%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN461-1 : 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 05:39:12 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.57s
% Output : Proof 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN461-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:35:53 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.57 % SZS status Unsatisfiable
% 0.19/0.57 % SZS output start Proof
% 0.19/0.57 tff(c0_1_type, type, (
% 0.19/0.57 c0_1: $i > $o)).
% 0.19/0.57 tff(c1_1_type, type, (
% 0.19/0.57 c1_1: $i > $o)).
% 0.19/0.57 tff(c2_1_type, type, (
% 0.19/0.57 c2_1: $i > $o)).
% 0.19/0.57 tff(c3_1_type, type, (
% 0.19/0.57 c3_1: $i > $o)).
% 0.19/0.57 tff(ndr1_0_type, type, (
% 0.19/0.57 ndr1_0: $o)).
% 0.19/0.57 tff(a1200_type, type, (
% 0.19/0.57 a1200: $i)).
% 0.19/0.57 tff(hskp17_type, type, (
% 0.19/0.57 hskp17: $o)).
% 0.19/0.57 tff(a1174_type, type, (
% 0.19/0.57 a1174: $i)).
% 0.19/0.57 tff(a1194_type, type, (
% 0.19/0.57 a1194: $i)).
% 0.19/0.57 tff(hskp3_type, type, (
% 0.19/0.57 hskp3: $o)).
% 0.19/0.57 tff(a1168_type, type, (
% 0.19/0.57 a1168: $i)).
% 0.19/0.57 tff(hskp22_type, type, (
% 0.19/0.57 hskp22: $o)).
% 0.19/0.57 tff(a1211_type, type, (
% 0.19/0.57 a1211: $i)).
% 0.19/0.57 tff(hskp0_type, type, (
% 0.19/0.57 hskp0: $o)).
% 0.19/0.57 tff(hskp14_type, type, (
% 0.19/0.57 hskp14: $o)).
% 0.19/0.57 tff(hskp23_type, type, (
% 0.19/0.57 hskp23: $o)).
% 0.19/0.57 tff(hskp19_type, type, (
% 0.19/0.57 hskp19: $o)).
% 0.19/0.57 tff(a1169_type, type, (
% 0.19/0.57 a1169: $i)).
% 0.19/0.57 tff(hskp1_type, type, (
% 0.19/0.57 hskp1: $o)).
% 0.19/0.57 tff(a1204_type, type, (
% 0.19/0.57 a1204: $i)).
% 0.19/0.57 tff(hskp28_type, type, (
% 0.19/0.57 hskp28: $o)).
% 0.19/0.57 tff(hskp8_type, type, (
% 0.19/0.57 hskp8: $o)).
% 0.19/0.57 tff(a1218_type, type, (
% 0.19/0.57 a1218: $i)).
% 0.19/0.57 tff(a1199_type, type, (
% 0.19/0.57 a1199: $i)).
% 0.19/0.57 tff(hskp16_type, type, (
% 0.19/0.57 hskp16: $o)).
% 0.19/0.57 tff(a1184_type, type, (
% 0.19/0.57 a1184: $i)).
% 0.19/0.57 tff(hskp10_type, type, (
% 0.19/0.57 hskp10: $o)).
% 0.19/0.57 tff(hskp13_type, type, (
% 0.19/0.57 hskp13: $o)).
% 0.19/0.57 tff(a1192_type, type, (
% 0.19/0.57 a1192: $i)).
% 0.19/0.57 tff(hskp2_type, type, (
% 0.19/0.57 hskp2: $o)).
% 0.19/0.57 tff(a1172_type, type, (
% 0.19/0.57 a1172: $i)).
% 0.19/0.57 tff(a1236_type, type, (
% 0.19/0.57 a1236: $i)).
% 0.19/0.57 tff(a1180_type, type, (
% 0.19/0.57 a1180: $i)).
% 0.19/0.57 tff(a1190_type, type, (
% 0.19/0.57 a1190: $i)).
% 0.19/0.57 tff(hskp26_type, type, (
% 0.19/0.57 hskp26: $o)).
% 0.19/0.57 tff(a1176_type, type, (
% 0.19/0.57 a1176: $i)).
% 0.19/0.57 tff(a1178_type, type, (
% 0.19/0.57 a1178: $i)).
% 0.19/0.57 tff(hskp6_type, type, (
% 0.19/0.57 hskp6: $o)).
% 0.19/0.57 tff(a1205_type, type, (
% 0.19/0.57 a1205: $i)).
% 0.19/0.57 tff(hskp20_type, type, (
% 0.19/0.57 hskp20: $o)).
% 0.19/0.57 tff(hskp12_type, type, (
% 0.19/0.57 hskp12: $o)).
% 0.19/0.57 tff(a1207_type, type, (
% 0.19/0.57 a1207: $i)).
% 0.19/0.57 tff(hskp21_type, type, (
% 0.19/0.57 hskp21: $o)).
% 0.19/0.57 tff(a1187_type, type, (
% 0.19/0.57 a1187: $i)).
% 0.19/0.57 tff(hskp4_type, type, (
% 0.19/0.57 hskp4: $o)).
% 0.19/0.57 tff(a1175_type, type, (
% 0.19/0.57 a1175: $i)).
% 0.19/0.57 tff(hskp5_type, type, (
% 0.19/0.57 hskp5: $o)).
% 0.19/0.57 tff(a1182_type, type, (
% 0.19/0.57 a1182: $i)).
% 0.19/0.57 tff(hskp25_type, type, (
% 0.19/0.57 hskp25: $o)).
% 0.19/0.57 tff(1,plain,
% 0.19/0.57 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(2,plain,
% 0.19/0.57 (![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.57 tff(3,plain,
% 0.19/0.57 (![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(4,plain,
% 0.19/0.57 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(5,plain,
% 0.19/0.57 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.57 tff(6,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.19/0.57 tff(7,plain,
% 0.19/0.57 (![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.57 tff(8,plain,
% 0.19/0.57 (![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.57 tff(9,plain,(
% 0.19/0.57 ![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[8])).
% 0.19/0.57 tff(10,plain,
% 0.19/0.57 (![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.57 tff(11,assumption,(c2_1(a1174)), introduced(assumption)).
% 0.19/0.57 tff(12,plain,
% 0.19/0.57 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(13,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.57 tff(14,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(15,plain,
% 0.19/0.57 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(16,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.57 tff(17,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 0.19/0.57 tff(18,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.57 tff(19,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.57 tff(20,plain,(
% 0.19/0.57 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[19])).
% 0.19/0.57 tff(21,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.19/0.57 tff(22,assumption,(~hskp3), introduced(assumption)).
% 0.19/0.57 tff(23,assumption,(~hskp17), introduced(assumption)).
% 0.19/0.57 tff(24,assumption,(hskp22), introduced(assumption)).
% 0.19/0.57 tff(25,plain,
% 0.19/0.57 (((~hskp22) | (~c1_1(a1211))) <=> ((~hskp22) | (~c1_1(a1211)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(26,plain,
% 0.19/0.57 (((~c1_1(a1211)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a1211)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(27,axiom,((~c1_1(a1211)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.19/0.57 tff(28,plain,
% 0.19/0.57 ((~hskp22) | (~c1_1(a1211))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.57 tff(29,plain,
% 0.19/0.57 ((~hskp22) | (~c1_1(a1211))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.19/0.57 tff(30,plain,
% 0.19/0.57 (~c1_1(a1211)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[29, 24])).
% 0.19/0.57 tff(31,plain,
% 0.19/0.57 (((~hskp22) | c3_1(a1211)) <=> ((~hskp22) | c3_1(a1211))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(32,axiom,((~hskp22) | c3_1(a1211)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.19/0.57 tff(33,plain,
% 0.19/0.57 ((~hskp22) | c3_1(a1211)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.57 tff(34,plain,
% 0.19/0.57 ((~hskp22) | c3_1(a1211)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[33, 31])).
% 0.19/0.57 tff(35,plain,
% 0.19/0.57 ((~hskp22) | c3_1(a1211)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.19/0.57 tff(36,plain,
% 0.19/0.57 ((~hskp22) | c3_1(a1211)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.57 tff(37,plain,
% 0.19/0.57 ((~hskp22) | c3_1(a1211)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.19/0.57 tff(38,plain,
% 0.19/0.57 (c3_1(a1211)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[37, 24])).
% 0.19/0.57 tff(39,plain,
% 0.19/0.57 (((~hskp22) | c0_1(a1211)) <=> ((~hskp22) | c0_1(a1211))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(40,axiom,((~hskp22) | c0_1(a1211)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.19/0.57 tff(41,plain,
% 0.19/0.57 ((~hskp22) | c0_1(a1211)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.57 tff(42,plain,
% 0.19/0.57 ((~hskp22) | c0_1(a1211)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[41, 39])).
% 0.19/0.57 tff(43,plain,
% 0.19/0.57 ((~hskp22) | c0_1(a1211)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[42, 39])).
% 0.19/0.57 tff(44,plain,
% 0.19/0.57 ((~hskp22) | c0_1(a1211)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.57 tff(45,plain,
% 0.19/0.57 ((~hskp22) | c0_1(a1211)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[44, 39])).
% 0.19/0.57 tff(46,plain,
% 0.19/0.57 (c0_1(a1211)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[45, 24])).
% 0.19/0.57 tff(47,assumption,(~c2_1(a1211)), introduced(assumption)).
% 0.19/0.57 tff(48,plain,
% 0.19/0.57 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(49,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.57 tff(50,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(51,plain,
% 0.19/0.57 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(52,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.57 tff(53,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.19/0.57 tff(54,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.57 tff(55,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.19/0.57 tff(56,plain,(
% 0.19/0.57 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[55])).
% 0.19/0.57 tff(57,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.19/0.57 tff(58,plain,
% 0.19/0.57 (^[U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(59,plain,
% 0.19/0.57 (![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.57 tff(60,plain,
% 0.19/0.57 (![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(61,plain,
% 0.19/0.57 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(62,plain,
% 0.19/0.57 (![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.57 tff(63,axiom,(![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.19/0.57 tff(64,plain,
% 0.19/0.57 (![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.57 tff(65,plain,
% 0.19/0.57 (![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.19/0.57 tff(66,plain,(
% 0.19/0.57 ![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[65])).
% 0.19/0.58 tff(67,plain,
% 0.19/0.58 (![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.19/0.58 tff(68,plain,
% 0.19/0.58 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(69,plain,
% 0.19/0.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.58 tff(70,plain,
% 0.19/0.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(71,plain,
% 0.19/0.58 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | 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)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(72,plain,
% 0.19/0.58 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.58 tff(73,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 0.19/0.58 tff(74,plain,
% 0.19/0.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.58 tff(75,plain,
% 0.19/0.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.19/0.58 tff(76,plain,(
% 0.19/0.58 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.19/0.58 inference(skolemize,[status(sab)],[75])).
% 0.19/0.58 tff(77,plain,
% 0.19/0.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.19/0.58 tff(78,assumption,(~hskp0), introduced(assumption)).
% 0.19/0.58 tff(79,assumption,(~hskp14), introduced(assumption)).
% 0.19/0.58 tff(80,plain,
% 0.19/0.58 (^[U: $i] : refl((hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(81,plain,
% 0.19/0.58 (![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.58 tff(82,plain,
% 0.19/0.58 (![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(83,plain,
% 0.19/0.58 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp23) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp23))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp23) <=> (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp23) <=> (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(84,plain,
% 0.19/0.58 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp23) <=> ![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.58 tff(85,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.19/0.58 tff(86,plain,
% 0.19/0.58 (![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.58 tff(87,plain,
% 0.19/0.58 (![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.19/0.58 tff(88,plain,(
% 0.19/0.58 ![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.19/0.58 inference(skolemize,[status(sab)],[87])).
% 0.19/0.58 tff(89,plain,
% 0.19/0.58 (![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.19/0.58 tff(90,plain,
% 0.19/0.58 ((hskp14 | hskp1 | hskp0) <=> (hskp14 | hskp1 | hskp0)),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(91,plain,
% 0.19/0.58 (((hskp0 | hskp1) | hskp14) <=> (hskp14 | hskp1 | hskp0)),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(92,axiom,((hskp0 | hskp1) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 0.19/0.58 tff(93,plain,
% 0.19/0.58 (hskp14 | hskp1 | hskp0),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.58 tff(94,plain,
% 0.19/0.58 (hskp14 | hskp1 | hskp0),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[93, 90])).
% 0.19/0.58 tff(95,plain,
% 0.19/0.58 (hskp14 | hskp1 | hskp0),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.19/0.58 tff(96,plain,
% 0.19/0.58 (hskp14 | hskp1 | hskp0),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[95, 90])).
% 0.19/0.58 tff(97,plain,
% 0.19/0.58 (hskp14 | hskp1 | hskp0),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[96, 90])).
% 0.19/0.58 tff(98,plain,
% 0.19/0.58 (hskp1),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[97, 79, 78])).
% 0.19/0.58 tff(99,plain,
% 0.19/0.58 (((~hskp1) | (~c3_1(a1169))) <=> ((~hskp1) | (~c3_1(a1169)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(100,plain,
% 0.19/0.58 (((~c3_1(a1169)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a1169)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(101,axiom,((~c3_1(a1169)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.19/0.58 tff(102,plain,
% 0.19/0.58 ((~hskp1) | (~c3_1(a1169))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.58 tff(103,plain,
% 0.19/0.58 ((~hskp1) | (~c3_1(a1169))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.19/0.58 tff(104,plain,
% 0.19/0.58 (~c3_1(a1169)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[103, 98])).
% 0.19/0.58 tff(105,plain,
% 0.19/0.58 (((~hskp1) | (~c2_1(a1169))) <=> ((~hskp1) | (~c2_1(a1169)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(106,plain,
% 0.19/0.58 (((~c2_1(a1169)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a1169)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(107,axiom,((~c2_1(a1169)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.19/0.58 tff(108,plain,
% 0.19/0.58 ((~hskp1) | (~c2_1(a1169))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.58 tff(109,plain,
% 0.19/0.58 ((~hskp1) | (~c2_1(a1169))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[108, 105])).
% 0.19/0.58 tff(110,plain,
% 0.19/0.58 (~c2_1(a1169)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[109, 98])).
% 0.19/0.58 tff(111,plain,
% 0.19/0.58 (((~hskp1) | c1_1(a1169)) <=> ((~hskp1) | c1_1(a1169))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(112,axiom,((~hskp1) | c1_1(a1169)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.19/0.58 tff(113,plain,
% 0.19/0.58 ((~hskp1) | c1_1(a1169)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.58 tff(114,plain,
% 0.19/0.58 ((~hskp1) | c1_1(a1169)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[113, 111])).
% 0.19/0.58 tff(115,plain,
% 0.19/0.58 ((~hskp1) | c1_1(a1169)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[114, 111])).
% 0.19/0.58 tff(116,plain,
% 0.19/0.58 ((~hskp1) | c1_1(a1169)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.19/0.58 tff(117,plain,
% 0.19/0.58 ((~hskp1) | c1_1(a1169)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[116, 111])).
% 0.19/0.58 tff(118,plain,
% 0.19/0.58 (c1_1(a1169)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[117, 98])).
% 0.19/0.58 tff(119,plain,
% 0.19/0.58 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(120,plain,
% 0.19/0.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[119])).
% 0.19/0.58 tff(121,plain,
% 0.19/0.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(122,plain,
% 0.19/0.58 (^[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) | c1_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(123,plain,
% 0.19/0.58 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[122])).
% 0.19/0.58 tff(124,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 0.19/0.58 tff(125,plain,
% 0.19/0.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.58 tff(126,plain,
% 0.19/0.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.19/0.58 tff(127,plain,(
% 0.19/0.58 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.19/0.58 inference(skolemize,[status(sab)],[126])).
% 0.19/0.58 tff(128,plain,
% 0.19/0.58 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.19/0.58 tff(129,assumption,(hskp19), introduced(assumption)).
% 0.19/0.58 tff(130,plain,
% 0.19/0.58 (((~hskp19) | (~c2_1(a1204))) <=> ((~hskp19) | (~c2_1(a1204)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(131,plain,
% 0.19/0.58 (((~c2_1(a1204)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a1204)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(132,axiom,((~c2_1(a1204)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 0.19/0.58 tff(133,plain,
% 0.19/0.58 ((~hskp19) | (~c2_1(a1204))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.58 tff(134,plain,
% 0.19/0.58 ((~hskp19) | (~c2_1(a1204))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[133, 130])).
% 0.19/0.58 tff(135,plain,
% 0.19/0.58 (~c2_1(a1204)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[134, 129])).
% 0.19/0.58 tff(136,plain,
% 0.19/0.58 (((~hskp19) | (~c1_1(a1204))) <=> ((~hskp19) | (~c1_1(a1204)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(137,plain,
% 0.19/0.58 (((~c1_1(a1204)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a1204)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(138,axiom,((~c1_1(a1204)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 0.19/0.58 tff(139,plain,
% 0.19/0.58 ((~hskp19) | (~c1_1(a1204))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.58 tff(140,plain,
% 0.19/0.58 ((~hskp19) | (~c1_1(a1204))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[139, 136])).
% 0.19/0.58 tff(141,plain,
% 0.19/0.58 (~c1_1(a1204)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[140, 129])).
% 0.19/0.58 tff(142,plain,
% 0.19/0.58 (((~hskp19) | c3_1(a1204)) <=> ((~hskp19) | c3_1(a1204))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(143,axiom,((~hskp19) | c3_1(a1204)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.19/0.58 tff(144,plain,
% 0.19/0.58 ((~hskp19) | c3_1(a1204)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.19/0.58 tff(145,plain,
% 0.19/0.58 ((~hskp19) | c3_1(a1204)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[144, 142])).
% 0.19/0.58 tff(146,plain,
% 0.19/0.58 ((~hskp19) | c3_1(a1204)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[145, 142])).
% 0.19/0.58 tff(147,plain,
% 0.19/0.58 ((~hskp19) | c3_1(a1204)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.19/0.58 tff(148,plain,
% 0.19/0.58 ((~hskp19) | c3_1(a1204)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[147, 142])).
% 0.19/0.58 tff(149,plain,
% 0.19/0.58 (c3_1(a1204)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[148, 129])).
% 0.19/0.58 tff(150,assumption,(~ndr1_0), introduced(assumption)).
% 0.19/0.58 tff(151,plain,
% 0.19/0.58 (((~hskp28) | ndr1_0) <=> ((~hskp28) | ndr1_0)),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(152,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 0.19/0.58 tff(153,plain,
% 0.19/0.58 ((~hskp28) | ndr1_0),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.58 tff(154,plain,
% 0.19/0.58 ((~hskp28) | ndr1_0),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[153, 151])).
% 0.19/0.58 tff(155,plain,
% 0.19/0.58 ((~hskp28) | ndr1_0),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[154, 151])).
% 0.19/0.58 tff(156,plain,
% 0.19/0.58 ((~hskp28) | ndr1_0),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.19/0.58 tff(157,plain,
% 0.19/0.58 ((~hskp28) | ndr1_0),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[156, 151])).
% 0.19/0.58 tff(158,plain,
% 0.19/0.58 (~hskp28),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[157, 150])).
% 0.19/0.58 tff(159,plain,
% 0.19/0.58 ((ndr1_0 | (~hskp8)) <=> (ndr1_0 | (~hskp8))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(160,plain,
% 0.19/0.58 (((~hskp8) | ndr1_0) <=> (ndr1_0 | (~hskp8))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(161,axiom,((~hskp8) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause22')).
% 0.19/0.58 tff(162,plain,
% 0.19/0.58 (ndr1_0 | (~hskp8)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.19/0.58 tff(163,plain,
% 0.19/0.58 (ndr1_0 | (~hskp8)),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[162, 159])).
% 0.19/0.58 tff(164,plain,
% 0.19/0.58 (~hskp8),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[163, 150])).
% 0.19/0.58 tff(165,plain,
% 0.19/0.58 ((hskp28 | hskp8) <=> (hskp28 | hskp8)),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(166,axiom,(hskp28 | hskp8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.19/0.58 tff(167,plain,
% 0.19/0.58 (hskp28 | hskp8),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.58 tff(168,plain,
% 0.19/0.58 ($false),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[167, 164, 158])).
% 0.19/0.58 tff(169,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.19/0.58 tff(170,plain,
% 0.19/0.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | c0_1(a1204) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | c0_1(a1204) | (~c3_1(a1204)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(171,plain,
% 0.19/0.58 ((hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c3_1(a1204)) | c2_1(a1204) | c1_1(a1204) | c0_1(a1204)) <=> (hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | c0_1(a1204) | (~c3_1(a1204)))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(172,plain,
% 0.43/0.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c3_1(a1204)) | c2_1(a1204) | c1_1(a1204) | c0_1(a1204))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | c0_1(a1204) | (~c3_1(a1204))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[171])).
% 0.43/0.58 tff(173,plain,
% 0.43/0.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c3_1(a1204)) | c2_1(a1204) | c1_1(a1204) | c0_1(a1204))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | c0_1(a1204) | (~c3_1(a1204)))),
% 0.43/0.58 inference(transitivity,[status(thm)],[172, 170])).
% 0.43/0.58 tff(174,plain,
% 0.43/0.58 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c3_1(a1204)) | c2_1(a1204) | c1_1(a1204) | c0_1(a1204))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(175,plain,
% 0.43/0.58 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | c0_1(a1204) | (~c3_1(a1204))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.43/0.58 tff(176,plain,
% 0.43/0.58 (c0_1(a1204)),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[175, 169, 78, 149, 141, 135, 128])).
% 0.43/0.58 tff(177,plain,
% 0.43/0.58 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | (~c0_1(a1204)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | (~c0_1(a1204)))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(178,plain,
% 0.43/0.58 ((hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c0_1(a1204))) <=> (hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | (~c0_1(a1204)))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(179,plain,
% 0.43/0.58 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c0_1(a1204)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | (~c0_1(a1204))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[178])).
% 0.43/0.58 tff(180,plain,
% 0.43/0.58 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c0_1(a1204)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | (~c0_1(a1204)))),
% 0.43/0.58 inference(transitivity,[status(thm)],[179, 177])).
% 0.43/0.58 tff(181,plain,
% 0.43/0.58 ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c0_1(a1204)))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(182,plain,
% 0.43/0.58 ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | (~c0_1(a1204))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.43/0.58 tff(183,plain,
% 0.43/0.58 ($false),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[182, 169, 78, 141, 135, 67, 176])).
% 0.43/0.58 tff(184,plain,((~hskp19) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.43/0.58 tff(185,plain,
% 0.43/0.58 (~hskp19),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[184, 78])).
% 0.43/0.58 tff(186,plain,
% 0.43/0.58 (((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp23 | hskp19 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)))) <=> ((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp23 | hskp19 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(187,plain,
% 0.43/0.58 ((hskp23 | hskp19 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c1_1(a1169))) <=> (hskp23 | hskp19 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(188,plain,
% 0.43/0.58 (((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp23 | hskp19 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c1_1(a1169)))) <=> ((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp23 | hskp19 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[187])).
% 0.43/0.58 tff(189,plain,
% 0.43/0.58 (((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp23 | hskp19 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c1_1(a1169)))) <=> ((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp23 | hskp19 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)))),
% 0.43/0.58 inference(transitivity,[status(thm)],[188, 186])).
% 0.43/0.58 tff(190,plain,
% 0.43/0.58 ((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp23 | hskp19 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c1_1(a1169)))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(191,plain,
% 0.43/0.58 ((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp23 | hskp19 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.43/0.58 tff(192,plain,
% 0.43/0.58 (hskp23),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[191, 169, 185, 118, 110, 104, 89])).
