (~c3_1(a1267)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[2003, 159, 24, 1996, 1995, 1466, 1452, 44, 1997])).
% 0.81/1.02 tff(2005,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c0_1(a1267)) | c3_1(a1267))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c0_1(a1267)) | c3_1(a1267))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(2006,plain,
% 0.81/1.02 (((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1212) | c3_1(a1212) | (~c1_1(a1212))) <=> (c1_1(a1267) | c2_1(a1267) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c0_1(a1267)) | c3_1(a1267))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(2007,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1212) | c3_1(a1212) | (~c1_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c0_1(a1267)) | c3_1(a1267)))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[2006])).
% 0.81/1.02 tff(2008,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1212) | c3_1(a1212) | (~c1_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c0_1(a1267)) | c3_1(a1267))),
% 0.81/1.02 inference(transitivity,[status(thm)],[2007, 2005])).
% 0.81/1.02 tff(2009,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1212) | c3_1(a1212) | (~c1_1(a1212)))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(2010,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c0_1(a1267)) | c3_1(a1267)),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[2009, 2008])).
% 0.81/1.02 tff(2011,plain,
% 0.81/1.02 (~c1_1(a1212)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[2010, 159, 1466, 1453, 1452, 1903, 1897, 846, 2004])).
% 0.81/1.02 tff(2012,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(2013,plain,
% 0.81/1.02 ((hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212))) <=> (hskp9 | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(2014,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[2013])).
% 0.81/1.02 tff(2015,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.81/1.02 inference(transitivity,[status(thm)],[2014, 2012])).
% 0.81/1.02 tff(2016,plain,
% 0.81/1.02 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212)))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(2017,plain,
% 0.81/1.02 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 0.81/1.02 tff(2018,plain,
% 0.81/1.02 (hskp9 | c1_1(a1212)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[2017, 159, 1996, 1994, 1911, 1897, 1266, 1997])).
% 0.81/1.02 tff(2019,plain,
% 0.81/1.02 (hskp9),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[2018, 2011])).
% 0.81/1.02 tff(2020,plain,
% 0.81/1.02 (~c0_1(a1219)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[768, 2019])).
% 0.81/1.02 tff(2021,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(2022,plain,
% 0.81/1.02 ((hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212))) <=> (hskp14 | c2_1(a1224) | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(2023,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[2022])).
% 0.81/1.02 tff(2024,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 0.81/1.02 inference(transitivity,[status(thm)],[2023, 2021])).
% 0.81/1.02 tff(2025,plain,
% 0.81/1.02 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212)))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(2026,plain,
% 0.81/1.02 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 0.81/1.02 tff(2027,plain,
% 0.81/1.02 (hskp14 | c1_1(a1212)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[2026, 159, 1921, 1920, 1911, 1919, 1897, 613])).
% 0.81/1.02 tff(2028,plain,
% 0.81/1.02 (hskp14),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[2027, 2011])).
% 0.81/1.02 tff(2029,plain,
% 0.81/1.02 (~c2_1(a1232)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[385, 2028])).
% 0.81/1.02 tff(2030,plain,
% 0.81/1.02 (~c0_1(a1232)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[417, 2028])).
% 0.81/1.03 tff(2031,plain,
% 0.81/1.03 (c2_1(a1219)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[747, 2019])).
% 0.81/1.03 tff(2032,plain,
% 0.81/1.03 (c1_1(a1219)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[755, 2019])).
% 0.81/1.03 tff(2033,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2034,plain,
% 0.81/1.03 (((~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232)) <=> (c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2035,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 0.81/1.03 inference(monotonicity,[status(thm)],[2034])).
% 0.81/1.03 tff(2036,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.81/1.03 inference(transitivity,[status(thm)],[2035, 2033])).
% 0.81/1.03 tff(2037,plain,
% 0.81/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))),
% 0.81/1.03 inference(quant_inst,[status(thm)],[])).
% 0.81/1.03 tff(2038,plain,
% 0.81/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 0.81/1.03 tff(2039,plain,
% 0.81/1.03 (c1_1(a1232)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2038, 159, 1996, 1994, 2032, 2031, 2030, 2029, 2020, 34, 1997])).
% 0.81/1.03 tff(2040,plain,
% 0.81/1.03 (c3_1(a1219)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[859, 2032, 2004, 1453, 1452, 2020, 1466])).
% 0.81/1.03 tff(2041,plain,
% 0.81/1.03 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.81/1.03 inference(bind,[status(th)],[])).
% 0.81/1.03 tff(2042,plain,
% 0.81/1.03 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/1.03 inference(quant_intro,[status(thm)],[2041])).
