%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN501-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:39:22 AM UTC 2025
% Result : Unsatisfiable 0.85s 1.02s
% Output : Proof 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN501-1 : TPTP v9.0.0. Released v2.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:38:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.85/1.02 % SZS status Unsatisfiable
% 0.85/1.02 % SZS output start Proof
% 0.85/1.02 tff(c3_1_type, type, (
% 0.85/1.02 c3_1: $i > $o)).
% 0.85/1.02 tff(a108_type, type, (
% 0.85/1.02 a108: $i)).
% 0.85/1.02 tff(a129_type, type, (
% 0.85/1.02 a129: $i)).
% 0.85/1.02 tff(c2_1_type, type, (
% 0.85/1.02 c2_1: $i > $o)).
% 0.85/1.02 tff(c0_1_type, type, (
% 0.85/1.02 c0_1: $i > $o)).
% 0.85/1.02 tff(c1_1_type, type, (
% 0.85/1.02 c1_1: $i > $o)).
% 0.85/1.02 tff(ndr1_0_type, type, (
% 0.85/1.02 ndr1_0: $o)).
% 0.85/1.02 tff(hskp18_type, type, (
% 0.85/1.02 hskp18: $o)).
% 0.85/1.02 tff(a130_type, type, (
% 0.85/1.02 a130: $i)).
% 0.85/1.02 tff(a132_type, type, (
% 0.85/1.02 a132: $i)).
% 0.85/1.02 tff(hskp19_type, type, (
% 0.85/1.02 hskp19: $o)).
% 0.85/1.02 tff(hskp20_type, type, (
% 0.85/1.02 hskp20: $o)).
% 0.85/1.02 tff(hskp4_type, type, (
% 0.85/1.02 hskp4: $o)).
% 0.85/1.02 tff(hskp0_type, type, (
% 0.85/1.02 hskp0: $o)).
% 0.85/1.02 tff(a97_type, type, (
% 0.85/1.02 a97: $i)).
% 0.85/1.02 tff(a124_type, type, (
% 0.85/1.02 a124: $i)).
% 0.85/1.02 tff(hskp17_type, type, (
% 0.85/1.02 hskp17: $o)).
% 0.85/1.02 tff(a106_type, type, (
% 0.85/1.02 a106: $i)).
% 0.85/1.02 tff(hskp7_type, type, (
% 0.85/1.02 hskp7: $o)).
% 0.85/1.02 tff(a138_type, type, (
% 0.85/1.02 a138: $i)).
% 0.85/1.02 tff(a137_type, type, (
% 0.85/1.02 a137: $i)).
% 0.85/1.02 tff(hskp28_type, type, (
% 0.85/1.02 hskp28: $o)).
% 0.85/1.02 tff(a103_type, type, (
% 0.85/1.02 a103: $i)).
% 0.85/1.02 tff(a112_type, type, (
% 0.85/1.02 a112: $i)).
% 0.85/1.02 tff(hskp11_type, type, (
% 0.85/1.03 hskp11: $o)).
% 0.85/1.03 tff(hskp22_type, type, (
% 0.85/1.03 hskp22: $o)).
% 0.85/1.03 tff(a173_type, type, (
% 0.85/1.03 a173: $i)).
% 0.85/1.03 tff(a136_type, type, (
% 0.85/1.03 a136: $i)).
% 0.85/1.03 tff(hskp16_type, type, (
% 0.85/1.03 hskp16: $o)).
% 0.85/1.03 tff(a122_type, type, (
% 0.85/1.03 a122: $i)).
% 0.85/1.03 tff(hskp21_type, type, (
% 0.85/1.03 hskp21: $o)).
% 0.85/1.03 tff(hskp25_type, type, (
% 0.85/1.03 hskp25: $o)).
% 0.85/1.03 tff(a105_type, type, (
% 0.85/1.03 a105: $i)).
% 0.85/1.03 tff(hskp6_type, type, (
% 0.85/1.03 hskp6: $o)).
% 0.85/1.03 tff(hskp2_type, type, (
% 0.85/1.03 hskp2: $o)).
% 0.85/1.03 tff(a99_type, type, (
% 0.85/1.03 a99: $i)).
% 0.85/1.03 tff(a107_type, type, (
% 0.85/1.03 a107: $i)).
% 0.85/1.03 tff(hskp8_type, type, (
% 0.85/1.03 hskp8: $o)).
% 0.85/1.03 tff(a104_type, type, (
% 0.85/1.03 a104: $i)).
% 0.85/1.03 tff(hskp5_type, type, (
% 0.85/1.03 hskp5: $o)).
% 0.85/1.03 tff(hskp9_type, type, (
% 0.85/1.03 hskp9: $o)).
% 0.85/1.03 tff(a98_type, type, (
% 0.85/1.03 a98: $i)).
% 0.85/1.03 tff(hskp1_type, type, (
% 0.85/1.03 hskp1: $o)).
% 0.85/1.03 tff(a101_type, type, (
% 0.85/1.03 a101: $i)).
% 0.85/1.03 tff(hskp27_type, type, (
% 0.85/1.03 hskp27: $o)).
% 0.85/1.03 tff(a147_type, type, (
% 0.85/1.03 a147: $i)).
% 0.85/1.03 tff(hskp24_type, type, (
% 0.85/1.03 hskp24: $o)).
% 0.85/1.03 tff(1,plain,
% 0.85/1.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(2,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[1])).
% 0.85/1.03 tff(3,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(4,plain,
% 0.85/1.03 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(5,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[4])).
% 0.85/1.03 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 0.85/1.03 tff(7,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.85/1.03 tff(8,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.85/1.03 tff(9,plain,(
% 0.85/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(skolemize,[status(sab)],[8])).
% 0.85/1.03 tff(10,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.85/1.03 tff(11,plain,
% 0.85/1.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(12,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[11])).
% 0.85/1.03 tff(13,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(14,plain,
% 0.85/1.03 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(15,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[14])).
% 0.85/1.03 tff(16,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 0.85/1.03 tff(17,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.85/1.03 tff(18,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.85/1.03 tff(19,plain,(
% 0.85/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(skolemize,[status(sab)],[18])).
% 0.85/1.03 tff(20,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.85/1.03 tff(21,plain,
% 0.85/1.03 (^[U: $i] : refl((hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(22,plain,
% 0.85/1.03 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[21])).
% 0.85/1.03 tff(23,plain,
% 0.85/1.03 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(24,plain,
% 0.85/1.03 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19) <=> ((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp19))), rewrite(((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(25,plain,
% 0.85/1.03 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[24])).
% 0.85/1.03 tff(26,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.85/1.03 tff(27,plain,
% 0.85/1.03 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.85/1.03 tff(28,plain,
% 0.85/1.03 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.85/1.03 tff(29,plain,(
% 0.85/1.03 ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.85/1.03 inference(skolemize,[status(sab)],[28])).
% 0.85/1.03 tff(30,plain,
% 0.85/1.03 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.85/1.03 tff(31,assumption,(~c2_1(a97)), introduced(assumption)).
% 0.85/1.03 tff(32,plain,
% 0.85/1.03 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(33,plain,
% 0.85/1.03 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[32])).
% 0.85/1.03 tff(34,plain,
% 0.85/1.03 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(35,plain,
% 0.85/1.03 (^[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(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(36,plain,
% 0.85/1.03 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[35])).
% 0.85/1.03 tff(37,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 0.85/1.03 tff(38,plain,
% 0.85/1.03 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.85/1.03 tff(39,plain,
% 0.85/1.03 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.85/1.03 tff(40,plain,(
% 0.85/1.03 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.85/1.03 inference(skolemize,[status(sab)],[39])).
% 0.85/1.03 tff(41,plain,
% 0.85/1.03 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.85/1.03 tff(42,plain,
% 0.85/1.03 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(43,plain,
% 0.85/1.03 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[42])).
% 0.85/1.03 tff(44,plain,
% 0.85/1.03 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(45,plain,
% 0.85/1.03 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp17) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp17))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(46,plain,
% 0.85/1.03 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[45])).
% 0.85/1.03 tff(47,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 0.85/1.03 tff(48,plain,
% 0.85/1.03 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.85/1.03 tff(49,plain,
% 0.85/1.03 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.85/1.03 tff(50,plain,(
% 0.85/1.03 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.03 inference(skolemize,[status(sab)],[49])).
% 0.85/1.03 tff(51,plain,
% 0.85/1.03 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.85/1.03 tff(52,assumption,(~hskp18), introduced(assumption)).
% 0.85/1.03 tff(53,assumption,(~c3_1(a97)), introduced(assumption)).
% 0.85/1.03 tff(54,assumption,(~c0_1(a97)), introduced(assumption)).
% 0.85/1.03 tff(55,plain,
% 0.85/1.03 (((~hskp0) | c0_1(a97)) <=> ((~hskp0) | c0_1(a97))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(56,axiom,((~hskp0) | c0_1(a97)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.85/1.03 tff(57,plain,
% 0.85/1.03 ((~hskp0) | c0_1(a97)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.85/1.03 tff(58,plain,
% 0.85/1.03 ((~hskp0) | c0_1(a97)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[57, 55])).
% 0.85/1.03 tff(59,plain,
% 0.85/1.03 ((~hskp0) | c0_1(a97)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.85/1.03 tff(60,plain,
% 0.85/1.03 ((~hskp0) | c0_1(a97)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.85/1.03 tff(61,plain,
% 0.85/1.03 ((~hskp0) | c0_1(a97)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.85/1.03 tff(62,plain,
% 0.85/1.03 (~hskp0),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[61, 54])).
% 0.85/1.03 tff(63,plain,
% 0.85/1.03 (^[U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(64,plain,
% 0.85/1.03 (![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[63])).
% 0.85/1.03 tff(65,plain,
% 0.85/1.03 (![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(66,plain,
% 0.85/1.03 (^[U: $i] : 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)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(67,plain,
% 0.85/1.03 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[66])).
% 0.85/1.03 tff(68,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 0.85/1.03 tff(69,plain,
% 0.85/1.03 (![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.85/1.03 tff(70,plain,
% 0.85/1.03 (![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.85/1.03 tff(71,plain,(
% 0.85/1.03 ![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(skolemize,[status(sab)],[70])).
% 0.85/1.03 tff(72,plain,
% 0.85/1.03 (![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.85/1.03 tff(73,assumption,(hskp4), introduced(assumption)).
% 0.85/1.03 tff(74,plain,
% 0.85/1.03 (((~hskp4) | (~c3_1(a103))) <=> ((~hskp4) | (~c3_1(a103)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(75,plain,
% 0.85/1.03 (((~c3_1(a103)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a103)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(76,axiom,((~c3_1(a103)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.85/1.03 tff(77,plain,
% 0.85/1.03 ((~hskp4) | (~c3_1(a103))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.85/1.03 tff(78,plain,
% 0.85/1.03 ((~hskp4) | (~c3_1(a103))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[77, 74])).
% 0.85/1.03 tff(79,plain,
% 0.85/1.03 (~c3_1(a103)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[78, 73])).
% 0.85/1.03 tff(80,plain,
% 0.85/1.03 (((~hskp4) | c0_1(a103)) <=> ((~hskp4) | c0_1(a103))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(81,axiom,((~hskp4) | c0_1(a103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.85/1.03 tff(82,plain,
% 0.85/1.03 ((~hskp4) | c0_1(a103)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.85/1.03 tff(83,plain,
% 0.85/1.03 ((~hskp4) | c0_1(a103)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[82, 80])).
% 0.85/1.03 tff(84,plain,
% 0.85/1.03 ((~hskp4) | c0_1(a103)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.85/1.03 tff(85,plain,
% 0.85/1.03 ((~hskp4) | c0_1(a103)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.85/1.03 tff(86,plain,
% 0.85/1.03 ((~hskp4) | c0_1(a103)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[85, 80])).
% 0.85/1.03 tff(87,plain,
% 0.85/1.03 (c0_1(a103)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[86, 73])).
% 0.85/1.03 tff(88,assumption,(~hskp0), introduced(assumption)).
% 0.85/1.03 tff(89,assumption,(~ndr1_0), introduced(assumption)).
% 0.85/1.03 tff(90,plain,
% 0.85/1.03 ((ndr1_0 | (~hskp4)) <=> (ndr1_0 | (~hskp4))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(91,plain,
% 0.85/1.03 (((~hskp4) | ndr1_0) <=> (ndr1_0 | (~hskp4))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(92,axiom,((~hskp4) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause27')).
% 0.85/1.03 tff(93,plain,
% 0.85/1.03 (ndr1_0 | (~hskp4)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.85/1.03 tff(94,plain,
% 0.85/1.03 (ndr1_0 | (~hskp4)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[93, 90])).
% 0.85/1.03 tff(95,plain,
% 0.85/1.03 (~hskp4),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[94, 89])).
% 0.85/1.03 tff(96,plain,
% 0.85/1.03 ((ndr1_0 | (~hskp28)) <=> (ndr1_0 | (~hskp28))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(97,plain,
% 0.85/1.03 (((~hskp28) | ndr1_0) <=> (ndr1_0 | (~hskp28))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(98,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 0.85/1.03 tff(99,plain,
% 0.85/1.03 (ndr1_0 | (~hskp28)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.85/1.03 tff(100,plain,
% 0.85/1.03 (ndr1_0 | (~hskp28)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[99, 96])).
% 0.85/1.03 tff(101,plain,
% 0.85/1.03 (~hskp28),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[100, 89])).
% 0.85/1.03 tff(102,plain,
% 0.85/1.03 ((ndr1_0 | (~hskp22)) <=> (ndr1_0 | (~hskp22))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(103,plain,
% 0.85/1.03 (((~hskp22) | ndr1_0) <=> (ndr1_0 | (~hskp22))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(104,axiom,((~hskp22) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause9')).
% 0.85/1.03 tff(105,plain,
% 0.85/1.03 (ndr1_0 | (~hskp22)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.85/1.03 tff(106,plain,
% 0.85/1.03 (ndr1_0 | (~hskp22)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[105, 102])).
% 0.85/1.03 tff(107,plain,
% 0.85/1.03 (~hskp22),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[106, 89])).
% 0.85/1.03 tff(108,plain,
% 0.85/1.03 ((hskp28 | hskp22 | hskp4) <=> (hskp28 | hskp22 | hskp4)),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(109,plain,
% 0.85/1.03 (((hskp28 | hskp4) | hskp22) <=> (hskp28 | hskp22 | hskp4)),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(110,axiom,((hskp28 | hskp4) | hskp22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 0.85/1.03 tff(111,plain,
% 0.85/1.03 (hskp28 | hskp22 | hskp4),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.85/1.03 tff(112,plain,
% 0.85/1.03 (hskp28 | hskp22 | hskp4),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[111, 108])).
% 0.85/1.03 tff(113,plain,
% 0.85/1.03 (hskp28 | hskp22 | hskp4),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.85/1.03 tff(114,plain,
% 0.85/1.03 (hskp28 | hskp22 | hskp4),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[113, 108])).
% 0.85/1.03 tff(115,plain,
% 0.85/1.03 (hskp28 | hskp22 | hskp4),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[114, 108])).
% 0.85/1.03 tff(116,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[115, 107, 101, 95])).
% 0.85/1.03 tff(117,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(118,plain,
% 0.85/1.03 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(119,plain,
% 0.85/1.03 ((hskp0 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103))) <=> (hskp0 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(120,plain,
% 0.85/1.03 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[119])).
% 0.85/1.03 tff(121,plain,
% 0.85/1.03 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[120, 118])).
% 0.85/1.03 tff(122,plain,
% 0.85/1.03 ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(123,plain,
% 0.85/1.03 ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.85/1.03 tff(124,plain,
% 0.85/1.03 (~c1_1(a103)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[123, 117, 88, 87, 79, 72])).
% 0.85/1.03 tff(125,plain,
% 0.85/1.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(126,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[125])).
% 0.85/1.03 tff(127,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(128,plain,
% 0.85/1.03 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | 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(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | 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(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(129,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[128])).
% 0.85/1.03 tff(130,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 0.85/1.03 tff(131,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.85/1.03 tff(132,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.85/1.03 tff(133,plain,(
% 0.85/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(skolemize,[status(sab)],[132])).
% 0.85/1.03 tff(134,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.85/1.03 tff(135,assumption,(~hskp22), introduced(assumption)).
% 0.85/1.03 tff(136,assumption,(~hskp28), introduced(assumption)).
% 0.85/1.03 tff(137,plain,
% 0.85/1.03 (hskp4),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[115, 136, 135])).
% 0.85/1.03 tff(138,plain,
% 0.85/1.03 (~c3_1(a103)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[78, 137])).
% 0.85/1.03 tff(139,plain,
% 0.85/1.03 (((~hskp4) | c2_1(a103)) <=> ((~hskp4) | c2_1(a103))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(140,axiom,((~hskp4) | c2_1(a103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.85/1.03 tff(141,plain,
% 0.85/1.03 ((~hskp4) | c2_1(a103)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.85/1.04 tff(142,plain,
% 0.85/1.04 ((~hskp4) | c2_1(a103)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[141, 139])).
% 0.85/1.04 tff(143,plain,
% 0.85/1.04 ((~hskp4) | c2_1(a103)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[142, 139])).
% 0.85/1.04 tff(144,plain,
% 0.85/1.04 ((~hskp4) | c2_1(a103)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.85/1.04 tff(145,plain,
% 0.85/1.04 ((~hskp4) | c2_1(a103)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[144, 139])).
% 0.85/1.04 tff(146,plain,
% 0.85/1.04 (c2_1(a103)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[145, 137])).
% 0.85/1.04 tff(147,plain,
% 0.85/1.04 (c0_1(a103)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[86, 137])).
% 0.85/1.04 tff(148,assumption,(~c3_1(a103)), introduced(assumption)).
% 0.85/1.04 tff(149,assumption,(c0_1(a103)), introduced(assumption)).
% 0.85/1.04 tff(150,plain,
% 0.85/1.04 (hskp0 | (~c1_1(a103))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[123, 117, 149, 148, 72])).
% 0.85/1.04 tff(151,plain,
% 0.85/1.04 (~c1_1(a103)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[150, 88])).
% 0.85/1.04 tff(152,plain,
% 0.85/1.04 (^[U: $i] : refl((hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(153,plain,
% 0.85/1.04 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[152])).
% 0.85/1.04 tff(154,plain,
% 0.85/1.04 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(155,plain,
% 0.85/1.04 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp22))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp22) | hskp21) <=> ((hskp22 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21))), rewrite(((hskp22 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21) <=> (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp22) | hskp21) <=> (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(156,plain,
% 0.85/1.04 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp22) | hskp21) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[155])).
% 0.85/1.04 tff(157,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp22) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 0.85/1.04 tff(158,plain,
% 0.85/1.04 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.85/1.04 tff(159,plain,
% 0.85/1.04 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.85/1.04 tff(160,plain,(
% 0.85/1.04 ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.04 inference(skolemize,[status(sab)],[159])).
% 0.85/1.04 tff(161,plain,
% 0.85/1.04 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[160, 153])).
% 0.85/1.04 tff(162,assumption,(c2_1(a103)), introduced(assumption)).
% 0.85/1.04 tff(163,plain,
% 0.85/1.04 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | c1_1(a103))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | c1_1(a103))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(164,plain,
% 0.85/1.04 ((hskp22 | hskp21 | (~ndr1_0) | c1_1(a103) | c3_1(a103) | (~c2_1(a103))) <=> (hskp22 | hskp21 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | c1_1(a103))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(165,plain,
% 0.85/1.04 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a103) | c3_1(a103) | (~c2_1(a103)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | c1_1(a103)))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[164])).
% 0.85/1.04 tff(166,plain,
% 0.85/1.04 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a103) | c3_1(a103) | (~c2_1(a103)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | c1_1(a103))),
% 0.85/1.04 inference(transitivity,[status(thm)],[165, 163])).
% 0.85/1.04 tff(167,plain,
% 0.85/1.04 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a103) | c3_1(a103) | (~c2_1(a103)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(168,plain,
% 0.85/1.04 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | c1_1(a103)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.85/1.04 tff(169,plain,
% 0.85/1.04 (hskp21 | c1_1(a103)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[168, 117, 135, 162, 148, 161])).
% 0.85/1.04 tff(170,plain,
% 0.85/1.04 (hskp21),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[169, 151])).
% 0.85/1.04 tff(171,plain,
% 0.85/1.04 (((~hskp21) | (~c2_1(a136))) <=> ((~hskp21) | (~c2_1(a136)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(172,plain,
% 0.85/1.04 (((~c2_1(a136)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a136)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(173,axiom,((~c2_1(a136)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 0.85/1.04 tff(174,plain,
% 0.85/1.04 ((~hskp21) | (~c2_1(a136))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.85/1.04 tff(175,plain,
% 0.85/1.04 ((~hskp21) | (~c2_1(a136))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[174, 171])).
% 0.85/1.04 tff(176,plain,
% 0.85/1.04 (~c2_1(a136)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[175, 170])).
% 0.85/1.04 tff(177,plain,
% 0.85/1.04 (((~hskp21) | (~c1_1(a136))) <=> ((~hskp21) | (~c1_1(a136)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(178,plain,
% 0.85/1.04 (((~c1_1(a136)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a136)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(179,axiom,((~c1_1(a136)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.85/1.04 tff(180,plain,
% 0.85/1.04 ((~hskp21) | (~c1_1(a136))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.85/1.04 tff(181,plain,
% 0.85/1.04 ((~hskp21) | (~c1_1(a136))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[180, 177])).
% 0.85/1.04 tff(182,plain,
% 0.85/1.04 (~c1_1(a136)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[181, 170])).
% 0.85/1.04 tff(183,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a136) | c2_1(a136) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a136) | c2_1(a136) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a136)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(184,plain,
% 0.85/1.04 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136))) <=> (c1_1(a136) | c2_1(a136) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a136)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(185,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a136) | c2_1(a136) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a136))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[184])).
% 0.85/1.04 tff(186,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a136) | c2_1(a136) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a136)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[185, 183])).
% 0.85/1.04 tff(187,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(188,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a136) | c2_1(a136) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a136))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.85/1.04 tff(189,plain,
% 0.85/1.04 (~c0_1(a136)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[188, 117, 149, 162, 182, 176, 148, 134, 151])).
% 0.85/1.04 tff(190,plain,
% 0.85/1.04 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(191,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[190])).
% 0.85/1.04 tff(192,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(193,plain,
% 0.85/1.04 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(194,plain,
% 0.85/1.04 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[193])).
% 0.85/1.04 tff(195,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.85/1.04 tff(196,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.85/1.04 tff(197,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.85/1.04 tff(198,plain,(
% 0.85/1.04 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.04 inference(skolemize,[status(sab)],[197])).
% 0.85/1.04 tff(199,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.85/1.04 tff(200,plain,
% 0.85/1.04 (((~hskp21) | c3_1(a136)) <=> ((~hskp21) | c3_1(a136))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(201,axiom,((~hskp21) | c3_1(a136)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.85/1.04 tff(202,plain,
% 0.85/1.04 ((~hskp21) | c3_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.85/1.04 tff(203,plain,
% 0.85/1.04 ((~hskp21) | c3_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[202, 200])).
% 0.85/1.04 tff(204,plain,
% 0.85/1.04 ((~hskp21) | c3_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[203, 200])).
% 0.85/1.04 tff(205,plain,
% 0.85/1.04 ((~hskp21) | c3_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.85/1.04 tff(206,plain,
% 0.85/1.04 ((~hskp21) | c3_1(a136)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[205, 200])).
% 0.85/1.04 tff(207,plain,
% 0.85/1.04 (c3_1(a136)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[206, 170])).
% 0.85/1.04 tff(208,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a136) | c2_1(a136) | (~ndr1_0) | c0_1(a136) | (~c3_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a136) | c2_1(a136) | (~ndr1_0) | c0_1(a136) | (~c3_1(a136)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(209,plain,
% 0.85/1.04 ((hskp0 | (~ndr1_0) | c2_1(a136) | c0_1(a136) | (~c3_1(a136)) | c2_1(a136) | c1_1(a136) | c0_1(a136)) <=> (hskp0 | c1_1(a136) | c2_1(a136) | (~ndr1_0) | c0_1(a136) | (~c3_1(a136)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(210,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a136) | c0_1(a136) | (~c3_1(a136)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a136) | c2_1(a136) | (~ndr1_0) | c0_1(a136) | (~c3_1(a136))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[209])).
% 0.85/1.04 tff(211,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a136) | c0_1(a136) | (~c3_1(a136)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a136) | c2_1(a136) | (~ndr1_0) | c0_1(a136) | (~c3_1(a136)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[210, 208])).
% 0.85/1.04 tff(212,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a136) | c0_1(a136) | (~c3_1(a136)) | c2_1(a136) | c1_1(a136) | c0_1(a136))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(213,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a136) | c2_1(a136) | (~ndr1_0) | c0_1(a136) | (~c3_1(a136))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.85/1.04 tff(214,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[213, 117, 88, 207, 182, 176, 199, 189])).
% 0.85/1.04 tff(215,plain,(hskp0 | (~c0_1(a103)) | (~c2_1(a103)) | c3_1(a103) | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(216,plain,
% 0.85/1.04 (hskp0),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[215, 147, 146, 138, 135])).
% 0.85/1.04 tff(217,plain,
% 0.85/1.04 (((~hskp0) | (~c3_1(a97))) <=> ((~hskp0) | (~c3_1(a97)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(218,plain,
% 0.85/1.04 (((~c3_1(a97)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a97)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(219,axiom,((~c3_1(a97)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.85/1.04 tff(220,plain,
% 0.85/1.04 ((~hskp0) | (~c3_1(a97))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.85/1.04 tff(221,plain,
% 0.85/1.04 ((~hskp0) | (~c3_1(a97))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[220, 217])).
% 0.85/1.04 tff(222,plain,
% 0.85/1.04 (~c3_1(a97)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[221, 216])).