% 0.43/0.58 tff(193,plain,
% 0.43/0.58 (^[U: $i] : refl((hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 0.43/0.58 inference(bind,[status(th)],[])).
% 0.43/0.58 tff(194,plain,
% 0.43/0.58 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.43/0.58 inference(quant_intro,[status(thm)],[193])).
% 0.43/0.58 tff(195,plain,
% 0.43/0.58 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(196,plain,
% 0.43/0.58 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | 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))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp3) <=> ((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite(((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp3) <=> (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 0.43/0.58 inference(bind,[status(th)],[])).
% 0.43/0.58 tff(197,plain,
% 0.43/0.58 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp3) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.43/0.58 inference(quant_intro,[status(thm)],[196])).
% 0.43/0.58 tff(198,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.43/0.58 tff(199,plain,
% 0.43/0.58 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.43/0.59 tff(200,plain,
% 0.43/0.59 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.43/0.59 tff(201,plain,(
% 0.43/0.59 ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.43/0.59 inference(skolemize,[status(sab)],[200])).
% 0.43/0.59 tff(202,plain,
% 0.43/0.59 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[201, 194])).
% 0.43/0.59 tff(203,assumption,(hskp23), introduced(assumption)).
% 0.43/0.59 tff(204,plain,
% 0.43/0.59 (((~hskp23) | (~c3_1(a1218))) <=> ((~hskp23) | (~c3_1(a1218)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(205,plain,
% 0.43/0.59 (((~c3_1(a1218)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1218)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(206,axiom,((~c3_1(a1218)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.43/0.59 tff(207,plain,
% 0.43/0.59 ((~hskp23) | (~c3_1(a1218))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.43/0.59 tff(208,plain,
% 0.43/0.59 ((~hskp23) | (~c3_1(a1218))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[207, 204])).
% 0.43/0.59 tff(209,plain,
% 0.43/0.59 (~c3_1(a1218)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[208, 203])).
% 0.43/0.59 tff(210,plain,
% 0.43/0.59 (((~hskp23) | (~c1_1(a1218))) <=> ((~hskp23) | (~c1_1(a1218)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(211,plain,
% 0.43/0.59 (((~c1_1(a1218)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a1218)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(212,axiom,((~c1_1(a1218)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.43/0.59 tff(213,plain,
% 0.43/0.59 ((~hskp23) | (~c1_1(a1218))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.43/0.59 tff(214,plain,
% 0.43/0.59 ((~hskp23) | (~c1_1(a1218))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[213, 210])).
% 0.43/0.59 tff(215,plain,
% 0.43/0.59 (~c1_1(a1218)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[214, 203])).
% 0.43/0.59 tff(216,plain,
% 0.43/0.59 (((~hskp23) | (~c0_1(a1218))) <=> ((~hskp23) | (~c0_1(a1218)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(217,plain,
% 0.43/0.59 (((~c0_1(a1218)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a1218)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(218,axiom,((~c0_1(a1218)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.43/0.59 tff(219,plain,
% 0.43/0.59 ((~hskp23) | (~c0_1(a1218))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.43/0.59 tff(220,plain,
% 0.43/0.59 ((~hskp23) | (~c0_1(a1218))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[219, 216])).
% 0.43/0.59 tff(221,plain,
% 0.43/0.59 (~c0_1(a1218)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[220, 203])).
% 0.43/0.59 tff(222,plain,
% 0.43/0.59 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | c0_1(a1218) | c1_1(a1218) | c3_1(a1218) | (~ndr1_0))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp0 | c0_1(a1218) | c1_1(a1218) | c3_1(a1218) | (~ndr1_0))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(223,plain,
% 0.43/0.59 ((hskp3 | hskp0 | (~ndr1_0) | c3_1(a1218) | c1_1(a1218) | c0_1(a1218)) <=> (hskp3 | hskp0 | c0_1(a1218) | c1_1(a1218) | c3_1(a1218) | (~ndr1_0))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(224,plain,
% 0.43/0.59 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | (~ndr1_0) | c3_1(a1218) | c1_1(a1218) | c0_1(a1218))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | c0_1(a1218) | c1_1(a1218) | c3_1(a1218) | (~ndr1_0)))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[223])).
% 0.43/0.59 tff(225,plain,
% 0.43/0.59 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | (~ndr1_0) | c3_1(a1218) | c1_1(a1218) | c0_1(a1218))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp0 | c0_1(a1218) | c1_1(a1218) | c3_1(a1218) | (~ndr1_0))),
% 0.43/0.59 inference(transitivity,[status(thm)],[224, 222])).
% 0.43/0.59 tff(226,plain,
% 0.43/0.59 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | (~ndr1_0) | c3_1(a1218) | c1_1(a1218) | c0_1(a1218))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(227,plain,
% 0.43/0.59 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp0 | c0_1(a1218) | c1_1(a1218) | c3_1(a1218) | (~ndr1_0)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.43/0.59 tff(228,plain,
% 0.43/0.59 ($false),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[227, 169, 22, 78, 221, 215, 209, 202])).
% 0.43/0.59 tff(229,plain,((~hskp23) | hskp3 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.43/0.59 tff(230,plain,
% 0.43/0.59 (hskp3),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[229, 192, 78])).
% 0.43/0.59 tff(231,plain,
% 0.43/0.59 (^[U: $i] : refl((hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(232,plain,
% 0.43/0.59 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[231])).
% 0.43/0.59 tff(233,plain,
% 0.43/0.59 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(234,plain,
% 0.43/0.59 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) | hskp14) <=> ((hskp22 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp14))), rewrite(((hskp22 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp14) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) | hskp14) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(235,plain,
% 0.43/0.59 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) | hskp14) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[234])).
% 0.43/0.59 tff(236,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 0.43/0.59 tff(237,plain,
% 0.43/0.59 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.43/0.59 tff(238,plain,
% 0.43/0.59 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[237, 233])).
% 0.43/0.59 tff(239,plain,(
% 0.43/0.59 ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.43/0.59 inference(skolemize,[status(sab)],[238])).
% 0.43/0.59 tff(240,plain,
% 0.43/0.59 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[239, 232])).
% 0.43/0.59 tff(241,assumption,(hskp3), introduced(assumption)).
% 0.43/0.59 tff(242,plain,
% 0.43/0.59 (((~hskp3) | (~c3_1(a1174))) <=> ((~hskp3) | (~c3_1(a1174)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(243,plain,
% 0.43/0.59 (((~c3_1(a1174)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a1174)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(244,axiom,((~c3_1(a1174)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.43/0.59 tff(245,plain,
% 0.43/0.59 ((~hskp3) | (~c3_1(a1174))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.43/0.59 tff(246,plain,
% 0.43/0.59 ((~hskp3) | (~c3_1(a1174))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[245, 242])).
% 0.43/0.59 tff(247,plain,
% 0.43/0.59 (~c3_1(a1174)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[246, 241])).
% 0.43/0.59 tff(248,plain,
% 0.43/0.59 (((~hskp3) | c0_1(a1174)) <=> ((~hskp3) | c0_1(a1174))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(249,axiom,((~hskp3) | c0_1(a1174)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.43/0.59 tff(250,plain,
% 0.43/0.59 ((~hskp3) | c0_1(a1174)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.43/0.59 tff(251,plain,
% 0.43/0.59 ((~hskp3) | c0_1(a1174)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[250, 248])).
% 0.43/0.59 tff(252,plain,
% 0.43/0.59 ((~hskp3) | c0_1(a1174)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[251, 248])).
% 0.43/0.59 tff(253,plain,
% 0.43/0.59 ((~hskp3) | c0_1(a1174)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[252, 248])).
% 0.43/0.59 tff(254,plain,
% 0.43/0.59 ((~hskp3) | c0_1(a1174)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[253, 248])).
% 0.43/0.59 tff(255,plain,
% 0.43/0.59 (c0_1(a1174)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[254, 241])).
% 0.43/0.59 tff(256,assumption,(~hskp22), introduced(assumption)).
% 0.43/0.59 tff(257,plain,
% 0.43/0.59 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | (~c2_1(a1174)) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | (~c2_1(a1174)) | (~c0_1(a1174)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(258,plain,
% 0.43/0.59 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c2_1(a1174))) <=> (hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | (~c2_1(a1174)) | (~c0_1(a1174)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(259,plain,
% 0.43/0.59 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c2_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | (~c2_1(a1174)) | (~c0_1(a1174))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[258])).
% 0.43/0.59 tff(260,plain,
% 0.43/0.59 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c2_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | (~c2_1(a1174)) | (~c0_1(a1174)))),
% 0.43/0.59 inference(transitivity,[status(thm)],[259, 257])).
% 0.43/0.59 tff(261,plain,
% 0.43/0.59 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c2_1(a1174)))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(262,plain,
% 0.43/0.59 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | (~c2_1(a1174)) | (~c0_1(a1174))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.43/0.59 tff(263,plain,
% 0.43/0.59 (~c2_1(a1174)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[262, 169, 256, 79, 255, 247, 240])).
% 0.43/0.59 tff(264,plain,
% 0.43/0.59 (^[U: $i] : refl((hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(265,plain,
% 0.43/0.59 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[264])).
% 0.43/0.59 tff(266,plain,
% 0.43/0.59 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(267,plain,
% 0.43/0.59 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp14) <=> ((hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp14))), rewrite(((hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp14) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp14) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(268,plain,
% 0.43/0.59 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp14) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[267])).
% 0.43/0.59 tff(269,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.43/0.59 tff(270,plain,
% 0.43/0.59 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.43/0.59 tff(271,plain,
% 0.43/0.59 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[270, 266])).
% 0.43/0.59 tff(272,plain,(
% 0.43/0.59 ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.43/0.59 inference(skolemize,[status(sab)],[271])).
% 0.43/0.59 tff(273,plain,
% 0.43/0.59 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[272, 265])).
% 0.43/0.59 tff(274,plain,
% 0.43/0.59 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(275,plain,
% 0.43/0.59 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174))) <=> (hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(276,plain,
% 0.43/0.59 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[275])).
% 0.43/0.59 tff(277,plain,
% 0.43/0.59 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.43/0.59 inference(transitivity,[status(thm)],[276, 274])).
% 0.43/0.59 tff(278,plain,
% 0.43/0.59 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(279,plain,
% 0.43/0.59 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.43/0.59 tff(280,plain,
% 0.43/0.59 ($false),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[279, 169, 256, 79, 255, 247, 273, 263])).
% 0.43/0.59 tff(281,plain,((~hskp3) | hskp22 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.43/0.59 tff(282,plain,
% 0.43/0.59 (hskp22),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[281, 230, 79])).
% 0.43/0.59 tff(283,plain,
% 0.43/0.59 (~c1_1(a1211)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[29, 282])).
% 0.43/0.59 tff(284,plain,
% 0.43/0.59 (c0_1(a1211)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[45, 282])).
% 0.43/0.59 tff(285,plain,
% 0.43/0.59 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | c1_1(a1211) | (~ndr1_0) | (~c0_1(a1211)) | c2_1(a1211))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1211) | (~ndr1_0) | (~c0_1(a1211)) | c2_1(a1211))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(286,plain,
% 0.43/0.59 ((hskp0 | (~ndr1_0) | c1_1(a1211) | c2_1(a1211) | (~c0_1(a1211))) <=> (hskp0 | c1_1(a1211) | (~ndr1_0) | (~c0_1(a1211)) | c2_1(a1211))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(287,plain,
% 0.43/0.59 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1211) | c2_1(a1211) | (~c0_1(a1211)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | c1_1(a1211) | (~ndr1_0) | (~c0_1(a1211)) | c2_1(a1211)))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[286])).
% 0.43/0.59 tff(288,plain,
% 0.43/0.59 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1211) | c2_1(a1211) | (~c0_1(a1211)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1211) | (~ndr1_0) | (~c0_1(a1211)) | c2_1(a1211))),
% 0.43/0.59 inference(transitivity,[status(thm)],[287, 285])).
% 0.43/0.59 tff(289,plain,
% 0.43/0.59 ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1211) | c2_1(a1211) | (~c0_1(a1211)))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(290,plain,
% 0.43/0.59 ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1211) | (~ndr1_0) | (~c0_1(a1211)) | c2_1(a1211)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.43/0.59 tff(291,plain,
% 0.43/0.59 (c2_1(a1211)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[290, 169, 78, 284, 283, 67])).
% 0.43/0.59 tff(292,plain,
% 0.43/0.59 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(293,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[292])).
% 0.43/0.59 tff(294,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(295,plain,
% 0.43/0.59 (^[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))) <=> ((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_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))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_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))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_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))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_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))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(296,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[295])).
% 0.43/0.59 tff(297,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.43/0.60 tff(298,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.43/0.60 tff(299,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[298, 294])).
% 0.43/0.60 tff(300,plain,(
% 0.43/0.60 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.43/0.60 inference(skolemize,[status(sab)],[299])).
% 0.43/0.60 tff(301,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[300, 293])).
% 0.43/0.60 tff(302,plain,
% 0.43/0.60 (((~hskp3) | c1_1(a1174)) <=> ((~hskp3) | c1_1(a1174))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(303,axiom,((~hskp3) | c1_1(a1174)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.43/0.60 tff(304,plain,
% 0.43/0.60 ((~hskp3) | c1_1(a1174)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.43/0.60 tff(305,plain,
% 0.43/0.60 ((~hskp3) | c1_1(a1174)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[304, 302])).
% 0.43/0.60 tff(306,plain,
% 0.43/0.60 ((~hskp3) | c1_1(a1174)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[305, 302])).
% 0.43/0.60 tff(307,plain,
% 0.43/0.60 ((~hskp3) | c1_1(a1174)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[306, 302])).
% 0.43/0.60 tff(308,plain,
% 0.43/0.60 ((~hskp3) | c1_1(a1174)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[307, 302])).
% 0.43/0.60 tff(309,plain,
% 0.43/0.60 (c1_1(a1174)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[308, 230])).
% 0.43/0.60 tff(310,plain,
% 0.43/0.60 (c0_1(a1174)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[254, 230])).
% 0.43/0.60 tff(311,plain,
% 0.43/0.60 (c3_1(a1211)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[37, 282])).
% 0.43/0.60 tff(312,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | (~c3_1(a1211)) | (~c0_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | (~c3_1(a1211)) | (~c0_1(a1211)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(313,plain,
% 0.43/0.60 (((~ndr1_0) | (~c0_1(a1174)) | (~c1_1(a1174)) | (~c2_1(a1174)) | c2_1(a1169) | c3_1(a1169) | (~c1_1(a1169)) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211))) <=> (c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | (~c3_1(a1211)) | (~c0_1(a1211)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(314,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c0_1(a1174)) | (~c1_1(a1174)) | (~c2_1(a1174)) | c2_1(a1169) | c3_1(a1169) | (~c1_1(a1169)) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | (~c3_1(a1211)) | (~c0_1(a1211))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[313])).
% 0.43/0.60 tff(315,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c0_1(a1174)) | (~c1_1(a1174)) | (~c2_1(a1174)) | c2_1(a1169) | c3_1(a1169) | (~c1_1(a1169)) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | (~c3_1(a1211)) | (~c0_1(a1211)))),
% 0.43/0.60 inference(transitivity,[status(thm)],[314, 312])).
% 0.43/0.60 tff(316,plain,
% 0.43/0.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c0_1(a1174)) | (~c1_1(a1174)) | (~c2_1(a1174)) | c2_1(a1169) | c3_1(a1169) | (~c1_1(a1169)) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(317,plain,
% 0.43/0.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | (~c3_1(a1211)) | (~c0_1(a1211))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.43/0.60 tff(318,plain,
% 0.43/0.60 (~c2_1(a1174)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[317, 169, 284, 311, 310, 309, 118, 283, 110, 104, 301])).
% 0.43/0.60 tff(319,plain,
% 0.43/0.60 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(320,plain,
% 0.43/0.60 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[319])).
% 0.43/0.60 tff(321,plain,
% 0.43/0.60 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(322,plain,
% 0.43/0.60 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(323,plain,
% 0.43/0.60 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[322])).
% 0.43/0.60 tff(324,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 0.43/0.60 tff(325,plain,
% 0.43/0.60 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.43/0.60 tff(326,plain,
% 0.43/0.60 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[325, 321])).
% 0.43/0.60 tff(327,plain,(
% 0.43/0.60 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.43/0.60 inference(skolemize,[status(sab)],[326])).
% 0.43/0.60 tff(328,plain,
% 0.43/0.60 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[327, 320])).
% 0.43/0.60 tff(329,plain,
% 0.43/0.60 (~c3_1(a1174)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[246, 230])).
% 0.43/0.60 tff(330,assumption,(hskp17), introduced(assumption)).
% 0.43/0.60 tff(331,plain,
% 0.43/0.60 (((~hskp17) | (~c2_1(a1200))) <=> ((~hskp17) | (~c2_1(a1200)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(332,plain,
% 0.43/0.60 (((~c2_1(a1200)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a1200)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(333,axiom,((~c2_1(a1200)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 0.43/0.60 tff(334,plain,
% 0.43/0.60 ((~hskp17) | (~c2_1(a1200))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.43/0.60 tff(335,plain,
% 0.43/0.60 ((~hskp17) | (~c2_1(a1200))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[334, 331])).
% 0.43/0.60 tff(336,plain,
% 0.43/0.60 (~c2_1(a1200)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[335, 330])).
% 0.43/0.60 tff(337,plain,
% 0.43/0.60 (((~hskp17) | (~c1_1(a1200))) <=> ((~hskp17) | (~c1_1(a1200)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(338,plain,
% 0.43/0.60 (((~c1_1(a1200)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1200)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(339,axiom,((~c1_1(a1200)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.43/0.60 tff(340,plain,
% 0.43/0.60 ((~hskp17) | (~c1_1(a1200))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.43/0.60 tff(341,plain,
% 0.43/0.60 ((~hskp17) | (~c1_1(a1200))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[340, 337])).
% 0.43/0.60 tff(342,plain,
% 0.43/0.60 (~c1_1(a1200)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[341, 330])).
% 0.43/0.60 tff(343,plain,
% 0.43/0.60 (((~hskp17) | c0_1(a1200)) <=> ((~hskp17) | c0_1(a1200))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(344,axiom,((~hskp17) | c0_1(a1200)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.43/0.60 tff(345,plain,
% 0.43/0.60 ((~hskp17) | c0_1(a1200)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.43/0.60 tff(346,plain,
% 0.43/0.60 ((~hskp17) | c0_1(a1200)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[345, 343])).
% 0.43/0.60 tff(347,plain,
% 0.43/0.60 ((~hskp17) | c0_1(a1200)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[346, 343])).
% 0.43/0.60 tff(348,plain,
% 0.43/0.60 ((~hskp17) | c0_1(a1200)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[347, 343])).
% 0.43/0.60 tff(349,plain,
% 0.43/0.60 ((~hskp17) | c0_1(a1200)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[348, 343])).
% 0.43/0.60 tff(350,plain,
% 0.43/0.60 (c0_1(a1200)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[349, 330])).
% 0.43/0.60 tff(351,plain,
% 0.43/0.60 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c0_1(a1200)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c0_1(a1200)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(352,plain,
% 0.43/0.60 ((hskp0 | (~ndr1_0) | c1_1(a1200) | c2_1(a1200) | (~c0_1(a1200))) <=> (hskp0 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c0_1(a1200)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(353,plain,
% 0.43/0.60 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1200) | c2_1(a1200) | (~c0_1(a1200)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c0_1(a1200))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[352])).
% 0.43/0.60 tff(354,plain,
% 0.43/0.60 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1200) | c2_1(a1200) | (~c0_1(a1200)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c0_1(a1200)))),
% 0.43/0.60 inference(transitivity,[status(thm)],[353, 351])).
% 0.43/0.60 tff(355,plain,
% 0.43/0.60 ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1200) | c2_1(a1200) | (~c0_1(a1200)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(356,plain,
% 0.43/0.60 ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c0_1(a1200))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.43/0.60 tff(357,plain,
% 0.43/0.60 ($false),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[356, 169, 78, 350, 342, 336, 67])).
% 0.43/0.60 tff(358,plain,((~hskp17) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.43/0.60 tff(359,plain,
% 0.43/0.60 (~hskp17),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[358, 78])).
% 0.43/0.60 tff(360,plain,
% 0.43/0.60 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a1211) | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c0_1(a1211)) | (~c2_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a1211) | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(361,plain,
% 0.43/0.60 ((hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211))) <=> (hskp17 | c1_1(a1211) | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(362,plain,
% 0.43/0.60 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a1211) | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c0_1(a1211)) | (~c2_1(a1211))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[361])).
% 0.43/0.60 tff(363,plain,
% 0.43/0.60 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a1211) | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.43/0.60 inference(transitivity,[status(thm)],[362, 360])).
% 0.43/0.60 tff(364,plain,
% 0.43/0.60 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(365,plain,
% 0.43/0.60 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a1211) | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c0_1(a1211)) | (~c2_1(a1211))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.43/0.60 tff(366,plain,
% 0.43/0.60 ($false),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[365, 169, 359, 284, 310, 283, 329, 328, 318, 291])).
% 0.43/0.60 tff(367,plain,(hskp14 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.43/0.60 tff(368,plain,
% 0.43/0.60 (hskp14),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[367, 78])).
% 0.43/0.60 tff(369,plain,
% 0.43/0.60 (((~hskp14) | (~c1_1(a1194))) <=> ((~hskp14) | (~c1_1(a1194)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(370,plain,
% 0.43/0.60 (((~c1_1(a1194)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a1194)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(371,axiom,((~c1_1(a1194)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.43/0.60 tff(372,plain,
% 0.43/0.60 ((~hskp14) | (~c1_1(a1194))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.43/0.60 tff(373,plain,
% 0.43/0.60 ((~hskp14) | (~c1_1(a1194))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[372, 369])).
% 0.43/0.60 tff(374,plain,
% 0.43/0.60 (~c1_1(a1194)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[373, 368])).
% 0.43/0.60 tff(375,plain,
% 0.43/0.60 (((~hskp14) | (~c0_1(a1194))) <=> ((~hskp14) | (~c0_1(a1194)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(376,plain,
% 0.43/0.60 (((~c0_1(a1194)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a1194)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(377,axiom,((~c0_1(a1194)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.43/0.60 tff(378,plain,
% 0.43/0.60 ((~hskp14) | (~c0_1(a1194))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.43/0.60 tff(379,plain,
% 0.43/0.60 ((~hskp14) | (~c0_1(a1194))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[378, 375])).
% 0.43/0.60 tff(380,plain,
% 0.43/0.60 (~c0_1(a1194)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[379, 368])).
% 0.43/0.60 tff(381,plain,
% 0.43/0.60 (((~hskp14) | c2_1(a1194)) <=> ((~hskp14) | c2_1(a1194))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(382,axiom,((~hskp14) | c2_1(a1194)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 0.43/0.60 tff(383,plain,
% 0.43/0.60 ((~hskp14) | c2_1(a1194)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.43/0.60 tff(384,plain,
% 0.43/0.60 ((~hskp14) | c2_1(a1194)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[383, 381])).
% 0.43/0.60 tff(385,plain,
% 0.43/0.60 ((~hskp14) | c2_1(a1194)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[384, 381])).
% 0.43/0.60 tff(386,plain,
% 0.43/0.60 ((~hskp14) | c2_1(a1194)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[385, 381])).
% 0.43/0.60 tff(387,plain,
% 0.43/0.60 ((~hskp14) | c2_1(a1194)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[386, 381])).
% 0.43/0.60 tff(388,plain,
% 0.43/0.60 (c2_1(a1194)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[387, 368])).