% 0.81/1.03 tff(2043,plain,
% 0.81/1.03 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2044,plain,
% 0.81/1.03 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.81/1.03 inference(bind,[status(th)],[])).
% 0.81/1.03 tff(2045,plain,
% 0.81/1.03 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/1.03 inference(quant_intro,[status(thm)],[2044])).
% 0.81/1.03 tff(2046,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 0.81/1.03 tff(2047,plain,
% 0.81/1.03 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 0.81/1.03 tff(2048,plain,
% 0.81/1.03 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2047, 2043])).
% 0.81/1.03 tff(2049,plain,(
% 0.81/1.03 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/1.03 inference(skolemize,[status(sab)],[2048])).
% 0.81/1.03 tff(2050,plain,
% 0.81/1.03 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2049, 2042])).
% 0.81/1.03 tff(2051,plain,
% 0.81/1.03 (c3_1(a1232)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[393, 2028])).
% 0.81/1.03 tff(2052,plain,
% 0.81/1.03 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2053,plain,
% 0.81/1.03 ((hskp3 | (~ndr1_0) | c0_1(a1219) | (~c2_1(a1219)) | (~c3_1(a1219)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232))) <=> (hskp3 | c0_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2054,plain,
% 0.81/1.03 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1219) | (~c2_1(a1219)) | (~c3_1(a1219)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1232)) | (~c1_1(a1232))))),
% 0.81/1.03 inference(monotonicity,[status(thm)],[2053])).
% 0.81/1.03 tff(2055,plain,
% 0.81/1.03 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1219) | (~c2_1(a1219)) | (~c3_1(a1219)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.81/1.03 inference(transitivity,[status(thm)],[2054, 2052])).
% 0.81/1.03 tff(2056,plain,
% 0.81/1.03 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1219) | (~c2_1(a1219)) | (~c3_1(a1219)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.81/1.03 inference(quant_inst,[status(thm)],[])).
% 0.81/1.03 tff(2057,plain,
% 0.81/1.03 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1232)) | (~c1_1(a1232))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 0.81/1.03 tff(2058,plain,
% 0.81/1.03 (hskp3),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2057, 159, 2051, 2031, 2030, 2020, 2050, 2040, 2039])).
% 0.81/1.03 tff(2059,plain,
% 0.81/1.03 (((~hskp3) | (~c3_1(a1210))) <=> ((~hskp3) | (~c3_1(a1210)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2060,plain,
% 0.81/1.03 (((~c3_1(a1210)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a1210)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2061,axiom,((~c3_1(a1210)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.81/1.03 tff(2062,plain,
% 0.81/1.03 ((~hskp3) | (~c3_1(a1210))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2061, 2060])).
% 0.81/1.03 tff(2063,plain,
% 0.81/1.03 ((~hskp3) | (~c3_1(a1210))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2062, 2059])).
% 0.81/1.03 tff(2064,plain,
% 0.81/1.03 (~c3_1(a1210)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2063, 2058])).
% 0.81/1.03 tff(2065,plain,
% 0.81/1.03 (((~hskp3) | c1_1(a1210)) <=> ((~hskp3) | c1_1(a1210))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2066,axiom,((~hskp3) | c1_1(a1210)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.81/1.03 tff(2067,plain,
% 0.81/1.03 ((~hskp3) | c1_1(a1210)),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2066, 2065])).
% 0.81/1.03 tff(2068,plain,
% 0.81/1.03 ((~hskp3) | c1_1(a1210)),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2067, 2065])).
% 0.81/1.03 tff(2069,plain,
% 0.81/1.03 ((~hskp3) | c1_1(a1210)),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2068, 2065])).
% 0.81/1.03 tff(2070,plain,
% 0.81/1.03 ((~hskp3) | c1_1(a1210)),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2069, 2065])).
% 0.81/1.03 tff(2071,plain,
% 0.81/1.03 ((~hskp3) | c1_1(a1210)),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2070, 2065])).
% 0.81/1.03 tff(2072,plain,
% 0.81/1.03 (c1_1(a1210)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2071, 2058])).
% 0.81/1.03 tff(2073,plain,
% 0.81/1.03 (((~hskp3) | c0_1(a1210)) <=> ((~hskp3) | c0_1(a1210))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2074,axiom,((~hskp3) | c0_1(a1210)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.81/1.03 tff(2075,plain,
% 0.81/1.03 ((~hskp3) | c0_1(a1210)),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 0.81/1.03 tff(2076,plain,
% 0.81/1.03 ((~hskp3) | c0_1(a1210)),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2075, 2073])).
% 0.81/1.03 tff(2077,plain,
% 0.81/1.03 ((~hskp3) | c0_1(a1210)),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2076, 2073])).