% 0.85/1.04 tff(223,plain,
% 0.85/1.04 (((~hskp0) | (~c2_1(a97))) <=> ((~hskp0) | (~c2_1(a97)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(224,plain,
% 0.85/1.04 (((~c2_1(a97)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a97)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(225,axiom,((~c2_1(a97)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.85/1.04 tff(226,plain,
% 0.85/1.04 ((~hskp0) | (~c2_1(a97))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.85/1.04 tff(227,plain,
% 0.85/1.04 ((~hskp0) | (~c2_1(a97))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[226, 223])).
% 0.85/1.04 tff(228,plain,
% 0.85/1.04 (~c2_1(a97)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[227, 216])).
% 0.85/1.04 tff(229,plain,
% 0.85/1.04 (c0_1(a97)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[61, 216])).
% 0.85/1.04 tff(230,assumption,(~c1_1(a97)), introduced(assumption)).
% 0.85/1.04 tff(231,assumption,(c0_1(a97)), introduced(assumption)).
% 0.85/1.04 tff(232,assumption,(hskp19), introduced(assumption)).
% 0.85/1.04 tff(233,plain,
% 0.85/1.04 (((~hskp19) | (~c2_1(a130))) <=> ((~hskp19) | (~c2_1(a130)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(234,plain,
% 0.85/1.04 (((~c2_1(a130)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a130)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(235,axiom,((~c2_1(a130)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.85/1.04 tff(236,plain,
% 0.85/1.04 ((~hskp19) | (~c2_1(a130))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.85/1.04 tff(237,plain,
% 0.85/1.04 ((~hskp19) | (~c2_1(a130))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[236, 233])).
% 0.85/1.04 tff(238,plain,
% 0.85/1.04 (~c2_1(a130)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[237, 232])).
% 0.85/1.04 tff(239,plain,
% 0.85/1.04 (((~hskp19) | c3_1(a130)) <=> ((~hskp19) | c3_1(a130))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(240,axiom,((~hskp19) | c3_1(a130)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.85/1.04 tff(241,plain,
% 0.85/1.04 ((~hskp19) | c3_1(a130)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.85/1.04 tff(242,plain,
% 0.85/1.04 ((~hskp19) | c3_1(a130)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[241, 239])).
% 0.85/1.04 tff(243,plain,
% 0.85/1.04 ((~hskp19) | c3_1(a130)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[242, 239])).
% 0.85/1.04 tff(244,plain,
% 0.85/1.04 ((~hskp19) | c3_1(a130)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[243, 239])).
% 0.85/1.04 tff(245,plain,
% 0.85/1.04 ((~hskp19) | c3_1(a130)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[244, 239])).
% 0.85/1.04 tff(246,plain,
% 0.85/1.04 (c3_1(a130)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[245, 232])).
% 0.85/1.04 tff(247,plain,
% 0.85/1.04 (((~hskp19) | c1_1(a130)) <=> ((~hskp19) | c1_1(a130))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(248,axiom,((~hskp19) | c1_1(a130)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 0.85/1.04 tff(249,plain,
% 0.85/1.04 ((~hskp19) | c1_1(a130)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.85/1.04 tff(250,plain,
% 0.85/1.04 ((~hskp19) | c1_1(a130)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[249, 247])).
% 0.85/1.04 tff(251,plain,
% 0.85/1.04 ((~hskp19) | c1_1(a130)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[250, 247])).
% 0.85/1.04 tff(252,plain,
% 0.85/1.04 ((~hskp19) | c1_1(a130)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.85/1.04 tff(253,plain,
% 0.85/1.04 ((~hskp19) | c1_1(a130)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[252, 247])).
% 0.85/1.04 tff(254,plain,
% 0.85/1.04 (c1_1(a130)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[253, 232])).
% 0.85/1.04 tff(255,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a130) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c3_1(a130)) | (~c1_1(a130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c3_1(a130)) | (~c1_1(a130)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(256,plain,
% 0.85/1.04 (((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a97) | c3_1(a97) | (~c0_1(a97))) <=> (c2_1(a130) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c3_1(a130)) | (~c1_1(a130)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(257,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a97) | c3_1(a97) | (~c0_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a130) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c3_1(a130)) | (~c1_1(a130))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[256])).
% 0.85/1.04 tff(258,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a97) | c3_1(a97) | (~c0_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c3_1(a130)) | (~c1_1(a130)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[257, 255])).
% 0.85/1.04 tff(259,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a97) | c3_1(a97) | (~c0_1(a97)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(260,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c3_1(a130)) | (~c1_1(a130))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.85/1.04 tff(261,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[260, 117, 254, 246, 231, 238, 31, 53, 20, 230])).
% 0.85/1.04 tff(262,plain,((~hskp19) | (~c0_1(a97)) | c2_1(a97) | c3_1(a97) | c1_1(a97)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(263,plain,
% 0.85/1.04 (~hskp19),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[262, 230, 31, 53, 231])).
% 0.85/1.04 tff(264,plain,
% 0.85/1.04 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | c1_1(a97))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp18 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | c1_1(a97))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(265,plain,
% 0.85/1.04 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a97) | c1_1(a97) | c3_1(a97)) <=> (hskp19 | hskp18 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | c1_1(a97))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(266,plain,
% 0.85/1.04 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a97) | c1_1(a97) | c3_1(a97))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | c1_1(a97)))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[265])).
% 0.85/1.04 tff(267,plain,
% 0.85/1.04 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a97) | c1_1(a97) | c3_1(a97))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp18 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | c1_1(a97))),
% 0.85/1.04 inference(transitivity,[status(thm)],[266, 264])).
% 0.85/1.04 tff(268,plain,
% 0.85/1.04 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a97) | c1_1(a97) | c3_1(a97))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(269,plain,
% 0.85/1.04 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp18 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | c1_1(a97)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.85/1.04 tff(270,plain,
% 0.85/1.04 (hskp19 | hskp18 | c1_1(a97)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[269, 117, 31, 53, 30])).
% 0.85/1.04 tff(271,plain,
% 0.85/1.04 (hskp18),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[270, 263, 230])).
% 0.85/1.04 tff(272,plain,
% 0.85/1.04 (((~hskp18) | (~c1_1(a129))) <=> ((~hskp18) | (~c1_1(a129)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(273,plain,
% 0.85/1.04 (((~c1_1(a129)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a129)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(274,axiom,((~c1_1(a129)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 0.85/1.04 tff(275,plain,
% 0.85/1.04 ((~hskp18) | (~c1_1(a129))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.85/1.04 tff(276,plain,
% 0.85/1.04 ((~hskp18) | (~c1_1(a129))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[275, 272])).
% 0.85/1.04 tff(277,plain,
% 0.85/1.04 (~c1_1(a129)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[276, 271])).
% 0.85/1.04 tff(278,plain,
% 0.85/1.04 (((~hskp18) | c2_1(a129)) <=> ((~hskp18) | c2_1(a129))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(279,axiom,((~hskp18) | c2_1(a129)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.85/1.04 tff(280,plain,
% 0.85/1.04 ((~hskp18) | c2_1(a129)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.85/1.04 tff(281,plain,
% 0.85/1.04 ((~hskp18) | c2_1(a129)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[280, 278])).
% 0.85/1.04 tff(282,plain,
% 0.85/1.04 ((~hskp18) | c2_1(a129)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[281, 278])).
% 0.85/1.04 tff(283,plain,
% 0.85/1.04 ((~hskp18) | c2_1(a129)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[282, 278])).
% 0.85/1.04 tff(284,plain,
% 0.85/1.04 ((~hskp18) | c2_1(a129)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[283, 278])).
% 0.85/1.04 tff(285,plain,
% 0.85/1.04 (c2_1(a129)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[284, 271])).
% 0.85/1.04 tff(286,plain,
% 0.85/1.04 (((~hskp18) | c0_1(a129)) <=> ((~hskp18) | c0_1(a129))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(287,axiom,((~hskp18) | c0_1(a129)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 0.85/1.04 tff(288,plain,
% 0.85/1.04 ((~hskp18) | c0_1(a129)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.85/1.04 tff(289,plain,
% 0.85/1.04 ((~hskp18) | c0_1(a129)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[288, 286])).
% 0.85/1.04 tff(290,plain,
% 0.85/1.04 ((~hskp18) | c0_1(a129)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[289, 286])).
% 0.85/1.04 tff(291,plain,
% 0.85/1.04 ((~hskp18) | c0_1(a129)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[290, 286])).
% 0.85/1.04 tff(292,plain,
% 0.85/1.04 ((~hskp18) | c0_1(a129)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[291, 286])).
% 0.85/1.04 tff(293,plain,
% 0.85/1.04 (c0_1(a129)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[292, 271])).
% 0.85/1.04 tff(294,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a129) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a129) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a129)) | (~c0_1(a129)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(295,plain,
% 0.85/1.04 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97))) <=> (c1_1(a129) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a129)) | (~c0_1(a129)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(296,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a129) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a129)) | (~c0_1(a129))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[295])).
% 0.85/1.04 tff(297,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a129) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a129)) | (~c0_1(a129)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[296, 294])).
% 0.85/1.04 tff(298,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(299,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a129) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a129)) | (~c0_1(a129))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.85/1.05 tff(300,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[299, 117, 293, 285, 149, 162, 231, 277, 148, 31, 134, 230])).
% 0.85/1.05 tff(301,plain,(c1_1(a97) | (~c0_1(a103)) | (~c2_1(a103)) | (~c0_1(a97)) | c3_1(a103) | c2_1(a97) | c3_1(a97)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(302,plain,
% 0.85/1.05 (c1_1(a97)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[301, 147, 146, 229, 138, 228, 222])).
% 0.85/1.05 tff(303,assumption,(c1_1(a97)), introduced(assumption)).
% 0.85/1.05 tff(304,plain,
% 0.85/1.05 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(305,plain,
% 0.85/1.05 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[304])).
% 0.85/1.05 tff(306,plain,
% 0.85/1.05 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(307,plain,
% 0.85/1.05 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_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)) | (~c3_1(V))) | 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) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp28) <=> (hskp28 | (~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)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(308,plain,
% 0.85/1.05 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[307])).
% 0.85/1.05 tff(309,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 0.85/1.05 tff(310,plain,
% 0.85/1.05 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.85/1.05 tff(311,plain,
% 0.85/1.05 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[310, 306])).
% 0.85/1.05 tff(312,plain,(
% 0.85/1.05 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.85/1.05 inference(skolemize,[status(sab)],[311])).
% 0.85/1.05 tff(313,plain,
% 0.85/1.05 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[312, 305])).
% 0.85/1.05 tff(314,assumption,(hskp21), introduced(assumption)).
% 0.85/1.05 tff(315,plain,
% 0.85/1.05 (~c2_1(a136)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[175, 314])).
% 0.85/1.05 tff(316,plain,
% 0.85/1.05 (~c1_1(a136)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[181, 314])).
% 0.85/1.05 tff(317,plain,
% 0.85/1.05 (c3_1(a136)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[206, 314])).
% 0.85/1.05 tff(318,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a136) | c2_1(a136) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a136) | c2_1(a136) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a136)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(319,plain,
% 0.85/1.05 ((hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a136) | c1_1(a136) | (~c3_1(a136))) <=> (hskp28 | c1_1(a136) | c2_1(a136) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a136)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(320,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a136) | c1_1(a136) | (~c3_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a136) | c2_1(a136) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a136))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[319])).
% 0.85/1.05 tff(321,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a136) | c1_1(a136) | (~c3_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a136) | c2_1(a136) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a136)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[320, 318])).
% 0.85/1.05 tff(322,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a136) | c1_1(a136) | (~c3_1(a136)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(323,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a136) | c2_1(a136) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a136))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.85/1.05 tff(324,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[323, 117, 136, 317, 231, 316, 315, 31, 313, 303])).
% 0.85/1.05 tff(325,plain,((~hskp21) | hskp28 | (~c0_1(a97)) | c2_1(a97) | (~c1_1(a97))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(326,plain,
% 0.85/1.05 (~hskp21),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[325, 136, 229, 228, 302])).
% 0.85/1.05 tff(327,assumption,(~c1_1(a103)), introduced(assumption)).
% 0.85/1.05 tff(328,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(329,plain,
% 0.85/1.05 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97))) <=> (c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(330,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[329])).
% 0.85/1.05 tff(331,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103))),
% 0.85/1.05 inference(transitivity,[status(thm)],[330, 328])).
% 0.85/1.05 tff(332,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(333,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.85/1.05 tff(334,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[333, 117, 149, 162, 231, 148, 31, 134, 327, 230])).
% 0.85/1.05 tff(335,plain,(c1_1(a103) | (~c0_1(a103)) | (~c2_1(a103)) | (~c0_1(a97)) | c3_1(a103) | c2_1(a97) | c1_1(a97)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(336,plain,
% 0.85/1.05 (c1_1(a97)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[335, 327, 146, 229, 138, 228, 147])).
% 0.85/1.05 tff(337,plain,
% 0.85/1.05 (hskp21 | c1_1(a103)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[168, 117, 135, 146, 138, 161])).
% 0.85/1.05 tff(338,plain,
% 0.85/1.05 (hskp21),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[337, 327])).
% 0.85/1.05 tff(339,plain,
% 0.85/1.05 (~c2_1(a136)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[175, 338])).
% 0.85/1.05 tff(340,plain,
% 0.85/1.05 (~c1_1(a136)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[181, 338])).
% 0.85/1.05 tff(341,plain,
% 0.85/1.05 (c3_1(a136)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[206, 338])).
% 0.85/1.05 tff(342,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[323, 117, 136, 341, 229, 340, 339, 228, 313, 336])).
% 0.85/1.05 tff(343,plain,(c1_1(a103) | hskp28 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(344,plain,
% 0.85/1.05 (c1_1(a103)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[343, 136, 135])).
% 0.85/1.05 tff(345,plain,
% 0.85/1.05 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(346,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[345])).
% 0.85/1.05 tff(347,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(348,plain,
% 0.85/1.05 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(349,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[348])).
% 0.85/1.05 tff(350,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 0.85/1.05 tff(351,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.85/1.05 tff(352,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[351, 347])).
% 0.85/1.05 tff(353,plain,(
% 0.85/1.05 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.85/1.05 inference(skolemize,[status(sab)],[352])).
% 0.85/1.05 tff(354,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[353, 346])).
% 0.85/1.05 tff(355,plain,
% 0.85/1.05 (^[U: $i] : refl((hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(356,plain,
% 0.85/1.05 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[355])).
% 0.85/1.05 tff(357,plain,
% 0.85/1.05 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(358,plain,
% 0.85/1.05 (^[U: $i] : 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)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(359,plain,
% 0.85/1.05 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) <=> ![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[358])).
% 0.85/1.05 tff(360,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 0.85/1.05 tff(361,plain,
% 0.85/1.05 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.85/1.05 tff(362,plain,
% 0.85/1.05 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[361, 357])).
% 0.85/1.05 tff(363,plain,(
% 0.85/1.05 ![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.05 inference(skolemize,[status(sab)],[362])).
% 0.85/1.05 tff(364,plain,
% 0.85/1.05 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[363, 356])).
% 0.85/1.05 tff(365,plain,
% 0.85/1.05 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(366,plain,
% 0.85/1.05 ((hskp6 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103))) <=> (hskp6 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(367,plain,
% 0.85/1.05 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[366])).
% 0.85/1.05 tff(368,plain,
% 0.85/1.05 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[367, 365])).
% 0.85/1.05 tff(369,plain,
% 0.85/1.05 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(370,plain,
% 0.85/1.05 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.85/1.05 tff(371,plain,
% 0.85/1.05 (hskp6 | (~c1_1(a103))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[370, 117, 147, 138, 364])).
% 0.85/1.05 tff(372,plain,
% 0.85/1.05 (hskp6),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[371, 344])).
% 0.85/1.05 tff(373,plain,
% 0.85/1.05 (((~hskp6) | (~c3_1(a105))) <=> ((~hskp6) | (~c3_1(a105)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(374,plain,
% 0.85/1.05 (((~c3_1(a105)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a105)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(375,axiom,((~c3_1(a105)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.85/1.05 tff(376,plain,
% 0.85/1.05 ((~hskp6) | (~c3_1(a105))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.85/1.05 tff(377,plain,
% 0.85/1.05 ((~hskp6) | (~c3_1(a105))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[376, 373])).
% 0.85/1.05 tff(378,plain,
% 0.85/1.05 (~c3_1(a105)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[377, 372])).
% 0.85/1.05 tff(379,plain,
% 0.85/1.05 (((~hskp6) | c2_1(a105)) <=> ((~hskp6) | c2_1(a105))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(380,axiom,((~hskp6) | c2_1(a105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.85/1.05 tff(381,plain,
% 0.85/1.05 ((~hskp6) | c2_1(a105)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.85/1.05 tff(382,plain,
% 0.85/1.05 ((~hskp6) | c2_1(a105)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[381, 379])).
% 0.85/1.05 tff(383,plain,
% 0.85/1.05 ((~hskp6) | c2_1(a105)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[382, 379])).
% 0.85/1.05 tff(384,plain,
% 0.85/1.05 ((~hskp6) | c2_1(a105)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[383, 379])).
% 0.85/1.05 tff(385,plain,
% 0.85/1.05 ((~hskp6) | c2_1(a105)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[384, 379])).
% 0.85/1.05 tff(386,plain,
% 0.85/1.05 (c2_1(a105)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[385, 372])).
% 0.85/1.05 tff(387,plain,
% 0.85/1.05 (((~hskp6) | c1_1(a105)) <=> ((~hskp6) | c1_1(a105))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(388,axiom,((~hskp6) | c1_1(a105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.85/1.05 tff(389,plain,
% 0.85/1.05 ((~hskp6) | c1_1(a105)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.85/1.05 tff(390,plain,
% 0.85/1.05 ((~hskp6) | c1_1(a105)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[389, 387])).
% 0.85/1.05 tff(391,plain,
% 0.85/1.05 ((~hskp6) | c1_1(a105)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[390, 387])).
% 0.85/1.05 tff(392,plain,
% 0.85/1.05 ((~hskp6) | c1_1(a105)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[391, 387])).
% 0.85/1.05 tff(393,plain,
% 0.85/1.05 ((~hskp6) | c1_1(a105)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[392, 387])).
% 0.85/1.05 tff(394,plain,
% 0.85/1.05 (c1_1(a105)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[393, 372])).
% 0.85/1.05 tff(395,assumption,(~c1_1(a122)), introduced(assumption)).
% 0.85/1.05 tff(396,plain,
% 0.85/1.05 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(397,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[396])).
% 0.85/1.05 tff(398,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(399,plain,
% 0.85/1.05 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(400,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[399])).
% 0.85/1.05 tff(401,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 0.85/1.05 tff(402,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.85/1.05 tff(403,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[402, 398])).
% 0.85/1.05 tff(404,plain,(
% 0.85/1.05 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.85/1.05 inference(skolemize,[status(sab)],[403])).
% 0.85/1.05 tff(405,plain,
% 0.85/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[404, 397])).
% 0.85/1.05 tff(406,assumption,(~c3_1(a105)), introduced(assumption)).
% 0.85/1.05 tff(407,assumption,(~c2_1(a122)), introduced(assumption)).
% 0.85/1.05 tff(408,assumption,(c2_1(a105)), introduced(assumption)).
% 0.85/1.05 tff(409,assumption,(c1_1(a105)), introduced(assumption)).
% 0.85/1.05 tff(410,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a122) | c2_1(a122) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)) | c3_1(a122))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a122) | c2_1(a122) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)) | c3_1(a122))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(411,plain,
% 0.85/1.05 (((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | c3_1(a122)) <=> (c1_1(a122) | c2_1(a122) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)) | c3_1(a122))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(412,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | c3_1(a122))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a122) | c2_1(a122) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)) | c3_1(a122)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[411])).
% 0.85/1.05 tff(413,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | c3_1(a122))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a122) | c2_1(a122) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)) | c3_1(a122))),
% 0.85/1.05 inference(transitivity,[status(thm)],[412, 410])).
% 0.85/1.05 tff(414,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | c3_1(a122))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(415,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a122) | c2_1(a122) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)) | c3_1(a122)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.85/1.05 tff(416,plain,
% 0.85/1.05 (c3_1(a122)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[415, 117, 409, 408, 395, 407, 406, 31, 53, 405, 303])).
% 0.85/1.05 tff(417,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a122) | c2_1(a122) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a122) | c2_1(a122) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(418,plain,
% 0.85/1.05 ((hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | (~c3_1(a122))) <=> (hskp28 | c1_1(a122) | c2_1(a122) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(419,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | (~c3_1(a122)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a122) | c2_1(a122) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[418])).
% 0.85/1.06 tff(420,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | (~c3_1(a122)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a122) | c2_1(a122) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[419, 417])).
% 0.85/1.06 tff(421,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | (~c3_1(a122)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(422,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a122) | c2_1(a122) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.85/1.06 tff(423,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[422, 117, 136, 231, 395, 407, 31, 313, 303, 416])).
% 0.85/1.06 tff(424,plain,(c2_1(a122) | hskp28 | (~c0_1(a97)) | c1_1(a122) | c2_1(a97) | (~c1_1(a97)) | (~c1_1(a105)) | (~c2_1(a105)) | c3_1(a105) | c3_1(a97)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(425,plain,
% 0.85/1.06 (c2_1(a122)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[424, 395, 229, 136, 228, 302, 394, 386, 378, 222])).
% 0.85/1.06 tff(426,plain,
% 0.85/1.06 (((~hskp16) | (~c2_1(a122))) <=> ((~hskp16) | (~c2_1(a122)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(427,plain,
% 0.85/1.06 (((~c2_1(a122)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a122)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(428,axiom,((~c2_1(a122)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.85/1.06 tff(429,plain,
% 0.85/1.06 ((~hskp16) | (~c2_1(a122))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[428, 427])).
% 0.85/1.06 tff(430,plain,
% 0.85/1.06 ((~hskp16) | (~c2_1(a122))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[429, 426])).
% 0.85/1.06 tff(431,plain,
% 0.85/1.06 (~hskp16),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[430, 425])).
% 0.85/1.06 tff(432,plain,
% 0.85/1.06 (^[U: $i] : refl((hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(433,plain,
% 0.85/1.06 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[432])).
% 0.85/1.06 tff(434,plain,
% 0.85/1.06 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(435,plain,
% 0.85/1.06 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp25) <=> ((hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp25))), rewrite(((hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp25) <=> (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(436,plain,
% 0.85/1.06 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp25) <=> ![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[435])).
% 0.85/1.06 tff(437,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 0.85/1.06 tff(438,plain,
% 0.85/1.06 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.85/1.06 tff(439,plain,
% 0.85/1.06 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[438, 434])).
% 0.85/1.06 tff(440,plain,(
% 0.85/1.06 ![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(skolemize,[status(sab)],[439])).
% 0.85/1.06 tff(441,plain,
% 0.85/1.06 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[440, 433])).
% 0.85/1.06 tff(442,plain,
% 0.85/1.06 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(443,plain,
% 0.85/1.06 ((hskp25 | hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103))) <=> (hskp25 | hskp16 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(444,plain,
% 0.85/1.06 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[443])).
% 0.85/1.06 tff(445,plain,
% 0.85/1.06 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[444, 442])).
% 0.85/1.06 tff(446,plain,
% 0.85/1.06 ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(447,plain,
% 0.85/1.06 ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.85/1.06 tff(448,plain,
% 0.85/1.06 (hskp25 | hskp16),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[447, 117, 147, 146, 138, 441])).
% 0.85/1.06 tff(449,plain,
% 0.85/1.06 (hskp25),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[448, 431])).
% 0.85/1.06 tff(450,plain,
% 0.85/1.06 (((~hskp25) | (~c0_1(a173))) <=> ((~hskp25) | (~c0_1(a173)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(451,plain,
% 0.85/1.06 (((~c0_1(a173)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a173)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(452,axiom,((~c0_1(a173)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.85/1.06 tff(453,plain,
% 0.85/1.06 ((~hskp25) | (~c0_1(a173))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.85/1.06 tff(454,plain,
% 0.85/1.06 ((~hskp25) | (~c0_1(a173))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[453, 450])).
% 0.85/1.06 tff(455,plain,
% 0.85/1.06 (~c0_1(a173)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[454, 449])).
% 0.85/1.06 tff(456,plain,
% 0.85/1.06 (((~hskp25) | c1_1(a173)) <=> ((~hskp25) | c1_1(a173))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(457,axiom,((~hskp25) | c1_1(a173)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.85/1.06 tff(458,plain,
% 0.85/1.06 ((~hskp25) | c1_1(a173)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.85/1.06 tff(459,plain,
% 0.85/1.06 ((~hskp25) | c1_1(a173)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[458, 456])).
% 0.85/1.06 tff(460,plain,
% 0.85/1.06 ((~hskp25) | c1_1(a173)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[459, 456])).
% 0.85/1.06 tff(461,plain,
% 0.85/1.06 ((~hskp25) | c1_1(a173)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[460, 456])).
% 0.85/1.06 tff(462,plain,
% 0.85/1.06 ((~hskp25) | c1_1(a173)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[461, 456])).
% 0.85/1.06 tff(463,plain,
% 0.85/1.06 (c1_1(a173)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[462, 449])).
% 0.85/1.06 tff(464,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a173) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c2_1(a173)) | (~c1_1(a173)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a173) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c2_1(a173)) | (~c1_1(a173)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(465,plain,
% 0.85/1.06 (((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a173) | (~c2_1(a173)) | (~c1_1(a173))) <=> (c0_1(a173) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c2_1(a173)) | (~c1_1(a173)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(466,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a173) | (~c2_1(a173)) | (~c1_1(a173)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a173) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c2_1(a173)) | (~c1_1(a173))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[465])).