% 0.43/0.60 tff(389,plain,
% 0.43/0.60 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp0 | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | c3_1(a1194) | (~c2_1(a1194)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp0 | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(390,plain,
% 0.43/0.60 ((hskp0 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194)) <=> (hskp0 | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(391,plain,
% 0.43/0.60 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp0 | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | c3_1(a1194) | (~c2_1(a1194))))),
% 0.45/0.60 inference(monotonicity,[status(thm)],[390])).
% 0.45/0.60 tff(392,plain,
% 0.45/0.60 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp0 | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.45/0.60 inference(transitivity,[status(thm)],[391, 389])).
% 0.45/0.60 tff(393,plain,
% 0.45/0.60 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194))),
% 0.45/0.60 inference(quant_inst,[status(thm)],[])).
% 0.45/0.60 tff(394,plain,
% 0.45/0.60 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp0 | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | c3_1(a1194) | (~c2_1(a1194))),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.45/0.60 tff(395,plain,
% 0.45/0.60 (c3_1(a1194)),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[394, 169, 78, 388, 380, 374, 77])).
% 0.45/0.60 tff(396,plain,
% 0.45/0.60 (~hskp23),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[229, 22, 78])).
% 0.45/0.60 tff(397,assumption,(hskp1), introduced(assumption)).
% 0.45/0.60 tff(398,plain,
% 0.45/0.60 (~c3_1(a1169)),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[103, 397])).
% 0.45/0.60 tff(399,plain,
% 0.45/0.60 (~c2_1(a1169)),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[109, 397])).
% 0.45/0.60 tff(400,plain,
% 0.45/0.60 (c1_1(a1169)),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[117, 397])).
% 0.45/0.60 tff(401,assumption,(~hskp19), introduced(assumption)).
% 0.45/0.60 tff(402,assumption,(~hskp23), introduced(assumption)).
% 0.45/0.60 tff(403,plain,
% 0.45/0.60 ($false),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[191, 169, 402, 401, 400, 399, 398, 89])).
% 0.45/0.60 tff(404,plain,((~hskp1) | hskp23 | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.45/0.60 tff(405,plain,
% 0.45/0.60 (~hskp1),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[404, 396, 185])).
% 0.45/0.60 tff(406,plain,
% 0.45/0.60 ((hskp17 | hskp16 | hskp1) <=> (hskp17 | hskp16 | hskp1)),
% 0.45/0.60 inference(rewrite,[status(thm)],[])).
% 0.45/0.60 tff(407,plain,
% 0.45/0.60 (((hskp17 | hskp1) | hskp16) <=> (hskp17 | hskp16 | hskp1)),
% 0.45/0.60 inference(rewrite,[status(thm)],[])).
% 0.45/0.60 tff(408,plain,
% 0.45/0.60 ((hskp17 | hskp1) <=> (hskp17 | hskp1)),
% 0.45/0.60 inference(rewrite,[status(thm)],[])).
% 0.45/0.60 tff(409,plain,
% 0.45/0.60 (((hskp17 | hskp1) | hskp16) <=> ((hskp17 | hskp1) | hskp16)),
% 0.45/0.60 inference(monotonicity,[status(thm)],[408])).
% 0.45/0.60 tff(410,plain,
% 0.45/0.60 (((hskp17 | hskp1) | hskp16) <=> (hskp17 | hskp16 | hskp1)),
% 0.45/0.60 inference(transitivity,[status(thm)],[409, 407])).
% 0.45/0.60 tff(411,axiom,((hskp17 | hskp1) | hskp16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 0.45/0.60 tff(412,plain,
% 0.45/0.60 (hskp17 | hskp16 | hskp1),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.45/0.60 tff(413,plain,
% 0.45/0.60 (hskp17 | hskp16 | hskp1),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[412, 406])).
% 0.45/0.60 tff(414,plain,
% 0.45/0.60 (hskp17 | hskp16 | hskp1),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[413, 406])).
% 0.45/0.60 tff(415,plain,
% 0.45/0.60 (hskp17 | hskp16 | hskp1),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[414, 406])).
% 0.45/0.60 tff(416,plain,
% 0.45/0.60 (hskp17 | hskp16 | hskp1),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[415, 406])).
% 0.45/0.60 tff(417,plain,
% 0.45/0.60 (hskp16),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[416, 405, 359])).
% 0.45/0.60 tff(418,plain,
% 0.45/0.60 (((~hskp16) | (~c3_1(a1199))) <=> ((~hskp16) | (~c3_1(a1199)))),
% 0.45/0.60 inference(rewrite,[status(thm)],[])).
% 0.45/0.60 tff(419,plain,
% 0.45/0.60 (((~c3_1(a1199)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a1199)))),
% 0.45/0.60 inference(rewrite,[status(thm)],[])).
% 0.45/0.60 tff(420,axiom,((~c3_1(a1199)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.45/0.60 tff(421,plain,
% 0.45/0.60 ((~hskp16) | (~c3_1(a1199))),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.45/0.60 tff(422,plain,
% 0.45/0.60 ((~hskp16) | (~c3_1(a1199))),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[421, 418])).
% 0.45/0.60 tff(423,plain,
% 0.45/0.60 (~c3_1(a1199)),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[422, 417])).
% 0.45/0.60 tff(424,plain,
% 0.45/0.60 (((~hskp16) | (~c0_1(a1199))) <=> ((~hskp16) | (~c0_1(a1199)))),
% 0.45/0.60 inference(rewrite,[status(thm)],[])).
% 0.45/0.60 tff(425,plain,
% 0.45/0.60 (((~c0_1(a1199)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a1199)))),
% 0.45/0.60 inference(rewrite,[status(thm)],[])).
% 0.45/0.60 tff(426,axiom,((~c0_1(a1199)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.45/0.60 tff(427,plain,
% 0.45/0.60 ((~hskp16) | (~c0_1(a1199))),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.45/0.60 tff(428,plain,
% 0.45/0.60 ((~hskp16) | (~c0_1(a1199))),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[427, 424])).
% 0.45/0.60 tff(429,plain,
% 0.45/0.60 (~c0_1(a1199)),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[428, 417])).
% 0.45/0.60 tff(430,plain,
% 0.45/0.60 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | c1_1(a1199))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp0 | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | c1_1(a1199))),
% 0.45/0.60 inference(rewrite,[status(thm)],[])).
% 0.45/0.60 tff(431,plain,
% 0.45/0.60 ((hskp3 | hskp0 | (~ndr1_0) | c3_1(a1199) | c1_1(a1199) | c0_1(a1199)) <=> (hskp3 | hskp0 | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | c1_1(a1199))),
% 0.45/0.60 inference(rewrite,[status(thm)],[])).
% 0.45/0.60 tff(432,plain,
% 0.45/0.60 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | (~ndr1_0) | c3_1(a1199) | c1_1(a1199) | c0_1(a1199))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | c1_1(a1199)))),
% 0.45/0.60 inference(monotonicity,[status(thm)],[431])).
% 0.45/0.60 tff(433,plain,
% 0.45/0.60 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | (~ndr1_0) | c3_1(a1199) | c1_1(a1199) | c0_1(a1199))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp0 | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | c1_1(a1199))),
% 0.45/0.60 inference(transitivity,[status(thm)],[432, 430])).
% 0.45/0.60 tff(434,plain,
% 0.45/0.60 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | (~ndr1_0) | c3_1(a1199) | c1_1(a1199) | c0_1(a1199))),
% 0.45/0.60 inference(quant_inst,[status(thm)],[])).
% 0.45/0.60 tff(435,plain,
% 0.45/0.60 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp0 | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | c1_1(a1199)),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[434, 433])).
% 0.45/0.60 tff(436,plain,
% 0.45/0.60 (c1_1(a1199)),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[435, 169, 22, 78, 429, 423, 202])).
% 0.45/0.60 tff(437,plain,
% 0.45/0.60 (((~hskp16) | c2_1(a1199)) <=> ((~hskp16) | c2_1(a1199))),
% 0.45/0.60 inference(rewrite,[status(thm)],[])).
% 0.45/0.60 tff(438,axiom,((~hskp16) | c2_1(a1199)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 0.45/0.60 tff(439,plain,
% 0.45/0.60 ((~hskp16) | c2_1(a1199)),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.45/0.60 tff(440,plain,
% 0.45/0.60 ((~hskp16) | c2_1(a1199)),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[439, 437])).
% 0.45/0.60 tff(441,plain,
% 0.45/0.60 ((~hskp16) | c2_1(a1199)),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[440, 437])).
% 0.45/0.60 tff(442,plain,
% 0.45/0.60 ((~hskp16) | c2_1(a1199)),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[441, 437])).
% 0.45/0.60 tff(443,plain,
% 0.45/0.60 ((~hskp16) | c2_1(a1199)),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[442, 437])).
% 0.45/0.60 tff(444,plain,
% 0.45/0.60 (c2_1(a1199)),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[443, 417])).
% 0.45/0.60 tff(445,plain,
% 0.45/0.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1199) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c3_1(a1194)) | (~c2_1(a1194)) | (~c1_1(a1199)) | (~c2_1(a1199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1199) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c3_1(a1194)) | (~c2_1(a1194)) | (~c1_1(a1199)) | (~c2_1(a1199)))),
% 0.45/0.60 inference(rewrite,[status(thm)],[])).
% 0.45/0.60 tff(446,plain,
% 0.45/0.60 (((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194))) <=> (c3_1(a1199) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c3_1(a1194)) | (~c2_1(a1194)) | (~c1_1(a1199)) | (~c2_1(a1199)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(447,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1199) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c3_1(a1194)) | (~c2_1(a1194)) | (~c1_1(a1199)) | (~c2_1(a1199))))),
% 0.45/0.61 inference(monotonicity,[status(thm)],[446])).
% 0.45/0.61 tff(448,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1199) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c3_1(a1194)) | (~c2_1(a1194)) | (~c1_1(a1199)) | (~c2_1(a1199)))),
% 0.45/0.61 inference(transitivity,[status(thm)],[447, 445])).
% 0.45/0.61 tff(449,plain,
% 0.45/0.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))),
% 0.45/0.61 inference(quant_inst,[status(thm)],[])).
% 0.45/0.61 tff(450,plain,
% 0.45/0.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1199) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c3_1(a1194)) | (~c2_1(a1194)) | (~c1_1(a1199)) | (~c2_1(a1199))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.45/0.61 tff(451,plain,
% 0.45/0.61 ($false),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[450, 169, 444, 388, 423, 380, 374, 21, 395, 436])).
% 0.45/0.61 tff(452,plain,(hskp3 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.45/0.61 tff(453,plain,
% 0.45/0.61 (hskp3),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[452, 78])).
% 0.45/0.61 tff(454,plain,
% 0.45/0.61 (~c3_1(a1174)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[246, 453])).
% 0.45/0.61 tff(455,plain,
% 0.45/0.61 (c1_1(a1174)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[308, 453])).
% 0.45/0.61 tff(456,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1194) | c1_1(a1194) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c3_1(a1194)) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1194) | c1_1(a1194) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c3_1(a1194)) | (~c2_1(a1194)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(457,plain,
% 0.45/0.61 (((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194))) <=> (c0_1(a1194) | c1_1(a1194) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c3_1(a1194)) | (~c2_1(a1194)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(458,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1194) | c1_1(a1194) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c3_1(a1194)) | (~c2_1(a1194))))),
% 0.45/0.61 inference(monotonicity,[status(thm)],[457])).
% 0.45/0.61 tff(459,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1194) | c1_1(a1194) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c3_1(a1194)) | (~c2_1(a1194)))),
% 0.45/0.61 inference(transitivity,[status(thm)],[458, 456])).
% 0.45/0.61 tff(460,plain,
% 0.45/0.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))),
% 0.45/0.61 inference(quant_inst,[status(thm)],[])).
% 0.45/0.61 tff(461,plain,
% 0.45/0.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1194) | c1_1(a1194) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c3_1(a1194)) | (~c2_1(a1194))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.45/0.61 tff(462,plain,
% 0.45/0.61 (~c2_1(a1174)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[461, 169, 388, 455, 380, 374, 454, 21, 395])).
% 0.45/0.61 tff(463,plain,
% 0.45/0.61 (^[U: $i] : refl((hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(464,plain,
% 0.45/0.61 (![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[463])).
% 0.45/0.61 tff(465,plain,
% 0.45/0.61 (![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(466,plain,
% 0.45/0.61 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp17) <=> ((hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp17))), rewrite(((hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp17) <=> (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp17) <=> (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(467,plain,
% 0.45/0.61 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp17) <=> ![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[466])).
% 0.45/0.61 tff(468,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.45/0.61 tff(469,plain,
% 0.45/0.61 (![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.45/0.61 tff(470,plain,
% 0.45/0.61 (![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[469, 465])).
% 0.45/0.61 tff(471,plain,(
% 0.45/0.61 ![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.45/0.61 inference(skolemize,[status(sab)],[470])).
% 0.45/0.61 tff(472,plain,
% 0.45/0.61 (![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[471, 464])).
% 0.45/0.61 tff(473,plain,
% 0.45/0.61 (c0_1(a1174)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[254, 453])).
% 0.45/0.61 tff(474,plain,
% 0.45/0.61 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(475,plain,
% 0.45/0.61 ((hskp22 | hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174))) <=> (hskp22 | hskp17 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(476,plain,
% 0.45/0.61 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174))))),
% 0.45/0.61 inference(monotonicity,[status(thm)],[475])).
% 0.45/0.61 tff(477,plain,
% 0.45/0.61 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.45/0.61 inference(transitivity,[status(thm)],[476, 474])).
% 0.45/0.61 tff(478,plain,
% 0.45/0.61 ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.45/0.61 inference(quant_inst,[status(thm)],[])).
% 0.45/0.61 tff(479,plain,
% 0.45/0.61 ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.45/0.61 tff(480,plain,
% 0.45/0.61 (hskp22 | c2_1(a1174)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[479, 169, 359, 473, 454, 472])).
% 0.45/0.61 tff(481,plain,
% 0.45/0.61 (hskp22),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[480, 462])).
% 0.45/0.61 tff(482,plain,
% 0.45/0.61 (~c1_1(a1211)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[29, 481])).
% 0.45/0.61 tff(483,plain,
% 0.45/0.61 (c0_1(a1211)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[45, 481])).
% 0.45/0.61 tff(484,plain,
% 0.45/0.61 (c2_1(a1211)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[290, 169, 78, 483, 482, 67])).
% 0.45/0.61 tff(485,plain,
% 0.45/0.61 ($false),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[365, 169, 359, 483, 473, 482, 454, 328, 462, 484])).
% 0.45/0.61 tff(486,plain,(hskp0), inference(lemma,lemma(discharge,[]))).
% 0.45/0.61 tff(487,plain,
% 0.45/0.61 (((~hskp0) | (~c2_1(a1168))) <=> ((~hskp0) | (~c2_1(a1168)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(488,plain,
% 0.45/0.61 (((~c2_1(a1168)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1168)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(489,axiom,((~c2_1(a1168)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 0.45/0.61 tff(490,plain,
% 0.45/0.61 ((~hskp0) | (~c2_1(a1168))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.45/0.61 tff(491,plain,
% 0.45/0.61 ((~hskp0) | (~c2_1(a1168))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[490, 487])).
% 0.45/0.61 tff(492,plain,
% 0.45/0.61 (~c2_1(a1168)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[491, 486])).
% 0.45/0.61 tff(493,assumption,(~c1_1(a1211)), introduced(assumption)).
% 0.45/0.61 tff(494,plain,
% 0.45/0.61 (((~hskp0) | c1_1(a1168)) <=> ((~hskp0) | c1_1(a1168))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(495,axiom,((~hskp0) | c1_1(a1168)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.45/0.61 tff(496,plain,
% 0.45/0.61 ((~hskp0) | c1_1(a1168)),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.45/0.61 tff(497,plain,
% 0.45/0.61 ((~hskp0) | c1_1(a1168)),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[496, 494])).
% 0.45/0.61 tff(498,plain,
% 0.45/0.61 ((~hskp0) | c1_1(a1168)),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[497, 494])).
% 0.45/0.61 tff(499,plain,
% 0.45/0.61 ((~hskp0) | c1_1(a1168)),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[498, 494])).
% 0.45/0.61 tff(500,plain,
% 0.45/0.61 ((~hskp0) | c1_1(a1168)),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[499, 494])).
% 0.45/0.61 tff(501,plain,
% 0.45/0.61 (c1_1(a1168)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[500, 486])).
% 0.45/0.61 tff(502,plain,
% 0.45/0.61 (((~hskp0) | c0_1(a1168)) <=> ((~hskp0) | c0_1(a1168))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(503,axiom,((~hskp0) | c0_1(a1168)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.45/0.61 tff(504,plain,
% 0.45/0.61 ((~hskp0) | c0_1(a1168)),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.45/0.61 tff(505,plain,
% 0.45/0.61 ((~hskp0) | c0_1(a1168)),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[504, 502])).
% 0.45/0.61 tff(506,plain,
% 0.45/0.61 ((~hskp0) | c0_1(a1168)),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[505, 502])).
% 0.45/0.61 tff(507,plain,
% 0.45/0.61 ((~hskp0) | c0_1(a1168)),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[506, 502])).
% 0.45/0.61 tff(508,plain,
% 0.45/0.61 ((~hskp0) | c0_1(a1168)),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[507, 502])).
% 0.45/0.61 tff(509,plain,
% 0.45/0.61 (c0_1(a1168)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[508, 486])).
% 0.45/0.61 tff(510,assumption,(c3_1(a1211)), introduced(assumption)).
% 0.45/0.61 tff(511,assumption,(c0_1(a1211)), introduced(assumption)).
% 0.45/0.61 tff(512,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1211) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1211) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(513,plain,
% 0.45/0.61 (((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211) | c1_1(a1211) | (~c0_1(a1211))) <=> (c1_1(a1211) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(514,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211) | c1_1(a1211) | (~c0_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1211) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211)))),
% 0.45/0.61 inference(monotonicity,[status(thm)],[513])).
% 0.45/0.61 tff(515,plain,
% 0.45/0.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211) | c1_1(a1211) | (~c0_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1211) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211))),
% 0.45/0.61 inference(transitivity,[status(thm)],[514, 512])).
% 0.45/0.61 tff(516,plain,
% 0.45/0.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211) | c1_1(a1211) | (~c0_1(a1211)))),
% 0.45/0.61 inference(quant_inst,[status(thm)],[])).
% 0.45/0.61 tff(517,plain,
% 0.45/0.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1211) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211)),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.45/0.61 tff(518,plain,
% 0.45/0.61 ($false),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[517, 169, 511, 510, 509, 501, 493, 492, 57, 47])).
% 0.45/0.61 tff(519,plain,(c2_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.61 tff(520,plain,
% 0.45/0.61 (c2_1(a1211)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[519, 46, 38, 30])).
% 0.45/0.61 tff(521,plain,
% 0.45/0.61 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(522,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[521])).
% 0.45/0.61 tff(523,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(524,plain,
% 0.45/0.61 (^[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) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_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))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_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))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(525,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[524])).
% 0.45/0.61 tff(526,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 0.45/0.61 tff(527,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.45/0.61 tff(528,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[527, 523])).
% 0.45/0.61 tff(529,plain,(
% 0.45/0.61 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.61 inference(skolemize,[status(sab)],[528])).
% 0.45/0.61 tff(530,plain,
% 0.45/0.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[529, 522])).
% 0.45/0.61 tff(531,plain,
% 0.45/0.61 (c2_1(a1211)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[519, 511, 510, 493])).
% 0.45/0.61 tff(532,assumption,(~hskp1), introduced(assumption)).
% 0.45/0.61 tff(533,assumption,(hskp13), introduced(assumption)).
% 0.45/0.61 tff(534,plain,
% 0.45/0.61 (((~hskp13) | (~c2_1(a1192))) <=> ((~hskp13) | (~c2_1(a1192)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(535,plain,
% 0.45/0.61 (((~c2_1(a1192)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a1192)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(536,axiom,((~c2_1(a1192)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 0.45/0.61 tff(537,plain,
% 0.45/0.61 ((~hskp13) | (~c2_1(a1192))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.45/0.62 tff(538,plain,
% 0.45/0.62 ((~hskp13) | (~c2_1(a1192))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[537, 534])).
% 0.45/0.62 tff(539,plain,
% 0.45/0.62 (~c2_1(a1192)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[538, 533])).
% 0.45/0.62 tff(540,plain,
% 0.45/0.62 (((~hskp13) | (~c0_1(a1192))) <=> ((~hskp13) | (~c0_1(a1192)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(541,plain,
% 0.45/0.62 (((~c0_1(a1192)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a1192)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(542,axiom,((~c0_1(a1192)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.45/0.62 tff(543,plain,
% 0.45/0.62 ((~hskp13) | (~c0_1(a1192))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[542, 541])).
% 0.45/0.62 tff(544,plain,
% 0.45/0.62 ((~hskp13) | (~c0_1(a1192))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[543, 540])).
% 0.45/0.62 tff(545,plain,
% 0.45/0.62 (~c0_1(a1192)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[544, 533])).
% 0.45/0.62 tff(546,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | c3_1(a1192) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | c3_1(a1192) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(547,plain,
% 0.45/0.62 (((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1192) | c0_1(a1192) | c3_1(a1192)) <=> (c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | c3_1(a1192) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(548,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1192) | c0_1(a1192) | c3_1(a1192))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | c3_1(a1192) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[547])).
% 0.45/0.62 tff(549,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1192) | c0_1(a1192) | c3_1(a1192))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | c3_1(a1192) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.62 inference(transitivity,[status(thm)],[548, 546])).
% 0.45/0.62 tff(550,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1192) | c0_1(a1192) | c3_1(a1192))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(551,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | c3_1(a1192) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.45/0.62 tff(552,plain,
% 0.45/0.62 (c3_1(a1192)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[551, 169, 511, 510, 493, 545, 539, 530, 531])).
% 0.45/0.62 tff(553,plain,
% 0.45/0.62 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(554,plain,
% 0.45/0.62 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[553])).
% 0.45/0.62 tff(555,plain,
% 0.45/0.62 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(556,plain,
% 0.45/0.62 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(557,plain,
% 0.45/0.62 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[556])).
% 0.45/0.62 tff(558,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 0.45/0.62 tff(559,plain,
% 0.45/0.62 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[558, 557])).
% 0.45/0.62 tff(560,plain,
% 0.45/0.62 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[559, 555])).
% 0.45/0.62 tff(561,plain,(
% 0.45/0.62 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.45/0.62 inference(skolemize,[status(sab)],[560])).
% 0.45/0.62 tff(562,plain,
% 0.45/0.62 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[561, 554])).
% 0.45/0.62 tff(563,plain,
% 0.45/0.62 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | (~c3_1(a1192)) | (~c3_1(a1211)) | (~c2_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | (~c3_1(a1192)) | (~c3_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(564,plain,
% 0.45/0.62 ((hskp1 | (~ndr1_0) | c1_1(a1211) | (~c3_1(a1211)) | (~c2_1(a1211)) | c2_1(a1192) | c0_1(a1192) | (~c3_1(a1192))) <=> (hskp1 | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | (~c3_1(a1192)) | (~c3_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(565,plain,
% 0.45/0.62 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1211) | (~c3_1(a1211)) | (~c2_1(a1211)) | c2_1(a1192) | c0_1(a1192) | (~c3_1(a1192)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | (~c3_1(a1192)) | (~c3_1(a1211)) | (~c2_1(a1211))))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[564])).
% 0.45/0.62 tff(566,plain,
% 0.45/0.62 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1211) | (~c3_1(a1211)) | (~c2_1(a1211)) | c2_1(a1192) | c0_1(a1192) | (~c3_1(a1192)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | (~c3_1(a1192)) | (~c3_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.62 inference(transitivity,[status(thm)],[565, 563])).