% 0.81/1.03 tff(2078,plain,
% 0.81/1.03 ((~hskp3) | c0_1(a1210)),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2077, 2073])).
% 0.81/1.03 tff(2079,plain,
% 0.81/1.03 ((~hskp3) | c0_1(a1210)),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2078, 2073])).
% 0.81/1.03 tff(2080,plain,
% 0.81/1.03 (c0_1(a1210)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2079, 2058])).
% 0.81/1.03 tff(2081,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c3_1(a1210) | (~ndr1_0) | (~c1_1(a1210)) | c2_1(a1210) | (~c0_1(a1210)) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c3_1(a1210) | (~ndr1_0) | (~c1_1(a1210)) | c2_1(a1210) | (~c0_1(a1210)) | (~c0_1(a1267)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2082,plain,
% 0.81/1.03 (((~ndr1_0) | c3_1(a1210) | (~c1_1(a1210)) | (~c0_1(a1210)) | c3_1(a1210) | c2_1(a1210) | (~c1_1(a1210)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267))) <=> (c1_1(a1267) | c2_1(a1267) | c3_1(a1210) | (~ndr1_0) | (~c1_1(a1210)) | c2_1(a1210) | (~c0_1(a1210)) | (~c0_1(a1267)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2083,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1210) | (~c1_1(a1210)) | (~c0_1(a1210)) | c3_1(a1210) | c2_1(a1210) | (~c1_1(a1210)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c3_1(a1210) | (~ndr1_0) | (~c1_1(a1210)) | c2_1(a1210) | (~c0_1(a1210)) | (~c0_1(a1267))))),
% 0.81/1.03 inference(monotonicity,[status(thm)],[2082])).
% 0.81/1.03 tff(2084,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1210) | (~c1_1(a1210)) | (~c0_1(a1210)) | c3_1(a1210) | c2_1(a1210) | (~c1_1(a1210)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c3_1(a1210) | (~ndr1_0) | (~c1_1(a1210)) | c2_1(a1210) | (~c0_1(a1210)) | (~c0_1(a1267)))),
% 0.81/1.03 inference(transitivity,[status(thm)],[2083, 2081])).
% 0.81/1.03 tff(2085,plain,
% 0.81/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1210) | (~c1_1(a1210)) | (~c0_1(a1210)) | c3_1(a1210) | c2_1(a1210) | (~c1_1(a1210)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))),
% 0.81/1.03 inference(quant_inst,[status(thm)],[])).
% 0.81/1.03 tff(2086,plain,
% 0.81/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c3_1(a1210) | (~ndr1_0) | (~c1_1(a1210)) | c2_1(a1210) | (~c0_1(a1210)) | (~c0_1(a1267))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2085, 2084])).
% 0.81/1.03 tff(2087,plain,
% 0.81/1.03 (c2_1(a1210)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2086, 159, 1466, 2080, 2072, 1453, 1452, 2064, 1372])).
% 0.81/1.03 tff(2088,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c1_1(a1210)) | (~c2_1(a1210)) | (~c0_1(a1210)) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c1_1(a1210)) | (~c2_1(a1210)) | (~c0_1(a1210)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2089,plain,
% 0.81/1.03 (((~ndr1_0) | (~c2_1(a1210)) | (~c1_1(a1210)) | (~c0_1(a1210)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c1_1(a1210)) | (~c2_1(a1210)) | (~c0_1(a1210)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2090,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1210)) | (~c1_1(a1210)) | (~c0_1(a1210)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c1_1(a1210)) | (~c2_1(a1210)) | (~c0_1(a1210)) | (~c3_1(a1232)) | (~c1_1(a1232))))),
% 0.81/1.03 inference(monotonicity,[status(thm)],[2089])).
% 0.81/1.03 tff(2091,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1210)) | (~c1_1(a1210)) | (~c0_1(a1210)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c1_1(a1210)) | (~c2_1(a1210)) | (~c0_1(a1210)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 0.81/1.03 inference(transitivity,[status(thm)],[2090, 2088])).
% 0.81/1.03 tff(2092,plain,
% 0.81/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1210)) | (~c1_1(a1210)) | (~c0_1(a1210)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 0.81/1.03 inference(quant_inst,[status(thm)],[])).
% 0.81/1.03 tff(2093,plain,
% 0.81/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c1_1(a1210)) | (~c2_1(a1210)) | (~c0_1(a1210)) | (~c3_1(a1232)) | (~c1_1(a1232))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 0.81/1.03 tff(2094,plain,
% 0.81/1.03 ($false),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2093, 159, 2051, 2080, 2072, 2030, 2029, 352, 2039, 2087])).