% 0.85/1.06 tff(467,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a173) | (~c2_1(a173)) | (~c1_1(a173)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a173) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c2_1(a173)) | (~c1_1(a173)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[466, 464])).
% 0.85/1.06 tff(468,plain,
% 0.85/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a173) | (~c2_1(a173)) | (~c1_1(a173)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(469,plain,
% 0.85/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a173) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c2_1(a173)) | (~c1_1(a173))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.85/1.06 tff(470,plain,
% 0.85/1.06 (~c2_1(a173)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[469, 117, 463, 147, 146, 229, 455, 228, 354, 344, 302])).
% 0.85/1.06 tff(471,assumption,(~hskp21), introduced(assumption)).
% 0.85/1.06 tff(472,plain,
% 0.85/1.06 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | c3_1(a122))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | c3_1(a122))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(473,plain,
% 0.85/1.06 ((hskp22 | hskp21 | (~ndr1_0) | c1_1(a122) | c3_1(a122) | (~c2_1(a122))) <=> (hskp22 | hskp21 | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | c3_1(a122))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(474,plain,
% 0.85/1.06 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a122) | c3_1(a122) | (~c2_1(a122)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | c3_1(a122)))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[473])).
% 0.85/1.06 tff(475,plain,
% 0.85/1.06 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a122) | c3_1(a122) | (~c2_1(a122)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | c3_1(a122))),
% 0.85/1.06 inference(transitivity,[status(thm)],[474, 472])).
% 0.85/1.06 tff(476,plain,
% 0.85/1.06 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a122) | c3_1(a122) | (~c2_1(a122)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(477,plain,
% 0.85/1.06 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | c3_1(a122)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.85/1.06 tff(478,plain,
% 0.85/1.06 ((~c2_1(a122)) | c3_1(a122)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[477, 117, 135, 471, 395, 161])).
% 0.85/1.06 tff(479,plain,
% 0.85/1.06 (c3_1(a122)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[478, 425])).
% 0.85/1.06 tff(480,plain,
% 0.85/1.06 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(481,plain,
% 0.85/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[480])).
% 0.85/1.06 tff(482,plain,
% 0.85/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(483,plain,
% 0.85/1.06 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(484,plain,
% 0.85/1.06 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[483])).
% 0.85/1.06 tff(485,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 0.85/1.06 tff(486,plain,
% 0.85/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.85/1.06 tff(487,plain,
% 0.85/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[486, 482])).
% 0.85/1.06 tff(488,plain,(
% 0.85/1.06 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.85/1.06 inference(skolemize,[status(sab)],[487])).
% 0.85/1.06 tff(489,plain,
% 0.85/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[488, 481])).
% 0.85/1.06 tff(490,plain,
% 0.85/1.06 (((~hskp25) | (~c3_1(a173))) <=> ((~hskp25) | (~c3_1(a173)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(491,plain,
% 0.85/1.06 (((~c3_1(a173)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a173)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(492,axiom,((~c3_1(a173)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 0.85/1.06 tff(493,plain,
% 0.85/1.06 ((~hskp25) | (~c3_1(a173))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.85/1.06 tff(494,plain,
% 0.85/1.06 ((~hskp25) | (~c3_1(a173))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[493, 490])).
% 0.85/1.06 tff(495,plain,
% 0.85/1.06 (~c3_1(a173)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[494, 449])).
% 0.85/1.06 tff(496,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | (~c0_1(a122)) | (~c3_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | (~c0_1(a122)) | (~c3_1(a122)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(497,plain,
% 0.85/1.06 (((~ndr1_0) | (~c2_1(a122)) | (~c3_1(a122)) | (~c0_1(a122)) | c1_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c1_1(a122) | (~c0_1(a122)) | (~c2_1(a122))) <=> (c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | (~c0_1(a122)) | (~c3_1(a122)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(498,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a122)) | (~c3_1(a122)) | (~c0_1(a122)) | c1_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c1_1(a122) | (~c0_1(a122)) | (~c2_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | (~c0_1(a122)) | (~c3_1(a122))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[497])).
% 0.85/1.06 tff(499,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a122)) | (~c3_1(a122)) | (~c0_1(a122)) | c1_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c1_1(a122) | (~c0_1(a122)) | (~c2_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | (~c0_1(a122)) | (~c3_1(a122)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[498, 496])).
% 0.85/1.06 tff(500,plain,
% 0.85/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a122)) | (~c3_1(a122)) | (~c0_1(a122)) | c1_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c1_1(a122) | (~c0_1(a122)) | (~c2_1(a122)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(501,plain,
% 0.85/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | (~c0_1(a122)) | (~c3_1(a122))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.85/1.06 tff(502,plain,
% 0.85/1.06 (~c0_1(a122)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[501, 117, 395, 425, 10, 479])).
% 0.85/1.06 tff(503,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a122) | c0_1(a173) | c3_1(a173) | (~c2_1(a122)) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)) | c2_1(a173))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a122) | c0_1(a173) | c3_1(a173) | (~c2_1(a122)) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)) | c2_1(a173))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(504,plain,
% 0.85/1.06 (((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c2_1(a173) | c0_1(a173) | c3_1(a173)) <=> (c0_1(a122) | c0_1(a173) | c3_1(a173) | (~c2_1(a122)) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)) | c2_1(a173))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(505,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c2_1(a173) | c0_1(a173) | c3_1(a173))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a122) | c0_1(a173) | c3_1(a173) | (~c2_1(a122)) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)) | c2_1(a173)))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[504])).
% 0.85/1.06 tff(506,plain,
% 0.85/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c2_1(a173) | c0_1(a173) | c3_1(a173))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a122) | c0_1(a173) | c3_1(a173) | (~c2_1(a122)) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)) | c2_1(a173))),
% 0.85/1.06 inference(transitivity,[status(thm)],[505, 503])).
% 0.85/1.06 tff(507,plain,
% 0.85/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c2_1(a173) | c0_1(a173) | c3_1(a173))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(508,plain,
% 0.85/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a122) | c0_1(a173) | c3_1(a173) | (~c2_1(a122)) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)) | c2_1(a173)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[507, 506])).
% 0.85/1.06 tff(509,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[508, 117, 502, 229, 455, 495, 425, 228, 489, 302, 479, 470])).
% 0.85/1.06 tff(510,plain,(c1_1(a122) | hskp22 | hskp21 | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(511,plain,
% 0.85/1.06 (c1_1(a122)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[510, 326, 135, 136])).
% 0.85/1.06 tff(512,plain,
% 0.85/1.06 (((~hskp16) | (~c1_1(a122))) <=> ((~hskp16) | (~c1_1(a122)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(513,plain,
% 0.85/1.06 (((~c1_1(a122)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a122)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(514,axiom,((~c1_1(a122)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 0.85/1.06 tff(515,plain,
% 0.85/1.06 ((~hskp16) | (~c1_1(a122))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.85/1.06 tff(516,plain,
% 0.85/1.06 ((~hskp16) | (~c1_1(a122))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[515, 512])).
% 0.85/1.06 tff(517,plain,
% 0.85/1.06 (~hskp16),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[516, 511])).
% 0.85/1.06 tff(518,plain,
% 0.85/1.06 (c1_1(a122)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[510, 471, 135, 136])).
% 0.85/1.06 tff(519,plain,
% 0.85/1.06 (~hskp16),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[516, 518])).
% 0.85/1.06 tff(520,plain,
% 0.85/1.06 (hskp25),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[448, 519])).
% 0.85/1.06 tff(521,plain,
% 0.85/1.06 (~c0_1(a173)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[454, 520])).
% 0.85/1.06 tff(522,plain,
% 0.85/1.06 (c1_1(a173)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[462, 520])).
% 0.85/1.06 tff(523,plain,
% 0.85/1.06 (~c2_1(a173)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[469, 117, 522, 147, 146, 229, 521, 228, 354, 344, 302])).
% 0.85/1.06 tff(524,plain,
% 0.85/1.06 (^[U: $i] : refl((hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(525,plain,
% 0.85/1.06 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[524])).
% 0.85/1.06 tff(526,plain,
% 0.85/1.06 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(527,plain,
% 0.85/1.06 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp16) | hskp2) <=> ((hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp2))), rewrite(((hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp2) <=> (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp16) | hskp2) <=> (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(528,plain,
% 0.85/1.06 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp16) | hskp2) <=> ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[527])).
% 0.85/1.06 tff(529,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp16) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 0.85/1.06 tff(530,plain,
% 0.85/1.06 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.85/1.06 tff(531,plain,
% 0.85/1.06 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[530, 526])).
% 0.85/1.06 tff(532,plain,(
% 0.85/1.06 ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.85/1.06 inference(skolemize,[status(sab)],[531])).
% 0.85/1.06 tff(533,plain,
% 0.85/1.06 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[532, 525])).
% 0.85/1.06 tff(534,plain,
% 0.85/1.06 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp16 | hskp2 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp16 | hskp2 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(535,plain,
% 0.85/1.06 ((hskp16 | hskp2 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97))) <=> (hskp16 | hskp2 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(536,plain,
% 0.85/1.07 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp16 | hskp2 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[535])).
% 0.85/1.07 tff(537,plain,
% 0.85/1.07 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp16 | hskp2 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[536, 534])).
% 0.85/1.07 tff(538,plain,
% 0.85/1.07 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(539,plain,
% 0.85/1.07 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp16 | hskp2 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.85/1.07 tff(540,plain,
% 0.85/1.07 (hskp16 | hskp2),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[539, 117, 229, 228, 222, 533])).
% 0.85/1.07 tff(541,plain,
% 0.85/1.07 (hskp2),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[540, 519])).
% 0.85/1.07 tff(542,plain,
% 0.85/1.07 (((~hskp2) | c2_1(a99)) <=> ((~hskp2) | c2_1(a99))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(543,axiom,((~hskp2) | c2_1(a99)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.85/1.07 tff(544,plain,
% 0.85/1.07 ((~hskp2) | c2_1(a99)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[543, 542])).
% 0.85/1.07 tff(545,plain,
% 0.85/1.07 ((~hskp2) | c2_1(a99)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[544, 542])).
% 0.85/1.07 tff(546,plain,
% 0.85/1.07 ((~hskp2) | c2_1(a99)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[545, 542])).
% 0.85/1.07 tff(547,plain,
% 0.85/1.07 ((~hskp2) | c2_1(a99)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[546, 542])).
% 0.85/1.07 tff(548,plain,
% 0.85/1.07 ((~hskp2) | c2_1(a99)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[547, 542])).
% 0.85/1.07 tff(549,plain,
% 0.85/1.07 (c2_1(a99)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[548, 541])).
% 0.85/1.07 tff(550,assumption,(~c1_1(a99)), introduced(assumption)).
% 0.85/1.07 tff(551,plain,
% 0.85/1.07 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(552,plain,
% 0.85/1.07 ((hskp22 | hskp21 | (~ndr1_0) | c1_1(a99) | c3_1(a99) | (~c2_1(a99))) <=> (hskp22 | hskp21 | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(553,plain,
% 0.85/1.07 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a99) | c3_1(a99) | (~c2_1(a99)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99)))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[552])).
% 0.85/1.07 tff(554,plain,
% 0.85/1.07 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a99) | c3_1(a99) | (~c2_1(a99)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99))),
% 0.85/1.07 inference(transitivity,[status(thm)],[553, 551])).
% 0.85/1.07 tff(555,plain,
% 0.85/1.07 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a99) | c3_1(a99) | (~c2_1(a99)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(556,plain,
% 0.85/1.07 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.85/1.07 tff(557,plain,
% 0.85/1.07 (hskp21 | (~c2_1(a99)) | c3_1(a99)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[556, 117, 135, 550, 161])).
% 0.85/1.07 tff(558,plain,
% 0.85/1.07 (c3_1(a99)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[557, 549, 471])).
% 0.85/1.07 tff(559,plain,
% 0.85/1.07 (((~hskp2) | (~c0_1(a99))) <=> ((~hskp2) | (~c0_1(a99)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(560,plain,
% 0.85/1.07 (((~c0_1(a99)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a99)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(561,axiom,((~c0_1(a99)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.85/1.07 tff(562,plain,
% 0.85/1.07 ((~hskp2) | (~c0_1(a99))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[561, 560])).
% 0.85/1.07 tff(563,plain,
% 0.85/1.07 ((~hskp2) | (~c0_1(a99))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[562, 559])).
% 0.85/1.07 tff(564,plain,
% 0.85/1.07 (~c0_1(a99)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[563, 541])).
% 0.85/1.07 tff(565,plain,
% 0.85/1.07 (~c3_1(a173)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[494, 520])).
% 0.85/1.07 tff(566,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a173) | c3_1(a173) | c0_1(a99) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a173) | c3_1(a173) | c0_1(a99) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(567,plain,
% 0.85/1.07 (((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173) | c0_1(a173) | c3_1(a173)) <=> (c0_1(a173) | c3_1(a173) | c0_1(a99) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(568,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173) | c0_1(a173) | c3_1(a173))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a173) | c3_1(a173) | c0_1(a99) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173)))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[567])).
% 0.85/1.07 tff(569,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173) | c0_1(a173) | c3_1(a173))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a173) | c3_1(a173) | c0_1(a99) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173))),
% 0.85/1.07 inference(transitivity,[status(thm)],[568, 566])).
% 0.85/1.07 tff(570,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173) | c0_1(a173) | c3_1(a173))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(571,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a173) | c3_1(a173) | c0_1(a99) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.85/1.07 tff(572,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[571, 117, 549, 229, 521, 565, 564, 228, 489, 558, 302, 523])).
% 0.85/1.07 tff(573,plain,(hskp21 | hskp22 | c1_1(a99) | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(574,plain,
% 0.85/1.07 (c1_1(a99)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[573, 326, 135, 136])).
% 0.85/1.07 tff(575,plain,
% 0.85/1.07 (((~hskp2) | (~c1_1(a99))) <=> ((~hskp2) | (~c1_1(a99)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(576,plain,
% 0.85/1.07 (((~c1_1(a99)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a99)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(577,axiom,((~c1_1(a99)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.85/1.07 tff(578,plain,
% 0.85/1.07 ((~hskp2) | (~c1_1(a99))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.85/1.07 tff(579,plain,
% 0.85/1.07 ((~hskp2) | (~c1_1(a99))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[578, 575])).
% 0.85/1.07 tff(580,plain,
% 0.85/1.07 (~hskp2),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[579, 574])).
% 0.85/1.07 tff(581,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[540, 580, 517])).
% 0.85/1.07 tff(582,plain,(hskp28 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(583,plain,
% 0.85/1.07 (hskp28),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[582, 135])).
% 0.85/1.07 tff(584,plain,
% 0.85/1.07 (((~hskp28) | c0_1(a137)) <=> ((~hskp28) | c0_1(a137))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(585,axiom,((~hskp28) | c0_1(a137)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 0.85/1.07 tff(586,plain,
% 0.85/1.07 ((~hskp28) | c0_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.85/1.07 tff(587,plain,
% 0.85/1.07 ((~hskp28) | c0_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[586, 584])).
% 0.85/1.07 tff(588,plain,
% 0.85/1.07 ((~hskp28) | c0_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[587, 584])).
% 0.85/1.07 tff(589,plain,
% 0.85/1.07 ((~hskp28) | c0_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[588, 584])).
% 0.85/1.07 tff(590,plain,
% 0.85/1.07 ((~hskp28) | c0_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[589, 584])).
% 0.85/1.07 tff(591,plain,
% 0.85/1.07 (c0_1(a137)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[590, 583])).
% 0.85/1.07 tff(592,plain,
% 0.85/1.07 (((~hskp28) | c2_1(a137)) <=> ((~hskp28) | c2_1(a137))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(593,axiom,((~hskp28) | c2_1(a137)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.85/1.07 tff(594,plain,
% 0.85/1.07 ((~hskp28) | c2_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[593, 592])).
% 0.85/1.07 tff(595,plain,
% 0.85/1.07 ((~hskp28) | c2_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[594, 592])).
% 0.85/1.07 tff(596,plain,
% 0.85/1.07 ((~hskp28) | c2_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[595, 592])).
% 0.85/1.07 tff(597,plain,
% 0.85/1.07 ((~hskp28) | c2_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[596, 592])).
% 0.85/1.07 tff(598,plain,
% 0.85/1.07 ((~hskp28) | c2_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[597, 592])).
% 0.85/1.07 tff(599,plain,
% 0.85/1.07 (c2_1(a137)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[598, 583])).
% 0.85/1.07 tff(600,plain,
% 0.85/1.07 (((~hskp28) | c1_1(a137)) <=> ((~hskp28) | c1_1(a137))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(601,axiom,((~hskp28) | c1_1(a137)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.85/1.07 tff(602,plain,
% 0.85/1.07 ((~hskp28) | c1_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.85/1.07 tff(603,plain,
% 0.85/1.07 ((~hskp28) | c1_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[602, 600])).
% 0.85/1.07 tff(604,plain,
% 0.85/1.07 ((~hskp28) | c1_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[603, 600])).
% 0.85/1.07 tff(605,plain,
% 0.85/1.07 ((~hskp28) | c1_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[604, 600])).
% 0.85/1.07 tff(606,plain,
% 0.85/1.07 ((~hskp28) | c1_1(a137)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[605, 600])).
% 0.85/1.07 tff(607,plain,
% 0.85/1.07 (c1_1(a137)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[606, 583])).
% 0.85/1.07 tff(608,plain,
% 0.85/1.07 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a137)) | c3_1(a137) | (~c1_1(a137)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a137)) | c3_1(a137) | (~c1_1(a137)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(609,plain,
% 0.85/1.07 ((hskp0 | (~ndr1_0) | c3_1(a137) | (~c0_1(a137)) | (~c1_1(a137))) <=> (hskp0 | (~ndr1_0) | (~c0_1(a137)) | c3_1(a137) | (~c1_1(a137)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(610,plain,
% 0.85/1.07 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a137) | (~c0_1(a137)) | (~c1_1(a137)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a137)) | c3_1(a137) | (~c1_1(a137))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[609])).
% 0.85/1.07 tff(611,plain,
% 0.85/1.07 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a137) | (~c0_1(a137)) | (~c1_1(a137)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a137)) | c3_1(a137) | (~c1_1(a137)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[610, 608])).
% 0.85/1.07 tff(612,plain,
% 0.85/1.07 ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a137) | (~c0_1(a137)) | (~c1_1(a137)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(613,plain,
% 0.85/1.07 ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a137)) | c3_1(a137) | (~c1_1(a137))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.85/1.07 tff(614,plain,
% 0.85/1.07 (hskp0 | c3_1(a137)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[613, 117, 591, 607, 72])).
% 0.85/1.07 tff(615,plain,
% 0.85/1.07 (c3_1(a137)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[614, 88])).
% 0.85/1.07 tff(616,assumption,(c0_1(a137)), introduced(assumption)).
% 0.85/1.07 tff(617,assumption,(c3_1(a137)), introduced(assumption)).
% 0.85/1.07 tff(618,assumption,(c1_1(a137)), introduced(assumption)).
% 0.85/1.07 tff(619,assumption,(c2_1(a137)), introduced(assumption)).
% 0.85/1.07 tff(620,assumption,(hskp18), introduced(assumption)).
% 0.85/1.07 tff(621,plain,
% 0.85/1.07 (~c1_1(a129)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[276, 620])).
% 0.85/1.07 tff(622,plain,
% 0.85/1.07 (c0_1(a129)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[292, 620])).
% 0.85/1.07 tff(623,plain,
% 0.85/1.07 (c2_1(a129)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[284, 620])).
% 0.85/1.07 tff(624,assumption,(~c1_1(a129)), introduced(assumption)).
% 0.85/1.07 tff(625,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c3_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c3_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(626,plain,
% 0.85/1.07 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129))) <=> (c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c3_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(627,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c3_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[626])).
% 0.85/1.07 tff(628,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c3_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[627, 625])).
% 0.85/1.07 tff(629,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(630,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c3_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.85/1.07 tff(631,plain,
% 0.85/1.07 ((~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[630, 117, 616, 619, 624, 10, 617])).
% 0.85/1.07 tff(632,plain,
% 0.85/1.07 (~c3_1(a129)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[631, 623, 622])).
% 0.85/1.07 tff(633,plain,
% 0.85/1.07 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(634,plain,
% 0.85/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[633])).
% 0.85/1.07 tff(635,plain,
% 0.85/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(636,plain,
% 0.85/1.07 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(637,plain,
% 0.85/1.07 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[636])).
% 0.85/1.07 tff(638,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 0.85/1.07 tff(639,plain,
% 0.85/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[638, 637])).
% 0.85/1.07 tff(640,plain,
% 0.85/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[639, 635])).
% 0.85/1.07 tff(641,plain,(
% 0.85/1.07 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.07 inference(skolemize,[status(sab)],[640])).
% 0.85/1.07 tff(642,plain,
% 0.85/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[641, 634])).
% 0.85/1.07 tff(643,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(644,plain,
% 0.85/1.07 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129))) <=> (c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(645,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[644])).
% 0.85/1.07 tff(646,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 0.85/1.07 inference(transitivity,[status(thm)],[645, 643])).
% 0.85/1.07 tff(647,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(648,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[647, 646])).
% 0.85/1.07 tff(649,plain,
% 0.85/1.07 ((~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[648, 117, 618, 619, 624, 642, 617])).
% 0.85/1.07 tff(650,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[649, 632, 623, 622])).
% 0.85/1.07 tff(651,plain,((~hskp18) | (~c1_1(a137)) | (~c2_1(a137)) | c1_1(a129) | (~c3_1(a137)) | (~c0_1(a137))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(652,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[651, 621, 620, 619, 618, 617, 616])).
% 0.85/1.07 tff(653,plain,((~hskp18) | (~c2_1(a137)) | (~c1_1(a137)) | (~c3_1(a137)) | (~c0_1(a137))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(654,plain,
% 0.85/1.07 (~hskp18),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[653, 615, 607, 599, 591])).
% 0.85/1.07 tff(655,plain,
% 0.85/1.07 (hskp0 | c3_1(a137)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[613, 117, 616, 618, 72])).
% 0.85/1.07 tff(656,plain,
% 0.85/1.07 (c3_1(a137)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[655, 88])).
% 0.85/1.07 tff(657,plain,
% 0.85/1.07 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(658,plain,
% 0.85/1.07 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[657])).
% 0.85/1.07 tff(659,plain,
% 0.85/1.07 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(660,plain,
% 0.85/1.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_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) | (~c3_1(U)) | (~c0_1(U)) | (~c1_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)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp18) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(661,plain,
% 0.85/1.07 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[660])).
% 0.85/1.07 tff(662,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 0.85/1.07 tff(663,plain,
% 0.85/1.07 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.85/1.07 tff(664,plain,
% 0.85/1.07 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[663, 659])).
% 0.85/1.08 tff(665,plain,(
% 0.85/1.08 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.85/1.08 inference(skolemize,[status(sab)],[664])).
% 0.85/1.08 tff(666,plain,
% 0.85/1.08 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[665, 658])).
% 0.85/1.08 tff(667,assumption,(hskp20), introduced(assumption)).
% 0.85/1.08 tff(668,plain,
% 0.85/1.08 (((~hskp20) | (~c3_1(a132))) <=> ((~hskp20) | (~c3_1(a132)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(669,plain,
% 0.85/1.08 (((~c3_1(a132)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a132)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(670,axiom,((~c3_1(a132)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.85/1.08 tff(671,plain,
% 0.85/1.08 ((~hskp20) | (~c3_1(a132))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.85/1.08 tff(672,plain,
% 0.85/1.08 ((~hskp20) | (~c3_1(a132))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[671, 668])).
% 0.85/1.08 tff(673,plain,
% 0.85/1.08 (~c3_1(a132)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[672, 667])).
% 0.85/1.08 tff(674,plain,
% 0.85/1.08 (((~hskp20) | (~c1_1(a132))) <=> ((~hskp20) | (~c1_1(a132)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(675,plain,
% 0.85/1.08 (((~c1_1(a132)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a132)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(676,axiom,((~c1_1(a132)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 0.85/1.08 tff(677,plain,
% 0.85/1.08 ((~hskp20) | (~c1_1(a132))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[676, 675])).
% 0.85/1.08 tff(678,plain,
% 0.85/1.08 ((~hskp20) | (~c1_1(a132))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[677, 674])).
% 0.85/1.08 tff(679,plain,
% 0.85/1.08 (~c1_1(a132)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[678, 667])).
% 0.85/1.08 tff(680,plain,
% 0.85/1.08 (~hskp18),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[653, 656, 618, 619, 616])).
% 0.85/1.08 tff(681,plain,
% 0.85/1.08 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a132)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(682,plain,
% 0.85/1.08 ((hskp18 | (~ndr1_0) | (~c3_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132))) <=> (hskp18 | c1_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a132)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(683,plain,
% 0.85/1.08 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a132))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[682])).
% 0.85/1.08 tff(684,plain,
% 0.85/1.08 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a132)))),
% 0.85/1.08 inference(transitivity,[status(thm)],[683, 681])).
% 0.85/1.08 tff(685,plain,
% 0.85/1.08 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))),
% 0.85/1.08 inference(quant_inst,[status(thm)],[])).
% 0.85/1.08 tff(686,plain,
% 0.85/1.08 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a132))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[685, 684])).
% 0.85/1.08 tff(687,plain,
% 0.85/1.08 (~c0_1(a132)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[686, 117, 680, 616, 618, 679, 673, 666, 656])).
% 0.85/1.08 tff(688,plain,
% 0.85/1.08 (((~hskp20) | (~c2_1(a132))) <=> ((~hskp20) | (~c2_1(a132)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(689,plain,
% 0.85/1.08 (((~c2_1(a132)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a132)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(690,axiom,((~c2_1(a132)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.85/1.08 tff(691,plain,
% 0.85/1.08 ((~hskp20) | (~c2_1(a132))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.85/1.08 tff(692,plain,
% 0.85/1.08 ((~hskp20) | (~c2_1(a132))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[691, 688])).