% 0.45/0.62 tff(567,plain,
% 0.45/0.62 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1211) | (~c3_1(a1211)) | (~c2_1(a1211)) | c2_1(a1192) | c0_1(a1192) | (~c3_1(a1192)))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(568,plain,
% 0.45/0.62 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | (~c3_1(a1192)) | (~c3_1(a1211)) | (~c2_1(a1211))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.45/0.62 tff(569,plain,
% 0.45/0.62 ($false),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[568, 169, 532, 510, 493, 545, 539, 562, 531, 552])).
% 0.45/0.62 tff(570,plain,((~hskp13) | hskp1 | (~c3_1(a1211)) | c1_1(a1211) | (~c0_1(a1211))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.62 tff(571,plain,
% 0.45/0.62 (~hskp13),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[570, 532, 510, 493, 511])).
% 0.45/0.62 tff(572,plain,
% 0.45/0.62 (^[U: $i] : refl((hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(573,plain,
% 0.45/0.62 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[572])).
% 0.45/0.62 tff(574,plain,
% 0.45/0.62 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(575,plain,
% 0.45/0.62 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp13))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp10) <=> ((hskp13 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp10))), rewrite(((hskp13 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp10) <=> (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp10) <=> (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(576,plain,
% 0.45/0.62 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp10) <=> ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[575])).
% 0.45/0.62 tff(577,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 0.45/0.62 tff(578,plain,
% 0.45/0.62 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.45/0.62 tff(579,plain,
% 0.45/0.62 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[578, 574])).
% 0.45/0.62 tff(580,plain,(
% 0.45/0.62 ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.62 inference(skolemize,[status(sab)],[579])).
% 0.45/0.62 tff(581,plain,
% 0.45/0.62 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[580, 573])).
% 0.45/0.62 tff(582,plain,
% 0.45/0.62 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(583,plain,
% 0.45/0.62 ((hskp13 | hskp10 | (~ndr1_0) | (~c0_1(a1211)) | (~c3_1(a1211)) | (~c2_1(a1211))) <=> (hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(584,plain,
% 0.45/0.62 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(a1211)) | (~c3_1(a1211)) | (~c2_1(a1211)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[583])).
% 0.45/0.62 tff(585,plain,
% 0.45/0.62 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(a1211)) | (~c3_1(a1211)) | (~c2_1(a1211)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.62 inference(transitivity,[status(thm)],[584, 582])).
% 0.45/0.62 tff(586,plain,
% 0.45/0.62 ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(a1211)) | (~c3_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(587,plain,
% 0.45/0.62 ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.45/0.62 tff(588,plain,
% 0.45/0.62 (hskp13 | hskp10 | (~c2_1(a1211))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[587, 169, 511, 510, 581])).
% 0.45/0.62 tff(589,plain,
% 0.45/0.62 (hskp10),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[588, 571, 531])).
% 0.45/0.62 tff(590,plain,
% 0.45/0.62 (((~hskp10) | (~c2_1(a1184))) <=> ((~hskp10) | (~c2_1(a1184)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(591,plain,
% 0.45/0.62 (((~c2_1(a1184)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a1184)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(592,axiom,((~c2_1(a1184)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.45/0.62 tff(593,plain,
% 0.45/0.62 ((~hskp10) | (~c2_1(a1184))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.45/0.62 tff(594,plain,
% 0.45/0.62 ((~hskp10) | (~c2_1(a1184))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[593, 590])).
% 0.45/0.62 tff(595,plain,
% 0.45/0.62 (~c2_1(a1184)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[594, 589])).
% 0.45/0.62 tff(596,plain,
% 0.45/0.62 (((~hskp10) | (~c0_1(a1184))) <=> ((~hskp10) | (~c0_1(a1184)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(597,plain,
% 0.45/0.62 (((~c0_1(a1184)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a1184)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(598,axiom,((~c0_1(a1184)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.45/0.62 tff(599,plain,
% 0.45/0.62 ((~hskp10) | (~c0_1(a1184))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[598, 597])).
% 0.45/0.62 tff(600,plain,
% 0.45/0.62 ((~hskp10) | (~c0_1(a1184))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[599, 596])).
% 0.45/0.62 tff(601,plain,
% 0.45/0.62 (~c0_1(a1184)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[600, 589])).
% 0.45/0.62 tff(602,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1211) | c0_1(a1184) | c2_1(a1184) | (~ndr1_0) | c3_1(a1184) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c0_1(a1184) | c2_1(a1184) | (~ndr1_0) | c3_1(a1184) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(603,plain,
% 0.45/0.62 (((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1184) | c0_1(a1184) | c3_1(a1184)) <=> (c1_1(a1211) | c0_1(a1184) | c2_1(a1184) | (~ndr1_0) | c3_1(a1184) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(604,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1184) | c0_1(a1184) | c3_1(a1184))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1211) | c0_1(a1184) | c2_1(a1184) | (~ndr1_0) | c3_1(a1184) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[603])).
% 0.45/0.62 tff(605,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1184) | c0_1(a1184) | c3_1(a1184))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c0_1(a1184) | c2_1(a1184) | (~ndr1_0) | c3_1(a1184) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.62 inference(transitivity,[status(thm)],[604, 602])).
% 0.45/0.62 tff(606,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1184) | c0_1(a1184) | c3_1(a1184))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(607,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c0_1(a1184) | c2_1(a1184) | (~ndr1_0) | c3_1(a1184) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[606, 605])).
% 0.45/0.62 tff(608,plain,
% 0.45/0.62 (c3_1(a1184)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[607, 169, 511, 510, 493, 601, 595, 530, 531])).
% 0.45/0.62 tff(609,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1211) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c0_1(a1200)) | (~c3_1(a1211)) | (~c0_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1211) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c0_1(a1200)) | (~c3_1(a1211)) | (~c0_1(a1211)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(610,plain,
% 0.45/0.62 (((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200))) <=> (c1_1(a1211) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c0_1(a1200)) | (~c3_1(a1211)) | (~c0_1(a1211)))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(611,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1211) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c0_1(a1200)) | (~c3_1(a1211)) | (~c0_1(a1211))))),
% 0.45/0.62 inference(monotonicity,[status(thm)],[610])).
% 0.45/0.62 tff(612,plain,
% 0.45/0.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1211) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c0_1(a1200)) | (~c3_1(a1211)) | (~c0_1(a1211)))),
% 0.45/0.62 inference(transitivity,[status(thm)],[611, 609])).
% 0.45/0.62 tff(613,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(614,plain,
% 0.45/0.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1211) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c0_1(a1200)) | (~c3_1(a1211)) | (~c0_1(a1211))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.45/0.62 tff(615,plain,
% 0.45/0.62 ($false),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[614, 169, 511, 510, 350, 509, 501, 493, 342, 336, 492, 57])).
% 0.45/0.62 tff(616,plain,((~hskp17) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.62 tff(617,plain,
% 0.45/0.63 (~hskp17),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[616, 511, 510, 493])).
% 0.45/0.63 tff(618,plain,
% 0.45/0.63 (hskp16),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[416, 532, 617])).
% 0.45/0.63 tff(619,plain,
% 0.45/0.63 (c2_1(a1199)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[443, 618])).
% 0.45/0.63 tff(620,plain,
% 0.45/0.63 (~c3_1(a1199)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[422, 618])).
% 0.45/0.63 tff(621,plain,
% 0.45/0.63 (~c0_1(a1199)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[428, 618])).
% 0.45/0.63 tff(622,plain,
% 0.45/0.63 ((hskp17 | hskp13 | hskp2) <=> (hskp17 | hskp13 | hskp2)),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(623,plain,
% 0.45/0.63 (((hskp17 | hskp13) | hskp2) <=> (hskp17 | hskp13 | hskp2)),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(624,plain,
% 0.45/0.63 ((hskp17 | hskp13) <=> (hskp17 | hskp13)),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(625,plain,
% 0.45/0.63 (((hskp17 | hskp13) | hskp2) <=> ((hskp17 | hskp13) | hskp2)),
% 0.45/0.63 inference(monotonicity,[status(thm)],[624])).
% 0.45/0.63 tff(626,plain,
% 0.45/0.63 (((hskp17 | hskp13) | hskp2) <=> (hskp17 | hskp13 | hskp2)),
% 0.45/0.63 inference(transitivity,[status(thm)],[625, 623])).
% 0.45/0.63 tff(627,axiom,((hskp17 | hskp13) | hskp2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 0.45/0.63 tff(628,plain,
% 0.45/0.63 (hskp17 | hskp13 | hskp2),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[627, 626])).
% 0.45/0.63 tff(629,plain,
% 0.45/0.63 (hskp17 | hskp13 | hskp2),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[628, 622])).
% 0.45/0.63 tff(630,plain,
% 0.45/0.63 (hskp17 | hskp13 | hskp2),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[629, 622])).
% 0.45/0.63 tff(631,plain,
% 0.45/0.63 (hskp17 | hskp13 | hskp2),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[630, 622])).
% 0.45/0.63 tff(632,plain,
% 0.45/0.63 (hskp17 | hskp13 | hskp2),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[631, 622])).
% 0.45/0.63 tff(633,plain,
% 0.45/0.63 (hskp2),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[632, 571, 617])).
% 0.45/0.63 tff(634,assumption,(~c1_1(a1199)), introduced(assumption)).
% 0.45/0.63 tff(635,plain,
% 0.45/0.63 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(636,plain,
% 0.45/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[635])).
% 0.45/0.63 tff(637,plain,
% 0.45/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(638,plain,
% 0.45/0.63 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(639,plain,
% 0.45/0.63 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[638])).
% 0.45/0.63 tff(640,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 0.45/0.63 tff(641,plain,
% 0.45/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[640, 639])).
% 0.45/0.63 tff(642,plain,
% 0.45/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[641, 637])).
% 0.45/0.63 tff(643,plain,(
% 0.45/0.63 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.63 inference(skolemize,[status(sab)],[642])).
% 0.45/0.63 tff(644,plain,
% 0.45/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[643, 636])).
% 0.45/0.63 tff(645,assumption,(hskp2), introduced(assumption)).
% 0.45/0.63 tff(646,plain,
% 0.45/0.63 (((~hskp2) | (~c0_1(a1172))) <=> ((~hskp2) | (~c0_1(a1172)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(647,plain,
% 0.45/0.63 (((~c0_1(a1172)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a1172)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(648,axiom,((~c0_1(a1172)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.45/0.63 tff(649,plain,
% 0.45/0.63 ((~hskp2) | (~c0_1(a1172))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[648, 647])).
% 0.45/0.63 tff(650,plain,
% 0.45/0.63 ((~hskp2) | (~c0_1(a1172))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[649, 646])).
% 0.45/0.63 tff(651,plain,
% 0.45/0.63 (~c0_1(a1172)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[650, 645])).
% 0.45/0.63 tff(652,assumption,(~c3_1(a1199)), introduced(assumption)).
% 0.45/0.63 tff(653,assumption,(~c0_1(a1199)), introduced(assumption)).
% 0.45/0.63 tff(654,plain,
% 0.45/0.63 (((~hskp2) | c3_1(a1172)) <=> ((~hskp2) | c3_1(a1172))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(655,axiom,((~hskp2) | c3_1(a1172)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.45/0.63 tff(656,plain,
% 0.45/0.63 ((~hskp2) | c3_1(a1172)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[655, 654])).
% 0.45/0.63 tff(657,plain,
% 0.45/0.63 ((~hskp2) | c3_1(a1172)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[656, 654])).
% 0.45/0.63 tff(658,plain,
% 0.45/0.63 ((~hskp2) | c3_1(a1172)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[657, 654])).
% 0.45/0.63 tff(659,plain,
% 0.45/0.63 ((~hskp2) | c3_1(a1172)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[658, 654])).
% 0.45/0.63 tff(660,plain,
% 0.45/0.63 ((~hskp2) | c3_1(a1172)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[659, 654])).
% 0.45/0.63 tff(661,plain,
% 0.45/0.63 (c3_1(a1172)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[660, 645])).
% 0.45/0.63 tff(662,plain,
% 0.45/0.63 (((~hskp2) | c2_1(a1172)) <=> ((~hskp2) | c2_1(a1172))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(663,axiom,((~hskp2) | c2_1(a1172)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.45/0.63 tff(664,plain,
% 0.45/0.63 ((~hskp2) | c2_1(a1172)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[663, 662])).
% 0.45/0.63 tff(665,plain,
% 0.45/0.63 ((~hskp2) | c2_1(a1172)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[664, 662])).
% 0.45/0.63 tff(666,plain,
% 0.45/0.63 ((~hskp2) | c2_1(a1172)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[665, 662])).
% 0.45/0.63 tff(667,plain,
% 0.45/0.63 ((~hskp2) | c2_1(a1172)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[666, 662])).
% 0.45/0.63 tff(668,plain,
% 0.45/0.63 ((~hskp2) | c2_1(a1172)),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[667, 662])).
% 0.45/0.63 tff(669,plain,
% 0.45/0.63 (c2_1(a1172)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[668, 645])).
% 0.45/0.63 tff(670,assumption,(c2_1(a1199)), introduced(assumption)).
% 0.45/0.63 tff(671,plain,
% 0.45/0.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1199) | c3_1(a1199) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c1_1(a1199) | (~c2_1(a1199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1199) | c3_1(a1199) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c1_1(a1199) | (~c2_1(a1199)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(672,plain,
% 0.45/0.63 (((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199)) <=> (c0_1(a1199) | c3_1(a1199) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c1_1(a1199) | (~c2_1(a1199)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(673,plain,
% 0.45/0.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1199) | c3_1(a1199) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c1_1(a1199) | (~c2_1(a1199))))),
% 0.45/0.63 inference(monotonicity,[status(thm)],[672])).
% 0.45/0.63 tff(674,plain,
% 0.45/0.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1199) | c3_1(a1199) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c1_1(a1199) | (~c2_1(a1199)))),
% 0.45/0.63 inference(transitivity,[status(thm)],[673, 671])).
% 0.45/0.63 tff(675,plain,
% 0.45/0.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(676,plain,
% 0.45/0.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1199) | c3_1(a1199) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c1_1(a1199) | (~c2_1(a1199))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.45/0.63 tff(677,plain,
% 0.45/0.63 ($false),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[676, 169, 670, 669, 661, 653, 652, 651, 644, 634])).
% 0.45/0.63 tff(678,plain,((~hskp2) | (~c2_1(a1199)) | c0_1(a1199) | c3_1(a1199) | c1_1(a1199)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.63 tff(679,plain,
% 0.45/0.63 (c1_1(a1199)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[678, 633, 621, 620, 619])).
% 0.45/0.63 tff(680,plain,
% 0.45/0.63 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(681,plain,
% 0.45/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[680])).
% 0.45/0.63 tff(682,plain,
% 0.45/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(683,plain,
% 0.45/0.63 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(684,plain,
% 0.45/0.63 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[683])).
% 0.45/0.63 tff(685,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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','clause168')).
% 0.45/0.63 tff(686,plain,
% 0.45/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[685, 684])).
% 0.45/0.63 tff(687,plain,
% 0.45/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[686, 682])).
% 0.45/0.63 tff(688,plain,(
% 0.45/0.63 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.45/0.63 inference(skolemize,[status(sab)],[687])).
% 0.45/0.63 tff(689,plain,
% 0.45/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[688, 681])).
% 0.45/0.63 tff(690,plain,
% 0.45/0.63 (((~hskp10) | (~c1_1(a1184))) <=> ((~hskp10) | (~c1_1(a1184)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(691,plain,
% 0.45/0.63 (((~c1_1(a1184)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1184)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(692,axiom,((~c1_1(a1184)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.45/0.63 tff(693,plain,
% 0.45/0.63 ((~hskp10) | (~c1_1(a1184))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[692, 691])).
% 0.45/0.63 tff(694,plain,
% 0.45/0.63 ((~hskp10) | (~c1_1(a1184))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[693, 690])).
% 0.45/0.63 tff(695,plain,
% 0.45/0.63 (~c1_1(a1184)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[694, 589])).
% 0.45/0.63 tff(696,plain,
% 0.45/0.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1199) | c0_1(a1184) | c1_1(a1184) | c2_1(a1184) | (~ndr1_0) | (~c3_1(a1184)) | (~c1_1(a1199)) | (~c2_1(a1199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1199) | c0_1(a1184) | c1_1(a1184) | c2_1(a1184) | (~ndr1_0) | (~c3_1(a1184)) | (~c1_1(a1199)) | (~c2_1(a1199)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(697,plain,
% 0.45/0.63 (((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c2_1(a1184) | c0_1(a1184) | (~c3_1(a1184)) | c2_1(a1184) | c1_1(a1184) | c0_1(a1184)) <=> (c3_1(a1199) | c0_1(a1184) | c1_1(a1184) | c2_1(a1184) | (~ndr1_0) | (~c3_1(a1184)) | (~c1_1(a1199)) | (~c2_1(a1199)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(698,plain,
% 0.45/0.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c2_1(a1184) | c0_1(a1184) | (~c3_1(a1184)) | c2_1(a1184) | c1_1(a1184) | c0_1(a1184))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1199) | c0_1(a1184) | c1_1(a1184) | c2_1(a1184) | (~ndr1_0) | (~c3_1(a1184)) | (~c1_1(a1199)) | (~c2_1(a1199))))),
% 0.45/0.63 inference(monotonicity,[status(thm)],[697])).
% 0.45/0.63 tff(699,plain,
% 0.45/0.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c2_1(a1184) | c0_1(a1184) | (~c3_1(a1184)) | c2_1(a1184) | c1_1(a1184) | c0_1(a1184))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1199) | c0_1(a1184) | c1_1(a1184) | c2_1(a1184) | (~ndr1_0) | (~c3_1(a1184)) | (~c1_1(a1199)) | (~c2_1(a1199)))),
% 0.45/0.63 inference(transitivity,[status(thm)],[698, 696])).
% 0.45/0.63 tff(700,plain,
% 0.45/0.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c2_1(a1184) | c0_1(a1184) | (~c3_1(a1184)) | c2_1(a1184) | c1_1(a1184) | c0_1(a1184))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(701,plain,
% 0.45/0.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1199) | c0_1(a1184) | c1_1(a1184) | c2_1(a1184) | (~ndr1_0) | (~c3_1(a1184)) | (~c1_1(a1199)) | (~c2_1(a1199))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.45/0.63 tff(702,plain,
% 0.45/0.63 ($false),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[701, 169, 619, 620, 601, 695, 595, 689, 679, 608])).
% 0.45/0.63 tff(703,plain,(hskp1 | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.63 tff(704,plain,
% 0.45/0.63 (hskp1),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[703, 46, 38, 30])).
% 0.45/0.63 tff(705,plain,
% 0.45/0.63 (~c3_1(a1169)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[103, 704])).
% 0.45/0.63 tff(706,plain,
% 0.45/0.63 (~c2_1(a1169)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[109, 704])).
% 0.45/0.63 tff(707,plain,
% 0.45/0.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(708,plain,
% 0.45/0.63 (((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1169) | c0_1(a1169) | c3_1(a1169)) <=> (c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(709,plain,
% 0.45/0.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1169) | c0_1(a1169) | c3_1(a1169))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))))),
% 0.45/0.63 inference(monotonicity,[status(thm)],[708])).
% 0.45/0.63 tff(710,plain,
% 0.45/0.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1169) | c0_1(a1169) | c3_1(a1169))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.63 inference(transitivity,[status(thm)],[709, 707])).
% 0.45/0.63 tff(711,plain,
% 0.45/0.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1169) | c0_1(a1169) | c3_1(a1169))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(712,plain,
% 0.45/0.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[711, 710])).
% 0.45/0.63 tff(713,plain,
% 0.45/0.63 (c0_1(a1169)),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[712, 169, 46, 38, 30, 706, 705, 530, 520])).
% 0.45/0.63 tff(714,plain,
% 0.45/0.63 (~hskp17),
% 0.45/0.63 inference(unit_resolution,[status(thm)],[616, 46, 38, 30])).
% 0.45/0.63 tff(715,plain,
% 0.45/0.63 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)) | (~c0_1(a1211)) | (~c2_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(716,plain,
% 0.45/0.63 ((hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211))) <=> (hskp17 | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(717,plain,
% 0.45/0.64 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)) | (~c0_1(a1211)) | (~c2_1(a1211))))),
% 0.45/0.64 inference(monotonicity,[status(thm)],[716])).
% 0.45/0.64 tff(718,plain,
% 0.45/0.64 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.45/0.64 inference(transitivity,[status(thm)],[717, 715])).
% 0.45/0.64 tff(719,plain,
% 0.45/0.64 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(720,plain,
% 0.45/0.64 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)) | (~c0_1(a1211)) | (~c2_1(a1211))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[719, 718])).
% 0.45/0.64 tff(721,plain,
% 0.45/0.64 ($false),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[720, 169, 714, 46, 30, 706, 705, 328, 713, 520])).
% 0.45/0.64 tff(722,plain,(~hskp22), inference(lemma,lemma(discharge,[]))).
% 0.45/0.64 tff(723,plain,
% 0.45/0.64 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(724,plain,
% 0.45/0.64 ((hskp22 | hskp17 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168))) <=> (hskp22 | hskp17 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(725,plain,
% 0.45/0.64 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168))))),
% 0.45/0.64 inference(monotonicity,[status(thm)],[724])).
% 0.45/0.64 tff(726,plain,
% 0.45/0.64 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))),
% 0.45/0.64 inference(transitivity,[status(thm)],[725, 723])).
% 0.45/0.64 tff(727,plain,
% 0.45/0.64 ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168)))),
% 0.45/0.64 inference(quant_inst,[status(thm)],[])).
% 0.45/0.64 tff(728,plain,
% 0.45/0.64 ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[727, 726])).
% 0.45/0.64 tff(729,plain,
% 0.45/0.64 (hskp22 | hskp17 | c3_1(a1168)),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[728, 169, 509, 492, 472])).
% 0.45/0.64 tff(730,plain,
% 0.45/0.64 (hskp17 | c3_1(a1168)),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[729, 722])).
% 0.45/0.64 tff(731,plain,
% 0.45/0.64 (c3_1(a1168)),
% 0.45/0.64 inference(unit_resolution,[status(thm)],[730, 23])).
% 0.45/0.64 tff(732,plain,
% 0.45/0.64 (^[U: $i] : refl((hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(733,plain,
% 0.45/0.64 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.64 inference(quant_intro,[status(thm)],[732])).
% 0.45/0.64 tff(734,plain,
% 0.45/0.64 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(735,plain,
% 0.45/0.64 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp22))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp2) <=> ((hskp22 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp2))), rewrite(((hskp22 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp2) <=> (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp2) <=> (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(736,plain,
% 0.45/0.64 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp2) <=> ![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.64 inference(quant_intro,[status(thm)],[735])).
% 0.45/0.64 tff(737,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 0.45/0.64 tff(738,plain,
% 0.45/0.64 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.45/0.64 tff(739,plain,
% 0.45/0.64 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[738, 734])).
% 0.45/0.64 tff(740,plain,(
% 0.45/0.64 ![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.64 inference(skolemize,[status(sab)],[739])).
% 0.45/0.64 tff(741,plain,
% 0.45/0.64 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.45/0.64 inference(modus_ponens,[status(thm)],[740, 733])).
% 0.45/0.64 tff(742,plain,
% 0.45/0.64 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.45/0.64 inference(bind,[status(th)],[])).
% 0.45/0.64 tff(743,plain,
% 0.45/0.64 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.45/0.64 inference(quant_intro,[status(thm)],[742])).