% 0.81/1.03 tff(2095,plain,(hskp26 | hskp6 | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.81/1.03 tff(2096,plain,
% 0.81/1.03 (hskp6),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2095, 1946, 198])).
% 0.81/1.03 tff(2097,plain,
% 0.81/1.03 (c1_1(a1215)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[97, 2096])).
% 0.81/1.03 tff(2098,plain,
% 0.81/1.03 (c2_1(a1215)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[105, 2096])).
% 0.81/1.03 tff(2099,plain,
% 0.81/1.03 (~c3_1(a1215)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[89, 2096])).
% 0.81/1.03 tff(2100,plain,
% 0.81/1.03 ((~hskp25) | c3_1(a1215) | hskp15 | hskp28 | (~c1_1(a1215)) | c0_1(a1215)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[916, 1921, 1920, 1919])).
% 0.81/1.03 tff(2101,plain,
% 0.81/1.03 (c0_1(a1215)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2100, 75, 198, 2097, 1982, 2099])).
% 0.81/1.03 tff(2102,plain,
% 0.81/1.03 (~hskp4),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[368, 2101, 198, 2098, 2097])).
% 0.81/1.03 tff(2103,plain,
% 0.81/1.03 (hskp15 | hskp4 | (~c3_1(a1267))),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[886, 159, 1949, 1948, 379])).
% 0.81/1.03 tff(2104,plain,
% 0.81/1.03 (~c3_1(a1267)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2103, 2102, 75])).
% 0.81/1.03 tff(2105,plain,
% 0.81/1.03 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1267) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2106,plain,
% 0.81/1.03 (((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267))) <=> (c2_1(a1267) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2107,plain,
% 0.81/1.03 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1267) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267)))),
% 0.81/1.03 inference(monotonicity,[status(thm)],[2106])).
% 0.81/1.03 tff(2108,plain,
% 0.81/1.03 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))),
% 0.81/1.03 inference(transitivity,[status(thm)],[2107, 2105])).
% 0.81/1.03 tff(2109,plain,
% 0.81/1.03 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))),
% 0.81/1.03 inference(quant_inst,[status(thm)],[])).
% 0.81/1.03 tff(2110,plain,
% 0.81/1.03 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267)),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 0.81/1.03 tff(2111,plain,
% 0.81/1.03 ($false),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2110, 159, 1950, 2097, 2098, 1948, 821, 2101, 2104])).
% 0.81/1.03 tff(2112,plain,(hskp15 | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.81/1.03 tff(2113,plain,
% 0.81/1.03 (hskp15),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2112, 198])).
% 0.81/1.03 tff(2114,plain,
% 0.81/1.03 (~c2_1(a1233)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[1169, 2113])).
% 0.81/1.03 tff(2115,plain,
% 0.81/1.03 (c1_1(a1233)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[1177, 2113])).
% 0.81/1.03 tff(2116,plain,
% 0.81/1.03 (c0_1(a1233)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[1185, 2113])).
% 0.81/1.03 tff(2117,plain,
% 0.81/1.03 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2118,plain,
% 0.81/1.03 ((hskp19 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204))) <=> (hskp19 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2119,plain,
% 0.81/1.03 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204))))),
% 0.81/1.03 inference(monotonicity,[status(thm)],[2118])).
% 0.81/1.03 tff(2120,plain,
% 0.81/1.03 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 0.81/1.03 inference(transitivity,[status(thm)],[2119, 2117])).
% 0.81/1.03 tff(2121,plain,
% 0.81/1.03 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))),
% 0.81/1.03 inference(quant_inst,[status(thm)],[])).
% 0.81/1.03 tff(2122,plain,
% 0.81/1.03 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2121, 2120])).
% 0.81/1.03 tff(2123,plain,
% 0.81/1.03 (hskp19),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2122, 159, 1984, 1983, 2116, 2115, 2114, 794, 1992])).
% 0.81/1.03 tff(2124,plain,
% 0.81/1.03 (~c3_1(a1247)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[518, 2123])).
% 0.81/1.03 tff(2125,plain,
% 0.81/1.03 (~c2_1(a1247)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[496, 2123])).
% 0.81/1.03 tff(2126,plain,
% 0.81/1.03 (c1_1(a1247)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[504, 2123])).
% 0.81/1.03 tff(2127,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)) | (~c0_1(a1267)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2128,plain,
% 0.81/1.03 (((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267))) <=> (c1_1(a1267) | c2_1(a1267) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)) | (~c0_1(a1267)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2129,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)) | (~c0_1(a1267))))),
% 0.81/1.03 inference(monotonicity,[status(thm)],[2128])).