% 0.85/1.08 tff(693,plain,
% 0.85/1.08 (~c2_1(a132)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[692, 667])).
% 0.92/1.08 tff(694,plain,
% 0.92/1.08 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp18 | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(695,plain,
% 0.92/1.08 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a132) | c1_1(a132) | c3_1(a132)) <=> (hskp19 | hskp18 | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(696,plain,
% 0.92/1.08 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a132) | c1_1(a132) | c3_1(a132))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0)))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[695])).
% 0.92/1.08 tff(697,plain,
% 0.92/1.08 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a132) | c1_1(a132) | c3_1(a132))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp18 | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0))),
% 0.92/1.08 inference(transitivity,[status(thm)],[696, 694])).
% 0.92/1.08 tff(698,plain,
% 0.92/1.08 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a132) | c1_1(a132) | c3_1(a132))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(699,plain,
% 0.92/1.08 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp18 | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[698, 697])).
% 0.92/1.08 tff(700,plain,
% 0.92/1.08 (hskp19),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[699, 117, 680, 679, 693, 673, 30])).
% 0.92/1.08 tff(701,plain,
% 0.92/1.08 (~c2_1(a130)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[237, 700])).
% 0.92/1.08 tff(702,plain,
% 0.92/1.08 (c3_1(a130)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[245, 700])).
% 0.92/1.08 tff(703,plain,
% 0.92/1.08 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a132) | c2_1(a132) | c2_1(a130) | (~ndr1_0) | c0_1(a130) | (~c3_1(a130)) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a132) | c2_1(a132) | c2_1(a130) | (~ndr1_0) | c0_1(a130) | (~c3_1(a130)) | c0_1(a132))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(704,plain,
% 0.92/1.08 ((hskp0 | (~ndr1_0) | c2_1(a130) | c0_1(a130) | (~c3_1(a130)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (hskp0 | c1_1(a132) | c2_1(a132) | c2_1(a130) | (~ndr1_0) | c0_1(a130) | (~c3_1(a130)) | c0_1(a132))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(705,plain,
% 0.92/1.08 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a130) | c0_1(a130) | (~c3_1(a130)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a132) | c2_1(a132) | c2_1(a130) | (~ndr1_0) | c0_1(a130) | (~c3_1(a130)) | c0_1(a132)))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[704])).
% 0.92/1.08 tff(706,plain,
% 0.92/1.08 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a130) | c0_1(a130) | (~c3_1(a130)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a132) | c2_1(a132) | c2_1(a130) | (~ndr1_0) | c0_1(a130) | (~c3_1(a130)) | c0_1(a132))),
% 0.92/1.08 inference(transitivity,[status(thm)],[705, 703])).
% 0.92/1.08 tff(707,plain,
% 0.92/1.08 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a130) | c0_1(a130) | (~c3_1(a130)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(708,plain,
% 0.92/1.08 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a132) | c2_1(a132) | c2_1(a130) | (~ndr1_0) | c0_1(a130) | (~c3_1(a130)) | c0_1(a132)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[707, 706])).
% 0.92/1.08 tff(709,plain,
% 0.92/1.08 (c0_1(a130)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[708, 117, 88, 702, 679, 693, 701, 199, 687])).
% 0.92/1.08 tff(710,plain,
% 0.92/1.08 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(711,plain,
% 0.92/1.08 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[710])).
% 0.92/1.08 tff(712,plain,
% 0.92/1.08 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(713,plain,
% 0.92/1.08 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~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))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp2))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(714,plain,
% 0.92/1.08 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[713])).
% 0.92/1.08 tff(715,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 0.92/1.08 tff(716,plain,
% 0.92/1.08 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[715, 714])).
% 0.92/1.08 tff(717,plain,
% 0.92/1.08 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[716, 712])).
% 0.92/1.08 tff(718,plain,(
% 0.92/1.08 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.08 inference(skolemize,[status(sab)],[717])).
% 0.92/1.08 tff(719,plain,
% 0.92/1.08 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[718, 711])).
% 0.92/1.08 tff(720,plain,
% 0.92/1.08 (c1_1(a130)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[253, 700])).
% 0.92/1.08 tff(721,plain,
% 0.92/1.08 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | (~c3_1(a130)) | (~c1_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(722,plain,
% 0.92/1.08 ((hskp2 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130))) <=> (hskp2 | c2_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(723,plain,
% 0.92/1.08 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | (~c3_1(a130)) | (~c1_1(a130))))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[722])).
% 0.92/1.08 tff(724,plain,
% 0.92/1.08 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 0.92/1.08 inference(transitivity,[status(thm)],[723, 721])).
% 0.92/1.08 tff(725,plain,
% 0.92/1.08 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(726,plain,
% 0.92/1.08 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | (~c3_1(a130)) | (~c1_1(a130))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[725, 724])).
% 0.92/1.08 tff(727,plain,
% 0.92/1.08 (hskp2),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[726, 117, 616, 618, 619, 720, 702, 701, 719])).
% 0.92/1.08 tff(728,plain,
% 0.92/1.08 (~c0_1(a99)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[563, 727])).
% 0.92/1.08 tff(729,plain,
% 0.92/1.08 (c2_1(a99)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[548, 727])).
% 0.92/1.08 tff(730,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(731,plain,
% 0.92/1.08 (((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a132) | c0_1(a132) | c3_1(a132)) <=> (c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(732,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132)))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[731])).
% 0.92/1.08 tff(733,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))),
% 0.92/1.08 inference(transitivity,[status(thm)],[732, 730])).
% 0.92/1.08 tff(734,plain,
% 0.92/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a132) | c0_1(a132) | c3_1(a132))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(735,plain,
% 0.92/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[734, 733])).
% 0.92/1.08 tff(736,plain,
% 0.92/1.08 (~c3_1(a99)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[735, 117, 720, 729, 693, 673, 701, 728, 489, 687, 709])).
% 0.92/1.08 tff(737,plain,
% 0.92/1.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(738,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[737])).
% 0.92/1.08 tff(739,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(740,plain,
% 0.92/1.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_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)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_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)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(741,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[740])).
% 0.92/1.08 tff(742,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 0.92/1.08 tff(743,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[742, 741])).
% 0.92/1.08 tff(744,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[743, 739])).
% 0.92/1.08 tff(745,plain,(
% 0.92/1.08 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.08 inference(skolemize,[status(sab)],[744])).
% 0.92/1.08 tff(746,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[745, 738])).
% 0.92/1.08 tff(747,plain,
% 0.92/1.08 (~c1_1(a99)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[579, 727])).
% 0.92/1.08 tff(748,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a132) | c2_1(a132) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a132) | c2_1(a132) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c0_1(a132))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(749,plain,
% 0.92/1.08 (((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (c1_1(a132) | c2_1(a132) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c0_1(a132))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(750,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a132) | c2_1(a132) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c0_1(a132)))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[749])).
% 0.92/1.08 tff(751,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a132) | c2_1(a132) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c0_1(a132))),
% 0.92/1.08 inference(transitivity,[status(thm)],[750, 748])).
% 0.92/1.08 tff(752,plain,
% 0.92/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(753,plain,
% 0.92/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a132) | c2_1(a132) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c0_1(a132)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[752, 751])).
% 0.92/1.08 tff(754,plain,
% 0.92/1.08 ($false),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[753, 117, 729, 679, 693, 728, 747, 746, 736, 687])).
% 0.92/1.08 tff(755,plain,((~hskp20) | hskp0 | (~c0_1(a137)) | (~c1_1(a137)) | (~c2_1(a137))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.08 tff(756,plain,
% 0.92/1.08 (~hskp20),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[755, 88, 591, 607, 599])).
% 0.92/1.08 tff(757,plain,
% 0.92/1.08 ((hskp20 | hskp18 | hskp4) <=> (hskp20 | hskp18 | hskp4)),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(758,plain,
% 0.92/1.08 (((hskp18 | hskp4) | hskp20) <=> (hskp20 | hskp18 | hskp4)),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(759,axiom,((hskp18 | hskp4) | hskp20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 0.92/1.08 tff(760,plain,
% 0.92/1.08 (hskp20 | hskp18 | hskp4),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[759, 758])).
% 0.92/1.08 tff(761,plain,
% 0.92/1.08 (hskp20 | hskp18 | hskp4),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[760, 757])).
% 0.92/1.08 tff(762,plain,
% 0.92/1.08 (hskp20 | hskp18 | hskp4),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[761, 757])).
% 0.92/1.08 tff(763,plain,
% 0.92/1.08 (hskp20 | hskp18 | hskp4),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[762, 757])).
% 0.92/1.08 tff(764,plain,
% 0.92/1.08 (hskp20 | hskp18 | hskp4),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[763, 757])).
% 0.92/1.08 tff(765,plain,
% 0.92/1.08 (hskp4),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[764, 756, 654])).
% 0.92/1.08 tff(766,plain,
% 0.92/1.08 (~c3_1(a103)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[78, 765])).
% 0.92/1.08 tff(767,plain,
% 0.92/1.08 (c0_1(a103)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[86, 765])).
% 0.92/1.08 tff(768,plain,
% 0.92/1.08 (c2_1(a103)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[145, 765])).
% 0.92/1.08 tff(769,plain,
% 0.92/1.08 ($false),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[215, 768, 767, 88, 766, 135])).
% 0.92/1.08 tff(770,plain,(hskp0 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.92/1.08 tff(771,plain,
% 0.92/1.08 (hskp0),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[770, 135])).
% 0.92/1.08 tff(772,plain,
% 0.92/1.08 (~c3_1(a97)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[221, 771])).
% 0.92/1.08 tff(773,plain,
% 0.92/1.08 (~c2_1(a97)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[227, 771])).
% 0.92/1.08 tff(774,plain,
% 0.92/1.08 (^[U: $i] : refl((hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(775,plain,
% 0.92/1.08 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[774])).
% 0.92/1.08 tff(776,plain,
% 0.92/1.08 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(777,plain,
% 0.92/1.08 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp11) <=> ((hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp11))), rewrite(((hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp11) <=> (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp11) <=> (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(778,plain,
% 0.92/1.09 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp11) <=> ![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[777])).
% 0.92/1.09 tff(779,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 0.92/1.09 tff(780,plain,
% 0.92/1.09 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[779, 778])).
% 0.92/1.09 tff(781,plain,
% 0.92/1.09 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[780, 776])).
% 0.92/1.09 tff(782,plain,(
% 0.92/1.09 ![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/1.09 inference(skolemize,[status(sab)],[781])).
% 0.92/1.09 tff(783,plain,
% 0.92/1.09 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[782, 775])).
% 0.92/1.09 tff(784,plain,
% 0.92/1.09 (c0_1(a97)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[61, 771])).
% 0.92/1.09 tff(785,plain,
% 0.92/1.09 (((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp18 | hskp11 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))) <=> ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp18 | hskp11 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(786,plain,
% 0.92/1.09 ((hskp18 | hskp11 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97))) <=> (hskp18 | hskp11 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(787,plain,
% 0.92/1.09 (((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)))) <=> ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp18 | hskp11 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[786])).
% 0.92/1.09 tff(788,plain,
% 0.92/1.09 (((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)))) <=> ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp18 | hskp11 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[787, 785])).
% 0.92/1.09 tff(789,plain,
% 0.92/1.09 ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(790,plain,
% 0.92/1.09 ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp18 | hskp11 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.92/1.09 tff(791,plain,
% 0.92/1.09 (hskp18 | hskp11),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[790, 117, 784, 773, 772, 783])).
% 0.92/1.09 tff(792,plain,
% 0.92/1.09 (hskp11),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[791, 52])).
% 0.92/1.09 tff(793,plain,
% 0.92/1.09 (((~hskp11) | (~c1_1(a112))) <=> ((~hskp11) | (~c1_1(a112)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(794,plain,
% 0.92/1.09 (((~c1_1(a112)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a112)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(795,axiom,((~c1_1(a112)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.92/1.09 tff(796,plain,
% 0.92/1.09 ((~hskp11) | (~c1_1(a112))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[795, 794])).
% 0.92/1.09 tff(797,plain,
% 0.92/1.09 ((~hskp11) | (~c1_1(a112))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[796, 793])).
% 0.92/1.09 tff(798,plain,
% 0.92/1.09 (~c1_1(a112)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[797, 792])).
% 0.92/1.09 tff(799,plain,
% 0.92/1.09 (((~hskp11) | (~c0_1(a112))) <=> ((~hskp11) | (~c0_1(a112)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(800,plain,
% 0.92/1.09 (((~c0_1(a112)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a112)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(801,axiom,((~c0_1(a112)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.92/1.09 tff(802,plain,
% 0.92/1.09 ((~hskp11) | (~c0_1(a112))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[801, 800])).
% 0.92/1.09 tff(803,plain,
% 0.92/1.09 ((~hskp11) | (~c0_1(a112))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[802, 799])).
% 0.92/1.09 tff(804,plain,
% 0.92/1.09 (~c0_1(a112)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[803, 792])).
% 0.92/1.09 tff(805,assumption,(~hskp4), introduced(assumption)).
% 0.92/1.09 tff(806,plain,
% 0.92/1.09 (hskp20),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[764, 52, 805])).
% 0.92/1.09 tff(807,plain,
% 0.92/1.09 (~c3_1(a132)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[672, 806])).
% 0.92/1.09 tff(808,plain,
% 0.92/1.09 (~c2_1(a132)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[692, 806])).
% 0.92/1.09 tff(809,plain,
% 0.92/1.09 (~c1_1(a132)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[678, 806])).
% 0.92/1.09 tff(810,plain,
% 0.92/1.09 (hskp19),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[699, 117, 52, 809, 808, 807, 30])).
% 0.92/1.09 tff(811,plain,
% 0.92/1.09 (c1_1(a97)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[262, 810, 31, 53, 231])).
% 0.92/1.09 tff(812,plain,
% 0.92/1.09 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(813,plain,
% 0.92/1.09 ((hskp6 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97))) <=> (hskp6 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(814,plain,
% 0.92/1.09 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[813])).
% 0.92/1.09 tff(815,plain,
% 0.92/1.09 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[814, 812])).
% 0.92/1.09 tff(816,plain,
% 0.92/1.09 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(817,plain,
% 0.92/1.09 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.92/1.09 tff(818,plain,
% 0.92/1.09 (hskp6 | (~c1_1(a97))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[817, 117, 231, 53, 364])).
% 0.92/1.09 tff(819,plain,
% 0.92/1.09 (hskp6),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[818, 811])).
% 0.92/1.09 tff(820,plain,
% 0.92/1.09 (~c3_1(a105)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[377, 819])).
% 0.92/1.09 tff(821,plain,
% 0.92/1.09 (c2_1(a105)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[385, 819])).
% 0.92/1.09 tff(822,plain,
% 0.92/1.09 (c1_1(a105)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[393, 819])).
% 0.92/1.09 tff(823,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a132) | c2_1(a132) | c3_1(a132) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a132) | c2_1(a132) | c3_1(a132) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(824,plain,
% 0.92/1.09 (((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a132) | c1_1(a132) | c3_1(a132)) <=> (c1_1(a132) | c2_1(a132) | c3_1(a132) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(825,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a132) | c1_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a132) | c2_1(a132) | c3_1(a132) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[824])).
% 0.92/1.09 tff(826,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a132) | c1_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a132) | c2_1(a132) | c3_1(a132) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[825, 823])).
% 0.92/1.09 tff(827,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a132) | c1_1(a132) | c3_1(a132))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(828,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a132) | c2_1(a132) | c3_1(a132) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[827, 826])).
% 0.92/1.09 tff(829,plain,
% 0.92/1.09 ($false),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[828, 117, 822, 821, 809, 808, 807, 820, 31, 53, 405, 811])).
% 0.92/1.09 tff(830,plain,(hskp18 | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.92/1.09 tff(831,plain,
% 0.92/1.09 (hskp18),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[830, 805, 772, 784, 773])).
% 0.92/1.09 tff(832,plain,
% 0.92/1.09 (~c1_1(a129)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[276, 831])).
% 0.92/1.09 tff(833,plain,
% 0.92/1.09 (c2_1(a129)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[284, 831])).
% 0.92/1.09 tff(834,plain,
% 0.92/1.09 (c0_1(a129)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[292, 831])).
% 0.92/1.09 tff(835,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(836,plain,
% 0.92/1.09 (((~ndr1_0) | (~c2_1(a129)) | (~c3_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129))) <=> (c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(837,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a129)) | (~c3_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[836])).
% 0.92/1.09 tff(838,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a129)) | (~c3_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[837, 835])).
% 0.92/1.09 tff(839,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a129)) | (~c3_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(840,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[839, 838])).
% 0.92/1.09 tff(841,plain,
% 0.92/1.09 (~c3_1(a129)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[840, 117, 834, 833, 832, 10])).
% 0.92/1.09 tff(842,plain,
% 0.92/1.09 (^[U: $i] : refl((hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(843,plain,
% 0.92/1.09 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[842])).
% 0.92/1.09 tff(844,plain,
% 0.92/1.09 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(845,plain,
% 0.92/1.09 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp7) <=> ((hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7))), rewrite(((hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp7) <=> (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(846,plain,
% 0.92/1.09 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp7) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[845])).
% 0.92/1.09 tff(847,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 0.92/1.09 tff(848,plain,
% 0.92/1.09 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[847, 846])).
% 0.92/1.09 tff(849,plain,
% 0.92/1.09 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[848, 844])).
% 0.92/1.09 tff(850,plain,(
% 0.92/1.09 ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(skolemize,[status(sab)],[849])).
% 0.92/1.09 tff(851,plain,
% 0.92/1.09 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[850, 843])).
% 0.92/1.09 tff(852,plain,
% 0.92/1.09 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(853,plain,
% 0.92/1.09 ((hskp7 | hskp4 | (~ndr1_0) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129))) <=> (hskp7 | hskp4 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(854,plain,
% 0.92/1.09 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[853])).
% 0.92/1.09 tff(855,plain,
% 0.92/1.09 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[854, 852])).
% 0.92/1.09 tff(856,plain,
% 0.92/1.09 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(857,plain,
% 0.92/1.09 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[856, 855])).
% 0.92/1.09 tff(858,plain,
% 0.92/1.09 (hskp7),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[857, 117, 805, 834, 833, 832, 851])).
% 0.92/1.09 tff(859,plain,
% 0.92/1.09 (((~hskp7) | c3_1(a106)) <=> ((~hskp7) | c3_1(a106))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(860,axiom,((~hskp7) | c3_1(a106)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.92/1.09 tff(861,plain,
% 0.92/1.09 ((~hskp7) | c3_1(a106)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[860, 859])).
% 0.92/1.09 tff(862,plain,
% 0.92/1.09 ((~hskp7) | c3_1(a106)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[861, 859])).
% 0.92/1.09 tff(863,plain,
% 0.92/1.09 ((~hskp7) | c3_1(a106)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[862, 859])).
% 0.92/1.09 tff(864,plain,
% 0.92/1.09 ((~hskp7) | c3_1(a106)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[863, 859])).
% 0.92/1.09 tff(865,plain,
% 0.92/1.09 ((~hskp7) | c3_1(a106)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[864, 859])).
% 0.92/1.09 tff(866,plain,
% 0.92/1.09 (c3_1(a106)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[865, 858])).
% 0.92/1.09 tff(867,plain,
% 0.92/1.09 (((~hskp7) | c2_1(a106)) <=> ((~hskp7) | c2_1(a106))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(868,axiom,((~hskp7) | c2_1(a106)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.92/1.09 tff(869,plain,
% 0.92/1.09 ((~hskp7) | c2_1(a106)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[868, 867])).
% 0.92/1.09 tff(870,plain,
% 0.92/1.09 ((~hskp7) | c2_1(a106)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[869, 867])).
% 0.92/1.09 tff(871,plain,
% 0.92/1.09 ((~hskp7) | c2_1(a106)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[870, 867])).
% 0.92/1.09 tff(872,plain,
% 0.92/1.09 ((~hskp7) | c2_1(a106)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[871, 867])).
% 0.92/1.09 tff(873,plain,
% 0.92/1.09 ((~hskp7) | c2_1(a106)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[872, 867])).
% 0.92/1.09 tff(874,plain,
% 0.92/1.09 (c2_1(a106)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[873, 858])).
% 0.92/1.09 tff(875,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(876,plain,
% 0.92/1.09 (((~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129))) <=> (c1_1(a129) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(877,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[876])).
% 0.92/1.09 tff(878,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 0.92/1.09 inference(transitivity,[status(thm)],[877, 875])).
% 0.92/1.09 tff(879,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(880,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[879, 878])).
% 0.92/1.09 tff(881,plain,
% 0.92/1.09 (~c1_1(a106)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[880, 117, 834, 833, 874, 866, 832, 642, 841])).
% 0.92/1.09 tff(882,plain,
% 0.92/1.09 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | c3_1(a129))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | c3_1(a129))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(883,plain,
% 0.92/1.09 ((hskp22 | hskp21 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c2_1(a129))) <=> (hskp22 | hskp21 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | c3_1(a129))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(884,plain,
% 0.92/1.09 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | c3_1(a129)))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[883])).
% 0.92/1.09 tff(885,plain,
% 0.92/1.09 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | c3_1(a129))),
% 0.92/1.09 inference(transitivity,[status(thm)],[884, 882])).
% 0.92/1.09 tff(886,plain,
% 0.92/1.09 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(887,plain,
% 0.92/1.09 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | c3_1(a129)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[886, 885])).
% 0.92/1.09 tff(888,plain,
% 0.92/1.09 (hskp21),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[887, 117, 135, 833, 832, 161, 841])).
% 0.92/1.09 tff(889,plain,
% 0.92/1.09 (~c2_1(a136)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[175, 888])).
% 0.92/1.09 tff(890,plain,
% 0.92/1.09 (~c1_1(a136)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[181, 888])).
% 0.92/1.09 tff(891,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a136) | c2_1(a136) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c0_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a136) | c2_1(a136) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c0_1(a136)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(892,plain,
% 0.92/1.09 (((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136))) <=> (c1_1(a136) | c2_1(a136) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c0_1(a136)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(893,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a136) | c2_1(a136) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c0_1(a136))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[892])).
% 0.92/1.09 tff(894,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a136) | c2_1(a136) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c0_1(a136)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[893, 891])).
% 0.92/1.09 tff(895,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(896,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a136) | c2_1(a136) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c0_1(a136))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[895, 894])).
% 0.92/1.09 tff(897,plain,
% 0.92/1.09 (~c0_1(a136)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[896, 117, 834, 833, 890, 889, 832, 134, 841])).
% 0.92/1.09 tff(898,plain,
% 0.92/1.09 (^[U: $i] : refl((hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(899,plain,
% 0.92/1.09 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[898])).
% 0.92/1.09 tff(900,plain,
% 0.92/1.09 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(901,plain,
% 0.92/1.09 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | 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)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp5) <=> ((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp5))), rewrite(((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp5) <=> (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp5) <=> (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(902,plain,
% 0.92/1.09 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp5) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[901])).
% 0.92/1.09 tff(903,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 0.92/1.09 tff(904,plain,
% 0.92/1.09 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[903, 902])).
% 0.92/1.09 tff(905,plain,
% 0.92/1.09 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[904, 900])).
% 0.92/1.09 tff(906,plain,(
% 0.92/1.09 ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(skolemize,[status(sab)],[905])).
% 0.92/1.09 tff(907,plain,
% 0.92/1.09 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[906, 899])).
% 0.92/1.10 tff(908,plain,
% 0.92/1.10 (((~hskp7) | (~c0_1(a106))) <=> ((~hskp7) | (~c0_1(a106)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(909,plain,
% 0.92/1.10 (((~c0_1(a106)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a106)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(910,axiom,((~c0_1(a106)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.92/1.10 tff(911,plain,
% 0.92/1.10 ((~hskp7) | (~c0_1(a106))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[910, 909])).
% 0.92/1.10 tff(912,plain,
% 0.92/1.10 ((~hskp7) | (~c0_1(a106))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[911, 908])).
% 0.92/1.10 tff(913,plain,
% 0.92/1.10 (~c0_1(a106)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[912, 858])).
% 0.92/1.10 tff(914,plain,
% 0.92/1.10 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp4 | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | c1_1(a106))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp4 | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | c1_1(a106))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(915,plain,
% 0.92/1.10 ((hskp5 | hskp4 | (~ndr1_0) | c1_1(a106) | c0_1(a106) | (~c2_1(a106))) <=> (hskp5 | hskp4 | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | c1_1(a106))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(916,plain,
% 0.92/1.10 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp4 | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | c1_1(a106)))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[915])).
% 0.92/1.10 tff(917,plain,
% 0.92/1.10 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp4 | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | c1_1(a106))),
% 0.92/1.10 inference(transitivity,[status(thm)],[916, 914])).
% 0.92/1.10 tff(918,plain,
% 0.92/1.10 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(919,plain,
% 0.92/1.10 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp4 | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | c1_1(a106)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[918, 917])).
% 0.92/1.10 tff(920,plain,
% 0.92/1.10 (hskp5),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[919, 117, 805, 874, 913, 907, 881])).
% 0.92/1.10 tff(921,plain,
% 0.92/1.10 (((~hskp5) | (~c3_1(a104))) <=> ((~hskp5) | (~c3_1(a104)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(922,plain,
% 0.92/1.10 (((~c3_1(a104)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a104)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(923,axiom,((~c3_1(a104)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.92/1.10 tff(924,plain,
% 0.92/1.10 ((~hskp5) | (~c3_1(a104))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[923, 922])).
% 0.92/1.10 tff(925,plain,
% 0.92/1.10 ((~hskp5) | (~c3_1(a104))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[924, 921])).
% 0.92/1.10 tff(926,plain,
% 0.92/1.10 (~c3_1(a104)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[925, 920])).