% 0.45/0.64 tff(744,plain,
% 0.45/0.64 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.45/0.64 inference(rewrite,[status(thm)],[])).
% 0.45/0.64 tff(745,plain,
% 0.45/0.64 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | 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)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | 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)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.49/0.64 inference(bind,[status(th)],[])).
% 0.49/0.64 tff(746,plain,
% 0.49/0.64 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.49/0.64 inference(quant_intro,[status(thm)],[745])).
% 0.49/0.64 tff(747,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 0.49/0.64 tff(748,plain,
% 0.49/0.64 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[747, 746])).
% 0.49/0.64 tff(749,plain,
% 0.49/0.64 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[748, 744])).
% 0.49/0.64 tff(750,plain,(
% 0.49/0.64 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.49/0.64 inference(skolemize,[status(sab)],[749])).
% 0.49/0.64 tff(751,plain,
% 0.49/0.64 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[750, 743])).
% 0.49/0.64 tff(752,assumption,(~hskp2), introduced(assumption)).
% 0.49/0.64 tff(753,plain,
% 0.49/0.64 (hskp13),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[632, 752, 23])).
% 0.49/0.64 tff(754,plain,
% 0.49/0.64 (~c0_1(a1192)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[544, 753])).
% 0.49/0.64 tff(755,plain,
% 0.49/0.64 (((~hskp13) | c1_1(a1192)) <=> ((~hskp13) | c1_1(a1192))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(756,axiom,((~hskp13) | c1_1(a1192)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.49/0.64 tff(757,plain,
% 0.49/0.64 ((~hskp13) | c1_1(a1192)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.49/0.64 tff(758,plain,
% 0.49/0.64 ((~hskp13) | c1_1(a1192)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[757, 755])).
% 0.49/0.64 tff(759,plain,
% 0.49/0.64 ((~hskp13) | c1_1(a1192)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[758, 755])).
% 0.49/0.64 tff(760,plain,
% 0.49/0.64 ((~hskp13) | c1_1(a1192)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[759, 755])).
% 0.49/0.64 tff(761,plain,
% 0.49/0.64 ((~hskp13) | c1_1(a1192)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[760, 755])).
% 0.49/0.64 tff(762,plain,
% 0.49/0.64 (c1_1(a1192)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[761, 753])).
% 0.49/0.64 tff(763,plain,
% 0.49/0.64 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1192) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c3_1(a1192) | (~c1_1(a1192)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1192) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c3_1(a1192) | (~c1_1(a1192)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(764,plain,
% 0.49/0.64 ((hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1192) | c3_1(a1192) | (~c1_1(a1192))) <=> (hskp3 | c0_1(a1192) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c3_1(a1192) | (~c1_1(a1192)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(765,plain,
% 0.49/0.64 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1192) | c3_1(a1192) | (~c1_1(a1192)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1192) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c3_1(a1192) | (~c1_1(a1192))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[764])).
% 0.49/0.64 tff(766,plain,
% 0.49/0.64 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1192) | c3_1(a1192) | (~c1_1(a1192)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1192) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c3_1(a1192) | (~c1_1(a1192)))),
% 0.49/0.64 inference(transitivity,[status(thm)],[765, 763])).
% 0.49/0.64 tff(767,plain,
% 0.49/0.64 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1192) | c3_1(a1192) | (~c1_1(a1192)))),
% 0.49/0.64 inference(quant_inst,[status(thm)],[])).
% 0.49/0.64 tff(768,plain,
% 0.49/0.64 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1192) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c3_1(a1192) | (~c1_1(a1192))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.49/0.64 tff(769,plain,
% 0.49/0.64 (c3_1(a1192)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[768, 169, 22, 762, 501, 754, 492, 751, 731])).
% 0.49/0.64 tff(770,plain,
% 0.49/0.64 (~c2_1(a1192)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[538, 753])).
% 0.49/0.64 tff(771,assumption,(c3_1(a1192)), introduced(assumption)).
% 0.49/0.64 tff(772,assumption,(hskp8), introduced(assumption)).
% 0.49/0.64 tff(773,plain,
% 0.49/0.64 (((~hskp8) | (~c3_1(a1180))) <=> ((~hskp8) | (~c3_1(a1180)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(774,plain,
% 0.49/0.64 (((~c3_1(a1180)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a1180)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(775,axiom,((~c3_1(a1180)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 0.49/0.64 tff(776,plain,
% 0.49/0.64 ((~hskp8) | (~c3_1(a1180))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.49/0.64 tff(777,plain,
% 0.49/0.64 ((~hskp8) | (~c3_1(a1180))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[776, 773])).
% 0.49/0.64 tff(778,plain,
% 0.49/0.64 (~c3_1(a1180)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[777, 772])).
% 0.49/0.64 tff(779,plain,
% 0.49/0.64 (((~hskp8) | (~c0_1(a1180))) <=> ((~hskp8) | (~c0_1(a1180)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(780,plain,
% 0.49/0.64 (((~c0_1(a1180)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a1180)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(781,axiom,((~c0_1(a1180)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.49/0.64 tff(782,plain,
% 0.49/0.64 ((~hskp8) | (~c0_1(a1180))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[781, 780])).
% 0.49/0.64 tff(783,plain,
% 0.49/0.64 ((~hskp8) | (~c0_1(a1180))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[782, 779])).
% 0.49/0.64 tff(784,plain,
% 0.49/0.64 (~c0_1(a1180)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[783, 772])).
% 0.49/0.64 tff(785,assumption,(~c2_1(a1192)), introduced(assumption)).
% 0.49/0.64 tff(786,plain,
% 0.49/0.64 (((~hskp8) | c1_1(a1180)) <=> ((~hskp8) | c1_1(a1180))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(787,axiom,((~hskp8) | c1_1(a1180)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 0.49/0.64 tff(788,plain,
% 0.49/0.64 ((~hskp8) | c1_1(a1180)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[787, 786])).
% 0.49/0.64 tff(789,plain,
% 0.49/0.64 ((~hskp8) | c1_1(a1180)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[788, 786])).
% 0.49/0.64 tff(790,plain,
% 0.49/0.64 ((~hskp8) | c1_1(a1180)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[789, 786])).
% 0.49/0.64 tff(791,plain,
% 0.49/0.64 ((~hskp8) | c1_1(a1180)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[790, 786])).
% 0.49/0.64 tff(792,plain,
% 0.49/0.64 ((~hskp8) | c1_1(a1180)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[791, 786])).
% 0.49/0.64 tff(793,plain,
% 0.49/0.64 (c1_1(a1180)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[792, 772])).
% 0.49/0.64 tff(794,assumption,(c1_1(a1192)), introduced(assumption)).
% 0.49/0.64 tff(795,plain,
% 0.49/0.64 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1192) | c0_1(a1180) | c3_1(a1180) | (~ndr1_0) | (~c1_1(a1180)) | (~c3_1(a1192)) | (~c1_1(a1192)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1192) | c0_1(a1180) | c3_1(a1180) | (~ndr1_0) | (~c1_1(a1180)) | (~c3_1(a1192)) | (~c1_1(a1192)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(796,plain,
% 0.49/0.64 ((hskp3 | (~ndr1_0) | c2_1(a1192) | (~c1_1(a1192)) | (~c3_1(a1192)) | c0_1(a1180) | c3_1(a1180) | (~c1_1(a1180))) <=> (hskp3 | c2_1(a1192) | c0_1(a1180) | c3_1(a1180) | (~ndr1_0) | (~c1_1(a1180)) | (~c3_1(a1192)) | (~c1_1(a1192)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(797,plain,
% 0.49/0.64 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1192) | (~c1_1(a1192)) | (~c3_1(a1192)) | c0_1(a1180) | c3_1(a1180) | (~c1_1(a1180)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1192) | c0_1(a1180) | c3_1(a1180) | (~ndr1_0) | (~c1_1(a1180)) | (~c3_1(a1192)) | (~c1_1(a1192))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[796])).
% 0.49/0.64 tff(798,plain,
% 0.49/0.64 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1192) | (~c1_1(a1192)) | (~c3_1(a1192)) | c0_1(a1180) | c3_1(a1180) | (~c1_1(a1180)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1192) | c0_1(a1180) | c3_1(a1180) | (~ndr1_0) | (~c1_1(a1180)) | (~c3_1(a1192)) | (~c1_1(a1192)))),
% 0.49/0.64 inference(transitivity,[status(thm)],[797, 795])).
% 0.49/0.64 tff(799,plain,
% 0.49/0.64 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1192) | (~c1_1(a1192)) | (~c3_1(a1192)) | c0_1(a1180) | c3_1(a1180) | (~c1_1(a1180)))),
% 0.49/0.64 inference(quant_inst,[status(thm)],[])).
% 0.49/0.64 tff(800,plain,
% 0.49/0.64 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1192) | c0_1(a1180) | c3_1(a1180) | (~ndr1_0) | (~c1_1(a1180)) | (~c3_1(a1192)) | (~c1_1(a1192))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.49/0.64 tff(801,plain,
% 0.49/0.64 ($false),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[800, 169, 22, 794, 793, 785, 784, 778, 751, 771])).
% 0.49/0.64 tff(802,plain,((~hskp8) | hskp3 | (~c1_1(a1192)) | c2_1(a1192) | (~c3_1(a1192))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.64 tff(803,plain,
% 0.49/0.64 (~hskp8),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[802, 762, 22, 770, 769])).
% 0.49/0.64 tff(804,plain,
% 0.49/0.64 (hskp28),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[167, 803])).
% 0.49/0.64 tff(805,plain,
% 0.49/0.64 (((~hskp28) | c3_1(a1236)) <=> ((~hskp28) | c3_1(a1236))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(806,axiom,((~hskp28) | c3_1(a1236)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 0.49/0.64 tff(807,plain,
% 0.49/0.64 ((~hskp28) | c3_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[806, 805])).
% 0.49/0.64 tff(808,plain,
% 0.49/0.64 ((~hskp28) | c3_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[807, 805])).
% 0.49/0.64 tff(809,plain,
% 0.49/0.64 ((~hskp28) | c3_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[808, 805])).
% 0.49/0.64 tff(810,plain,
% 0.49/0.64 ((~hskp28) | c3_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[809, 805])).
% 0.49/0.64 tff(811,plain,
% 0.49/0.64 ((~hskp28) | c3_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[810, 805])).
% 0.49/0.64 tff(812,plain,
% 0.49/0.64 (c3_1(a1236)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[811, 804])).
% 0.49/0.64 tff(813,plain,
% 0.49/0.64 (((~hskp28) | c2_1(a1236)) <=> ((~hskp28) | c2_1(a1236))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(814,axiom,((~hskp28) | c2_1(a1236)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 0.49/0.64 tff(815,plain,
% 0.49/0.64 ((~hskp28) | c2_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[814, 813])).
% 0.49/0.64 tff(816,plain,
% 0.49/0.64 ((~hskp28) | c2_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[815, 813])).
% 0.49/0.64 tff(817,plain,
% 0.49/0.64 ((~hskp28) | c2_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[816, 813])).
% 0.49/0.64 tff(818,plain,
% 0.49/0.64 ((~hskp28) | c2_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[817, 813])).
% 0.49/0.64 tff(819,plain,
% 0.49/0.64 ((~hskp28) | c2_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[818, 813])).
% 0.49/0.64 tff(820,plain,
% 0.49/0.64 (c2_1(a1236)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[819, 804])).
% 0.49/0.64 tff(821,plain,
% 0.49/0.64 (((~hskp28) | c0_1(a1236)) <=> ((~hskp28) | c0_1(a1236))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(822,axiom,((~hskp28) | c0_1(a1236)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 0.49/0.64 tff(823,plain,
% 0.49/0.64 ((~hskp28) | c0_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[822, 821])).
% 0.49/0.64 tff(824,plain,
% 0.49/0.64 ((~hskp28) | c0_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[823, 821])).
% 0.49/0.64 tff(825,plain,
% 0.49/0.64 ((~hskp28) | c0_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[824, 821])).
% 0.49/0.64 tff(826,plain,
% 0.49/0.64 ((~hskp28) | c0_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[825, 821])).
% 0.49/0.64 tff(827,plain,
% 0.49/0.64 ((~hskp28) | c0_1(a1236)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[826, 821])).
% 0.49/0.64 tff(828,plain,
% 0.49/0.64 (c0_1(a1236)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[827, 804])).
% 0.49/0.64 tff(829,plain,
% 0.49/0.64 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c2_1(a1236)) | (~c3_1(a1236)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c2_1(a1236)) | (~c3_1(a1236)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(830,plain,
% 0.49/0.64 ((hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c3_1(a1236)) | (~c2_1(a1236))) <=> (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c2_1(a1236)) | (~c3_1(a1236)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(831,plain,
% 0.49/0.64 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c3_1(a1236)) | (~c2_1(a1236)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c2_1(a1236)) | (~c3_1(a1236))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[830])).
% 0.49/0.64 tff(832,plain,
% 0.49/0.64 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c3_1(a1236)) | (~c2_1(a1236)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c2_1(a1236)) | (~c3_1(a1236)))),
% 0.49/0.65 inference(transitivity,[status(thm)],[831, 829])).
% 0.49/0.65 tff(833,plain,
% 0.49/0.65 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c3_1(a1236)) | (~c2_1(a1236)))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(834,plain,
% 0.49/0.65 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c2_1(a1236)) | (~c3_1(a1236))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[833, 832])).
% 0.49/0.65 tff(835,plain,
% 0.49/0.65 ($false),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[834, 169, 722, 752, 828, 820, 812, 741])).
% 0.49/0.65 tff(836,plain,(hskp2 | hskp3 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.49/0.65 tff(837,plain,
% 0.49/0.65 (hskp2),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[836, 23, 22])).
% 0.49/0.65 tff(838,assumption,(hskp16), introduced(assumption)).
% 0.49/0.65 tff(839,plain,
% 0.49/0.65 (c2_1(a1199)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[443, 838])).
% 0.49/0.65 tff(840,plain,
% 0.49/0.65 (~c3_1(a1199)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[422, 838])).
% 0.49/0.65 tff(841,plain,
% 0.49/0.65 (~c0_1(a1199)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[428, 838])).
% 0.49/0.65 tff(842,plain,
% 0.49/0.65 (c1_1(a1199)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[678, 841, 645, 840, 839])).
% 0.49/0.65 tff(843,assumption,(c3_1(a1168)), introduced(assumption)).
% 0.49/0.65 tff(844,plain,
% 0.49/0.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1199) | c3_1(a1199) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1199)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1199) | c3_1(a1199) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1199)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(845,plain,
% 0.49/0.65 ((hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199))) <=> (hskp3 | c0_1(a1199) | c3_1(a1199) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1199)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(846,plain,
% 0.49/0.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1199) | c3_1(a1199) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1199))))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[845])).
% 0.49/0.65 tff(847,plain,
% 0.49/0.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1199) | c3_1(a1199) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1199)))),
% 0.49/0.65 inference(transitivity,[status(thm)],[846, 844])).
% 0.49/0.65 tff(848,plain,
% 0.49/0.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199)))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(849,plain,
% 0.49/0.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1199) | c3_1(a1199) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1199))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[848, 847])).
% 0.49/0.65 tff(850,plain,
% 0.49/0.65 ($false),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[849, 169, 22, 501, 841, 840, 492, 751, 843, 842])).
% 0.49/0.65 tff(851,plain,((~hskp16) | hskp3 | (~c3_1(a1168)) | (~hskp2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.65 tff(852,plain,
% 0.49/0.65 (~hskp16),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[851, 731, 22, 837])).
% 0.49/0.65 tff(853,plain,
% 0.49/0.65 (hskp1),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[416, 852, 23])).
% 0.49/0.65 tff(854,plain,
% 0.49/0.65 (~c3_1(a1169)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[103, 853])).
% 0.49/0.65 tff(855,plain,
% 0.49/0.65 (~c2_1(a1169)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[109, 853])).
% 0.49/0.65 tff(856,plain,
% 0.49/0.65 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(857,plain,
% 0.49/0.65 ((hskp22 | hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169))) <=> (hskp22 | hskp17 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(858,plain,
% 0.49/0.65 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169))))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[857])).
% 0.49/0.65 tff(859,plain,
% 0.49/0.65 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))),
% 0.49/0.65 inference(transitivity,[status(thm)],[858, 856])).
% 0.49/0.65 tff(860,plain,
% 0.49/0.65 ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(861,plain,
% 0.49/0.65 ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[860, 859])).
% 0.49/0.65 tff(862,plain,
% 0.49/0.65 (~c0_1(a1169)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[861, 169, 722, 23, 855, 854, 472])).
% 0.49/0.65 tff(863,plain,
% 0.49/0.65 (c1_1(a1169)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[117, 853])).
% 0.49/0.65 tff(864,plain,
% 0.49/0.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c3_1(a1169) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1169)) | c0_1(a1169))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c3_1(a1169) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1169)) | c0_1(a1169))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(865,plain,
% 0.49/0.65 ((hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1169) | c3_1(a1169) | (~c1_1(a1169))) <=> (hskp3 | c3_1(a1169) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1169)) | c0_1(a1169))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(866,plain,
% 0.49/0.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1169) | c3_1(a1169) | (~c1_1(a1169)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c3_1(a1169) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1169)) | c0_1(a1169)))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[865])).
% 0.49/0.65 tff(867,plain,
% 0.49/0.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1169) | c3_1(a1169) | (~c1_1(a1169)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c3_1(a1169) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1169)) | c0_1(a1169))),
% 0.49/0.65 inference(transitivity,[status(thm)],[866, 864])).
% 0.49/0.65 tff(868,plain,
% 0.49/0.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1169) | c3_1(a1169) | (~c1_1(a1169)))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(869,plain,
% 0.49/0.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c3_1(a1169) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1169)) | c0_1(a1169)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[868, 867])).
% 0.49/0.65 tff(870,plain,
% 0.49/0.65 ($false),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[869, 169, 22, 863, 501, 854, 492, 751, 862, 731])).
% 0.49/0.65 tff(871,plain,(hskp17 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.49/0.65 tff(872,plain,
% 0.49/0.65 (hskp17),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[871, 22])).
% 0.49/0.65 tff(873,plain,
% 0.49/0.65 (~c2_1(a1200)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[335, 872])).
% 0.49/0.65 tff(874,plain,
% 0.49/0.65 (~c1_1(a1200)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[341, 872])).
% 0.49/0.65 tff(875,plain,
% 0.49/0.65 (c0_1(a1200)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[349, 872])).
% 0.49/0.65 tff(876,plain,
% 0.49/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1200)) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1200)) | (~c0_1(a1200)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(877,plain,
% 0.49/0.65 (((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200))) <=> (c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1200)) | (~c0_1(a1200)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(878,plain,
% 0.49/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1200)) | (~c0_1(a1200))))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[877])).
% 0.49/0.65 tff(879,plain,
% 0.49/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1200)) | (~c0_1(a1200)))),
% 0.49/0.65 inference(transitivity,[status(thm)],[878, 876])).
% 0.49/0.65 tff(880,plain,
% 0.49/0.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(881,plain,
% 0.49/0.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1200)) | (~c0_1(a1200))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[880, 879])).
% 0.49/0.65 tff(882,plain,
% 0.49/0.65 (~c3_1(a1200)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[881, 169, 875, 509, 501, 874, 873, 492, 57])).
% 0.49/0.65 tff(883,plain,
% 0.49/0.65 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(884,plain,
% 0.49/0.65 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[883])).
% 0.49/0.65 tff(885,plain,
% 0.49/0.65 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(886,plain,
% 0.49/0.65 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(887,plain,
% 0.49/0.65 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[886])).
% 0.49/0.65 tff(888,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.49/0.65 tff(889,plain,
% 0.49/0.65 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[888, 887])).
% 0.49/0.65 tff(890,plain,
% 0.49/0.65 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[889, 885])).
% 0.49/0.65 tff(891,plain,(
% 0.49/0.65 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.65 inference(skolemize,[status(sab)],[890])).
% 0.49/0.65 tff(892,plain,
% 0.49/0.65 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[891, 884])).
% 0.49/0.65 tff(893,plain,
% 0.49/0.65 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp6 | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | c3_1(a1200))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(894,plain,
% 0.49/0.65 ((hskp6 | (~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200)) <=> (hskp6 | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | c3_1(a1200))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(895,plain,
% 0.49/0.65 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | c3_1(a1200)))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[894])).
% 0.49/0.65 tff(896,plain,
% 0.49/0.65 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp6 | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | c3_1(a1200))),
% 0.49/0.65 inference(transitivity,[status(thm)],[895, 893])).
% 0.49/0.65 tff(897,plain,
% 0.49/0.65 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(898,plain,
% 0.49/0.65 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp6 | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | c3_1(a1200)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[897, 896])).
% 0.49/0.65 tff(899,plain,
% 0.49/0.65 (hskp6),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[898, 169, 509, 501, 874, 873, 492, 892, 882])).
% 0.49/0.65 tff(900,plain,
% 0.49/0.65 (((~hskp6) | (~c3_1(a1178))) <=> ((~hskp6) | (~c3_1(a1178)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(901,plain,
% 0.49/0.65 (((~c3_1(a1178)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a1178)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(902,axiom,((~c3_1(a1178)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 0.49/0.65 tff(903,plain,
% 0.49/0.65 ((~hskp6) | (~c3_1(a1178))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[902, 901])).
% 0.49/0.65 tff(904,plain,
% 0.49/0.65 ((~hskp6) | (~c3_1(a1178))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[903, 900])).
% 0.49/0.65 tff(905,plain,
% 0.49/0.65 (~c3_1(a1178)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[904, 899])).
% 0.49/0.66 tff(906,plain,
% 0.49/0.66 (^[U: $i] : refl((hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.49/0.66 inference(bind,[status(th)],[])).
% 0.49/0.66 tff(907,plain,
% 0.49/0.66 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.49/0.66 inference(quant_intro,[status(thm)],[906])).
% 0.49/0.66 tff(908,plain,
% 0.49/0.66 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(909,plain,
% 0.49/0.66 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp20))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp12) <=> ((hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp12))), rewrite(((hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp12) <=> (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp12) <=> (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.49/0.66 inference(bind,[status(th)],[])).
% 0.49/0.66 tff(910,plain,
% 0.49/0.66 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp12) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.49/0.66 inference(quant_intro,[status(thm)],[909])).
% 0.49/0.66 tff(911,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 0.49/0.66 tff(912,plain,
% 0.49/0.66 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[911, 910])).
% 0.49/0.66 tff(913,plain,
% 0.49/0.66 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[912, 908])).
% 0.49/0.66 tff(914,plain,(
% 0.49/0.66 ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.49/0.66 inference(skolemize,[status(sab)],[913])).
% 0.49/0.66 tff(915,plain,
% 0.49/0.66 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[914, 907])).
% 0.49/0.66 tff(916,plain,
% 0.49/0.66 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(917,plain,
% 0.49/0.66 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168))) <=> (hskp22 | hskp14 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(918,plain,
% 0.49/0.66 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168))))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[917])).
% 0.49/0.66 tff(919,plain,
% 0.49/0.66 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))),
% 0.49/0.66 inference(transitivity,[status(thm)],[918, 916])).
% 0.49/0.66 tff(920,plain,
% 0.49/0.66 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(921,plain,
% 0.49/0.66 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[920, 919])).
% 0.49/0.66 tff(922,plain,
% 0.49/0.66 (hskp22 | hskp14 | c3_1(a1168)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[921, 169, 509, 492, 273])).
% 0.49/0.66 tff(923,plain,
% 0.49/0.66 (c3_1(a1168)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[922, 256, 79])).
% 0.49/0.66 tff(924,assumption,(hskp6), introduced(assumption)).