% 0.81/1.03 tff(2130,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)) | (~c0_1(a1267)))),
% 0.81/1.03 inference(transitivity,[status(thm)],[2129, 2127])).
% 0.81/1.03 tff(2131,plain,
% 0.81/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))),
% 0.81/1.03 inference(quant_inst,[status(thm)],[])).
% 0.81/1.03 tff(2132,plain,
% 0.81/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)) | (~c0_1(a1267))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[2131, 2130])).
% 0.81/1.03 tff(2133,plain,
% 0.81/1.03 (~c0_1(a1247)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[2132, 159, 1950, 2126, 1949, 1948, 2125, 2124, 1372])).
% 0.81/1.03 tff(2134,plain,
% 0.81/1.03 ($false),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[525, 198, 159, 2125, 2124, 197, 2133])).
% 0.81/1.03 tff(2135,plain,(hskp28), inference(lemma,lemma(discharge,[]))).
% 0.81/1.03 tff(2136,plain,
% 0.81/1.03 (c1_1(a1214)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[284, 2135])).
% 0.81/1.03 tff(2137,plain,
% 0.81/1.03 (c3_1(a1214)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[276, 2135])).
% 0.81/1.03 tff(2138,plain,
% 0.81/1.03 (c0_1(a1214)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[292, 2135])).
% 0.81/1.03 tff(2139,plain,
% 0.81/1.03 (hskp26),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[1134, 1111, 2138, 2137, 2136])).
% 0.81/1.03 tff(2140,plain,
% 0.81/1.03 (c2_1(a1208)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[641, 2139])).
% 0.81/1.03 tff(2141,plain,
% 0.81/1.03 (c1_1(a1208)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[649, 2139])).
% 0.81/1.03 tff(2142,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | (~c2_1(a1212)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | (~c2_1(a1212)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2143,plain,
% 0.81/1.03 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212))) <=> (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | (~c2_1(a1212)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(2144,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | (~c2_1(a1212)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.81/1.04 inference(monotonicity,[status(thm)],[2143])).
% 0.81/1.04 tff(2145,plain,
% 0.81/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | (~c2_1(a1212)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.04 inference(transitivity,[status(thm)],[2144, 2142])).
% 0.81/1.04 tff(2146,plain,
% 0.81/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))),
% 0.81/1.04 inference(quant_inst,[status(thm)],[])).
% 0.81/1.04 tff(2147,plain,
% 0.81/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | (~c2_1(a1212)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.81/1.04 inference(modus_ponens,[status(thm)],[2146, 2145])).
% 0.81/1.04 tff(2148,plain,
% 0.81/1.04 (~c3_1(a1208)),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[2147, 159, 2138, 2136, 2137, 2141, 2140, 1911, 1903, 1897, 10])).
% 0.81/1.04 tff(2149,plain,
% 0.81/1.04 (c0_1(a1208)),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[657, 2139])).
% 0.81/1.04 tff(2150,plain,
% 0.81/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c0_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c0_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.04 inference(rewrite,[status(thm)],[])).
% 0.81/1.04 tff(2151,plain,
% 0.81/1.04 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1208)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257))) <=> (c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c0_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.04 inference(rewrite,[status(thm)],[])).
% 0.81/1.04 tff(2152,plain,
% 0.81/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1208)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c0_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.81/1.04 inference(monotonicity,[status(thm)],[2151])).
% 0.81/1.04 tff(2153,plain,
% 0.81/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1208)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c0_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.04 inference(transitivity,[status(thm)],[2152, 2150])).
% 0.81/1.04 tff(2154,plain,
% 0.81/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1208)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))),
% 0.81/1.04 inference(quant_inst,[status(thm)],[])).
% 0.81/1.04 tff(2155,plain,
% 0.81/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c0_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.81/1.04 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 0.81/1.04 tff(2156,plain,
% 0.81/1.04 ($false),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[2155, 159, 2138, 2136, 2137, 2149, 2140, 1126, 1123, 1122, 1109, 2148])).
% 0.81/1.04 tff(2157,plain,(hskp25), inference(lemma,lemma(discharge,[]))).
% 0.81/1.04 tff(2158,plain,
% 0.81/1.04 (c2_1(a1204)),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[700, 2157])).
% 0.81/1.04 tff(2159,assumption,(hskp9), introduced(assumption)).
% 0.81/1.04 tff(2160,plain,
% 0.81/1.04 (c2_1(a1219)),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[747, 2159])).
% 0.81/1.04 tff(2161,plain,
% 0.81/1.04 (c1_1(a1219)),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[755, 2159])).
% 0.81/1.04 tff(2162,plain,
% 0.81/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.04 inference(rewrite,[status(thm)],[])).