% 0.92/1.10 tff(927,plain,
% 0.92/1.10 (((~hskp5) | (~c0_1(a104))) <=> ((~hskp5) | (~c0_1(a104)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(928,plain,
% 0.92/1.10 (((~c0_1(a104)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a104)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(929,axiom,((~c0_1(a104)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 0.92/1.10 tff(930,plain,
% 0.92/1.10 ((~hskp5) | (~c0_1(a104))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[929, 928])).
% 0.92/1.10 tff(931,plain,
% 0.92/1.10 ((~hskp5) | (~c0_1(a104))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[930, 927])).
% 0.92/1.10 tff(932,plain,
% 0.92/1.10 (~c0_1(a104)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[931, 920])).
% 0.92/1.10 tff(933,plain,
% 0.92/1.10 (((~hskp5) | c2_1(a104)) <=> ((~hskp5) | c2_1(a104))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(934,axiom,((~hskp5) | c2_1(a104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.92/1.10 tff(935,plain,
% 0.92/1.10 ((~hskp5) | c2_1(a104)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[934, 933])).
% 0.92/1.10 tff(936,plain,
% 0.92/1.10 ((~hskp5) | c2_1(a104)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[935, 933])).
% 0.92/1.10 tff(937,plain,
% 0.92/1.10 ((~hskp5) | c2_1(a104)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[936, 933])).
% 0.92/1.10 tff(938,plain,
% 0.92/1.10 ((~hskp5) | c2_1(a104)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[937, 933])).
% 0.92/1.10 tff(939,plain,
% 0.92/1.10 ((~hskp5) | c2_1(a104)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[938, 933])).
% 0.92/1.10 tff(940,plain,
% 0.92/1.10 (c2_1(a104)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[939, 920])).
% 0.92/1.10 tff(941,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a136) | c2_1(a136) | c0_1(a106) | c0_1(a104) | c3_1(a104) | (~ndr1_0) | (~c2_1(a104)) | (~c2_1(a106)) | c1_1(a106) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a136) | c2_1(a136) | c0_1(a106) | c0_1(a104) | c3_1(a104) | (~ndr1_0) | (~c2_1(a104)) | (~c2_1(a106)) | c1_1(a106) | c0_1(a136))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(942,plain,
% 0.92/1.10 (((~ndr1_0) | c0_1(a104) | c3_1(a104) | (~c2_1(a104)) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)) | c2_1(a136) | c1_1(a136) | c0_1(a136)) <=> (c1_1(a136) | c2_1(a136) | c0_1(a106) | c0_1(a104) | c3_1(a104) | (~ndr1_0) | (~c2_1(a104)) | (~c2_1(a106)) | c1_1(a106) | c0_1(a136))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(943,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a104) | c3_1(a104) | (~c2_1(a104)) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a136) | c2_1(a136) | c0_1(a106) | c0_1(a104) | c3_1(a104) | (~ndr1_0) | (~c2_1(a104)) | (~c2_1(a106)) | c1_1(a106) | c0_1(a136)))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[942])).
% 0.92/1.10 tff(944,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a104) | c3_1(a104) | (~c2_1(a104)) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a136) | c2_1(a136) | c0_1(a106) | c0_1(a104) | c3_1(a104) | (~ndr1_0) | (~c2_1(a104)) | (~c2_1(a106)) | c1_1(a106) | c0_1(a136))),
% 0.92/1.10 inference(transitivity,[status(thm)],[943, 941])).
% 0.92/1.10 tff(945,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a104) | c3_1(a104) | (~c2_1(a104)) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)) | c2_1(a136) | c1_1(a136) | c0_1(a136))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(946,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a136) | c2_1(a136) | c0_1(a106) | c0_1(a104) | c3_1(a104) | (~ndr1_0) | (~c2_1(a104)) | (~c2_1(a106)) | c1_1(a106) | c0_1(a136)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.92/1.10 tff(947,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[946, 117, 874, 940, 890, 889, 913, 932, 926, 746, 897, 881])).
% 0.92/1.10 tff(948,plain,(hskp4 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.92/1.10 tff(949,plain,
% 0.92/1.10 (hskp4),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[948, 135])).
% 0.92/1.10 tff(950,plain,
% 0.92/1.10 (c0_1(a103)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[86, 949])).
% 0.92/1.10 tff(951,plain,
% 0.92/1.10 (~c3_1(a103)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[78, 949])).
% 0.92/1.10 tff(952,plain,
% 0.92/1.10 (c2_1(a103)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[145, 949])).
% 0.92/1.10 tff(953,plain,
% 0.92/1.10 (c1_1(a97)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[301, 952, 772, 784, 951, 773, 950])).
% 0.92/1.10 tff(954,plain,
% 0.92/1.10 (^[U: $i] : refl((hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(955,plain,
% 0.92/1.10 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[954])).
% 0.92/1.10 tff(956,plain,
% 0.92/1.10 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(957,plain,
% 0.92/1.10 (^[U: $i] : 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)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp8) <=> ((hskp18 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp8))), rewrite(((hskp18 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp8) <=> (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp8) <=> (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(958,plain,
% 0.92/1.10 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp8) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[957])).
% 0.92/1.10 tff(959,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 0.92/1.10 tff(960,plain,
% 0.92/1.10 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[959, 958])).
% 0.92/1.10 tff(961,plain,
% 0.92/1.10 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[960, 956])).
% 0.92/1.10 tff(962,plain,(
% 0.92/1.10 ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(skolemize,[status(sab)],[961])).
% 0.92/1.10 tff(963,plain,
% 0.92/1.10 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[962, 955])).
% 0.92/1.10 tff(964,plain,
% 0.92/1.10 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp18 | hskp8 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp18 | hskp8 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(965,plain,
% 0.92/1.10 ((hskp18 | hskp8 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97))) <=> (hskp18 | hskp8 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(966,plain,
% 0.92/1.10 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp18 | hskp8 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[965])).
% 0.92/1.10 tff(967,plain,
% 0.92/1.10 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp18 | hskp8 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[966, 964])).
% 0.92/1.10 tff(968,plain,
% 0.92/1.10 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(969,plain,
% 0.92/1.10 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp18 | hskp8 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[968, 967])).
% 0.92/1.10 tff(970,plain,
% 0.92/1.10 (hskp18 | hskp8 | (~c1_1(a97))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[969, 117, 784, 772, 963])).
% 0.92/1.10 tff(971,plain,
% 0.92/1.10 (hskp8),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[970, 52, 953])).
% 0.92/1.10 tff(972,plain,
% 0.92/1.10 (((~hskp8) | c3_1(a107)) <=> ((~hskp8) | c3_1(a107))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(973,axiom,((~hskp8) | c3_1(a107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.92/1.10 tff(974,plain,
% 0.92/1.10 ((~hskp8) | c3_1(a107)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[973, 972])).
% 0.92/1.10 tff(975,plain,
% 0.92/1.10 ((~hskp8) | c3_1(a107)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[974, 972])).
% 0.92/1.10 tff(976,plain,
% 0.92/1.10 ((~hskp8) | c3_1(a107)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[975, 972])).
% 0.92/1.10 tff(977,plain,
% 0.92/1.10 ((~hskp8) | c3_1(a107)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[976, 972])).
% 0.92/1.10 tff(978,plain,
% 0.92/1.10 ((~hskp8) | c3_1(a107)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[977, 972])).
% 0.92/1.10 tff(979,plain,
% 0.92/1.10 (c3_1(a107)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[978, 971])).
% 0.92/1.10 tff(980,plain,
% 0.92/1.10 (((~hskp11) | c3_1(a112)) <=> ((~hskp11) | c3_1(a112))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(981,axiom,((~hskp11) | c3_1(a112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.92/1.10 tff(982,plain,
% 0.92/1.10 ((~hskp11) | c3_1(a112)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[981, 980])).
% 0.92/1.10 tff(983,plain,
% 0.92/1.10 ((~hskp11) | c3_1(a112)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[982, 980])).
% 0.92/1.10 tff(984,plain,
% 0.92/1.10 ((~hskp11) | c3_1(a112)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[983, 980])).
% 0.92/1.10 tff(985,plain,
% 0.92/1.10 ((~hskp11) | c3_1(a112)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[984, 980])).
% 0.92/1.10 tff(986,plain,
% 0.92/1.10 ((~hskp11) | c3_1(a112)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[985, 980])).
% 0.92/1.10 tff(987,plain,
% 0.92/1.10 (c3_1(a112)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[986, 792])).
% 0.92/1.10 tff(988,plain,
% 0.92/1.10 (((~hskp8) | (~c2_1(a107))) <=> ((~hskp8) | (~c2_1(a107)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(989,plain,
% 0.92/1.10 (((~c2_1(a107)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a107)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(990,axiom,((~c2_1(a107)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.92/1.10 tff(991,plain,
% 0.92/1.10 ((~hskp8) | (~c2_1(a107))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[990, 989])).
% 0.92/1.10 tff(992,plain,
% 0.92/1.10 ((~hskp8) | (~c2_1(a107))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[991, 988])).
% 0.92/1.10 tff(993,plain,
% 0.92/1.10 (~c2_1(a107)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[992, 971])).
% 0.92/1.10 tff(994,assumption,(hskp9), introduced(assumption)).
% 0.92/1.10 tff(995,plain,
% 0.92/1.10 (((~hskp9) | (~c0_1(a108))) <=> ((~hskp9) | (~c0_1(a108)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(996,plain,
% 0.92/1.10 (((~c0_1(a108)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a108)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(997,axiom,((~c0_1(a108)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.92/1.10 tff(998,plain,
% 0.92/1.10 ((~hskp9) | (~c0_1(a108))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[997, 996])).
% 0.92/1.10 tff(999,plain,
% 0.92/1.10 ((~hskp9) | (~c0_1(a108))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[998, 995])).
% 0.92/1.10 tff(1000,plain,
% 0.92/1.10 (~c0_1(a108)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[999, 994])).
% 0.92/1.10 tff(1001,plain,
% 0.92/1.10 (((~hskp9) | c2_1(a108)) <=> ((~hskp9) | c2_1(a108))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(1002,axiom,((~hskp9) | c2_1(a108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.92/1.10 tff(1003,plain,
% 0.92/1.10 ((~hskp9) | c2_1(a108)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 0.92/1.10 tff(1004,plain,
% 0.92/1.10 ((~hskp9) | c2_1(a108)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1003, 1001])).
% 0.92/1.10 tff(1005,plain,
% 0.92/1.10 ((~hskp9) | c2_1(a108)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1004, 1001])).
% 0.92/1.10 tff(1006,plain,
% 0.92/1.10 ((~hskp9) | c2_1(a108)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1005, 1001])).
% 0.92/1.10 tff(1007,plain,
% 0.92/1.10 ((~hskp9) | c2_1(a108)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1006, 1001])).
% 0.92/1.10 tff(1008,plain,
% 0.92/1.10 (c2_1(a108)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[1007, 994])).
% 0.92/1.10 tff(1009,plain,
% 0.92/1.10 (((~hskp9) | c1_1(a108)) <=> ((~hskp9) | c1_1(a108))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(1010,axiom,((~hskp9) | c1_1(a108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.92/1.10 tff(1011,plain,
% 0.92/1.10 ((~hskp9) | c1_1(a108)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.92/1.10 tff(1012,plain,
% 0.92/1.10 ((~hskp9) | c1_1(a108)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1011, 1009])).
% 0.92/1.10 tff(1013,plain,
% 0.92/1.10 ((~hskp9) | c1_1(a108)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1012, 1009])).
% 0.92/1.10 tff(1014,plain,
% 0.92/1.10 ((~hskp9) | c1_1(a108)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1013, 1009])).
% 0.92/1.10 tff(1015,plain,
% 0.92/1.10 ((~hskp9) | c1_1(a108)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1014, 1009])).
% 0.92/1.10 tff(1016,plain,
% 0.92/1.10 (c1_1(a108)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[1015, 994])).
% 0.92/1.10 tff(1017,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a108) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a97)) | (~c1_1(a137)) | (~c1_1(a108)) | (~c2_1(a108)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a108) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a97)) | (~c1_1(a137)) | (~c1_1(a108)) | (~c2_1(a108)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(1018,plain,
% 0.92/1.10 (((~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108))) <=> (c0_1(a108) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a97)) | (~c1_1(a137)) | (~c1_1(a108)) | (~c2_1(a108)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(1019,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a108) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a97)) | (~c1_1(a137)) | (~c1_1(a108)) | (~c2_1(a108))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[1018])).
% 0.92/1.10 tff(1020,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a108) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a97)) | (~c1_1(a137)) | (~c1_1(a108)) | (~c2_1(a108)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[1019, 1017])).
% 0.92/1.10 tff(1021,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(1022,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a108) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a97)) | (~c1_1(a137)) | (~c1_1(a108)) | (~c2_1(a108))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 0.92/1.10 tff(1023,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[1022, 117, 616, 618, 619, 1016, 1008, 231, 1000, 31, 354, 303])).
% 0.92/1.10 tff(1024,plain,((~hskp9) | (~c0_1(a137)) | (~c1_1(a137)) | (~c2_1(a137)) | (~c0_1(a97)) | c2_1(a97) | (~c1_1(a97))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.10 tff(1025,plain,
% 0.92/1.10 (~hskp9),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[1024, 591, 607, 599, 784, 773, 953])).
% 0.92/1.10 tff(1026,plain,
% 0.92/1.10 (((~hskp8) | (~c0_1(a107))) <=> ((~hskp8) | (~c0_1(a107)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(1027,plain,
% 0.92/1.10 (((~c0_1(a107)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a107)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(1028,axiom,((~c0_1(a107)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.92/1.10 tff(1029,plain,
% 0.92/1.10 ((~hskp8) | (~c0_1(a107))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 0.92/1.10 tff(1030,plain,
% 0.92/1.10 ((~hskp8) | (~c0_1(a107))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1029, 1026])).
% 0.92/1.10 tff(1031,plain,
% 0.92/1.10 (~c0_1(a107)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[1030, 971])).
% 0.92/1.10 tff(1032,assumption,(~hskp17), introduced(assumption)).
% 0.92/1.10 tff(1033,plain,
% 0.92/1.10 (^[U: $i] : refl((hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(1034,plain,
% 0.92/1.10 (![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[1033])).
% 0.92/1.10 tff(1035,plain,
% 0.92/1.10 (![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(1036,plain,
% 0.92/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp17) <=> ((hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp17))), rewrite(((hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp17) <=> (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp17) <=> (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(1037,plain,
% 0.92/1.10 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp17) <=> ![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[1036])).
% 0.92/1.10 tff(1038,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 0.92/1.10 tff(1039,plain,
% 0.92/1.10 (![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.92/1.10 tff(1040,plain,
% 0.92/1.10 (![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1039, 1035])).
% 0.92/1.10 tff(1041,plain,(
% 0.92/1.10 ![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(skolemize,[status(sab)],[1040])).
% 0.92/1.10 tff(1042,plain,
% 0.92/1.10 (![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1041, 1034])).
% 0.92/1.10 tff(1043,assumption,(~c0_1(a112)), introduced(assumption)).
% 0.92/1.10 tff(1044,assumption,(c3_1(a112)), introduced(assumption)).
% 0.92/1.10 tff(1045,assumption,(~hskp9), introduced(assumption)).
% 0.92/1.10 tff(1046,plain,
% 0.92/1.10 (((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | c0_1(a112) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp9 | c0_1(a112) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(1047,plain,
% 0.92/1.10 ((hskp17 | hskp9 | (~ndr1_0) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112))) <=> (hskp17 | hskp9 | c0_1(a112) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(1048,plain,
% 0.92/1.10 (((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | (~ndr1_0) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | c0_1(a112) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[1047])).
% 0.92/1.10 tff(1049,plain,
% 0.92/1.10 (((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | (~ndr1_0) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp9 | c0_1(a112) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[1048, 1046])).
% 0.92/1.10 tff(1050,plain,
% 0.92/1.10 ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | (~ndr1_0) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(1051,plain,
% 0.92/1.10 ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp9 | c0_1(a112) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 0.92/1.10 tff(1052,plain,
% 0.92/1.10 (hskp17 | (~c2_1(a112))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[1051, 117, 1045, 1044, 1043, 1042])).
% 0.92/1.10 tff(1053,plain,
% 0.92/1.10 (~c2_1(a112)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[1052, 1032])).
% 0.92/1.10 tff(1054,plain,
% 0.92/1.10 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(1055,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[1054])).
% 0.92/1.10 tff(1056,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(1057,plain,
% 0.92/1.10 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(1058,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[1057])).
% 0.92/1.11 tff(1059,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 0.92/1.11 tff(1060,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 0.92/1.11 tff(1061,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1060, 1056])).
% 0.92/1.11 tff(1062,plain,(
% 0.92/1.11 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.92/1.11 inference(skolemize,[status(sab)],[1061])).
% 0.92/1.11 tff(1063,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1062, 1055])).
% 0.92/1.11 tff(1064,assumption,(~c0_1(a107)), introduced(assumption)).
% 0.92/1.11 tff(1065,assumption,(~c1_1(a112)), introduced(assumption)).
% 0.92/1.11 tff(1066,assumption,(c3_1(a107)), introduced(assumption)).
% 0.92/1.11 tff(1067,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a112) | c1_1(a112) | c0_1(a107) | (~ndr1_0) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | (~c3_1(a112)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a112) | c1_1(a112) | c0_1(a107) | (~ndr1_0) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | (~c3_1(a112)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1068,plain,
% 0.92/1.11 (((~ndr1_0) | c2_1(a112) | c1_1(a112) | (~c3_1(a112)) | c0_1(a107) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | c0_1(a112) | (~c3_1(a112))) <=> (c0_1(a112) | c1_1(a112) | c0_1(a107) | (~ndr1_0) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | (~c3_1(a112)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1069,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a112) | c1_1(a112) | (~c3_1(a112)) | c0_1(a107) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a112) | c1_1(a112) | c0_1(a107) | (~ndr1_0) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | (~c3_1(a112))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[1068])).
% 0.92/1.11 tff(1070,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a112) | c1_1(a112) | (~c3_1(a112)) | c0_1(a107) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a112) | c1_1(a112) | c0_1(a107) | (~ndr1_0) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | (~c3_1(a112)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[1069, 1067])).
% 0.92/1.11 tff(1071,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a112) | c1_1(a112) | (~c3_1(a112)) | c0_1(a107) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(1072,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a112) | c1_1(a112) | c0_1(a107) | (~ndr1_0) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | (~c3_1(a112))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 0.92/1.11 tff(1073,plain,
% 0.92/1.11 (~c1_1(a107)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1072, 117, 1044, 1066, 1043, 1065, 1064, 1063, 1053])).
% 0.92/1.11 tff(1074,plain,
% 0.92/1.11 ((hskp19 | hskp18 | hskp17) <=> (hskp19 | hskp18 | hskp17)),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1075,plain,
% 0.92/1.11 (((hskp18 | hskp19) | hskp17) <=> (hskp19 | hskp18 | hskp17)),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1076,axiom,((hskp18 | hskp19) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 0.92/1.11 tff(1077,plain,
% 0.92/1.11 (hskp19 | hskp18 | hskp17),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 0.92/1.11 tff(1078,plain,
% 0.92/1.11 (hskp19 | hskp18 | hskp17),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1077, 1074])).
% 0.92/1.11 tff(1079,plain,
% 0.92/1.11 (hskp19 | hskp18 | hskp17),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1078, 1074])).
% 0.92/1.11 tff(1080,plain,
% 0.92/1.11 (hskp19 | hskp18 | hskp17),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1079, 1074])).
% 0.92/1.11 tff(1081,plain,
% 0.92/1.11 (hskp19 | hskp18 | hskp17),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1080, 1074])).
% 0.92/1.11 tff(1082,plain,
% 0.92/1.11 (hskp19),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1081, 1032, 52])).
% 0.92/1.11 tff(1083,plain,
% 0.92/1.11 (~c2_1(a130)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[237, 1082])).
% 0.92/1.11 tff(1084,plain,
% 0.92/1.11 (c3_1(a130)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[245, 1082])).
% 0.92/1.11 tff(1085,plain,
% 0.92/1.11 (c1_1(a130)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[253, 1082])).
% 0.92/1.11 tff(1086,plain,
% 0.92/1.11 (hskp2),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[726, 117, 616, 618, 619, 1085, 1084, 1083, 719])).
% 0.92/1.11 tff(1087,plain,
% 0.92/1.11 (~c1_1(a99)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[579, 1086])).
% 0.92/1.11 tff(1088,plain,
% 0.92/1.11 (~c0_1(a99)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[563, 1086])).
% 0.92/1.11 tff(1089,assumption,(~c2_1(a107)), introduced(assumption)).
% 0.92/1.11 tff(1090,plain,
% 0.92/1.11 (c2_1(a99)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[548, 1086])).
% 0.92/1.11 tff(1091,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a107) | c2_1(a107) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c1_1(a107))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a107) | c2_1(a107) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c1_1(a107))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1092,plain,
% 0.92/1.11 (((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a107) | c1_1(a107) | c0_1(a107)) <=> (c0_1(a107) | c2_1(a107) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c1_1(a107))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1093,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a107) | c1_1(a107) | c0_1(a107))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a107) | c2_1(a107) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c1_1(a107)))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[1092])).
% 0.92/1.11 tff(1094,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a107) | c1_1(a107) | c0_1(a107))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a107) | c2_1(a107) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c1_1(a107))),
% 0.92/1.11 inference(transitivity,[status(thm)],[1093, 1091])).
% 0.92/1.11 tff(1095,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a107) | c1_1(a107) | c0_1(a107))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(1096,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a107) | c2_1(a107) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c1_1(a107)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1095, 1094])).
% 0.92/1.11 tff(1097,plain,
% 0.92/1.11 (c3_1(a99)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1096, 117, 1090, 1064, 1089, 1088, 1087, 746, 1073])).
% 0.92/1.11 tff(1098,plain,
% 0.92/1.11 (((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)))) <=> ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp9 | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1099,plain,
% 0.92/1.11 ((hskp17 | hskp9 | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99))) <=> (hskp17 | hskp9 | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1100,plain,
% 0.92/1.11 (((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)))) <=> ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[1099])).
% 0.92/1.11 tff(1101,plain,
% 0.92/1.11 (((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)))) <=> ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp9 | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[1100, 1098])).
% 0.92/1.11 tff(1102,plain,
% 0.92/1.11 ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(1103,plain,
% 0.92/1.11 ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp9 | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 0.92/1.11 tff(1104,plain,
% 0.92/1.11 ($false),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1103, 117, 1032, 1045, 1090, 1088, 1042, 1097])).
% 0.92/1.11 tff(1105,plain,(hskp17 | hskp9 | c0_1(a107) | c2_1(a107) | (~c0_1(a137)) | (~c1_1(a137)) | (~c2_1(a137)) | (~c3_1(a112)) | (~c3_1(a107)) | c0_1(a112) | c1_1(a112) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.92/1.11 tff(1106,plain,
% 0.92/1.11 (hskp17),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1105, 1031, 1025, 993, 591, 607, 599, 987, 979, 804, 798, 52])).
% 0.92/1.11 tff(1107,plain,
% 0.92/1.11 (((~hskp17) | (~c3_1(a124))) <=> ((~hskp17) | (~c3_1(a124)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1108,plain,
% 0.92/1.11 (((~c3_1(a124)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a124)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1109,axiom,((~c3_1(a124)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 0.92/1.11 tff(1110,plain,
% 0.92/1.11 ((~hskp17) | (~c3_1(a124))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 0.92/1.11 tff(1111,plain,
% 0.92/1.11 ((~hskp17) | (~c3_1(a124))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1110, 1107])).
% 0.92/1.11 tff(1112,plain,
% 0.92/1.11 (~c3_1(a124)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1111, 1106])).
% 0.92/1.11 tff(1113,plain,
% 0.92/1.11 (((~hskp17) | (~c1_1(a124))) <=> ((~hskp17) | (~c1_1(a124)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1114,plain,
% 0.92/1.11 (((~c1_1(a124)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a124)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1115,axiom,((~c1_1(a124)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 0.92/1.11 tff(1116,plain,
% 0.92/1.11 ((~hskp17) | (~c1_1(a124))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 0.92/1.11 tff(1117,plain,
% 0.92/1.11 ((~hskp17) | (~c1_1(a124))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1116, 1113])).
% 0.92/1.11 tff(1118,plain,
% 0.92/1.11 (~c1_1(a124)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1117, 1106])).
% 0.92/1.11 tff(1119,plain,
% 0.92/1.11 (((~hskp17) | c2_1(a124)) <=> ((~hskp17) | c2_1(a124))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1120,axiom,((~hskp17) | c2_1(a124)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.92/1.11 tff(1121,plain,
% 0.92/1.11 ((~hskp17) | c2_1(a124)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 0.92/1.11 tff(1122,plain,
% 0.92/1.11 ((~hskp17) | c2_1(a124)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1121, 1119])).
% 0.92/1.11 tff(1123,plain,
% 0.92/1.11 ((~hskp17) | c2_1(a124)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1122, 1119])).
% 0.92/1.11 tff(1124,plain,
% 0.92/1.11 ((~hskp17) | c2_1(a124)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1123, 1119])).
% 0.92/1.11 tff(1125,plain,
% 0.92/1.11 ((~hskp17) | c2_1(a124)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1124, 1119])).
% 0.92/1.11 tff(1126,plain,
% 0.92/1.11 (c2_1(a124)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1125, 1106])).
% 0.92/1.11 tff(1127,assumption,(~hskp19), introduced(assumption)).
% 0.92/1.11 tff(1128,plain,
% 0.92/1.11 (^[U: $i] : refl((hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(1129,plain,
% 0.92/1.11 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[1128])).
% 0.92/1.11 tff(1130,plain,
% 0.92/1.11 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1131,plain,
% 0.92/1.11 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp19) <=> ((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp19))), rewrite(((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp19) <=> (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp19) <=> (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(1132,plain,
% 0.92/1.11 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp19) <=> ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[1131])).