% 0.49/0.66 tff(925,plain,
% 0.49/0.66 (~c3_1(a1178)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[904, 924])).
% 0.49/0.66 tff(926,plain,
% 0.49/0.66 (((~hskp6) | c2_1(a1178)) <=> ((~hskp6) | c2_1(a1178))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(927,axiom,((~hskp6) | c2_1(a1178)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 0.49/0.66 tff(928,plain,
% 0.49/0.66 ((~hskp6) | c2_1(a1178)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[927, 926])).
% 0.49/0.66 tff(929,plain,
% 0.49/0.66 ((~hskp6) | c2_1(a1178)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[928, 926])).
% 0.49/0.66 tff(930,plain,
% 0.49/0.66 ((~hskp6) | c2_1(a1178)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[929, 926])).
% 0.49/0.66 tff(931,plain,
% 0.49/0.66 ((~hskp6) | c2_1(a1178)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[930, 926])).
% 0.49/0.66 tff(932,plain,
% 0.49/0.66 ((~hskp6) | c2_1(a1178)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[931, 926])).
% 0.49/0.66 tff(933,plain,
% 0.49/0.66 (c2_1(a1178)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[932, 924])).
% 0.49/0.66 tff(934,plain,
% 0.49/0.66 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | c3_1(a1178) | (~ndr1_0) | (~c0_1(a1178)) | (~c2_1(a1178)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp22 | hskp14 | c3_1(a1178) | (~ndr1_0) | (~c0_1(a1178)) | (~c2_1(a1178)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(935,plain,
% 0.49/0.66 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a1178) | (~c0_1(a1178)) | (~c2_1(a1178))) <=> (hskp22 | hskp14 | c3_1(a1178) | (~ndr1_0) | (~c0_1(a1178)) | (~c2_1(a1178)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(936,plain,
% 0.49/0.66 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1178) | (~c0_1(a1178)) | (~c2_1(a1178)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | c3_1(a1178) | (~ndr1_0) | (~c0_1(a1178)) | (~c2_1(a1178))))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[935])).
% 0.49/0.66 tff(937,plain,
% 0.49/0.66 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1178) | (~c0_1(a1178)) | (~c2_1(a1178)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp22 | hskp14 | c3_1(a1178) | (~ndr1_0) | (~c0_1(a1178)) | (~c2_1(a1178)))),
% 0.49/0.66 inference(transitivity,[status(thm)],[936, 934])).
% 0.49/0.66 tff(938,plain,
% 0.49/0.66 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1178) | (~c0_1(a1178)) | (~c2_1(a1178)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(939,plain,
% 0.49/0.66 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp22 | hskp14 | c3_1(a1178) | (~ndr1_0) | (~c0_1(a1178)) | (~c2_1(a1178))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[938, 937])).
% 0.49/0.66 tff(940,plain,
% 0.49/0.66 (~c0_1(a1178)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[939, 169, 256, 79, 933, 925, 240])).
% 0.49/0.66 tff(941,plain,
% 0.49/0.66 (((~hskp6) | c1_1(a1178)) <=> ((~hskp6) | c1_1(a1178))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(942,axiom,((~hskp6) | c1_1(a1178)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 0.49/0.66 tff(943,plain,
% 0.49/0.66 ((~hskp6) | c1_1(a1178)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[942, 941])).
% 0.49/0.66 tff(944,plain,
% 0.49/0.66 ((~hskp6) | c1_1(a1178)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[943, 941])).
% 0.49/0.66 tff(945,plain,
% 0.49/0.66 ((~hskp6) | c1_1(a1178)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[944, 941])).
% 0.49/0.66 tff(946,plain,
% 0.49/0.66 ((~hskp6) | c1_1(a1178)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[945, 941])).
% 0.49/0.66 tff(947,plain,
% 0.49/0.66 ((~hskp6) | c1_1(a1178)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[946, 941])).
% 0.49/0.66 tff(948,plain,
% 0.49/0.66 (c1_1(a1178)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[947, 924])).
% 0.49/0.66 tff(949,plain,
% 0.49/0.66 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c3_1(a1178) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | (~c1_1(a1178)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c3_1(a1178) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | (~c1_1(a1178)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(950,plain,
% 0.49/0.66 ((hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | c3_1(a1178) | (~c1_1(a1178))) <=> (hskp3 | c3_1(a1178) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | (~c1_1(a1178)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(951,plain,
% 0.49/0.66 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | c3_1(a1178) | (~c1_1(a1178)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c3_1(a1178) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | (~c1_1(a1178))))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[950])).
% 0.49/0.66 tff(952,plain,
% 0.49/0.66 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | c3_1(a1178) | (~c1_1(a1178)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c3_1(a1178) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | (~c1_1(a1178)))),
% 0.49/0.66 inference(transitivity,[status(thm)],[951, 949])).
% 0.49/0.66 tff(953,plain,
% 0.49/0.66 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | c3_1(a1178) | (~c1_1(a1178)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(954,plain,
% 0.49/0.66 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c3_1(a1178) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | (~c1_1(a1178))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.49/0.66 tff(955,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[954, 169, 22, 948, 501, 925, 492, 751, 940, 923])).
% 0.49/0.66 tff(956,plain,((~hskp6) | hskp3 | hskp22 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(957,plain,
% 0.49/0.66 (~hskp6),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[956, 256, 22, 79])).
% 0.49/0.66 tff(958,plain,
% 0.49/0.66 ((hskp21 | hskp14 | hskp6) <=> (hskp21 | hskp14 | hskp6)),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(959,plain,
% 0.49/0.66 (((hskp21 | hskp6) | hskp14) <=> (hskp21 | hskp14 | hskp6)),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(960,plain,
% 0.49/0.66 ((hskp6 | hskp21) <=> (hskp21 | hskp6)),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(961,plain,
% 0.49/0.66 (((hskp6 | hskp21) | hskp14) <=> ((hskp21 | hskp6) | hskp14)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[960])).
% 0.49/0.66 tff(962,plain,
% 0.49/0.66 (((hskp6 | hskp21) | hskp14) <=> (hskp21 | hskp14 | hskp6)),
% 0.49/0.66 inference(transitivity,[status(thm)],[961, 959])).
% 0.49/0.66 tff(963,axiom,((hskp6 | hskp21) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 0.49/0.66 tff(964,plain,
% 0.49/0.66 (hskp21 | hskp14 | hskp6),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[963, 962])).
% 0.49/0.66 tff(965,plain,
% 0.49/0.66 (hskp21 | hskp14 | hskp6),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[964, 958])).
% 0.49/0.66 tff(966,plain,
% 0.49/0.66 (hskp21 | hskp14 | hskp6),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[965, 958])).
% 0.49/0.66 tff(967,plain,
% 0.49/0.66 (hskp21 | hskp14 | hskp6),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[966, 958])).
% 0.49/0.66 tff(968,plain,
% 0.49/0.66 (hskp21 | hskp14 | hskp6),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[967, 958])).
% 0.49/0.66 tff(969,plain,
% 0.49/0.66 (hskp21),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[968, 957, 79])).
% 0.49/0.66 tff(970,plain,
% 0.49/0.66 (((~hskp21) | (~c1_1(a1207))) <=> ((~hskp21) | (~c1_1(a1207)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(971,plain,
% 0.49/0.66 (((~c1_1(a1207)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a1207)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(972,axiom,((~c1_1(a1207)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.49/0.66 tff(973,plain,
% 0.49/0.66 ((~hskp21) | (~c1_1(a1207))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[972, 971])).
% 0.49/0.66 tff(974,plain,
% 0.49/0.66 ((~hskp21) | (~c1_1(a1207))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[973, 970])).
% 0.49/0.66 tff(975,plain,
% 0.49/0.66 (~c1_1(a1207)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[974, 969])).
% 0.49/0.66 tff(976,plain,
% 0.49/0.66 (((~hskp21) | c3_1(a1207)) <=> ((~hskp21) | c3_1(a1207))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(977,axiom,((~hskp21) | c3_1(a1207)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.49/0.66 tff(978,plain,
% 0.49/0.66 ((~hskp21) | c3_1(a1207)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[977, 976])).
% 0.49/0.66 tff(979,plain,
% 0.49/0.66 ((~hskp21) | c3_1(a1207)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[978, 976])).
% 0.49/0.66 tff(980,plain,
% 0.49/0.66 ((~hskp21) | c3_1(a1207)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[979, 976])).
% 0.49/0.66 tff(981,plain,
% 0.49/0.66 ((~hskp21) | c3_1(a1207)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[980, 976])).
% 0.49/0.66 tff(982,plain,
% 0.49/0.66 ((~hskp21) | c3_1(a1207)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[981, 976])).
% 0.49/0.66 tff(983,plain,
% 0.49/0.66 (c3_1(a1207)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[982, 969])).
% 0.49/0.66 tff(984,plain,
% 0.49/0.66 (((~hskp21) | c2_1(a1207)) <=> ((~hskp21) | c2_1(a1207))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(985,axiom,((~hskp21) | c2_1(a1207)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 0.49/0.66 tff(986,plain,
% 0.49/0.66 ((~hskp21) | c2_1(a1207)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[985, 984])).
% 0.49/0.66 tff(987,plain,
% 0.49/0.66 ((~hskp21) | c2_1(a1207)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[986, 984])).
% 0.49/0.66 tff(988,plain,
% 0.49/0.66 ((~hskp21) | c2_1(a1207)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[987, 984])).
% 0.49/0.66 tff(989,plain,
% 0.49/0.66 ((~hskp21) | c2_1(a1207)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[988, 984])).
% 0.49/0.66 tff(990,plain,
% 0.49/0.66 ((~hskp21) | c2_1(a1207)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[989, 984])).
% 0.49/0.66 tff(991,plain,
% 0.49/0.66 (c2_1(a1207)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[990, 969])).
% 0.49/0.66 tff(992,plain,
% 0.49/0.66 (^[U: $i] : refl((hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 0.49/0.66 inference(bind,[status(th)],[])).
% 0.49/0.66 tff(993,plain,
% 0.49/0.66 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.49/0.66 inference(quant_intro,[status(thm)],[992])).
% 0.49/0.66 tff(994,plain,
% 0.49/0.66 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(995,plain,
% 0.49/0.66 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_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))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp6) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp6))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp6) <=> (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp6) <=> (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 0.49/0.66 inference(bind,[status(th)],[])).
% 0.49/0.66 tff(996,plain,
% 0.49/0.66 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp6) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.49/0.66 inference(quant_intro,[status(thm)],[995])).
% 0.49/0.66 tff(997,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.49/0.66 tff(998,plain,
% 0.49/0.66 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[997, 996])).
% 0.49/0.66 tff(999,plain,
% 0.49/0.66 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[998, 994])).
% 0.49/0.66 tff(1000,plain,(
% 0.49/0.66 ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.49/0.66 inference(skolemize,[status(sab)],[999])).
% 0.49/0.66 tff(1001,plain,
% 0.49/0.66 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1000, 993])).
% 0.49/0.66 tff(1002,assumption,(hskp12), introduced(assumption)).
% 0.49/0.66 tff(1003,plain,
% 0.49/0.66 (((~hskp12) | (~c3_1(a1187))) <=> ((~hskp12) | (~c3_1(a1187)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1004,plain,
% 0.49/0.66 (((~c3_1(a1187)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a1187)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1005,axiom,((~c3_1(a1187)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 0.49/0.66 tff(1006,plain,
% 0.49/0.66 ((~hskp12) | (~c3_1(a1187))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 0.49/0.66 tff(1007,plain,
% 0.49/0.66 ((~hskp12) | (~c3_1(a1187))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1006, 1003])).
% 0.49/0.66 tff(1008,plain,
% 0.49/0.66 (~c3_1(a1187)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1007, 1002])).
% 0.49/0.66 tff(1009,plain,
% 0.49/0.66 (((~hskp12) | (~c2_1(a1187))) <=> ((~hskp12) | (~c2_1(a1187)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1010,plain,
% 0.49/0.66 (((~c2_1(a1187)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a1187)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1011,axiom,((~c2_1(a1187)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 0.49/0.66 tff(1012,plain,
% 0.49/0.66 ((~hskp12) | (~c2_1(a1187))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 0.49/0.66 tff(1013,plain,
% 0.49/0.66 ((~hskp12) | (~c2_1(a1187))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1012, 1009])).
% 0.49/0.66 tff(1014,plain,
% 0.49/0.66 (~c2_1(a1187)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1013, 1002])).
% 0.49/0.66 tff(1015,plain,
% 0.49/0.66 (((~hskp12) | (~c0_1(a1187))) <=> ((~hskp12) | (~c0_1(a1187)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1016,plain,
% 0.49/0.66 (((~c0_1(a1187)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a1187)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1017,axiom,((~c0_1(a1187)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 0.49/0.66 tff(1018,plain,
% 0.49/0.66 ((~hskp12) | (~c0_1(a1187))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 0.49/0.66 tff(1019,plain,
% 0.49/0.66 ((~hskp12) | (~c0_1(a1187))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1018, 1015])).
% 0.49/0.66 tff(1020,plain,
% 0.49/0.66 (~c0_1(a1187)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1019, 1002])).
% 0.49/0.66 tff(1021,assumption,(~hskp6), introduced(assumption)).
% 0.49/0.66 tff(1022,plain,
% 0.49/0.66 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | c0_1(a1187) | c2_1(a1187) | c3_1(a1187) | (~ndr1_0))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | hskp3 | c0_1(a1187) | c2_1(a1187) | c3_1(a1187) | (~ndr1_0))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1023,plain,
% 0.49/0.66 ((hskp6 | hskp3 | (~ndr1_0) | c3_1(a1187) | c0_1(a1187) | c2_1(a1187)) <=> (hskp6 | hskp3 | c0_1(a1187) | c2_1(a1187) | c3_1(a1187) | (~ndr1_0))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1024,plain,
% 0.49/0.66 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a1187) | c0_1(a1187) | c2_1(a1187))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | c0_1(a1187) | c2_1(a1187) | c3_1(a1187) | (~ndr1_0)))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1023])).
% 0.49/0.66 tff(1025,plain,
% 0.49/0.66 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a1187) | c0_1(a1187) | c2_1(a1187))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | hskp3 | c0_1(a1187) | c2_1(a1187) | c3_1(a1187) | (~ndr1_0))),
% 0.49/0.66 inference(transitivity,[status(thm)],[1024, 1022])).
% 0.49/0.66 tff(1026,plain,
% 0.49/0.66 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a1187) | c0_1(a1187) | c2_1(a1187))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(1027,plain,
% 0.49/0.66 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | hskp3 | c0_1(a1187) | c2_1(a1187) | c3_1(a1187) | (~ndr1_0)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 0.49/0.66 tff(1028,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1027, 169, 1021, 22, 1020, 1014, 1008, 1001])).
% 0.49/0.66 tff(1029,plain,((~hskp12) | hskp6 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(1030,plain,
% 0.49/0.66 (~hskp12),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1029, 957, 22])).
% 0.49/0.66 tff(1031,plain,
% 0.49/0.66 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | (~c2_1(a1207)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | (~c2_1(a1207)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1032,plain,
% 0.49/0.66 ((hskp20 | hskp12 | (~ndr1_0) | c1_1(a1207) | (~c3_1(a1207)) | (~c2_1(a1207))) <=> (hskp20 | hskp12 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | (~c2_1(a1207)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1033,plain,
% 0.49/0.66 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c1_1(a1207) | (~c3_1(a1207)) | (~c2_1(a1207)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | (~c2_1(a1207))))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1032])).
% 0.49/0.66 tff(1034,plain,
% 0.49/0.66 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c1_1(a1207) | (~c3_1(a1207)) | (~c2_1(a1207)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | (~c2_1(a1207)))),
% 0.49/0.66 inference(transitivity,[status(thm)],[1033, 1031])).
% 0.49/0.66 tff(1035,plain,
% 0.49/0.66 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c1_1(a1207) | (~c3_1(a1207)) | (~c2_1(a1207)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(1036,plain,
% 0.49/0.66 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | (~c2_1(a1207))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 0.49/0.66 tff(1037,plain,
% 0.49/0.66 (hskp20),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1036, 169, 1030, 991, 983, 975, 915])).
% 0.49/0.66 tff(1038,plain,
% 0.49/0.66 (((~hskp20) | (~c2_1(a1205))) <=> ((~hskp20) | (~c2_1(a1205)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1039,plain,
% 0.49/0.66 (((~c2_1(a1205)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a1205)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1040,axiom,((~c2_1(a1205)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.49/0.66 tff(1041,plain,
% 0.49/0.66 ((~hskp20) | (~c2_1(a1205))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1040, 1039])).
% 0.49/0.66 tff(1042,plain,
% 0.49/0.66 ((~hskp20) | (~c2_1(a1205))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1041, 1038])).
% 0.49/0.66 tff(1043,plain,
% 0.49/0.66 (~c2_1(a1205)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1042, 1037])).
% 0.49/0.66 tff(1044,plain,
% 0.49/0.66 (((~hskp20) | c3_1(a1205)) <=> ((~hskp20) | c3_1(a1205))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1045,axiom,((~hskp20) | c3_1(a1205)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.49/0.66 tff(1046,plain,
% 0.49/0.66 ((~hskp20) | c3_1(a1205)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 0.49/0.66 tff(1047,plain,
% 0.49/0.66 ((~hskp20) | c3_1(a1205)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1046, 1044])).
% 0.49/0.66 tff(1048,plain,
% 0.49/0.66 ((~hskp20) | c3_1(a1205)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1047, 1044])).
% 0.49/0.66 tff(1049,plain,
% 0.49/0.66 ((~hskp20) | c3_1(a1205)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1048, 1044])).
% 0.49/0.66 tff(1050,plain,
% 0.49/0.66 ((~hskp20) | c3_1(a1205)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1049, 1044])).
% 0.49/0.66 tff(1051,plain,
% 0.49/0.66 (c3_1(a1205)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1050, 1037])).
% 0.49/0.66 tff(1052,plain,
% 0.49/0.66 (((~hskp20) | c1_1(a1205)) <=> ((~hskp20) | c1_1(a1205))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1053,axiom,((~hskp20) | c1_1(a1205)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.49/0.66 tff(1054,plain,
% 0.49/0.66 ((~hskp20) | c1_1(a1205)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 0.49/0.66 tff(1055,plain,
% 0.49/0.66 ((~hskp20) | c1_1(a1205)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1054, 1052])).
% 0.49/0.66 tff(1056,plain,
% 0.49/0.67 ((~hskp20) | c1_1(a1205)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1055, 1052])).
% 0.49/0.67 tff(1057,plain,
% 0.49/0.67 ((~hskp20) | c1_1(a1205)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1056, 1052])).
% 0.49/0.67 tff(1058,plain,
% 0.49/0.67 ((~hskp20) | c1_1(a1205)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1057, 1052])).
% 0.49/0.67 tff(1059,plain,
% 0.49/0.67 (c1_1(a1205)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1058, 1037])).
% 0.49/0.67 tff(1060,plain,
% 0.49/0.67 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c2_1(a1200) | (~ndr1_0) | c3_1(a1200) | (~c0_1(a1200)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1200) | (~ndr1_0) | c3_1(a1200) | (~c0_1(a1200)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1061,plain,
% 0.49/0.67 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a1200) | c2_1(a1200) | (~c0_1(a1200))) <=> (hskp22 | hskp14 | c2_1(a1200) | (~ndr1_0) | c3_1(a1200) | (~c0_1(a1200)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1062,plain,
% 0.49/0.67 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1200) | c2_1(a1200) | (~c0_1(a1200)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c2_1(a1200) | (~ndr1_0) | c3_1(a1200) | (~c0_1(a1200))))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1061])).
% 0.49/0.67 tff(1063,plain,
% 0.49/0.67 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1200) | c2_1(a1200) | (~c0_1(a1200)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1200) | (~ndr1_0) | c3_1(a1200) | (~c0_1(a1200)))),
% 0.49/0.67 inference(transitivity,[status(thm)],[1062, 1060])).
% 0.49/0.67 tff(1064,plain,
% 0.49/0.67 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1200) | c2_1(a1200) | (~c0_1(a1200)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(1065,plain,
% 0.49/0.67 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1200) | (~ndr1_0) | c3_1(a1200) | (~c0_1(a1200))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 0.49/0.67 tff(1066,plain,
% 0.49/0.67 (c3_1(a1200)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1065, 169, 256, 79, 350, 336, 273])).
% 0.49/0.67 tff(1067,plain,
% 0.49/0.67 ($false),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[881, 169, 350, 509, 501, 342, 336, 492, 57, 1066])).
% 0.49/0.67 tff(1068,plain,((~hskp17) | hskp22 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.49/0.67 tff(1069,plain,
% 0.49/0.67 (~hskp17),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1068, 256, 79])).
% 0.49/0.67 tff(1070,plain,
% 0.49/0.67 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1071,plain,
% 0.49/0.67 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169))) <=> (hskp22 | hskp14 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1072,plain,
% 0.49/0.67 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169))))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1071])).
% 0.49/0.67 tff(1073,plain,
% 0.49/0.67 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))),
% 0.49/0.67 inference(transitivity,[status(thm)],[1072, 1070])).
% 0.49/0.67 tff(1074,plain,
% 0.49/0.67 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(1075,plain,
% 0.49/0.67 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1074, 1073])).
% 0.49/0.67 tff(1076,plain,
% 0.49/0.67 (~c0_1(a1169)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1075, 169, 256, 79, 399, 398, 273])).
% 0.49/0.67 tff(1077,plain,
% 0.49/0.67 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | hskp3 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1078,plain,
% 0.49/0.67 ((hskp6 | hskp3 | (~ndr1_0) | c3_1(a1169) | c0_1(a1169) | c2_1(a1169)) <=> (hskp6 | hskp3 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1079,plain,
% 0.49/0.67 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a1169) | c0_1(a1169) | c2_1(a1169))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169)))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1078])).
% 0.49/0.67 tff(1080,plain,
% 0.49/0.67 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a1169) | c0_1(a1169) | c2_1(a1169))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | hskp3 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169))),
% 0.49/0.67 inference(transitivity,[status(thm)],[1079, 1077])).
% 0.49/0.67 tff(1081,plain,
% 0.49/0.67 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a1169) | c0_1(a1169) | c2_1(a1169))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(1082,plain,
% 0.49/0.67 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | hskp3 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 0.49/0.67 tff(1083,plain,
% 0.49/0.67 ($false),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1082, 169, 957, 22, 399, 398, 1001, 1076])).
% 0.49/0.67 tff(1084,plain,((~hskp1) | hskp3 | hskp22 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.49/0.67 tff(1085,plain,
% 0.49/0.67 (~hskp1),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1084, 256, 22, 79])).
% 0.49/0.67 tff(1086,plain,
% 0.49/0.67 (hskp16),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[416, 1085, 1069])).
% 0.49/0.67 tff(1087,plain,
% 0.49/0.67 (~c3_1(a1199)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[422, 1086])).
% 0.49/0.67 tff(1088,plain,
% 0.49/0.67 (~c0_1(a1199)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[428, 1086])).
% 0.49/0.67 tff(1089,plain,
% 0.49/0.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1205) | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | (~c1_1(a1199)) | (~c1_1(a1205)) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1205) | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | (~c1_1(a1199)) | (~c1_1(a1205)) | (~c3_1(a1205)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1090,plain,
% 0.49/0.67 ((hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199))) <=> (hskp3 | c2_1(a1205) | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | (~c1_1(a1199)) | (~c1_1(a1205)) | (~c3_1(a1205)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1091,plain,
% 0.49/0.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1205) | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | (~c1_1(a1199)) | (~c1_1(a1205)) | (~c3_1(a1205))))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1090])).