% 0.81/1.04 tff(2163,plain,
% 0.81/1.04 (((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212))) <=> (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.04 inference(rewrite,[status(thm)],[])).
% 0.81/1.04 tff(2164,plain,
% 0.81/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.81/1.04 inference(monotonicity,[status(thm)],[2163])).
% 0.81/1.04 tff(2165,plain,
% 0.81/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.04 inference(transitivity,[status(thm)],[2164, 2162])).
% 0.81/1.04 tff(2166,plain,
% 0.81/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))),
% 0.81/1.04 inference(quant_inst,[status(thm)],[])).
% 0.81/1.04 tff(2167,plain,
% 0.81/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.81/1.04 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 0.81/1.04 tff(2168,plain,
% 0.81/1.04 (~c3_1(a1219)),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[2167, 159, 2138, 2136, 2137, 2161, 2160, 1911, 1903, 1897, 10])).
% 0.81/1.04 tff(2169,plain,
% 0.81/1.04 (~c0_1(a1219)),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[768, 2159])).
% 0.81/1.04 tff(2170,plain,
% 0.81/1.04 (~c3_1(a1219)),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[2167, 159, 2138, 2136, 2137, 850, 1770, 1911, 1903, 1897, 10])).
% 0.81/1.04 tff(2171,plain,
% 0.81/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1219) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1219) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c3_1(a1219) | (~c1_1(a1219)))),
% 0.81/1.04 inference(rewrite,[status(thm)],[])).
% 0.81/1.04 tff(2172,plain,
% 0.81/1.04 (((~ndr1_0) | c3_1(a1219) | c0_1(a1219) | (~c1_1(a1219)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207)) <=> (c0_1(a1219) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c3_1(a1219) | (~c1_1(a1219)))),
% 0.81/1.04 inference(rewrite,[status(thm)],[])).
% 0.81/1.04 tff(2173,plain,
% 0.81/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1219) | c0_1(a1219) | (~c1_1(a1219)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1219) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c3_1(a1219) | (~c1_1(a1219))))),
% 0.81/1.04 inference(monotonicity,[status(thm)],[2172])).
% 0.81/1.04 tff(2174,plain,
% 0.81/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1219) | c0_1(a1219) | (~c1_1(a1219)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1219) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c3_1(a1219) | (~c1_1(a1219)))),
% 0.81/1.04 inference(transitivity,[status(thm)],[2173, 2171])).
% 0.81/1.04 tff(2175,plain,
% 0.81/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1219) | c0_1(a1219) | (~c1_1(a1219)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207))),
% 0.81/1.04 inference(quant_inst,[status(thm)],[])).
% 0.81/1.04 tff(2176,plain,
% 0.81/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1219) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c3_1(a1219) | (~c1_1(a1219))),
% 0.81/1.04 inference(modus_ponens,[status(thm)],[2175, 2174])).
% 0.81/1.04 tff(2177,plain,
% 0.81/1.04 (~c3_1(a1207)),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[2176, 159, 850, 847, 1042, 1036, 1030, 216, 2170])).
% 0.81/1.04 tff(2178,plain,
% 0.81/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.04 inference(rewrite,[status(thm)],[])).
% 0.81/1.04 tff(2179,plain,
% 0.81/1.04 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207)) <=> (c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.04 inference(rewrite,[status(thm)],[])).
% 0.81/1.04 tff(2180,plain,
% 0.81/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.81/1.04 inference(monotonicity,[status(thm)],[2179])).
% 0.81/1.04 tff(2181,plain,
% 0.81/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.81/1.04 inference(transitivity,[status(thm)],[2180, 2178])).
% 0.81/1.04 tff(2182,plain,
% 0.81/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207))),
% 0.81/1.04 inference(quant_inst,[status(thm)],[])).
% 0.81/1.04 tff(2183,plain,
% 0.81/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.81/1.04 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 0.81/1.04 tff(2184,plain,
% 0.81/1.04 ($false),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[2183, 159, 2138, 2136, 2137, 850, 1770, 1042, 1030, 74, 2170, 2177])).
% 0.81/1.04 tff(2185,plain,((~hskp2) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1219)), inference(lemma,lemma(discharge,[]))).
% 0.81/1.04 tff(2186,plain,
% 0.81/1.04 (~hskp2),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[2185, 2161, 2160, 2169])).
% 0.81/1.04 tff(2187,plain,
% 0.81/1.04 (hskp7 | hskp2),
% 0.81/1.04 inference(unit_resolution,[status(thm)],[1077, 159, 2138, 2136, 2137, 1071])).
% 0.88/1.04 tff(2188,plain,
% 0.88/1.04 (hskp7),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2187, 2186])).