% 0.92/1.11 tff(1133,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 0.92/1.11 tff(1134,plain,
% 0.92/1.11 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 0.92/1.11 tff(1135,plain,
% 0.92/1.11 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1134, 1130])).
% 0.92/1.11 tff(1136,plain,(
% 0.92/1.11 ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.92/1.11 inference(skolemize,[status(sab)],[1135])).
% 0.92/1.11 tff(1137,plain,
% 0.92/1.11 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1136, 1129])).
% 0.92/1.11 tff(1138,assumption,(~c3_1(a124)), introduced(assumption)).
% 0.92/1.11 tff(1139,assumption,(~c1_1(a124)), introduced(assumption)).
% 0.92/1.11 tff(1140,assumption,(c2_1(a124)), introduced(assumption)).
% 0.92/1.11 tff(1141,plain,
% 0.92/1.11 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp19 | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp19 | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1142,plain,
% 0.92/1.11 ((hskp19 | hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124))) <=> (hskp19 | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1143,plain,
% 0.92/1.11 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp19 | hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp19 | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[1142])).
% 0.92/1.11 tff(1144,plain,
% 0.92/1.11 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp19 | hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp19 | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[1143, 1141])).
% 0.92/1.11 tff(1145,plain,
% 0.92/1.11 ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp19 | hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(1146,plain,
% 0.92/1.11 ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp19 | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 0.92/1.11 tff(1147,plain,
% 0.92/1.11 (hskp19 | hskp1),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1146, 117, 1140, 1139, 1138, 1137])).
% 0.92/1.11 tff(1148,plain,
% 0.92/1.11 (hskp1),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1147, 1127])).
% 0.92/1.11 tff(1149,plain,
% 0.92/1.11 (((~hskp1) | (~c3_1(a98))) <=> ((~hskp1) | (~c3_1(a98)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1150,plain,
% 0.92/1.11 (((~c3_1(a98)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a98)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1151,axiom,((~c3_1(a98)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.92/1.11 tff(1152,plain,
% 0.92/1.11 ((~hskp1) | (~c3_1(a98))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 0.92/1.11 tff(1153,plain,
% 0.92/1.11 ((~hskp1) | (~c3_1(a98))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1152, 1149])).
% 0.92/1.11 tff(1154,plain,
% 0.92/1.11 (~c3_1(a98)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1153, 1148])).
% 0.92/1.11 tff(1155,plain,
% 0.92/1.11 (((~hskp1) | (~c1_1(a98))) <=> ((~hskp1) | (~c1_1(a98)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1156,plain,
% 0.92/1.11 (((~c1_1(a98)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a98)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1157,axiom,((~c1_1(a98)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.92/1.11 tff(1158,plain,
% 0.92/1.11 ((~hskp1) | (~c1_1(a98))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 0.92/1.11 tff(1159,plain,
% 0.92/1.11 ((~hskp1) | (~c1_1(a98))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1158, 1155])).
% 0.92/1.11 tff(1160,plain,
% 0.92/1.11 (~c1_1(a98)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1159, 1148])).
% 0.92/1.11 tff(1161,plain,
% 0.92/1.11 (((~hskp1) | c0_1(a98)) <=> ((~hskp1) | c0_1(a98))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1162,axiom,((~hskp1) | c0_1(a98)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.92/1.11 tff(1163,plain,
% 0.92/1.11 ((~hskp1) | c0_1(a98)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 0.92/1.11 tff(1164,plain,
% 0.92/1.11 ((~hskp1) | c0_1(a98)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1163, 1161])).
% 0.92/1.11 tff(1165,plain,
% 0.92/1.11 ((~hskp1) | c0_1(a98)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1164, 1161])).
% 0.92/1.11 tff(1166,plain,
% 0.92/1.11 ((~hskp1) | c0_1(a98)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1165, 1161])).
% 0.92/1.11 tff(1167,plain,
% 0.92/1.11 ((~hskp1) | c0_1(a98)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1166, 1161])).
% 0.92/1.11 tff(1168,plain,
% 0.92/1.11 (c0_1(a98)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1167, 1148])).
% 0.92/1.11 tff(1169,plain,
% 0.92/1.11 (^[U: $i] : refl((hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(1170,plain,
% 0.92/1.11 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[1169])).
% 0.92/1.11 tff(1171,plain,
% 0.92/1.11 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1172,plain,
% 0.92/1.11 (^[U: $i] : 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)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp19) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp19))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(1173,plain,
% 0.92/1.11 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp19) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[1172])).
% 0.92/1.11 tff(1174,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 0.92/1.11 tff(1175,plain,
% 0.92/1.11 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1174, 1173])).
% 0.92/1.11 tff(1176,plain,
% 0.92/1.11 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1175, 1171])).
% 0.92/1.11 tff(1177,plain,(
% 0.92/1.11 ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.11 inference(skolemize,[status(sab)],[1176])).
% 0.92/1.11 tff(1178,plain,
% 0.92/1.11 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1177, 1170])).
% 0.92/1.11 tff(1179,plain,
% 0.92/1.11 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1180,plain,
% 0.92/1.11 ((hskp27 | hskp19 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97))) <=> (hskp27 | hskp19 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1181,plain,
% 0.92/1.11 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[1180])).
% 0.92/1.11 tff(1182,plain,
% 0.92/1.11 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[1181, 1179])).
% 0.92/1.11 tff(1183,plain,
% 0.92/1.11 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(1184,plain,
% 0.92/1.11 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 0.92/1.11 tff(1185,plain,
% 0.92/1.11 (hskp27 | hskp19 | (~c1_1(a97))),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1184, 117, 231, 53, 1178])).
% 0.92/1.11 tff(1186,plain,
% 0.92/1.11 (hskp27),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1185, 1127, 303])).
% 0.92/1.11 tff(1187,plain,
% 0.92/1.11 (((~hskp27) | c3_1(a101)) <=> ((~hskp27) | c3_1(a101))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1188,axiom,((~hskp27) | c3_1(a101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.92/1.11 tff(1189,plain,
% 0.92/1.11 ((~hskp27) | c3_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 0.92/1.11 tff(1190,plain,
% 0.92/1.11 ((~hskp27) | c3_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1189, 1187])).
% 0.92/1.11 tff(1191,plain,
% 0.92/1.11 ((~hskp27) | c3_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1190, 1187])).
% 0.92/1.11 tff(1192,plain,
% 0.92/1.11 ((~hskp27) | c3_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1191, 1187])).
% 0.92/1.11 tff(1193,plain,
% 0.92/1.11 ((~hskp27) | c3_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1192, 1187])).
% 0.92/1.11 tff(1194,plain,
% 0.92/1.11 (c3_1(a101)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1193, 1186])).
% 0.92/1.11 tff(1195,plain,
% 0.92/1.11 (((~hskp27) | c1_1(a101)) <=> ((~hskp27) | c1_1(a101))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1196,axiom,((~hskp27) | c1_1(a101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.92/1.11 tff(1197,plain,
% 0.92/1.11 ((~hskp27) | c1_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 0.92/1.11 tff(1198,plain,
% 0.92/1.11 ((~hskp27) | c1_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1197, 1195])).
% 0.92/1.11 tff(1199,plain,
% 0.92/1.11 ((~hskp27) | c1_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1198, 1195])).
% 0.92/1.11 tff(1200,plain,
% 0.92/1.11 ((~hskp27) | c1_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1199, 1195])).
% 0.92/1.11 tff(1201,plain,
% 0.92/1.11 ((~hskp27) | c1_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1200, 1195])).
% 0.92/1.11 tff(1202,plain,
% 0.92/1.11 (c1_1(a101)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1201, 1186])).
% 0.92/1.11 tff(1203,plain,
% 0.92/1.11 (((~hskp27) | c0_1(a101)) <=> ((~hskp27) | c0_1(a101))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1204,axiom,((~hskp27) | c0_1(a101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 0.92/1.11 tff(1205,plain,
% 0.92/1.11 ((~hskp27) | c0_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 0.92/1.11 tff(1206,plain,
% 0.92/1.11 ((~hskp27) | c0_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1205, 1203])).
% 0.92/1.11 tff(1207,plain,
% 0.92/1.11 ((~hskp27) | c0_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1206, 1203])).
% 0.92/1.11 tff(1208,plain,
% 0.92/1.11 ((~hskp27) | c0_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1207, 1203])).
% 0.92/1.11 tff(1209,plain,
% 0.92/1.11 ((~hskp27) | c0_1(a101)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1208, 1203])).
% 0.92/1.11 tff(1210,plain,
% 0.92/1.11 (c0_1(a101)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1209, 1186])).
% 0.92/1.11 tff(1211,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a98) | c3_1(a98) | (~ndr1_0) | (~c0_1(a98)) | (~c0_1(a101)) | (~c1_1(a101)) | (~c3_1(a101)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a98) | c3_1(a98) | (~ndr1_0) | (~c0_1(a98)) | (~c0_1(a101)) | (~c1_1(a101)) | (~c3_1(a101)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1212,plain,
% 0.92/1.11 ((hskp18 | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a101)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98))) <=> (hskp18 | c1_1(a98) | c3_1(a98) | (~ndr1_0) | (~c0_1(a98)) | (~c0_1(a101)) | (~c1_1(a101)) | (~c3_1(a101)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(1213,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a101)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a98) | c3_1(a98) | (~ndr1_0) | (~c0_1(a98)) | (~c0_1(a101)) | (~c1_1(a101)) | (~c3_1(a101))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[1212])).
% 0.92/1.11 tff(1214,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a101)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a98) | c3_1(a98) | (~ndr1_0) | (~c0_1(a98)) | (~c0_1(a101)) | (~c1_1(a101)) | (~c3_1(a101)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[1213, 1211])).
% 0.92/1.11 tff(1215,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a101)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(1216,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a98) | c3_1(a98) | (~ndr1_0) | (~c0_1(a98)) | (~c0_1(a101)) | (~c1_1(a101)) | (~c3_1(a101))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 0.92/1.11 tff(1217,plain,
% 0.92/1.11 ($false),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1216, 117, 52, 1210, 1202, 1194, 1168, 1160, 1154, 666])).
% 0.92/1.11 tff(1218,plain,(hskp19 | hskp18 | (~c2_1(a124)) | c1_1(a124) | c3_1(a124) | (~c1_1(a97)) | (~c0_1(a97)) | c3_1(a97)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.11 tff(1219,plain,
% 0.92/1.11 (hskp19),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1218, 52, 1126, 1118, 1112, 953, 784, 772])).
% 0.92/1.11 tff(1220,plain,
% 0.92/1.11 (~c2_1(a130)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[237, 1219])).
% 0.92/1.11 tff(1221,plain,
% 0.92/1.11 (c3_1(a130)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[245, 1219])).
% 0.92/1.11 tff(1222,plain,
% 0.92/1.11 (c1_1(a130)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[253, 1219])).
% 0.92/1.11 tff(1223,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a130) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a130)) | (~c1_1(a130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1224,plain,
% 0.92/1.12 (((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124))) <=> (c2_1(a130) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1225,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a130) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a130)) | (~c1_1(a130))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[1224])).
% 0.92/1.12 tff(1226,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[1225, 1223])).
% 0.92/1.12 tff(1227,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(1228,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a130)) | (~c1_1(a130))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 0.92/1.12 tff(1229,plain,
% 0.92/1.12 (~c0_1(a124)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1228, 117, 1222, 1221, 784, 1220, 1118, 1112, 773, 772, 20])).
% 0.92/1.12 tff(1230,plain,
% 0.92/1.12 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(1231,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[1230])).
% 0.92/1.12 tff(1232,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1233,plain,
% 0.92/1.12 (^[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))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~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))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~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))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_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))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_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))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_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) | c3_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) | c3_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))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_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))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(1234,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[1233])).
% 0.92/1.12 tff(1235,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 0.92/1.12 tff(1236,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1235, 1234])).
% 0.92/1.12 tff(1237,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1236, 1232])).
% 0.92/1.12 tff(1238,plain,(
% 0.92/1.12 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(skolemize,[status(sab)],[1237])).
% 0.92/1.12 tff(1239,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1238, 1231])).
% 0.92/1.12 tff(1240,assumption,(hskp17), introduced(assumption)).
% 0.92/1.12 tff(1241,plain,
% 0.92/1.12 (~c3_1(a124)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1111, 1240])).
% 0.92/1.12 tff(1242,plain,
% 0.92/1.12 (~c1_1(a124)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1117, 1240])).
% 0.92/1.12 tff(1243,plain,
% 0.92/1.12 (c2_1(a124)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1125, 1240])).
% 0.92/1.12 tff(1244,plain,
% 0.92/1.12 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1245,plain,
% 0.92/1.12 ((hskp22 | hskp21 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124))) <=> (hskp22 | hskp21 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1246,plain,
% 0.92/1.12 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[1245])).
% 0.92/1.12 tff(1247,plain,
% 0.92/1.12 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[1246, 1244])).
% 0.92/1.12 tff(1248,plain,
% 0.92/1.12 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(1249,plain,
% 0.92/1.12 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 0.92/1.12 tff(1250,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1249, 117, 135, 471, 1243, 1242, 1241, 161])).
% 0.92/1.12 tff(1251,plain,((~hskp17) | hskp22 | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(1252,plain,
% 0.92/1.12 (hskp21),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1251, 1106, 135])).
% 0.92/1.12 tff(1253,plain,
% 0.92/1.12 (~c1_1(a136)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[181, 1252])).
% 0.92/1.12 tff(1254,plain,
% 0.92/1.12 (c3_1(a136)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[206, 1252])).
% 0.92/1.12 tff(1255,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a136) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | (~c0_1(a136)) | (~c3_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a136) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | (~c0_1(a136)) | (~c3_1(a136)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1256,plain,
% 0.92/1.12 (((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a136) | (~c3_1(a136)) | (~c0_1(a136)) | c1_1(a124) | c0_1(a124) | c3_1(a124)) <=> (c1_1(a136) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | (~c0_1(a136)) | (~c3_1(a136)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1257,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a136) | (~c3_1(a136)) | (~c0_1(a136)) | c1_1(a124) | c0_1(a124) | c3_1(a124))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a136) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | (~c0_1(a136)) | (~c3_1(a136))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[1256])).
% 0.92/1.12 tff(1258,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a136) | (~c3_1(a136)) | (~c0_1(a136)) | c1_1(a124) | c0_1(a124) | c3_1(a124))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a136) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | (~c0_1(a136)) | (~c3_1(a136)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[1257, 1255])).
% 0.92/1.12 tff(1259,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a136) | (~c3_1(a136)) | (~c0_1(a136)) | c1_1(a124) | c0_1(a124) | c3_1(a124))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(1260,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a136) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | (~c0_1(a136)) | (~c3_1(a136))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 0.92/1.12 tff(1261,plain,
% 0.92/1.12 (c0_1(a124) | (~c0_1(a136))),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1260, 117, 1254, 784, 1253, 1118, 1112, 772, 1239, 953])).
% 0.92/1.12 tff(1262,plain,
% 0.92/1.12 (~c0_1(a136)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1261, 1229])).
% 0.92/1.12 tff(1263,plain,
% 0.92/1.12 (~c2_1(a136)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[175, 1252])).
% 0.92/1.12 tff(1264,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a136) | c2_1(a136) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a136) | c2_1(a136) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124) | c0_1(a136))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1265,plain,
% 0.92/1.12 (((~ndr1_0) | c0_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)) | c2_1(a136) | c1_1(a136) | c0_1(a136)) <=> (c1_1(a136) | c2_1(a136) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124) | c0_1(a136))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1266,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a136) | c2_1(a136) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124) | c0_1(a136)))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[1265])).
% 0.92/1.12 tff(1267,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a136) | c2_1(a136) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124) | c0_1(a136))),
% 0.92/1.12 inference(transitivity,[status(thm)],[1266, 1264])).
% 0.92/1.12 tff(1268,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)) | c2_1(a136) | c1_1(a136) | c0_1(a136))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(1269,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a136) | c2_1(a136) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124) | c0_1(a136)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 0.92/1.12 tff(1270,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1269, 117, 1126, 1253, 1263, 1118, 1112, 746, 1229, 1262])).
% 0.92/1.12 tff(1271,plain,(hskp18 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(1272,plain,
% 0.92/1.12 (hskp18),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1271, 135])).
% 0.92/1.12 tff(1273,plain,
% 0.92/1.12 (~c1_1(a129)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[276, 1272])).
% 0.92/1.12 tff(1274,plain,
% 0.92/1.12 (c2_1(a129)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[284, 1272])).
% 0.92/1.12 tff(1275,plain,
% 0.92/1.12 (c0_1(a129)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[292, 1272])).
% 0.92/1.12 tff(1276,plain,
% 0.92/1.12 (~c3_1(a129)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[840, 117, 1275, 1274, 1273, 10])).
% 0.92/1.12 tff(1277,plain,
% 0.92/1.12 (hskp21),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[887, 117, 135, 1274, 1273, 161, 1276])).
% 0.92/1.12 tff(1278,plain,
% 0.92/1.12 (~c2_1(a136)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[175, 1277])).
% 0.92/1.12 tff(1279,plain,
% 0.92/1.12 (~c1_1(a136)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[181, 1277])).
% 0.92/1.12 tff(1280,plain,
% 0.92/1.12 (~c0_1(a136)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[896, 117, 1275, 1274, 1279, 1278, 1273, 134, 1276])).
% 0.92/1.12 tff(1281,assumption,(hskp16), introduced(assumption)).
% 0.92/1.12 tff(1282,plain,
% 0.92/1.12 (~c2_1(a122)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[430, 1281])).
% 0.92/1.12 tff(1283,plain,
% 0.92/1.12 (((~hskp16) | c0_1(a122)) <=> ((~hskp16) | c0_1(a122))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1284,axiom,((~hskp16) | c0_1(a122)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 0.92/1.12 tff(1285,plain,
% 0.92/1.12 ((~hskp16) | c0_1(a122)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 0.92/1.12 tff(1286,plain,
% 0.92/1.12 ((~hskp16) | c0_1(a122)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1285, 1283])).
% 0.92/1.12 tff(1287,plain,
% 0.92/1.12 ((~hskp16) | c0_1(a122)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1286, 1283])).
% 0.92/1.12 tff(1288,plain,
% 0.92/1.12 ((~hskp16) | c0_1(a122)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1287, 1283])).
% 0.92/1.12 tff(1289,plain,
% 0.92/1.12 ((~hskp16) | c0_1(a122)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1288, 1283])).
% 0.92/1.12 tff(1290,plain,
% 0.92/1.12 (c0_1(a122)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1289, 1281])).
% 0.92/1.12 tff(1291,plain,
% 0.92/1.12 (~c1_1(a122)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[516, 1281])).
% 0.92/1.12 tff(1292,assumption,(c0_1(a122)), introduced(assumption)).
% 0.92/1.12 tff(1293,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1294,plain,
% 0.92/1.12 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122))) <=> (c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1295,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[1294])).
% 0.92/1.12 tff(1296,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[1295, 1293])).
% 0.92/1.12 tff(1297,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(1298,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1297, 1296])).
% 0.92/1.12 tff(1299,plain,
% 0.92/1.12 ((~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129))),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1298, 117, 149, 162, 624, 395, 407, 148, 134])).
% 0.92/1.12 tff(1300,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1299, 623, 622, 1292])).
% 0.92/1.12 tff(1301,plain,((~hskp18) | (~c0_1(a122)) | (~c0_1(a103)) | (~c2_1(a103)) | c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(1302,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1301, 1291, 1290, 149, 162, 621, 620, 1282, 148])).
% 0.92/1.12 tff(1303,plain,((~hskp16) | (~c0_1(a103)) | (~c2_1(a103)) | (~hskp18) | c3_1(a103)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(1304,plain,
% 0.92/1.12 (~hskp16),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1303, 950, 952, 1272, 951])).
% 0.92/1.12 tff(1305,plain,
% 0.92/1.12 (hskp16 | hskp2),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[539, 117, 784, 773, 772, 533])).
% 0.92/1.12 tff(1306,plain,
% 0.92/1.12 (hskp2),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1305, 1304])).
% 0.92/1.12 tff(1307,plain,
% 0.92/1.12 (~c1_1(a99)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[579, 1306])).
% 0.92/1.12 tff(1308,plain,
% 0.92/1.12 (~c0_1(a99)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[563, 1306])).
% 0.92/1.12 tff(1309,plain,
% 0.92/1.12 (~c3_1(a137)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[653, 1272, 607, 599, 591])).
% 0.92/1.12 tff(1310,plain,
% 0.92/1.12 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | c3_1(a137))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | c3_1(a137))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1311,plain,
% 0.92/1.12 ((hskp25 | hskp16 | (~ndr1_0) | c3_1(a137) | (~c2_1(a137)) | (~c0_1(a137))) <=> (hskp25 | hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | c3_1(a137))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1312,plain,
% 0.92/1.12 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c3_1(a137) | (~c2_1(a137)) | (~c0_1(a137)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | c3_1(a137)))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[1311])).
% 0.92/1.12 tff(1313,plain,
% 0.92/1.12 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c3_1(a137) | (~c2_1(a137)) | (~c0_1(a137)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | c3_1(a137))),
% 0.92/1.12 inference(transitivity,[status(thm)],[1312, 1310])).
% 0.92/1.12 tff(1314,plain,
% 0.92/1.12 ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c3_1(a137) | (~c2_1(a137)) | (~c0_1(a137)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(1315,plain,
% 0.92/1.12 ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | c3_1(a137)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 0.92/1.12 tff(1316,plain,
% 0.92/1.12 (hskp25 | hskp16 | c3_1(a137)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1315, 117, 591, 599, 441])).
% 0.92/1.12 tff(1317,plain,
% 0.92/1.12 (hskp25),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1316, 1304, 1309])).
% 0.92/1.12 tff(1318,plain,
% 0.92/1.12 (~c3_1(a173)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[494, 1317])).
% 0.92/1.12 tff(1319,plain,
% 0.92/1.12 (~c0_1(a173)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[454, 1317])).
% 0.92/1.12 tff(1320,plain,
% 0.92/1.12 (c2_1(a99)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[548, 1306])).
% 0.92/1.12 tff(1321,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a173) | c3_1(a173) | c1_1(a136) | c2_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a136) | (~c2_1(a173)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a173) | c3_1(a173) | c1_1(a136) | c2_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a136) | (~c2_1(a173)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1322,plain,
% 0.92/1.12 (((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c2_1(a173)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a136) | c1_1(a136) | c0_1(a136)) <=> (c0_1(a173) | c3_1(a173) | c1_1(a136) | c2_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a136) | (~c2_1(a173)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1323,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c2_1(a173)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a173) | c3_1(a173) | c1_1(a136) | c2_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a136) | (~c2_1(a173))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[1322])).
% 0.92/1.12 tff(1324,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c2_1(a173)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a173) | c3_1(a173) | c1_1(a136) | c2_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a136) | (~c2_1(a173)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[1323, 1321])).
% 0.92/1.12 tff(1325,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c2_1(a173)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a136) | c1_1(a136) | c0_1(a136))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(1326,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a173) | c3_1(a173) | c1_1(a136) | c2_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a136) | (~c2_1(a173))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 0.92/1.12 tff(1327,plain,
% 0.92/1.12 (~c2_1(a173)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[1326, 117, 1320, 1319, 1318, 1279, 1278, 1308, 1307, 746, 1280])).
% 0.92/1.12 tff(1328,plain,
% 0.92/1.12 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(1329,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_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) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[1328])).
% 0.92/1.12 tff(1330,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_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) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(1331,plain,
% 0.92/1.12 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(1332,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_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) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[1331])).
% 0.92/1.12 tff(1333,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 0.92/1.12 tff(1334,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 0.92/1.12 tff(1335,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1334, 1330])).
% 0.92/1.12 tff(1336,plain,(
% 0.92/1.12 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(skolemize,[status(sab)],[1335])).
% 0.92/1.12 tff(1337,plain,
% 0.92/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[1336, 1329])).
% 0.92/1.12 tff(1338,plain,
% 0.92/1.12 (c3_1(a136)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[206, 1277])).
% 0.92/1.12 tff(1339,plain,
% 0.92/1.12 (c1_1(a173)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[462, 1317])).
% 0.92/1.13 tff(1340,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a173) | c3_1(a173) | c1_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | c3_1(a99) | c0_1(a136) | (~c3_1(a136)) | (~c1_1(a173)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a173) | c3_1(a173) | c1_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | c3_1(a99) | c0_1(a136) | (~c3_1(a136)) | (~c1_1(a173)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1341,plain,
% 0.92/1.13 (((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c1_1(a173)) | c1_1(a136) | c0_1(a136) | (~c3_1(a136)) | c1_1(a99) | c0_1(a99) | c3_1(a99)) <=> (c0_1(a173) | c3_1(a173) | c1_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | c3_1(a99) | c0_1(a136) | (~c3_1(a136)) | (~c1_1(a173)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1342,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c1_1(a173)) | c1_1(a136) | c0_1(a136) | (~c3_1(a136)) | c1_1(a99) | c0_1(a99) | c3_1(a99))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a173) | c3_1(a173) | c1_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | c3_1(a99) | c0_1(a136) | (~c3_1(a136)) | (~c1_1(a173))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[1341])).
% 0.92/1.13 tff(1343,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c1_1(a173)) | c1_1(a136) | c0_1(a136) | (~c3_1(a136)) | c1_1(a99) | c0_1(a99) | c3_1(a99))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a173) | c3_1(a173) | c1_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | c3_1(a99) | c0_1(a136) | (~c3_1(a136)) | (~c1_1(a173)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[1342, 1340])).