% 0.49/0.67 tff(1092,plain,
% 0.49/0.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1205) | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | (~c1_1(a1199)) | (~c1_1(a1205)) | (~c3_1(a1205)))),
% 0.49/0.67 inference(transitivity,[status(thm)],[1091, 1089])).
% 0.49/0.67 tff(1093,plain,
% 0.49/0.67 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(1094,plain,
% 0.49/0.67 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1205) | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | (~c1_1(a1199)) | (~c1_1(a1205)) | (~c3_1(a1205))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1093, 1092])).
% 0.49/0.67 tff(1095,plain,
% 0.49/0.67 (~c1_1(a1199)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1094, 169, 22, 1059, 1051, 1043, 1088, 1087, 751])).
% 0.49/0.67 tff(1096,plain,
% 0.49/0.67 (c2_1(a1199)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[443, 1086])).
% 0.49/0.67 tff(1097,plain,
% 0.49/0.67 (~hskp2),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[678, 1096, 1088, 1087, 1095])).
% 0.49/0.67 tff(1098,plain,
% 0.49/0.67 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1207)) | (~c0_1(a1207)) | (~c2_1(a1207)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1207)) | (~c0_1(a1207)) | (~c2_1(a1207)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1099,plain,
% 0.49/0.67 ((hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1207)) | (~c3_1(a1207)) | (~c2_1(a1207))) <=> (hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1207)) | (~c0_1(a1207)) | (~c2_1(a1207)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1100,plain,
% 0.49/0.67 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1207)) | (~c3_1(a1207)) | (~c2_1(a1207)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1207)) | (~c0_1(a1207)) | (~c2_1(a1207))))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1099])).
% 0.49/0.67 tff(1101,plain,
% 0.49/0.67 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1207)) | (~c3_1(a1207)) | (~c2_1(a1207)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1207)) | (~c0_1(a1207)) | (~c2_1(a1207)))),
% 0.49/0.67 inference(transitivity,[status(thm)],[1100, 1098])).
% 0.49/0.67 tff(1102,plain,
% 0.49/0.67 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1207)) | (~c3_1(a1207)) | (~c2_1(a1207)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(1103,plain,
% 0.49/0.67 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1207)) | (~c0_1(a1207)) | (~c2_1(a1207))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 0.49/0.67 tff(1104,plain,
% 0.49/0.67 (hskp2 | (~c0_1(a1207))),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1103, 169, 256, 991, 983, 741])).
% 0.49/0.67 tff(1105,plain,
% 0.49/0.67 (~c0_1(a1207)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1104, 1097])).
% 0.49/0.67 tff(1106,plain,
% 0.49/0.67 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.49/0.67 inference(bind,[status(th)],[])).
% 0.49/0.67 tff(1107,plain,
% 0.49/0.67 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.49/0.67 inference(quant_intro,[status(thm)],[1106])).
% 0.49/0.67 tff(1108,plain,
% 0.49/0.67 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1109,plain,
% 0.49/0.67 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.49/0.67 inference(bind,[status(th)],[])).
% 0.49/0.67 tff(1110,plain,
% 0.49/0.67 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.49/0.67 inference(quant_intro,[status(thm)],[1109])).
% 0.49/0.67 tff(1111,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 0.49/0.67 tff(1112,plain,
% 0.49/0.67 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 0.49/0.67 tff(1113,plain,
% 0.49/0.67 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1112, 1108])).
% 0.49/0.67 tff(1114,plain,(
% 0.49/0.67 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.49/0.67 inference(skolemize,[status(sab)],[1113])).
% 0.49/0.67 tff(1115,plain,
% 0.49/0.67 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1114, 1107])).
% 0.49/0.67 tff(1116,plain,
% 0.49/0.67 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1207) | (~c2_1(a1207)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1207) | (~c2_1(a1207)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1117,plain,
% 0.49/0.67 ((hskp4 | (~ndr1_0) | c1_1(a1207) | c0_1(a1207) | (~c3_1(a1207)) | c1_1(a1207) | c0_1(a1207) | (~c2_1(a1207))) <=> (hskp4 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1207) | (~c2_1(a1207)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1118,plain,
% 0.49/0.67 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a1207) | c0_1(a1207) | (~c3_1(a1207)) | c1_1(a1207) | c0_1(a1207) | (~c2_1(a1207)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1207) | (~c2_1(a1207))))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1117])).
% 0.49/0.67 tff(1119,plain,
% 0.49/0.67 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a1207) | c0_1(a1207) | (~c3_1(a1207)) | c1_1(a1207) | c0_1(a1207) | (~c2_1(a1207)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1207) | (~c2_1(a1207)))),
% 0.49/0.67 inference(transitivity,[status(thm)],[1118, 1116])).
% 0.49/0.67 tff(1120,plain,
% 0.49/0.67 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a1207) | c0_1(a1207) | (~c3_1(a1207)) | c1_1(a1207) | c0_1(a1207) | (~c2_1(a1207)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(1121,plain,
% 0.49/0.67 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1207) | (~c2_1(a1207))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 0.49/0.67 tff(1122,plain,
% 0.49/0.67 (hskp4 | c0_1(a1207)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1121, 169, 991, 983, 975, 1115])).
% 0.49/0.67 tff(1123,plain,
% 0.49/0.67 (hskp4),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1122, 1105])).
% 0.49/0.67 tff(1124,plain,
% 0.49/0.67 (((~hskp4) | (~c0_1(a1175))) <=> ((~hskp4) | (~c0_1(a1175)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1125,plain,
% 0.49/0.67 (((~c0_1(a1175)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a1175)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1126,axiom,((~c0_1(a1175)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.49/0.67 tff(1127,plain,
% 0.49/0.67 ((~hskp4) | (~c0_1(a1175))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 0.49/0.67 tff(1128,plain,
% 0.49/0.67 ((~hskp4) | (~c0_1(a1175))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1127, 1124])).
% 0.49/0.67 tff(1129,plain,
% 0.49/0.67 (~c0_1(a1175)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1128, 1123])).
% 0.49/0.67 tff(1130,assumption,(~c2_1(a1205)), introduced(assumption)).
% 0.49/0.67 tff(1131,assumption,(c3_1(a1205)), introduced(assumption)).
% 0.49/0.67 tff(1132,assumption,(c1_1(a1205)), introduced(assumption)).
% 0.49/0.67 tff(1133,assumption,(~c0_1(a1175)), introduced(assumption)).
% 0.49/0.67 tff(1134,assumption,(hskp4), introduced(assumption)).
% 0.49/0.67 tff(1135,plain,
% 0.49/0.67 (((~hskp4) | c2_1(a1175)) <=> ((~hskp4) | c2_1(a1175))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1136,axiom,((~hskp4) | c2_1(a1175)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.49/0.67 tff(1137,plain,
% 0.49/0.67 ((~hskp4) | c2_1(a1175)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1136, 1135])).
% 0.49/0.67 tff(1138,plain,
% 0.49/0.67 ((~hskp4) | c2_1(a1175)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1137, 1135])).
% 0.49/0.67 tff(1139,plain,
% 0.49/0.67 ((~hskp4) | c2_1(a1175)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1138, 1135])).
% 0.49/0.67 tff(1140,plain,
% 0.49/0.67 ((~hskp4) | c2_1(a1175)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1139, 1135])).
% 0.49/0.67 tff(1141,plain,
% 0.49/0.67 ((~hskp4) | c2_1(a1175)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1140, 1135])).
% 0.49/0.67 tff(1142,plain,
% 0.49/0.67 (c2_1(a1175)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1141, 1134])).
% 0.49/0.67 tff(1143,plain,
% 0.49/0.67 (((~hskp4) | c1_1(a1175)) <=> ((~hskp4) | c1_1(a1175))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1144,axiom,((~hskp4) | c1_1(a1175)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.49/0.67 tff(1145,plain,
% 0.49/0.67 ((~hskp4) | c1_1(a1175)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 0.49/0.67 tff(1146,plain,
% 0.49/0.67 ((~hskp4) | c1_1(a1175)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1145, 1143])).
% 0.49/0.67 tff(1147,plain,
% 0.49/0.67 ((~hskp4) | c1_1(a1175)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1146, 1143])).
% 0.49/0.67 tff(1148,plain,
% 0.49/0.67 ((~hskp4) | c1_1(a1175)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1147, 1143])).
% 0.49/0.67 tff(1149,plain,
% 0.49/0.67 ((~hskp4) | c1_1(a1175)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1148, 1143])).
% 0.49/0.67 tff(1150,plain,
% 0.49/0.67 (c1_1(a1175)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1149, 1134])).
% 0.49/0.67 tff(1151,plain,
% 0.49/0.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1205) | c0_1(a1175) | (~ndr1_0) | c3_1(a1175) | (~c1_1(a1175)) | (~c1_1(a1205)) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1205) | c0_1(a1175) | (~ndr1_0) | c3_1(a1175) | (~c1_1(a1175)) | (~c1_1(a1205)) | (~c3_1(a1205)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1152,plain,
% 0.49/0.67 ((hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1175) | c3_1(a1175) | (~c1_1(a1175))) <=> (hskp3 | c2_1(a1205) | c0_1(a1175) | (~ndr1_0) | c3_1(a1175) | (~c1_1(a1175)) | (~c1_1(a1205)) | (~c3_1(a1205)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1153,plain,
% 0.49/0.68 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1175) | c3_1(a1175) | (~c1_1(a1175)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1205) | c0_1(a1175) | (~ndr1_0) | c3_1(a1175) | (~c1_1(a1175)) | (~c1_1(a1205)) | (~c3_1(a1205))))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1152])).
% 0.49/0.68 tff(1154,plain,
% 0.49/0.68 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1175) | c3_1(a1175) | (~c1_1(a1175)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1205) | c0_1(a1175) | (~ndr1_0) | c3_1(a1175) | (~c1_1(a1175)) | (~c1_1(a1205)) | (~c3_1(a1205)))),
% 0.49/0.68 inference(transitivity,[status(thm)],[1153, 1151])).
% 0.49/0.68 tff(1155,plain,
% 0.49/0.68 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1175) | c3_1(a1175) | (~c1_1(a1175)))),
% 0.49/0.68 inference(quant_inst,[status(thm)],[])).
% 0.49/0.68 tff(1156,plain,
% 0.49/0.68 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1205) | c0_1(a1175) | (~ndr1_0) | c3_1(a1175) | (~c1_1(a1175)) | (~c1_1(a1205)) | (~c3_1(a1205))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 0.49/0.68 tff(1157,plain,
% 0.49/0.68 (c3_1(a1175) | (~c1_1(a1175))),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1156, 169, 22, 1132, 1131, 1130, 1133, 751])).
% 0.49/0.68 tff(1158,plain,
% 0.49/0.68 (c3_1(a1175)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1157, 1150])).
% 0.49/0.68 tff(1159,plain,
% 0.49/0.68 (~c1_1(a1199)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1094, 169, 22, 1132, 1131, 1130, 841, 840, 751])).
% 0.49/0.68 tff(1160,assumption,(c3_1(a1175)), introduced(assumption)).
% 0.49/0.68 tff(1161,assumption,(c2_1(a1175)), introduced(assumption)).
% 0.49/0.68 tff(1162,plain,
% 0.49/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1199) | c3_1(a1199) | c0_1(a1175) | (~ndr1_0) | (~c3_1(a1175)) | (~c2_1(a1175)) | c1_1(a1199) | (~c2_1(a1199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1199) | c3_1(a1199) | c0_1(a1175) | (~ndr1_0) | (~c3_1(a1175)) | (~c2_1(a1175)) | c1_1(a1199) | (~c2_1(a1199)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1163,plain,
% 0.49/0.68 (((~ndr1_0) | c0_1(a1175) | (~c3_1(a1175)) | (~c2_1(a1175)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199)) <=> (c0_1(a1199) | c3_1(a1199) | c0_1(a1175) | (~ndr1_0) | (~c3_1(a1175)) | (~c2_1(a1175)) | c1_1(a1199) | (~c2_1(a1199)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1164,plain,
% 0.49/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1175) | (~c3_1(a1175)) | (~c2_1(a1175)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1199) | c3_1(a1199) | c0_1(a1175) | (~ndr1_0) | (~c3_1(a1175)) | (~c2_1(a1175)) | c1_1(a1199) | (~c2_1(a1199))))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1163])).
% 0.49/0.68 tff(1165,plain,
% 0.49/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1175) | (~c3_1(a1175)) | (~c2_1(a1175)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1199) | c3_1(a1199) | c0_1(a1175) | (~ndr1_0) | (~c3_1(a1175)) | (~c2_1(a1175)) | c1_1(a1199) | (~c2_1(a1199)))),
% 0.49/0.68 inference(transitivity,[status(thm)],[1164, 1162])).
% 0.49/0.68 tff(1166,plain,
% 0.49/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1175) | (~c3_1(a1175)) | (~c2_1(a1175)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199))),
% 0.49/0.68 inference(quant_inst,[status(thm)],[])).
% 0.49/0.68 tff(1167,plain,
% 0.49/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1199) | c3_1(a1199) | c0_1(a1175) | (~ndr1_0) | (~c3_1(a1175)) | (~c2_1(a1175)) | c1_1(a1199) | (~c2_1(a1199))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 0.49/0.68 tff(1168,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1167, 169, 839, 1161, 841, 840, 1133, 644, 1160, 1159])).
% 0.49/0.68 tff(1169,plain,((~hskp16) | (~c2_1(a1175)) | c0_1(a1175) | (~c3_1(a1175)) | hskp3 | (~c1_1(a1205)) | (~c3_1(a1205)) | c2_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(1170,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1169, 1158, 1142, 838, 1133, 22, 1132, 1131, 1130])).
% 0.49/0.68 tff(1171,plain,((~hskp4) | (~hskp16) | c0_1(a1175) | hskp3 | (~c1_1(a1205)) | (~c3_1(a1205)) | c2_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(1172,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1171, 1129, 1123, 1086, 22, 1059, 1051, 1043])).
% 0.49/0.68 tff(1173,plain,(hskp22 | hskp3 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(1174,plain,
% 0.49/0.68 (hskp3 | hskp14),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1173, 722])).
% 0.49/0.68 tff(1175,plain,
% 0.49/0.68 (hskp14),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1174, 22])).
% 0.49/0.68 tff(1176,plain,
% 0.49/0.68 (~c1_1(a1194)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[373, 1175])).
% 0.49/0.68 tff(1177,plain,
% 0.49/0.68 (~c0_1(a1194)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[379, 1175])).
% 0.49/0.68 tff(1178,plain,
% 0.49/0.68 (c2_1(a1178)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[932, 899])).
% 0.49/0.68 tff(1179,plain,
% 0.49/0.68 (c1_1(a1178)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[947, 899])).
% 0.49/0.68 tff(1180,plain,
% 0.49/0.68 (c2_1(a1194)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[387, 1175])).
% 0.49/0.68 tff(1181,plain,
% 0.49/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1194) | c1_1(a1194) | c3_1(a1178) | (~ndr1_0) | (~c2_1(a1178)) | (~c1_1(a1178)) | (~c3_1(a1194)) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1194) | c1_1(a1194) | c3_1(a1178) | (~ndr1_0) | (~c2_1(a1178)) | (~c1_1(a1178)) | (~c3_1(a1194)) | (~c2_1(a1194)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1182,plain,
% 0.49/0.68 (((~ndr1_0) | c3_1(a1178) | (~c1_1(a1178)) | (~c2_1(a1178)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194))) <=> (c0_1(a1194) | c1_1(a1194) | c3_1(a1178) | (~ndr1_0) | (~c2_1(a1178)) | (~c1_1(a1178)) | (~c3_1(a1194)) | (~c2_1(a1194)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1183,plain,
% 0.49/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1178) | (~c1_1(a1178)) | (~c2_1(a1178)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1194) | c1_1(a1194) | c3_1(a1178) | (~ndr1_0) | (~c2_1(a1178)) | (~c1_1(a1178)) | (~c3_1(a1194)) | (~c2_1(a1194))))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1182])).
% 0.49/0.68 tff(1184,plain,
% 0.49/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1178) | (~c1_1(a1178)) | (~c2_1(a1178)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1194) | c1_1(a1194) | c3_1(a1178) | (~ndr1_0) | (~c2_1(a1178)) | (~c1_1(a1178)) | (~c3_1(a1194)) | (~c2_1(a1194)))),
% 0.49/0.68 inference(transitivity,[status(thm)],[1183, 1181])).
% 0.49/0.68 tff(1185,plain,
% 0.49/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1178) | (~c1_1(a1178)) | (~c2_1(a1178)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))),
% 0.49/0.68 inference(quant_inst,[status(thm)],[])).
% 0.49/0.68 tff(1186,plain,
% 0.49/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1194) | c1_1(a1194) | c3_1(a1178) | (~ndr1_0) | (~c2_1(a1178)) | (~c1_1(a1178)) | (~c3_1(a1194)) | (~c2_1(a1194))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 0.49/0.68 tff(1187,plain,
% 0.49/0.68 (~c3_1(a1194)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1186, 169, 1180, 1179, 1178, 1177, 1176, 905, 21])).
% 0.49/0.68 tff(1188,plain,
% 0.49/0.68 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(1189,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[1188])).
% 0.49/0.68 tff(1190,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1191,plain,
% 0.49/0.68 (^[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))) <=> ((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(1192,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[1191])).
% 0.49/0.68 tff(1193,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 0.49/0.68 tff(1194,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 0.49/0.68 tff(1195,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1194, 1190])).
% 0.49/0.68 tff(1196,plain,(
% 0.49/0.68 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.49/0.68 inference(skolemize,[status(sab)],[1195])).
% 0.49/0.68 tff(1197,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1196, 1189])).
% 0.49/0.68 tff(1198,plain,
% 0.49/0.68 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(1199,plain,
% 0.49/0.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[1198])).
% 0.49/0.68 tff(1200,plain,
% 0.49/0.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1201,plain,
% 0.49/0.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(1202,plain,
% 0.49/0.68 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[1201])).
% 0.49/0.68 tff(1203,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 0.49/0.68 tff(1204,plain,
% 0.49/0.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 0.49/0.68 tff(1205,plain,
% 0.49/0.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1204, 1200])).
% 0.49/0.68 tff(1206,plain,(
% 0.49/0.68 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.68 inference(skolemize,[status(sab)],[1205])).
% 0.49/0.68 tff(1207,plain,
% 0.49/0.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1206, 1199])).
% 0.49/0.68 tff(1208,plain,
% 0.49/0.68 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | c1_1(a1200) | c2_1(a1200) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c2_1(a1194)) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp5 | c1_1(a1200) | c2_1(a1200) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c2_1(a1194)) | c3_1(a1200))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1209,plain,
% 0.49/0.68 ((hskp5 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200)) <=> (hskp5 | c1_1(a1200) | c2_1(a1200) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c2_1(a1194)) | c3_1(a1200))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1210,plain,
% 0.49/0.68 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | c1_1(a1200) | c2_1(a1200) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c2_1(a1194)) | c3_1(a1200)))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1209])).
% 0.49/0.68 tff(1211,plain,
% 0.49/0.68 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp5 | c1_1(a1200) | c2_1(a1200) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c2_1(a1194)) | c3_1(a1200))),
% 0.49/0.68 inference(transitivity,[status(thm)],[1210, 1208])).
% 0.49/0.68 tff(1212,plain,
% 0.49/0.68 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))),
% 0.49/0.68 inference(quant_inst,[status(thm)],[])).
% 0.49/0.68 tff(1213,plain,
% 0.49/0.68 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp5 | c1_1(a1200) | c2_1(a1200) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c2_1(a1194)) | c3_1(a1200)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 0.49/0.68 tff(1214,plain,
% 0.49/0.68 (hskp5),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1213, 169, 1180, 874, 873, 1177, 1176, 1207, 882])).
% 0.49/0.68 tff(1215,plain,
% 0.49/0.68 (((~hskp5) | c2_1(a1176)) <=> ((~hskp5) | c2_1(a1176))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1216,axiom,((~hskp5) | c2_1(a1176)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.49/0.68 tff(1217,plain,
% 0.49/0.68 ((~hskp5) | c2_1(a1176)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 0.49/0.68 tff(1218,plain,
% 0.49/0.68 ((~hskp5) | c2_1(a1176)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1217, 1215])).
% 0.49/0.68 tff(1219,plain,
% 0.49/0.68 ((~hskp5) | c2_1(a1176)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1218, 1215])).
% 0.49/0.68 tff(1220,plain,
% 0.49/0.68 ((~hskp5) | c2_1(a1176)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1219, 1215])).
% 0.49/0.68 tff(1221,plain,
% 0.49/0.68 ((~hskp5) | c2_1(a1176)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1220, 1215])).
% 0.49/0.68 tff(1222,plain,
% 0.49/0.68 (c2_1(a1176)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1221, 1214])).
% 0.49/0.68 tff(1223,plain,
% 0.49/0.68 (((~hskp5) | c0_1(a1176)) <=> ((~hskp5) | c0_1(a1176))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1224,axiom,((~hskp5) | c0_1(a1176)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.49/0.68 tff(1225,plain,
% 0.49/0.68 ((~hskp5) | c0_1(a1176)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 0.49/0.68 tff(1226,plain,
% 0.49/0.68 ((~hskp5) | c0_1(a1176)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1225, 1223])).
% 0.49/0.68 tff(1227,plain,
% 0.49/0.68 ((~hskp5) | c0_1(a1176)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1226, 1223])).
% 0.49/0.68 tff(1228,plain,
% 0.49/0.68 ((~hskp5) | c0_1(a1176)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1227, 1223])).
% 0.49/0.68 tff(1229,plain,
% 0.49/0.68 ((~hskp5) | c0_1(a1176)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1228, 1223])).
% 0.49/0.68 tff(1230,plain,
% 0.49/0.68 (c0_1(a1176)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1229, 1214])).
% 0.49/0.68 tff(1231,plain,
% 0.49/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a1200) | c0_1(a1194) | (~ndr1_0) | (~c1_1(a1176)) | (~c2_1(a1176)) | (~c0_1(a1176)) | c3_1(a1194) | (~c2_1(a1194)) | c3_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a1200) | c0_1(a1194) | (~ndr1_0) | (~c1_1(a1176)) | (~c2_1(a1176)) | (~c0_1(a1176)) | c3_1(a1194) | (~c2_1(a1194)) | c3_1(a1200) | (~c0_1(a1200)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1232,plain,
% 0.49/0.68 (((~ndr1_0) | (~c0_1(a1176)) | (~c1_1(a1176)) | (~c2_1(a1176)) | c2_1(a1200) | c3_1(a1200) | (~c0_1(a1200)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194))) <=> (c2_1(a1200) | c0_1(a1194) | (~ndr1_0) | (~c1_1(a1176)) | (~c2_1(a1176)) | (~c0_1(a1176)) | c3_1(a1194) | (~c2_1(a1194)) | c3_1(a1200) | (~c0_1(a1200)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1233,plain,
% 0.49/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a1176)) | (~c1_1(a1176)) | (~c2_1(a1176)) | c2_1(a1200) | c3_1(a1200) | (~c0_1(a1200)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a1200) | c0_1(a1194) | (~ndr1_0) | (~c1_1(a1176)) | (~c2_1(a1176)) | (~c0_1(a1176)) | c3_1(a1194) | (~c2_1(a1194)) | c3_1(a1200) | (~c0_1(a1200))))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1232])).