% 0.88/1.04 tff(2189,plain,
% 0.88/1.04 (~c3_1(a1216)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1084, 2188])).
% 0.88/1.04 tff(2190,plain,
% 0.88/1.04 (~c2_1(a1216)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1090, 2188])).
% 0.88/1.04 tff(2191,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | c0_1(a1216) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | c0_1(a1216) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2192,plain,
% 0.88/1.04 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216)) <=> (c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | c0_1(a1216) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2193,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | c0_1(a1216) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2192])).
% 0.88/1.04 tff(2194,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | c0_1(a1216) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.88/1.04 inference(transitivity,[status(thm)],[2193, 2191])).
% 0.88/1.04 tff(2195,plain,
% 0.88/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(2196,plain,
% 0.88/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | c0_1(a1216) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 0.88/1.04 tff(2197,plain,
% 0.88/1.04 (c0_1(a1216)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2196, 159, 2138, 2136, 2137, 2161, 2160, 2190, 2189, 74, 2168])).
% 0.88/1.04 tff(2198,plain,
% 0.88/1.04 (~c1_1(a1216)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1153, 2188])).
% 0.88/1.04 tff(2199,assumption,(hskp27), introduced(assumption)).
% 0.88/1.04 tff(2200,plain,
% 0.88/1.04 (c3_1(a1213)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1555, 2199])).
% 0.88/1.04 tff(2201,plain,
% 0.88/1.04 (c2_1(a1213)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1563, 2199])).
% 0.88/1.04 tff(2202,plain,
% 0.88/1.04 (c1_1(a1213)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1571, 2199])).
% 0.88/1.04 tff(2203,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2204,plain,
% 0.88/1.04 (((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1219) | c3_1(a1219) | (~c2_1(a1219))) <=> (c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2205,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1219) | c3_1(a1219) | (~c2_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2204])).
% 0.88/1.04 tff(2206,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1219) | c3_1(a1219) | (~c2_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))),
% 0.88/1.04 inference(transitivity,[status(thm)],[2205, 2203])).
% 0.88/1.04 tff(2207,plain,
% 0.88/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1219) | c3_1(a1219) | (~c2_1(a1219)))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(2208,plain,
% 0.88/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 0.88/1.04 tff(2209,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2208, 159, 2138, 2136, 2137, 2202, 2201, 2200, 1770, 847, 10, 836])).
% 0.88/1.04 tff(2210,plain,((~hskp27) | (~c2_1(a1219)) | c0_1(a1219) | c3_1(a1219)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(2211,plain,
% 0.88/1.04 (~hskp27),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2210, 2160, 2169, 2168])).
% 0.88/1.04 tff(2212,plain,
% 0.88/1.04 ((hskp27 | hskp19 | hskp2) <=> (hskp27 | hskp19 | hskp2)),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2213,plain,
% 0.88/1.04 (((hskp27 | hskp19) | hskp2) <=> (hskp27 | hskp19 | hskp2)),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2214,plain,
% 0.88/1.04 ((hskp27 | hskp19) <=> (hskp27 | hskp19)),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2215,plain,
% 0.88/1.04 (((hskp27 | hskp19) | hskp2) <=> ((hskp27 | hskp19) | hskp2)),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2214])).
% 0.88/1.04 tff(2216,plain,
% 0.88/1.04 (((hskp27 | hskp19) | hskp2) <=> (hskp27 | hskp19 | hskp2)),
% 0.88/1.05 inference(transitivity,[status(thm)],[2215, 2213])).
% 0.88/1.05 tff(2217,axiom,((hskp27 | hskp19) | hskp2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.88/1.05 tff(2218,plain,
% 0.88/1.05 (hskp27 | hskp19 | hskp2),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2217, 2216])).
% 0.88/1.05 tff(2219,plain,
% 0.88/1.05 (hskp27 | hskp19 | hskp2),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2218, 2212])).
% 0.88/1.05 tff(2220,plain,
% 0.88/1.05 (hskp27 | hskp19 | hskp2),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2219, 2212])).
% 0.88/1.05 tff(2221,plain,
% 0.88/1.05 (hskp27 | hskp19 | hskp2),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2220, 2212])).
% 0.88/1.05 tff(2222,plain,
% 0.88/1.05 (hskp27 | hskp19 | hskp2),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2221, 2212])).
% 0.88/1.05 tff(2223,plain,
% 0.88/1.05 (hskp19),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2222, 2186, 2211])).
% 0.88/1.05 tff(2224,plain,
% 0.88/1.05 (~c3_1(a1247)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[518, 2223])).
% 0.88/1.05 tff(2225,plain,
% 0.88/1.05 (~c2_1(a1247)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[496, 2223])).