% 0.92/1.13 tff(1344,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c1_1(a173)) | c1_1(a136) | c0_1(a136) | (~c3_1(a136)) | c1_1(a99) | c0_1(a99) | c3_1(a99))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(1345,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a173) | c3_1(a173) | c1_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | c3_1(a99) | c0_1(a136) | (~c3_1(a136)) | (~c1_1(a173))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 0.92/1.13 tff(1346,plain,
% 0.92/1.13 (c3_1(a99)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1345, 117, 1339, 1338, 1319, 1318, 1279, 1308, 1307, 1337, 1280])).
% 0.92/1.13 tff(1347,plain,
% 0.92/1.13 ($false),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[571, 117, 1320, 784, 1319, 1318, 1308, 773, 489, 1346, 953, 1327])).
% 0.92/1.13 tff(1348,plain,(hskp22), inference(lemma,lemma(discharge,[]))).
% 0.92/1.13 tff(1349,plain,
% 0.92/1.13 (((~hskp22) | (~c2_1(a138))) <=> ((~hskp22) | (~c2_1(a138)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1350,plain,
% 0.92/1.13 (((~c2_1(a138)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a138)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1351,axiom,((~c2_1(a138)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.92/1.13 tff(1352,plain,
% 0.92/1.13 ((~hskp22) | (~c2_1(a138))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 0.92/1.13 tff(1353,plain,
% 0.92/1.13 ((~hskp22) | (~c2_1(a138))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1352, 1349])).
% 0.92/1.13 tff(1354,plain,
% 0.92/1.13 (~c2_1(a138)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1353, 1348])).
% 0.92/1.13 tff(1355,plain,
% 0.92/1.13 (c2_1(a103)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[145, 73])).
% 0.92/1.13 tff(1356,plain,
% 0.92/1.13 (((~hskp22) | c0_1(a138)) <=> ((~hskp22) | c0_1(a138))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1357,axiom,((~hskp22) | c0_1(a138)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 0.92/1.13 tff(1358,plain,
% 0.92/1.13 ((~hskp22) | c0_1(a138)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1357, 1356])).
% 0.92/1.13 tff(1359,plain,
% 0.92/1.13 ((~hskp22) | c0_1(a138)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1358, 1356])).
% 0.92/1.13 tff(1360,plain,
% 0.92/1.13 ((~hskp22) | c0_1(a138)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1359, 1356])).
% 0.92/1.13 tff(1361,plain,
% 0.92/1.13 ((~hskp22) | c0_1(a138)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1360, 1356])).
% 0.92/1.13 tff(1362,plain,
% 0.92/1.13 ((~hskp22) | c0_1(a138)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1361, 1356])).
% 0.92/1.13 tff(1363,plain,
% 0.92/1.13 (c0_1(a138)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1362, 1348])).
% 0.92/1.13 tff(1364,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a138) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1365,plain,
% 0.92/1.13 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138))) <=> (c2_1(a138) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1366,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a138) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | c1_1(a138) | (~c0_1(a138))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[1365])).
% 0.92/1.13 tff(1367,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[1366, 1364])).
% 0.92/1.13 tff(1368,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(1369,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | c1_1(a138) | (~c0_1(a138))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 0.92/1.13 tff(1370,plain,
% 0.92/1.13 (c1_1(a138)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1369, 117, 1363, 87, 1355, 1354, 79, 134, 124])).
% 0.92/1.13 tff(1371,plain,
% 0.92/1.13 (((~hskp22) | c3_1(a138)) <=> ((~hskp22) | c3_1(a138))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1372,axiom,((~hskp22) | c3_1(a138)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.92/1.13 tff(1373,plain,
% 0.92/1.13 ((~hskp22) | c3_1(a138)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1372, 1371])).
% 0.92/1.13 tff(1374,plain,
% 0.92/1.13 ((~hskp22) | c3_1(a138)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1373, 1371])).
% 0.92/1.13 tff(1375,plain,
% 0.92/1.13 ((~hskp22) | c3_1(a138)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1374, 1371])).
% 0.92/1.13 tff(1376,plain,
% 0.92/1.13 ((~hskp22) | c3_1(a138)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1375, 1371])).
% 0.92/1.13 tff(1377,plain,
% 0.92/1.13 ((~hskp22) | c3_1(a138)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1376, 1371])).
% 0.92/1.13 tff(1378,plain,
% 0.92/1.13 (c3_1(a138)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1377, 1348])).
% 0.92/1.13 tff(1379,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a138)) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a138)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1380,plain,
% 0.92/1.13 ((hskp18 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)) | c1_1(a103) | c3_1(a103) | (~c0_1(a103))) <=> (hskp18 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a138)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1381,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)) | c1_1(a103) | c3_1(a103) | (~c0_1(a103)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a138)) | (~c3_1(a138)) | (~c1_1(a138))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[1380])).
% 0.92/1.13 tff(1382,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)) | c1_1(a103) | c3_1(a103) | (~c0_1(a103)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a138)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[1381, 1379])).
% 0.92/1.13 tff(1383,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)) | c1_1(a103) | c3_1(a103) | (~c0_1(a103)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(1384,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a138)) | (~c3_1(a138)) | (~c1_1(a138))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 0.92/1.13 tff(1385,plain,
% 0.92/1.13 ($false),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1384, 117, 52, 1363, 1378, 87, 79, 666, 124, 1370])).
% 0.92/1.13 tff(1386,plain,((~hskp4) | hskp18 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.92/1.13 tff(1387,plain,
% 0.92/1.13 (~hskp4),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1386, 52, 62])).
% 0.92/1.13 tff(1388,plain,
% 0.92/1.13 (^[U: $i] : refl((hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(1389,plain,
% 0.92/1.13 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[1388])).
% 0.92/1.13 tff(1390,plain,
% 0.92/1.13 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1391,plain,
% 0.92/1.13 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp7) <=> ((hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7))), rewrite(((hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp7) <=> (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(1392,plain,
% 0.92/1.13 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp7) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[1391])).
% 0.92/1.13 tff(1393,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.92/1.13 tff(1394,plain,
% 0.92/1.13 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 0.92/1.13 tff(1395,plain,
% 0.92/1.13 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1394, 1390])).
% 0.92/1.13 tff(1396,plain,(
% 0.92/1.13 ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(skolemize,[status(sab)],[1395])).
% 0.92/1.13 tff(1397,plain,
% 0.92/1.13 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1396, 1389])).
% 0.92/1.13 tff(1398,plain,
% 0.92/1.13 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c3_1(a138)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c3_1(a138)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1399,plain,
% 0.92/1.13 ((hskp7 | hskp4 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138))) <=> (hskp7 | hskp4 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c3_1(a138)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1400,plain,
% 0.92/1.13 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c3_1(a138))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[1399])).
% 0.92/1.13 tff(1401,plain,
% 0.92/1.13 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c3_1(a138)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[1400, 1398])).
% 0.92/1.13 tff(1402,plain,
% 0.92/1.13 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(1403,plain,
% 0.92/1.13 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c3_1(a138))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1402, 1401])).
% 0.92/1.13 tff(1404,plain,
% 0.92/1.13 (hskp7 | hskp4),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1403, 117, 1363, 1378, 1354, 1397])).
% 0.92/1.13 tff(1405,plain,
% 0.92/1.13 (hskp7),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1404, 805])).
% 0.92/1.13 tff(1406,plain,
% 0.92/1.13 (~c0_1(a106)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[912, 1405])).
% 0.92/1.13 tff(1407,plain,
% 0.92/1.13 (c3_1(a106)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[865, 1405])).
% 0.92/1.13 tff(1408,plain,
% 0.92/1.13 (c2_1(a106)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[873, 1405])).
% 0.92/1.13 tff(1409,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a97) | c2_1(a138) | c0_1(a106) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a97) | c2_1(a138) | c0_1(a106) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1410,plain,
% 0.92/1.13 (((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a97) | c0_1(a97) | c3_1(a97)) <=> (c0_1(a97) | c2_1(a138) | c0_1(a106) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1411,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a97) | c0_1(a97) | c3_1(a97))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a97) | c2_1(a138) | c0_1(a106) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a138)) | (~c1_1(a138))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[1410])).
% 0.92/1.13 tff(1412,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a97) | c0_1(a97) | c3_1(a97))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a97) | c2_1(a138) | c0_1(a106) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[1411, 1409])).
% 0.92/1.13 tff(1413,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a97) | c0_1(a97) | c3_1(a97))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(1414,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a97) | c2_1(a138) | c0_1(a106) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a138)) | (~c1_1(a138))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 0.92/1.13 tff(1415,plain,
% 0.92/1.13 (~c1_1(a138)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1414, 117, 1363, 1408, 1407, 54, 1354, 1406, 31, 53, 489])).
% 0.92/1.13 tff(1416,plain,
% 0.92/1.13 (hskp20),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[764, 805, 52])).
% 0.92/1.13 tff(1417,plain,
% 0.92/1.13 (~c3_1(a132)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[672, 1416])).
% 0.92/1.13 tff(1418,plain,
% 0.92/1.13 (~c2_1(a132)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[692, 1416])).
% 0.92/1.13 tff(1419,plain,
% 0.92/1.13 (~c1_1(a132)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[678, 1416])).
% 0.92/1.13 tff(1420,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | c1_1(a132) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp17 | c1_1(a132) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1421,plain,
% 0.92/1.13 ((hskp17 | (~ndr1_0) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c1_1(a132) | c3_1(a132)) <=> (hskp17 | c1_1(a132) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1422,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | (~ndr1_0) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c1_1(a132) | c3_1(a132))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | c1_1(a132) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[1421])).
% 0.92/1.13 tff(1423,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | (~ndr1_0) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c1_1(a132) | c3_1(a132))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp17 | c1_1(a132) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[1422, 1420])).
% 0.92/1.13 tff(1424,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | (~ndr1_0) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c1_1(a132) | c3_1(a132))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(1425,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp17 | c1_1(a132) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 0.92/1.13 tff(1426,plain,
% 0.92/1.13 (hskp17),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1425, 117, 1408, 1407, 1419, 1418, 1417, 1406, 51])).
% 0.92/1.13 tff(1427,plain,
% 0.92/1.13 (~c3_1(a124)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1111, 1426])).
% 0.92/1.13 tff(1428,plain,
% 0.92/1.13 (~c1_1(a124)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1117, 1426])).
% 0.92/1.13 tff(1429,plain,
% 0.92/1.13 (c2_1(a124)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1125, 1426])).
% 0.92/1.13 tff(1430,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp4 | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1431,plain,
% 0.92/1.13 ((hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138))) <=> (hskp4 | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1432,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c1_1(a138) | (~c0_1(a138))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[1431])).
% 0.92/1.13 tff(1433,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp4 | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[1432, 1430])).
% 0.92/1.13 tff(1434,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(1435,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp4 | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c1_1(a138) | (~c0_1(a138))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 0.92/1.13 tff(1436,plain,
% 0.92/1.13 ($false),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1435, 117, 805, 1363, 1429, 1354, 1428, 1427, 41, 1415])).
% 0.92/1.13 tff(1437,plain,(hskp4 | c0_1(a97) | c2_1(a97) | c3_1(a97) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.92/1.13 tff(1438,plain,
% 0.92/1.13 (c3_1(a97)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1437, 1387, 31, 54, 52])).
% 0.92/1.13 tff(1439,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a97) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | c1_1(a97))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a97) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | c1_1(a97))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1440,plain,
% 0.92/1.13 ((hskp0 | (~ndr1_0) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)) | c2_1(a97) | c1_1(a97) | c0_1(a97)) <=> (hskp0 | c0_1(a97) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | c1_1(a97))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(1441,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)) | c2_1(a97) | c1_1(a97) | c0_1(a97))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a97) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | c1_1(a97)))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[1440])).
% 0.92/1.13 tff(1442,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)) | c2_1(a97) | c1_1(a97) | c0_1(a97))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a97) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | c1_1(a97))),
% 0.92/1.13 inference(transitivity,[status(thm)],[1441, 1439])).
% 0.92/1.13 tff(1443,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)) | c2_1(a97) | c1_1(a97) | c0_1(a97))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(1444,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a97) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | c1_1(a97)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 0.92/1.13 tff(1445,plain,
% 0.92/1.13 (hskp0 | c0_1(a97) | (~c3_1(a97)) | c1_1(a97)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1444, 117, 31, 199])).
% 0.92/1.13 tff(1446,plain,
% 0.92/1.13 (c1_1(a97)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1445, 1438, 54, 62])).
% 0.92/1.13 tff(1447,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a97) | c2_1(a138) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a97) | c2_1(a138) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1448,plain,
% 0.92/1.14 (((~ndr1_0) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)) | c2_1(a97) | c0_1(a97) | (~c3_1(a97))) <=> (c0_1(a97) | c2_1(a138) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1449,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a97) | c2_1(a138) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1448])).
% 0.92/1.14 tff(1450,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a97) | c2_1(a138) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1449, 1447])).
% 0.92/1.14 tff(1451,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1452,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a97) | c2_1(a138) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 0.92/1.14 tff(1453,plain,
% 0.92/1.14 ((~c3_1(a97)) | (~c1_1(a97)) | c1_1(a138)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1452, 117, 1378, 54, 1354, 31, 1063])).
% 0.92/1.14 tff(1454,plain,
% 0.92/1.14 (c1_1(a138)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1453, 1446, 1438])).
% 0.92/1.14 tff(1455,plain,
% 0.92/1.14 (hskp20),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[764, 1387, 52])).
% 0.92/1.14 tff(1456,plain,
% 0.92/1.14 (~c3_1(a132)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[672, 1455])).
% 0.92/1.14 tff(1457,plain,
% 0.92/1.14 (~c2_1(a132)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[692, 1455])).
% 0.92/1.14 tff(1458,plain,
% 0.92/1.14 (~c1_1(a132)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[678, 1455])).
% 0.92/1.14 tff(1459,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a132)) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a132)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1460,plain,
% 0.92/1.14 (((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132))) <=> (c2_1(a138) | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a132)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1461,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a132)) | (~c3_1(a138)) | (~c1_1(a138))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1460])).
% 0.92/1.14 tff(1462,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a132)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1461, 1459])).
% 0.92/1.14 tff(1463,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1464,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a132)) | (~c3_1(a138)) | (~c1_1(a138))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1463, 1462])).
% 0.92/1.14 tff(1465,plain,
% 0.92/1.14 (~c0_1(a132)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1464, 117, 1378, 1354, 1458, 1457, 1456, 20, 1454])).
% 0.92/1.14 tff(1466,plain,
% 0.92/1.14 (hskp7),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1404, 1387])).
% 0.92/1.14 tff(1467,plain,
% 0.92/1.14 (~c0_1(a106)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[912, 1466])).
% 0.92/1.14 tff(1468,plain,
% 0.92/1.14 (c3_1(a106)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[865, 1466])).
% 0.92/1.14 tff(1469,plain,
% 0.92/1.14 (c2_1(a106)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[873, 1466])).
% 0.92/1.14 tff(1470,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a138) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | c0_1(a132) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a138) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | c0_1(a132) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1471,plain,
% 0.92/1.14 (((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132)) <=> (c2_1(a138) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | c0_1(a132) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1472,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a138) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | c0_1(a132) | (~c0_1(a138)) | (~c1_1(a138))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1471])).
% 0.92/1.14 tff(1473,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a138) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | c0_1(a132) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1472, 1470])).
% 0.92/1.14 tff(1474,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1475,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a138) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | c0_1(a132) | (~c0_1(a138)) | (~c1_1(a138))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1474, 1473])).
% 0.92/1.14 tff(1476,plain,
% 0.92/1.14 ($false),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1475, 117, 1363, 1469, 1468, 1354, 1457, 1456, 1467, 489, 1454, 1465])).
% 0.92/1.14 tff(1477,plain,(hskp18 | c0_1(a97) | c2_1(a97)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.14 tff(1478,plain,
% 0.92/1.14 (hskp18),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1477, 54, 31])).
% 0.92/1.14 tff(1479,plain,
% 0.92/1.14 (~c1_1(a129)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[276, 1478])).
% 0.92/1.14 tff(1480,plain,
% 0.92/1.14 (c2_1(a129)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[284, 1478])).
% 0.92/1.14 tff(1481,plain,
% 0.92/1.14 (c0_1(a129)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[292, 1478])).
% 0.92/1.14 tff(1482,plain,
% 0.92/1.14 (~c3_1(a129)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[840, 117, 1481, 1480, 1479, 10])).
% 0.92/1.14 tff(1483,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1484,plain,
% 0.92/1.14 (((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138))) <=> (c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1485,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | c1_1(a138) | (~c0_1(a138))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1484])).
% 0.92/1.14 tff(1486,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1485, 1483])).
% 0.92/1.14 tff(1487,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1488,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | c1_1(a138) | (~c0_1(a138))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1487, 1486])).
% 0.92/1.14 tff(1489,plain,
% 0.92/1.14 (c1_1(a138)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1488, 117, 1363, 1481, 1480, 1354, 1479, 134, 1482])).
% 0.92/1.14 tff(1490,plain,
% 0.92/1.14 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(1491,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[1490])).
% 0.92/1.14 tff(1492,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1493,plain,
% 0.92/1.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(1494,plain,
% 0.92/1.14 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[1493])).
% 0.92/1.14 tff(1495,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 0.92/1.14 tff(1496,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 0.92/1.14 tff(1497,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1496, 1492])).
% 0.92/1.14 tff(1498,plain,(
% 0.92/1.14 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(skolemize,[status(sab)],[1497])).
% 0.92/1.14 tff(1499,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1498, 1491])).
% 0.92/1.14 tff(1500,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c2_1(a138) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c2_1(a138) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1501,plain,
% 0.92/1.14 ((hskp11 | (~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138))) <=> (hskp11 | c2_1(a138) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1502,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c2_1(a138) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1501])).
% 0.92/1.14 tff(1503,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c2_1(a138) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1502, 1500])).
% 0.92/1.14 tff(1504,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1505,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c2_1(a138) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 0.92/1.14 tff(1506,plain,
% 0.92/1.14 (hskp11),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1505, 117, 1378, 1481, 1480, 1354, 1499, 1489, 1482])).
% 0.92/1.14 tff(1507,plain,
% 0.92/1.14 (~c1_1(a112)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[797, 1506])).
% 0.92/1.14 tff(1508,plain,
% 0.92/1.14 (~c0_1(a112)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[803, 1506])).
% 0.92/1.14 tff(1509,plain,
% 0.92/1.14 (c3_1(a112)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[986, 1506])).
% 0.92/1.14 tff(1510,assumption,(~c2_1(a112)), introduced(assumption)).
% 0.92/1.14 tff(1511,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | c2_1(a112) | (~c3_1(a112)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | c2_1(a112) | (~c3_1(a112)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1512,plain,
% 0.92/1.14 ((hskp0 | (~ndr1_0) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)) | c2_1(a112) | c1_1(a112) | c0_1(a112)) <=> (hskp0 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | c2_1(a112) | (~c3_1(a112)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1513,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)) | c2_1(a112) | c1_1(a112) | c0_1(a112))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | c2_1(a112) | (~c3_1(a112))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1512])).
% 0.92/1.14 tff(1514,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)) | c2_1(a112) | c1_1(a112) | c0_1(a112))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | c2_1(a112) | (~c3_1(a112)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1513, 1511])).
% 0.92/1.14 tff(1515,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)) | c2_1(a112) | c1_1(a112) | c0_1(a112))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1516,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | c2_1(a112) | (~c3_1(a112))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 0.92/1.14 tff(1517,plain,
% 0.92/1.14 ($false),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1516, 117, 88, 1044, 1043, 1065, 199, 1510])).
% 0.92/1.14 tff(1518,plain,(c2_1(a112) | hskp0 | (~c3_1(a112)) | c0_1(a112) | c1_1(a112)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.14 tff(1519,plain,
% 0.92/1.14 (c2_1(a112)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1518, 62, 1509, 1508, 1507])).
% 0.92/1.14 tff(1520,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a97) | c2_1(a138) | c0_1(a112) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a97) | c2_1(a138) | c0_1(a112) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1521,plain,
% 0.92/1.14 (((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)) | c2_1(a97) | c0_1(a97) | c3_1(a97)) <=> (c0_1(a97) | c2_1(a138) | c0_1(a112) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1522,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)) | c2_1(a97) | c0_1(a97) | c3_1(a97))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a97) | c2_1(a138) | c0_1(a112) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)) | (~c0_1(a138)) | (~c1_1(a138))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1521])).
% 0.92/1.14 tff(1523,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)) | c2_1(a97) | c0_1(a97) | c3_1(a97))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a97) | c2_1(a138) | c0_1(a112) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1522, 1520])).
% 0.92/1.14 tff(1524,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)) | c2_1(a97) | c0_1(a97) | c3_1(a97))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1525,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a97) | c2_1(a138) | c0_1(a112) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)) | (~c0_1(a138)) | (~c1_1(a138))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1524, 1523])).
% 0.92/1.14 tff(1526,plain,
% 0.92/1.14 (c3_1(a97) | (~c2_1(a112))),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1525, 117, 1363, 1509, 54, 1354, 1508, 31, 489, 1489])).
% 0.92/1.14 tff(1527,plain,
% 0.92/1.14 (c3_1(a97)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1526, 1519])).
% 0.92/1.14 tff(1528,plain,
% 0.92/1.14 (c1_1(a97)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1445, 1527, 54, 62])).
% 0.92/1.14 tff(1529,plain,
% 0.92/1.14 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(1530,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[1529])).
% 0.92/1.14 tff(1531,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1532,plain,
% 0.92/1.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.92/1.15 inference(bind,[status(th)],[])).
% 0.92/1.15 tff(1533,plain,
% 0.92/1.15 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.15 inference(quant_intro,[status(thm)],[1532])).
% 0.92/1.15 tff(1534,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.92/1.15 tff(1535,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 0.92/1.15 tff(1536,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1535, 1531])).
% 0.92/1.15 tff(1537,plain,(
% 0.92/1.15 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.15 inference(skolemize,[status(sab)],[1536])).
% 0.92/1.15 tff(1538,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1537, 1530])).
% 0.92/1.15 tff(1539,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp0 | c0_1(a97) | c1_1(a129) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | (~c0_1(a129)) | c3_1(a129))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp0 | c0_1(a97) | c1_1(a129) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | (~c0_1(a129)) | c3_1(a129))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1540,plain,
% 0.92/1.15 ((hskp0 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97))) <=> (hskp0 | c0_1(a97) | c1_1(a129) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | (~c0_1(a129)) | c3_1(a129))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1541,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp0 | c0_1(a97) | c1_1(a129) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | (~c0_1(a129)) | c3_1(a129)))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[1540])).
% 0.92/1.15 tff(1542,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp0 | c0_1(a97) | c1_1(a129) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | (~c0_1(a129)) | c3_1(a129))),
% 0.92/1.15 inference(transitivity,[status(thm)],[1541, 1539])).
% 0.92/1.15 tff(1543,plain,
% 0.92/1.15 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(1544,plain,
% 0.92/1.15 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp0 | c0_1(a97) | c1_1(a129) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | (~c0_1(a129)) | c3_1(a129)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 0.92/1.15 tff(1545,plain,
% 0.92/1.15 ((~c3_1(a97)) | (~c1_1(a97))),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1544, 117, 62, 1481, 54, 1479, 1538, 1482])).
% 0.92/1.15 tff(1546,plain,
% 0.92/1.15 ($false),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1545, 1528, 1527])).
% 0.92/1.15 tff(1547,plain,(c0_1(a97) | c2_1(a97)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.15 tff(1548,plain,
% 0.92/1.15 (c0_1(a97)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1547, 31])).
% 0.92/1.15 tff(1549,plain,
% 0.92/1.15 (hskp4),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[830, 53, 1548, 52, 31])).
% 0.92/1.15 tff(1550,plain,
% 0.92/1.15 (c0_1(a103)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[86, 1549])).
% 0.92/1.15 tff(1551,plain,
% 0.92/1.15 (~c3_1(a103)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[78, 1549])).
% 0.92/1.15 tff(1552,plain,
% 0.92/1.15 (c2_1(a103)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[145, 1549])).
% 0.92/1.15 tff(1553,plain,
% 0.92/1.15 (c1_1(a97)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[301, 1552, 1548, 53, 1551, 31, 1550])).
% 0.92/1.15 tff(1554,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a138) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a138) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1555,plain,
% 0.92/1.15 ((hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a138) | c1_1(a138) | (~c3_1(a138))) <=> (hskp28 | c2_1(a138) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1556,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a138) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[1555])).
% 0.92/1.15 tff(1557,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a138) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[1556, 1554])).
% 0.92/1.15 tff(1558,plain,
% 0.92/1.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(1559,plain,
% 0.92/1.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a138) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1558, 1557])).
% 0.92/1.15 tff(1560,plain,
% 0.92/1.15 (hskp28 | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1559, 117, 1378, 1354, 31, 313])).
% 0.92/1.15 tff(1561,plain,
% 0.92/1.15 (c1_1(a138)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1560, 136, 1548, 1553])).
% 0.92/1.15 tff(1562,plain,
% 0.92/1.15 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.92/1.15 inference(bind,[status(th)],[])).
% 0.92/1.15 tff(1563,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.15 inference(quant_intro,[status(thm)],[1562])).
% 0.92/1.15 tff(1564,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1565,plain,
% 0.92/1.15 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.92/1.15 inference(bind,[status(th)],[])).
% 0.92/1.15 tff(1566,plain,
% 0.92/1.15 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.15 inference(quant_intro,[status(thm)],[1565])).
% 0.92/1.15 tff(1567,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 0.92/1.15 tff(1568,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1567, 1566])).
% 0.92/1.15 tff(1569,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1568, 1564])).
% 0.92/1.15 tff(1570,plain,(
% 0.92/1.15 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.15 inference(skolemize,[status(sab)],[1569])).
% 0.92/1.15 tff(1571,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1570, 1563])).
% 0.92/1.15 tff(1572,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a108) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a108) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1573,plain,
% 0.92/1.15 ((hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108))) <=> (hskp16 | c0_1(a108) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1574,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a108) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a108)) | (~c2_1(a108))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[1573])).