% 0.49/0.68 tff(1234,plain,
% 0.49/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a1176)) | (~c1_1(a1176)) | (~c2_1(a1176)) | c2_1(a1200) | c3_1(a1200) | (~c0_1(a1200)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a1200) | c0_1(a1194) | (~ndr1_0) | (~c1_1(a1176)) | (~c2_1(a1176)) | (~c0_1(a1176)) | c3_1(a1194) | (~c2_1(a1194)) | c3_1(a1200) | (~c0_1(a1200)))),
% 0.49/0.68 inference(transitivity,[status(thm)],[1233, 1231])).
% 0.49/0.68 tff(1235,plain,
% 0.49/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a1176)) | (~c1_1(a1176)) | (~c2_1(a1176)) | c2_1(a1200) | c3_1(a1200) | (~c0_1(a1200)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.49/0.68 inference(quant_inst,[status(thm)],[])).
% 0.49/0.68 tff(1236,plain,
% 0.49/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a1200) | c0_1(a1194) | (~ndr1_0) | (~c1_1(a1176)) | (~c2_1(a1176)) | (~c0_1(a1176)) | c3_1(a1194) | (~c2_1(a1194)) | c3_1(a1200) | (~c0_1(a1200))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1235, 1234])).
% 0.49/0.68 tff(1237,plain,
% 0.49/0.68 (~c1_1(a1176)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1236, 169, 875, 1180, 1230, 1222, 873, 1177, 1197, 1187, 882])).
% 0.49/0.68 tff(1238,plain,
% 0.49/0.68 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(1239,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[1238])).
% 0.49/0.69 tff(1240,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1241,plain,
% 0.49/0.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp26))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(1242,plain,
% 0.49/0.69 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[1241])).
% 0.49/0.69 tff(1243,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 0.49/0.69 tff(1244,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1243, 1242])).
% 0.49/0.69 tff(1245,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1244, 1240])).
% 0.49/0.69 tff(1246,plain,(
% 0.49/0.69 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.69 inference(skolemize,[status(sab)],[1245])).
% 0.49/0.69 tff(1247,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1246, 1239])).
% 0.49/0.69 tff(1248,plain,
% 0.49/0.69 (((~hskp5) | (~c3_1(a1176))) <=> ((~hskp5) | (~c3_1(a1176)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1249,plain,
% 0.49/0.69 (((~c3_1(a1176)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a1176)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1250,axiom,((~c3_1(a1176)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.49/0.69 tff(1251,plain,
% 0.49/0.69 ((~hskp5) | (~c3_1(a1176))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 0.49/0.69 tff(1252,plain,
% 0.49/0.69 ((~hskp5) | (~c3_1(a1176))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1251, 1248])).
% 0.49/0.69 tff(1253,plain,
% 0.49/0.69 (~c3_1(a1176)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1252, 1214])).
% 0.49/0.69 tff(1254,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp26 | c1_1(a1200) | c2_1(a1200) | c3_1(a1176) | (~ndr1_0) | c1_1(a1176) | (~c2_1(a1176)) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp26 | c1_1(a1200) | c2_1(a1200) | c3_1(a1176) | (~ndr1_0) | c1_1(a1176) | (~c2_1(a1176)) | c3_1(a1200))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1255,plain,
% 0.49/0.69 ((hskp26 | (~ndr1_0) | c3_1(a1176) | c1_1(a1176) | (~c2_1(a1176)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200)) <=> (hskp26 | c1_1(a1200) | c2_1(a1200) | c3_1(a1176) | (~ndr1_0) | c1_1(a1176) | (~c2_1(a1176)) | c3_1(a1200))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1256,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp26 | (~ndr1_0) | c3_1(a1176) | c1_1(a1176) | (~c2_1(a1176)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp26 | c1_1(a1200) | c2_1(a1200) | c3_1(a1176) | (~ndr1_0) | c1_1(a1176) | (~c2_1(a1176)) | c3_1(a1200)))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1255])).
% 0.49/0.69 tff(1257,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp26 | (~ndr1_0) | c3_1(a1176) | c1_1(a1176) | (~c2_1(a1176)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp26 | c1_1(a1200) | c2_1(a1200) | c3_1(a1176) | (~ndr1_0) | c1_1(a1176) | (~c2_1(a1176)) | c3_1(a1200))),
% 0.49/0.69 inference(transitivity,[status(thm)],[1256, 1254])).
% 0.49/0.69 tff(1258,plain,
% 0.49/0.69 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp26 | (~ndr1_0) | c3_1(a1176) | c1_1(a1176) | (~c2_1(a1176)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(1259,plain,
% 0.49/0.69 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp26 | c1_1(a1200) | c2_1(a1200) | c3_1(a1176) | (~ndr1_0) | c1_1(a1176) | (~c2_1(a1176)) | c3_1(a1200)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 0.49/0.69 tff(1260,plain,
% 0.49/0.69 (hskp26 | c1_1(a1176)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1259, 169, 1222, 874, 873, 1253, 1247, 882])).
% 0.49/0.69 tff(1261,plain,
% 0.49/0.69 (hskp26),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1260, 1237])).
% 0.49/0.69 tff(1262,plain,
% 0.49/0.69 (((~hskp26) | c3_1(a1190)) <=> ((~hskp26) | c3_1(a1190))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1263,axiom,((~hskp26) | c3_1(a1190)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.49/0.69 tff(1264,plain,
% 0.49/0.69 ((~hskp26) | c3_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1263, 1262])).
% 0.49/0.69 tff(1265,plain,
% 0.49/0.69 ((~hskp26) | c3_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1264, 1262])).
% 0.49/0.69 tff(1266,plain,
% 0.49/0.69 ((~hskp26) | c3_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1265, 1262])).
% 0.49/0.69 tff(1267,plain,
% 0.49/0.69 ((~hskp26) | c3_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1266, 1262])).
% 0.49/0.69 tff(1268,plain,
% 0.49/0.69 ((~hskp26) | c3_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1267, 1262])).
% 0.49/0.69 tff(1269,plain,
% 0.49/0.69 (c3_1(a1190)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1268, 1261])).
% 0.49/0.69 tff(1270,plain,
% 0.49/0.69 (((~hskp26) | c1_1(a1190)) <=> ((~hskp26) | c1_1(a1190))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1271,axiom,((~hskp26) | c1_1(a1190)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.49/0.69 tff(1272,plain,
% 0.49/0.69 ((~hskp26) | c1_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 0.49/0.69 tff(1273,plain,
% 0.49/0.69 ((~hskp26) | c1_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1272, 1270])).
% 0.49/0.69 tff(1274,plain,
% 0.49/0.69 ((~hskp26) | c1_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1273, 1270])).
% 0.49/0.69 tff(1275,plain,
% 0.49/0.69 ((~hskp26) | c1_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1274, 1270])).
% 0.49/0.69 tff(1276,plain,
% 0.49/0.69 ((~hskp26) | c1_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1275, 1270])).
% 0.49/0.69 tff(1277,plain,
% 0.49/0.69 (c1_1(a1190)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1276, 1261])).
% 0.49/0.69 tff(1278,plain,
% 0.49/0.69 (((~hskp26) | c0_1(a1190)) <=> ((~hskp26) | c0_1(a1190))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1279,axiom,((~hskp26) | c0_1(a1190)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.49/0.69 tff(1280,plain,
% 0.49/0.69 ((~hskp26) | c0_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 0.49/0.69 tff(1281,plain,
% 0.49/0.69 ((~hskp26) | c0_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1280, 1278])).
% 0.49/0.69 tff(1282,plain,
% 0.49/0.69 ((~hskp26) | c0_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1281, 1278])).
% 0.49/0.69 tff(1283,plain,
% 0.49/0.69 ((~hskp26) | c0_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1282, 1278])).
% 0.49/0.69 tff(1284,plain,
% 0.49/0.69 ((~hskp26) | c0_1(a1190)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1283, 1278])).
% 0.49/0.69 tff(1285,plain,
% 0.49/0.69 (c0_1(a1190)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1284, 1261])).
% 0.49/0.69 tff(1286,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c3_1(a1190)) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c0_1(a1200)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c3_1(a1190)) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c0_1(a1200)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1287,plain,
% 0.49/0.69 (((~ndr1_0) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c3_1(a1190)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200))) <=> (c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c3_1(a1190)) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c0_1(a1200)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1288,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c3_1(a1190)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c3_1(a1190)) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c0_1(a1200))))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1287])).
% 0.49/0.69 tff(1289,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c3_1(a1190)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c3_1(a1190)) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c0_1(a1200)))),
% 0.49/0.69 inference(transitivity,[status(thm)],[1288, 1286])).
% 0.49/0.69 tff(1290,plain,
% 0.49/0.69 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c3_1(a1190)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(1291,plain,
% 0.49/0.69 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c3_1(a1190)) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c0_1(a1200))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 0.49/0.69 tff(1292,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1291, 169, 1285, 1277, 1269, 875, 874, 873, 10])).
% 0.49/0.69 tff(1293,plain,(hskp3), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(1294,plain,
% 0.49/0.69 (~c3_1(a1174)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[246, 1293])).
% 0.49/0.69 tff(1295,plain,
% 0.49/0.69 ((~hskp3) | hskp14),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[281, 722])).
% 0.49/0.69 tff(1296,plain,
% 0.49/0.69 (hskp14),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1295, 1293])).
% 0.49/0.69 tff(1297,plain,
% 0.49/0.69 (~c1_1(a1194)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[373, 1296])).
% 0.49/0.69 tff(1298,plain,
% 0.49/0.69 (~c0_1(a1194)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[379, 1296])).
% 0.49/0.69 tff(1299,plain,
% 0.49/0.69 (c1_1(a1174)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[308, 1293])).
% 0.49/0.69 tff(1300,plain,
% 0.49/0.69 (c2_1(a1194)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[387, 1296])).
% 0.49/0.69 tff(1301,plain,
% 0.49/0.69 ((~c2_1(a1174)) | (~c3_1(a1194))),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[461, 169, 1300, 1299, 1298, 1297, 1294, 21])).
% 0.49/0.69 tff(1302,plain,
% 0.49/0.69 (~c3_1(a1194)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1301, 11])).
% 0.49/0.69 tff(1303,assumption,(~c0_1(a1182)), introduced(assumption)).
% 0.49/0.69 tff(1304,plain,
% 0.49/0.69 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(1305,plain,
% 0.49/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_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) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[1304])).
% 0.49/0.69 tff(1306,plain,
% 0.49/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_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) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1307,plain,
% 0.49/0.69 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(1308,plain,
% 0.49/0.69 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[1307])).
% 0.49/0.69 tff(1309,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.49/0.69 tff(1310,plain,
% 0.49/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1309, 1308])).
% 0.49/0.69 tff(1311,plain,
% 0.49/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1310, 1306])).
% 0.49/0.69 tff(1312,plain,(
% 0.49/0.69 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.49/0.69 inference(skolemize,[status(sab)],[1311])).
% 0.49/0.69 tff(1313,plain,
% 0.49/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1312, 1305])).
% 0.49/0.69 tff(1314,plain,
% 0.49/0.69 (c0_1(a1174)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[254, 1293])).
% 0.49/0.69 tff(1315,plain,
% 0.49/0.69 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(1316,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[1315])).
% 0.49/0.69 tff(1317,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1318,plain,
% 0.49/0.69 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp25) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp25))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(1319,plain,
% 0.49/0.69 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[1318])).
% 0.49/0.69 tff(1320,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 0.49/0.69 tff(1321,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 0.49/0.69 tff(1322,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1321, 1317])).
% 0.49/0.69 tff(1323,plain,(
% 0.49/0.69 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.49/0.69 inference(skolemize,[status(sab)],[1322])).
% 0.49/0.69 tff(1324,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1323, 1316])).
% 0.49/0.69 tff(1325,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp25 | c3_1(a1174) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c1_1(a1174)) | (~c0_1(a1174)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp25 | c3_1(a1174) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c1_1(a1174)) | (~c0_1(a1174)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1326,plain,
% 0.49/0.69 ((hskp25 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1168) | (~c1_1(a1168)) | (~c0_1(a1168))) <=> (hskp25 | c3_1(a1174) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c1_1(a1174)) | (~c0_1(a1174)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1327,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1168) | (~c1_1(a1168)) | (~c0_1(a1168)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp25 | c3_1(a1174) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c1_1(a1174)) | (~c0_1(a1174))))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1326])).
% 0.49/0.69 tff(1328,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1168) | (~c1_1(a1168)) | (~c0_1(a1168)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp25 | c3_1(a1174) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c1_1(a1174)) | (~c0_1(a1174)))),
% 0.49/0.69 inference(transitivity,[status(thm)],[1327, 1325])).
% 0.49/0.69 tff(1329,plain,
% 0.49/0.69 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1168) | (~c1_1(a1168)) | (~c0_1(a1168)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(1330,plain,
% 0.49/0.69 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp25 | c3_1(a1174) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c1_1(a1174)) | (~c0_1(a1174))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1329, 1328])).
% 0.49/0.69 tff(1331,plain,
% 0.49/0.69 (hskp25),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1330, 169, 1314, 1299, 509, 501, 1294, 492, 1324])).
% 0.49/0.69 tff(1332,plain,
% 0.49/0.69 (((~hskp25) | c3_1(a1182)) <=> ((~hskp25) | c3_1(a1182))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1333,axiom,((~hskp25) | c3_1(a1182)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.49/0.70 tff(1334,plain,
% 0.49/0.70 ((~hskp25) | c3_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 0.49/0.70 tff(1335,plain,
% 0.49/0.70 ((~hskp25) | c3_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1334, 1332])).
% 0.49/0.70 tff(1336,plain,
% 0.49/0.70 ((~hskp25) | c3_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1335, 1332])).
% 0.49/0.70 tff(1337,plain,
% 0.49/0.70 ((~hskp25) | c3_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1336, 1332])).
% 0.49/0.70 tff(1338,plain,
% 0.49/0.70 ((~hskp25) | c3_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1337, 1332])).
% 0.49/0.70 tff(1339,plain,
% 0.49/0.70 (c3_1(a1182)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1338, 1331])).
% 0.49/0.70 tff(1340,plain,
% 0.49/0.70 (((~hskp25) | c1_1(a1182)) <=> ((~hskp25) | c1_1(a1182))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1341,axiom,((~hskp25) | c1_1(a1182)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 0.49/0.70 tff(1342,plain,
% 0.49/0.70 ((~hskp25) | c1_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 0.49/0.70 tff(1343,plain,
% 0.49/0.70 ((~hskp25) | c1_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1342, 1340])).
% 0.49/0.70 tff(1344,plain,
% 0.49/0.70 ((~hskp25) | c1_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1343, 1340])).
% 0.49/0.70 tff(1345,plain,
% 0.49/0.70 ((~hskp25) | c1_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1344, 1340])).
% 0.49/0.70 tff(1346,plain,
% 0.49/0.70 ((~hskp25) | c1_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1345, 1340])).
% 0.49/0.70 tff(1347,plain,
% 0.49/0.70 (c1_1(a1182)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1346, 1331])).
% 0.49/0.70 tff(1348,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1349,plain,
% 0.49/0.70 (((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c3_1(a1174) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182))) <=> (c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1350,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c3_1(a1174) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1349])).
% 0.49/0.70 tff(1351,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c3_1(a1174) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[1350, 1348])).
% 0.49/0.70 tff(1352,plain,
% 0.49/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c3_1(a1174) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(1353,plain,
% 0.49/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 0.49/0.70 tff(1354,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1353, 169, 1347, 1339, 1314, 1299, 1294, 1313, 11, 1303])).
% 0.49/0.70 tff(1355,plain,(c0_1(a1182) | (~c2_1(a1174))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(1356,plain,
% 0.49/0.70 (c0_1(a1182)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1355, 11])).
% 0.49/0.70 tff(1357,plain,
% 0.49/0.70 (((~hskp25) | c2_1(a1182)) <=> ((~hskp25) | c2_1(a1182))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1358,axiom,((~hskp25) | c2_1(a1182)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.49/0.70 tff(1359,plain,
% 0.49/0.70 ((~hskp25) | c2_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 0.49/0.70 tff(1360,plain,
% 0.49/0.70 ((~hskp25) | c2_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1359, 1357])).
% 0.49/0.70 tff(1361,plain,
% 0.49/0.70 ((~hskp25) | c2_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1360, 1357])).
% 0.49/0.70 tff(1362,plain,
% 0.49/0.70 ((~hskp25) | c2_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1361, 1357])).
% 0.49/0.70 tff(1363,plain,
% 0.49/0.70 ((~hskp25) | c2_1(a1182)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1362, 1357])).
% 0.49/0.70 tff(1364,plain,
% 0.49/0.70 (c2_1(a1182)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1363, 1331])).
% 0.49/0.70 tff(1365,plain,
% 0.49/0.70 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1182)) | (~c0_1(a1182)) | (~c2_1(a1182)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1182)) | (~c0_1(a1182)) | (~c2_1(a1182)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1366,plain,
% 0.49/0.70 ((hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1182)) | (~c3_1(a1182)) | (~c2_1(a1182))) <=> (hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1182)) | (~c0_1(a1182)) | (~c2_1(a1182)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1367,plain,
% 0.49/0.70 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1182)) | (~c3_1(a1182)) | (~c2_1(a1182)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1182)) | (~c0_1(a1182)) | (~c2_1(a1182))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1366])).
% 0.49/0.70 tff(1368,plain,
% 0.49/0.70 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1182)) | (~c3_1(a1182)) | (~c2_1(a1182)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1182)) | (~c0_1(a1182)) | (~c2_1(a1182)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[1367, 1365])).
% 0.49/0.70 tff(1369,plain,
% 0.49/0.70 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1182)) | (~c3_1(a1182)) | (~c2_1(a1182)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(1370,plain,
% 0.49/0.70 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1182)) | (~c0_1(a1182)) | (~c2_1(a1182))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 0.49/0.70 tff(1371,plain,
% 0.49/0.70 (hskp2 | (~c0_1(a1182))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1370, 169, 722, 1364, 1339, 741])).
% 0.49/0.70 tff(1372,plain,
% 0.49/0.70 (hskp2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1371, 1356])).
% 0.49/0.70 tff(1373,plain,
% 0.49/0.70 (~c0_1(a1172)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[650, 1372])).
% 0.49/0.70 tff(1374,plain,
% 0.49/0.70 (c3_1(a1172)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[660, 1372])).
% 0.49/0.70 tff(1375,plain,
% 0.49/0.70 (c2_1(a1172)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[668, 1372])).
% 0.49/0.70 tff(1376,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1194) | c1_1(a1194) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c3_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1194) | c1_1(a1194) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1377,plain,
% 0.49/0.70 (((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194)) <=> (c0_1(a1194) | c1_1(a1194) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1378,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1194) | c1_1(a1194) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c3_1(a1194) | (~c2_1(a1194))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1377])).
% 0.49/0.70 tff(1379,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1194) | c1_1(a1194) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[1378, 1376])).
% 0.49/0.70 tff(1380,plain,
% 0.49/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(1381,plain,
% 0.49/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1194) | c1_1(a1194) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c3_1(a1194) | (~c2_1(a1194))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 0.49/0.70 tff(1382,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1381, 169, 1300, 1375, 1374, 1298, 1297, 1373, 644, 1302])).
% 0.49/0.70 tff(1383,plain,(~c2_1(a1174)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(1384,plain,
% 0.49/0.70 (hskp17 | c2_1(a1174)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[479, 169, 722, 1314, 1294, 472])).
% 0.49/0.70 tff(1385,plain,
% 0.49/0.70 (hskp17),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1384, 1383])).
% 0.49/0.70 tff(1386,plain,
% 0.49/0.70 (~c2_1(a1200)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[335, 1385])).
% 0.49/0.70 tff(1387,plain,
% 0.49/0.70 (~c1_1(a1200)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[341, 1385])).
% 0.49/0.70 tff(1388,plain,
% 0.49/0.70 (c0_1(a1200)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[349, 1385])).
% 0.49/0.70 tff(1389,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | (~c3_1(a1200)) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | (~c3_1(a1200)) | (~c0_1(a1200)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1390,plain,
% 0.49/0.70 (((~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200))) <=> (c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | (~c3_1(a1200)) | (~c0_1(a1200)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1391,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | (~c3_1(a1200)) | (~c0_1(a1200))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1390])).
% 0.49/0.70 tff(1392,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | (~c3_1(a1200)) | (~c0_1(a1200)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[1391, 1389])).
% 0.49/0.70 tff(1393,plain,
% 0.49/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(1394,plain,
% 0.49/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | (~c3_1(a1200)) | (~c0_1(a1200))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 0.49/0.70 tff(1395,plain,
% 0.49/0.70 (~c3_1(a1200)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1394, 169, 1388, 1314, 1299, 1387, 1386, 57, 1383])).
% 0.49/0.70 tff(1396,plain,
% 0.49/0.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp6 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | c3_1(a1200))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1397,plain,
% 0.49/0.70 ((hskp6 | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200)) <=> (hskp6 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | c3_1(a1200))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1398,plain,
% 0.49/0.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | c3_1(a1200)))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1397])).
% 0.49/0.70 tff(1399,plain,
% 0.49/0.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp6 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | c3_1(a1200))),
% 0.49/0.71 inference(transitivity,[status(thm)],[1398, 1396])).
% 0.49/0.71 tff(1400,plain,
% 0.49/0.71 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(1401,plain,
% 0.49/0.71 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp6 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | c3_1(a1200)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 0.49/0.71 tff(1402,plain,
% 0.49/0.71 (hskp6),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1401, 169, 1314, 1299, 1387, 1386, 892, 1383, 1395])).
% 0.49/0.71 tff(1403,plain,
% 0.49/0.71 (~c3_1(a1178)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[904, 1402])).
% 0.49/0.71 tff(1404,plain,
% 0.49/0.71 (c2_1(a1178)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[932, 1402])).
% 0.49/0.71 tff(1405,plain,
% 0.49/0.71 (c1_1(a1178)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[947, 1402])).
% 0.49/0.71 tff(1406,plain,
% 0.49/0.71 (~c3_1(a1194)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1186, 169, 1300, 1405, 1404, 1298, 1297, 1403, 21])).
% 0.49/0.71 tff(1407,plain,
% 0.49/0.71 (hskp5),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1213, 169, 1300, 1387, 1386, 1298, 1297, 1207, 1395])).
% 0.49/0.71 tff(1408,plain,
% 0.49/0.71 (c2_1(a1176)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1221, 1407])).
% 0.49/0.71 tff(1409,plain,
% 0.49/0.71 (c0_1(a1176)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1229, 1407])).
% 0.49/0.71 tff(1410,plain,
% 0.49/0.71 (~c1_1(a1176)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1236, 169, 1388, 1300, 1409, 1408, 1386, 1298, 1197, 1406, 1395])).
% 0.49/0.71 tff(1411,plain,
% 0.49/0.71 (~c3_1(a1176)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1252, 1407])).
% 0.49/0.71 tff(1412,plain,
% 0.49/0.71 (hskp26 | c1_1(a1176)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1259, 169, 1408, 1387, 1386, 1411, 1247, 1395])).
% 0.49/0.71 tff(1413,plain,
% 0.49/0.71 (hskp26),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1412, 1410])).
% 0.49/0.71 tff(1414,plain,
% 0.49/0.71 (c3_1(a1190)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1268, 1413])).
% 0.49/0.71 tff(1415,plain,
% 0.49/0.71 (c1_1(a1190)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1276, 1413])).
% 0.49/0.71 tff(1416,plain,
% 0.49/0.71 (c0_1(a1190)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1284, 1413])).
% 0.49/0.71 tff(1417,plain,
% 0.49/0.71 ($false),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1291, 169, 1416, 1415, 1414, 1388, 1387, 1386, 10])).
% 0.49/0.71 % SZS output end Proof
% 0.49/0.71 % E exiting
%------------------------------------------------------------------------------