% 0.88/1.05 tff(2226,plain,
% 0.88/1.05 (c1_1(a1247)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[504, 2223])).
% 0.88/1.05 tff(2227,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1247) | c3_1(a1247) | c1_1(a1216) | c2_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | (~c1_1(a1247)) | (~c0_1(a1247)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1247) | c3_1(a1247) | c1_1(a1216) | c2_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2228,plain,
% 0.88/1.05 (((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1216) | c1_1(a1216) | (~c0_1(a1216))) <=> (c2_1(a1247) | c3_1(a1247) | c1_1(a1216) | c2_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2229,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1216) | c1_1(a1216) | (~c0_1(a1216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1247) | c3_1(a1247) | c1_1(a1216) | c2_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | (~c1_1(a1247)) | (~c0_1(a1247))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[2228])).
% 0.88/1.05 tff(2230,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1216) | c1_1(a1216) | (~c0_1(a1216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1247) | c3_1(a1247) | c1_1(a1216) | c2_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 0.88/1.05 inference(transitivity,[status(thm)],[2229, 2227])).
% 0.88/1.05 tff(2231,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1216) | c1_1(a1216) | (~c0_1(a1216)))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(2232,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1247) | c3_1(a1247) | c1_1(a1216) | c2_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | (~c1_1(a1247)) | (~c0_1(a1247))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 0.88/1.05 tff(2233,plain,
% 0.88/1.05 (~c0_1(a1247)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2232, 159, 2226, 2225, 2224, 2198, 2190, 1372, 2197])).
% 0.88/1.05 tff(2234,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1247) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1247) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2235,plain,
% 0.88/1.05 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247)) <=> (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1247) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2236,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1247) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[2235])).
% 0.88/1.05 tff(2237,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1247) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 0.88/1.05 inference(transitivity,[status(thm)],[2236, 2234])).
% 0.88/1.05 tff(2238,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(2239,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1247) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2238, 2237])).
% 0.88/1.05 tff(2240,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2239, 159, 2138, 2136, 2137, 2161, 2160, 2225, 2224, 74, 2168, 2233])).
% 0.88/1.05 tff(2241,plain,(~hskp9), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(2242,plain,
% 0.88/1.05 (c0_1(a1204)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[691, 2157])).
% 0.88/1.05 tff(2243,plain,
% 0.88/1.05 (c3_1(a1204)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[708, 2157])).
% 0.88/1.05 tff(2244,assumption,(~hskp9), introduced(assumption)).
% 0.88/1.05 tff(2245,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2246,plain,
% 0.88/1.05 ((hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c0_1(a1212) | (~c1_1(a1212))) <=> (hskp9 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2247,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c0_1(a1212) | (~c1_1(a1212)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[2246])).
% 0.88/1.05 tff(2248,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c0_1(a1212) | (~c1_1(a1212)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 0.88/1.05 inference(transitivity,[status(thm)],[2247, 2245])).
% 0.88/1.05 tff(2249,plain,
% 0.88/1.05 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c0_1(a1212) | (~c1_1(a1212)))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(2250,plain,
% 0.88/1.05 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2249, 2248])).
% 0.88/1.05 tff(2251,plain,
% 0.88/1.05 (hskp9 | (~c1_1(a1212))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2250, 159, 732, 731, 730, 1903, 1897, 729])).
% 0.88/1.05 tff(2252,plain,
% 0.88/1.05 (~c1_1(a1212)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2251, 2244])).
% 0.88/1.05 tff(2253,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1204)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2254,plain,
% 0.88/1.05 (((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212))) <=> (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1204)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2255,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1204))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[2254])).
% 0.88/1.05 tff(2256,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1204)))),
% 0.88/1.05 inference(transitivity,[status(thm)],[2255, 2253])).
% 0.88/1.05 tff(2257,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(2258,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1204))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 0.88/1.05 tff(2259,plain,
% 0.88/1.05 (~c1_1(a1204)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2258, 159, 2138, 2136, 2137, 731, 730, 1911, 1903, 1897, 10])).
% 0.88/1.05 tff(2260,plain,
% 0.88/1.05 (hskp9 | c1_1(a1212)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2017, 159, 732, 730, 1911, 1897, 1266, 2259])).
% 0.88/1.05 tff(2261,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2260, 2252, 2244])).
% 0.88/1.05 tff(2262,plain,(hskp9 | (~c0_1(a1204)) | (~c3_1(a1204)) | (~c2_1(a1204))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(2263,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2262, 2243, 2242, 2241, 2158])).
% 0.88/1.05 % SZS output end Proof
% 0.88/1.06 % E exiting
%------------------------------------------------------------------------------