% 0.92/1.15 tff(1575,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a108) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[1574, 1572])).
% 0.92/1.15 tff(1576,plain,
% 0.92/1.15 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(1577,plain,
% 0.92/1.15 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a108) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a108)) | (~c2_1(a108))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 0.92/1.15 tff(1578,plain,
% 0.92/1.15 (hskp16),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1577, 117, 1016, 1008, 149, 162, 1000, 148, 1571])).
% 0.92/1.15 tff(1579,plain,
% 0.92/1.15 (c0_1(a122)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1289, 1578])).
% 0.92/1.15 tff(1580,assumption,(c1_1(a138)), introduced(assumption)).
% 0.92/1.15 tff(1581,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a138) | c0_1(a108) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a138) | c0_1(a108) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1582,plain,
% 0.92/1.15 (((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108))) <=> (c2_1(a138) | c0_1(a108) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1583,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a138) | c0_1(a108) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c0_1(a138)) | (~c1_1(a138))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[1582])).
% 0.92/1.15 tff(1584,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a138) | c0_1(a108) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[1583, 1581])).
% 0.92/1.15 tff(1585,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(1586,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a138) | c0_1(a108) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c0_1(a138)) | (~c1_1(a138))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1585, 1584])).
% 0.92/1.15 tff(1587,plain,
% 0.92/1.15 (~c1_1(a103)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1586, 117, 1363, 1016, 1008, 149, 162, 1354, 1000, 354, 1580])).
% 0.92/1.15 tff(1588,plain,
% 0.92/1.15 (~c1_1(a122)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[516, 1578])).
% 0.92/1.15 tff(1589,plain,
% 0.92/1.15 (~c2_1(a122)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[430, 1578])).
% 0.92/1.15 tff(1590,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a122)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1591,plain,
% 0.92/1.15 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122))) <=> (c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a122)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1592,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a122))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[1591])).
% 0.92/1.15 tff(1593,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a122)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[1592, 1590])).
% 0.92/1.15 tff(1594,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(1595,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a122))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 0.92/1.15 tff(1596,plain,
% 0.92/1.15 ($false),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1595, 117, 1292, 149, 162, 395, 407, 148, 134, 327])).
% 0.92/1.15 tff(1597,plain,(c1_1(a103) | (~c0_1(a122)) | (~c0_1(a103)) | (~c2_1(a103)) | c1_1(a122) | c2_1(a122) | c3_1(a103)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.15 tff(1598,plain,
% 0.92/1.15 ($false),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1597, 1589, 1588, 148, 162, 149, 1587, 1579])).
% 0.92/1.15 tff(1599,plain,((~hskp9) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a138))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.15 tff(1600,plain,
% 0.92/1.15 (~hskp9),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1599, 1561, 1552, 1550, 1551])).
% 0.92/1.15 tff(1601,plain,
% 0.92/1.15 (hskp18 | hskp11 | c3_1(a97) | (~c0_1(a97))),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[790, 117, 31, 783])).
% 0.92/1.15 tff(1602,plain,
% 0.92/1.15 (hskp11),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1601, 53, 1548, 52])).
% 0.92/1.15 tff(1603,plain,
% 0.92/1.15 (c3_1(a112)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[986, 1602])).
% 0.92/1.15 tff(1604,plain,
% 0.92/1.15 (hskp18 | hskp8 | c3_1(a97) | (~c1_1(a97))),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[969, 117, 1548, 963])).
% 0.92/1.15 tff(1605,plain,
% 0.92/1.15 (hskp8),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1604, 1553, 52, 53])).
% 0.92/1.15 tff(1606,plain,
% 0.92/1.15 (~c0_1(a107)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1030, 1605])).
% 0.92/1.15 tff(1607,plain,
% 0.92/1.15 (~c1_1(a112)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[797, 1602])).
% 0.92/1.15 tff(1608,plain,
% 0.92/1.15 (~c0_1(a112)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[803, 1602])).
% 0.92/1.15 tff(1609,plain,
% 0.92/1.15 (c3_1(a107)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[978, 1605])).
% 0.92/1.15 tff(1610,plain,
% 0.92/1.15 (~c2_1(a107)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[992, 1605])).
% 0.92/1.15 tff(1611,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a138) | c2_1(a107) | (~ndr1_0) | c1_1(a107) | (~c3_1(a107)) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a138) | c2_1(a107) | (~ndr1_0) | c1_1(a107) | (~c3_1(a107)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1612,plain,
% 0.92/1.15 ((hskp28 | (~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c2_1(a107) | c1_1(a107) | (~c3_1(a107))) <=> (hskp28 | c2_1(a138) | c2_1(a107) | (~ndr1_0) | c1_1(a107) | (~c3_1(a107)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1613,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c2_1(a107) | c1_1(a107) | (~c3_1(a107)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a138) | c2_1(a107) | (~ndr1_0) | c1_1(a107) | (~c3_1(a107)) | (~c0_1(a138)) | (~c1_1(a138))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[1612])).
% 0.92/1.15 tff(1614,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c2_1(a107) | c1_1(a107) | (~c3_1(a107)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a138) | c2_1(a107) | (~ndr1_0) | c1_1(a107) | (~c3_1(a107)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[1613, 1611])).
% 0.92/1.15 tff(1615,plain,
% 0.92/1.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c2_1(a107) | c1_1(a107) | (~c3_1(a107)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(1616,plain,
% 0.92/1.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a138) | c2_1(a107) | (~ndr1_0) | c1_1(a107) | (~c3_1(a107)) | (~c0_1(a138)) | (~c1_1(a138))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1615, 1614])).
% 0.92/1.15 tff(1617,plain,
% 0.92/1.15 (hskp28 | c1_1(a107) | (~c1_1(a138))),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1616, 117, 1363, 1609, 1354, 1610, 313])).
% 0.92/1.15 tff(1618,plain,
% 0.92/1.15 (c1_1(a107)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1617, 136, 1561])).
% 0.92/1.15 tff(1619,assumption,(c1_1(a107)), introduced(assumption)).
% 0.92/1.15 tff(1620,plain,
% 0.92/1.15 ($false),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1072, 117, 1044, 1066, 1043, 1065, 1064, 1063, 1619, 1510])).
% 0.92/1.15 tff(1621,plain,(c2_1(a112) | (~c3_1(a112)) | (~c3_1(a107)) | c0_1(a112) | c1_1(a112) | c0_1(a107) | (~c1_1(a107))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.15 tff(1622,plain,
% 0.92/1.15 (c2_1(a112)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1621, 1618, 1609, 1608, 1607, 1606, 1603])).
% 0.92/1.15 tff(1623,plain,
% 0.92/1.15 (hskp17 | hskp9 | (~c2_1(a112))),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1051, 117, 1603, 1608, 1042])).
% 0.92/1.15 tff(1624,plain,
% 0.92/1.15 (hskp17),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1623, 1622, 1600])).
% 0.92/1.15 tff(1625,plain,
% 0.92/1.15 (~c1_1(a124)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1117, 1624])).
% 0.92/1.15 tff(1626,plain,
% 0.92/1.15 (~c3_1(a124)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1111, 1624])).
% 0.92/1.15 tff(1627,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1628,plain,
% 0.92/1.15 (((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124))) <=> (c2_1(a138) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1629,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a138)) | (~c1_1(a138))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[1628])).
% 0.92/1.15 tff(1630,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[1629, 1627])).
% 0.92/1.15 tff(1631,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(1632,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a138)) | (~c1_1(a138))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 0.92/1.15 tff(1633,plain,
% 0.92/1.15 (c3_1(a124) | (~c0_1(a124))),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1632, 117, 1378, 1548, 1354, 1139, 31, 53, 20, 1580])).
% 0.92/1.15 tff(1634,plain,
% 0.92/1.15 (~c0_1(a124)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1633, 1138])).
% 0.92/1.15 tff(1635,plain,
% 0.92/1.15 (hskp6 | c3_1(a97) | (~c1_1(a97))),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[817, 117, 1548, 364])).
% 0.92/1.15 tff(1636,plain,
% 0.92/1.15 (hskp6),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1635, 1553, 53])).
% 0.92/1.15 tff(1637,plain,
% 0.92/1.15 (c1_1(a105)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[393, 1636])).
% 0.92/1.15 tff(1638,plain,
% 0.92/1.15 (~c3_1(a105)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[377, 1636])).
% 0.92/1.15 tff(1639,plain,
% 0.92/1.15 (c2_1(a105)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[385, 1636])).
% 0.92/1.15 tff(1640,assumption,(~c2_1(a124)), introduced(assumption)).
% 0.92/1.15 tff(1641,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a124) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a124) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1642,plain,
% 0.92/1.15 (((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a124) | c1_1(a124) | c3_1(a124)) <=> (c2_1(a124) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1643,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a124) | c1_1(a124) | c3_1(a124))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a124) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105))))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[1642])).
% 0.92/1.16 tff(1644,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a124) | c1_1(a124) | c3_1(a124))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a124) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))),
% 0.92/1.16 inference(transitivity,[status(thm)],[1643, 1641])).
% 0.92/1.16 tff(1645,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a124) | c1_1(a124) | c3_1(a124))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(1646,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a124) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 0.92/1.16 tff(1647,plain,
% 0.92/1.16 ($false),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1646, 117, 1640, 409, 408, 1139, 1138, 406, 31, 53, 405, 303])).
% 0.92/1.16 tff(1648,plain,(c2_1(a124) | (~c1_1(a105)) | (~c2_1(a105)) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~c1_1(a97))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.16 tff(1649,plain,
% 0.92/1.16 (c2_1(a124)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1648, 1138, 1553, 1639, 1139, 1638, 31, 53, 1637])).
% 0.92/1.16 tff(1650,plain,
% 0.92/1.16 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(1651,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[1650])).
% 0.92/1.16 tff(1652,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1653,plain,
% 0.92/1.16 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.92/1.16 inference(bind,[status(th)],[])).
% 0.92/1.16 tff(1654,plain,
% 0.92/1.16 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.16 inference(quant_intro,[status(thm)],[1653])).
% 0.92/1.16 tff(1655,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 0.92/1.16 tff(1656,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[1655, 1654])).
% 0.92/1.16 tff(1657,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[1656, 1652])).
% 0.92/1.16 tff(1658,plain,(
% 0.92/1.16 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.16 inference(skolemize,[status(sab)],[1657])).
% 0.92/1.16 tff(1659,plain,
% 0.92/1.16 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[1658, 1651])).
% 0.92/1.16 tff(1660,plain,
% 0.92/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1661,plain,
% 0.92/1.16 ((hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124))) <=> (hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1662,plain,
% 0.92/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124)))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[1661])).
% 0.92/1.16 tff(1663,plain,
% 0.92/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124))),
% 0.92/1.16 inference(transitivity,[status(thm)],[1662, 1660])).
% 0.92/1.16 tff(1664,plain,
% 0.92/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(1665,plain,
% 0.92/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 0.92/1.16 tff(1666,plain,
% 0.92/1.16 (hskp1 | c3_1(a124) | (~c2_1(a124)) | c0_1(a124)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1665, 117, 1139, 1659])).
% 0.92/1.16 tff(1667,plain,
% 0.92/1.16 (hskp1),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1666, 1649, 1138, 1634])).
% 0.92/1.16 tff(1668,plain,
% 0.92/1.16 (~c3_1(a98)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1153, 1667])).
% 0.92/1.16 tff(1669,plain,
% 0.92/1.16 (~c1_1(a98)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1159, 1667])).
% 0.92/1.16 tff(1670,plain,
% 0.92/1.16 (hskp19),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1218, 1649, 53, 1139, 1138, 1553, 1548, 52])).
% 0.92/1.16 tff(1671,plain,
% 0.92/1.16 (~c2_1(a130)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[237, 1670])).
% 0.92/1.16 tff(1672,plain,
% 0.92/1.16 (c0_1(a98)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1167, 1667])).
% 0.92/1.16 tff(1673,plain,
% 0.92/1.16 (c3_1(a130)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[245, 1670])).
% 0.92/1.16 tff(1674,plain,
% 0.92/1.16 (c1_1(a130)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[253, 1670])).
% 0.92/1.16 tff(1675,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a130) | c1_1(a98) | c3_1(a98) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a98)) | (~c3_1(a130)) | (~c1_1(a130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c1_1(a98) | c3_1(a98) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a98)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1676,plain,
% 0.92/1.16 (((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98))) <=> (c2_1(a130) | c1_1(a98) | c3_1(a98) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a98)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1677,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a130) | c1_1(a98) | c3_1(a98) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a98)) | (~c3_1(a130)) | (~c1_1(a130))))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[1676])).
% 0.92/1.16 tff(1678,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c1_1(a98) | c3_1(a98) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a98)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 0.92/1.16 inference(transitivity,[status(thm)],[1677, 1675])).
% 0.92/1.16 tff(1679,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98)))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(1680,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c1_1(a98) | c3_1(a98) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a98)) | (~c3_1(a130)) | (~c1_1(a130))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 0.92/1.16 tff(1681,plain,
% 0.92/1.16 ($false),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1680, 117, 1674, 1673, 1672, 1548, 1671, 1669, 1668, 31, 53, 20])).
% 0.92/1.16 tff(1682,plain,(c3_1(a124) | c2_1(a97) | c3_1(a97) | c1_1(a124) | hskp18 | (~c1_1(a138))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.16 tff(1683,plain,
% 0.92/1.16 ($false),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1682, 1626, 1625, 53, 31, 52, 1561])).
% 0.92/1.16 tff(1684,plain,(hskp28 | c3_1(a97) | c2_1(a97) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.92/1.16 tff(1685,plain,
% 0.92/1.16 (hskp28),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1684, 53, 31, 52])).
% 0.92/1.16 tff(1686,plain,
% 0.92/1.16 (c1_1(a137)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[606, 1685])).
% 0.92/1.16 tff(1687,plain,
% 0.92/1.16 (c2_1(a137)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[598, 1685])).
% 0.92/1.16 tff(1688,plain,
% 0.92/1.16 (c0_1(a137)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[590, 1685])).
% 0.92/1.16 tff(1689,plain,
% 0.92/1.16 (~hskp9),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1024, 1686, 1553, 1687, 1548, 31, 1688])).
% 0.92/1.16 tff(1690,plain,
% 0.92/1.16 (hskp17),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1105, 1689, 52, 1603, 1610, 1688, 1687, 1606, 1609, 1608, 1607, 1686])).
% 0.92/1.16 tff(1691,plain,
% 0.92/1.16 (~c1_1(a124)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1117, 1690])).
% 0.92/1.16 tff(1692,plain,
% 0.92/1.16 (~c3_1(a124)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1111, 1690])).
% 0.92/1.16 tff(1693,plain,
% 0.92/1.16 (~c1_1(a138)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1682, 1692, 53, 31, 52, 1691])).
% 0.92/1.16 tff(1694,plain,
% 0.92/1.16 (c2_1(a124)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1125, 1690])).
% 0.92/1.16 tff(1695,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1696,plain,
% 0.92/1.16 (((~ndr1_0) | c3_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138))) <=> (c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1697,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a138) | (~c0_1(a138))))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[1696])).
% 0.92/1.16 tff(1698,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.16 inference(transitivity,[status(thm)],[1697, 1695])).
% 0.92/1.16 tff(1699,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(1700,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a138) | (~c0_1(a138))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[1699, 1698])).
% 0.92/1.16 tff(1701,plain,
% 0.92/1.16 (~c0_1(a124)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1700, 117, 1363, 1694, 1354, 1691, 1692, 134, 1693])).
% 0.92/1.16 tff(1702,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | c1_1(a138) | (~c0_1(a138)) | (~c3_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | c1_1(a138) | (~c0_1(a138)) | (~c3_1(a138)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1703,plain,
% 0.92/1.16 (((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a124) | c0_1(a124) | c3_1(a124)) <=> (c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | c1_1(a138) | (~c0_1(a138)) | (~c3_1(a138)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1704,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a124) | c0_1(a124) | c3_1(a124))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | c1_1(a138) | (~c0_1(a138)) | (~c3_1(a138))))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[1703])).
% 0.92/1.16 tff(1705,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a124) | c0_1(a124) | c3_1(a124))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | c1_1(a138) | (~c0_1(a138)) | (~c3_1(a138)))),
% 0.92/1.16 inference(transitivity,[status(thm)],[1704, 1702])).
% 0.92/1.16 tff(1706,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a124) | c0_1(a124) | c3_1(a124))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(1707,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | c1_1(a138) | (~c0_1(a138)) | (~c3_1(a138))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 0.92/1.16 tff(1708,plain,
% 0.92/1.16 ($false),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1707, 117, 1363, 1378, 1548, 1691, 1692, 53, 1239, 1553, 1693, 1701])).
% 0.92/1.16 tff(1709,plain,(c3_1(a97) | c2_1(a97) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.92/1.16 tff(1710,plain,
% 0.92/1.16 (c3_1(a97)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1709, 52, 31])).
% 0.92/1.16 tff(1711,plain,
% 0.92/1.16 (~hskp0),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[221, 1710])).
% 0.92/1.16 tff(1712,plain,
% 0.92/1.16 (~hskp4),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1386, 1711, 52])).
% 0.92/1.16 tff(1713,plain,
% 0.92/1.16 (hskp7),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1404, 1712])).
% 0.92/1.16 tff(1714,plain,
% 0.92/1.16 (~c0_1(a106)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[912, 1713])).
% 0.92/1.16 tff(1715,plain,
% 0.92/1.16 (hskp20),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[764, 1712, 52])).
% 0.92/1.16 tff(1716,plain,
% 0.92/1.16 (~c3_1(a132)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[672, 1715])).
% 0.92/1.16 tff(1717,plain,
% 0.92/1.16 (~c2_1(a132)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[692, 1715])).
% 0.92/1.16 tff(1718,plain,
% 0.92/1.16 (~c1_1(a132)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[678, 1715])).
% 0.92/1.16 tff(1719,plain,
% 0.92/1.16 (c3_1(a106)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[865, 1713])).
% 0.92/1.16 tff(1720,plain,
% 0.92/1.16 (c2_1(a106)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[873, 1713])).
% 0.92/1.16 tff(1721,plain,
% 0.92/1.16 (hskp17),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1425, 117, 1720, 1719, 1718, 1717, 1716, 1714, 51])).
% 0.92/1.16 tff(1722,plain,
% 0.92/1.16 (~c3_1(a124)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1111, 1721])).
% 0.92/1.16 tff(1723,plain,
% 0.92/1.16 (~c1_1(a124)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1117, 1721])).
% 0.92/1.16 tff(1724,plain,
% 0.92/1.16 (c2_1(a124)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1125, 1721])).
% 0.92/1.16 tff(1725,plain,
% 0.92/1.16 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | c1_1(a132) | c2_1(a132) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp4 | c1_1(a132) | c2_1(a132) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a132)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1726,plain,
% 0.92/1.16 ((hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a132) | c1_1(a132) | (~c0_1(a132))) <=> (hskp4 | c1_1(a132) | c2_1(a132) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a132)))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1727,plain,
% 0.92/1.16 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a132) | c1_1(a132) | (~c0_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | c1_1(a132) | c2_1(a132) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a132))))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[1726])).
% 0.92/1.16 tff(1728,plain,
% 0.92/1.16 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a132) | c1_1(a132) | (~c0_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp4 | c1_1(a132) | c2_1(a132) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a132)))),
% 0.92/1.16 inference(transitivity,[status(thm)],[1727, 1725])).
% 0.92/1.16 tff(1729,plain,
% 0.92/1.16 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a132) | c1_1(a132) | (~c0_1(a132)))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(1730,plain,
% 0.92/1.16 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp4 | c1_1(a132) | c2_1(a132) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a132))),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[1729, 1728])).
% 0.92/1.16 tff(1731,plain,
% 0.92/1.16 (~c0_1(a132)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1730, 117, 1712, 1724, 1718, 1717, 1723, 1722, 41])).
% 0.92/1.16 tff(1732,plain,
% 0.92/1.16 (hskp19),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[699, 117, 52, 1718, 1717, 1716, 30])).
% 0.92/1.16 tff(1733,plain,
% 0.92/1.16 (~c2_1(a130)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[237, 1732])).
% 0.92/1.16 tff(1734,plain,
% 0.92/1.16 (c1_1(a130)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[253, 1732])).
% 0.92/1.16 tff(1735,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1736,plain,
% 0.92/1.16 (((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132)) <=> (c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))),
% 0.92/1.16 inference(rewrite,[status(thm)],[])).
% 0.92/1.16 tff(1737,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132)))),
% 0.92/1.16 inference(monotonicity,[status(thm)],[1736])).
% 0.92/1.16 tff(1738,plain,
% 0.92/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))),
% 0.92/1.16 inference(transitivity,[status(thm)],[1737, 1735])).
% 0.92/1.16 tff(1739,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132))),
% 0.92/1.16 inference(quant_inst,[status(thm)],[])).
% 0.92/1.16 tff(1740,plain,
% 0.92/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132)),
% 0.92/1.16 inference(modus_ponens,[status(thm)],[1739, 1738])).
% 0.92/1.16 tff(1741,plain,
% 0.92/1.16 (~c0_1(a130)),
% 0.92/1.16 inference(unit_resolution,[status(thm)],[1740, 117, 1734, 1720, 1719, 1717, 1716, 1733, 1714, 489, 1731])).
% 1.01/1.17 tff(1742,plain,
% 1.01/1.17 (c3_1(a130)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[245, 1732])).
% 1.01/1.17 tff(1743,plain,
% 1.01/1.17 ($false),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[708, 117, 1711, 1742, 1718, 1717, 1733, 199, 1731, 1741])).
% 1.01/1.17 tff(1744,plain,(hskp18 | c2_1(a97)), inference(lemma,lemma(discharge,[]))).
% 1.01/1.17 tff(1745,plain,
% 1.01/1.17 (hskp18),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1744, 31])).
% 1.01/1.17 tff(1746,plain,
% 1.01/1.17 (~c1_1(a129)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[276, 1745])).
% 1.01/1.17 tff(1747,plain,
% 1.01/1.17 (c2_1(a129)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[284, 1745])).
% 1.01/1.17 tff(1748,plain,
% 1.01/1.17 (c0_1(a129)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[292, 1745])).
% 1.01/1.17 tff(1749,plain,
% 1.01/1.17 (~c3_1(a129)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[840, 117, 1748, 1747, 1746, 10])).
% 1.01/1.17 tff(1750,plain,
% 1.01/1.17 (c1_1(a138)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1488, 117, 1363, 1748, 1747, 1354, 1746, 134, 1749])).
% 1.01/1.17 tff(1751,plain,
% 1.01/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a129) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a129) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1752,plain,
% 1.01/1.17 (((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a129) | c3_1(a129) | (~c0_1(a129))) <=> (c2_1(a138) | c1_1(a129) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1753,plain,
% 1.01/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a129) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138))))),
% 1.01/1.17 inference(monotonicity,[status(thm)],[1752])).
% 1.01/1.17 tff(1754,plain,
% 1.01/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a129) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.01/1.17 inference(transitivity,[status(thm)],[1753, 1751])).
% 1.01/1.17 tff(1755,plain,
% 1.01/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(1756,plain,
% 1.01/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a129) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1755, 1754])).
% 1.01/1.17 tff(1757,plain,
% 1.01/1.17 (c3_1(a97) | (~c1_1(a138))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1756, 117, 1378, 1748, 1548, 1354, 1746, 31, 20, 1749])).
% 1.01/1.17 tff(1758,plain,
% 1.01/1.17 (c3_1(a97)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1757, 1750])).
% 1.01/1.17 tff(1759,plain,
% 1.01/1.17 (~hskp0),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[221, 1758])).
% 1.01/1.17 tff(1760,plain,
% 1.01/1.17 (hskp11),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1505, 117, 1378, 1748, 1747, 1354, 1499, 1750, 1749])).
% 1.01/1.17 tff(1761,plain,
% 1.01/1.17 (~c1_1(a112)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[797, 1760])).
% 1.01/1.17 tff(1762,plain,
% 1.01/1.17 (~c0_1(a112)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[803, 1760])).
% 1.01/1.17 tff(1763,plain,
% 1.01/1.17 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.01/1.17 inference(bind,[status(th)],[])).
% 1.01/1.17 tff(1764,plain,
% 1.01/1.17 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.01/1.17 inference(quant_intro,[status(thm)],[1763])).
% 1.01/1.17 tff(1765,plain,
% 1.01/1.17 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1766,plain,
% 1.01/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp24) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp24))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.01/1.17 inference(bind,[status(th)],[])).
% 1.01/1.17 tff(1767,plain,
% 1.01/1.17 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.01/1.17 inference(quant_intro,[status(thm)],[1766])).
% 1.01/1.17 tff(1768,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.01/1.17 tff(1769,plain,
% 1.01/1.17 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1768, 1767])).
% 1.01/1.17 tff(1770,plain,
% 1.01/1.17 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1769, 1765])).
% 1.01/1.17 tff(1771,plain,(
% 1.01/1.17 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.01/1.17 inference(skolemize,[status(sab)],[1770])).
% 1.01/1.17 tff(1772,plain,
% 1.01/1.17 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1771, 1764])).
% 1.01/1.17 tff(1773,plain,
% 1.01/1.17 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c0_1(a138)) | (~c3_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c0_1(a138)) | (~c3_1(a138)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1774,plain,
% 1.01/1.17 ((hskp24 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129))) <=> (hskp24 | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c0_1(a138)) | (~c3_1(a138)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1775,plain,
% 1.01/1.17 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c0_1(a138)) | (~c3_1(a138))))),
% 1.01/1.17 inference(monotonicity,[status(thm)],[1774])).
% 1.01/1.17 tff(1776,plain,
% 1.01/1.17 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c0_1(a138)) | (~c3_1(a138)))),
% 1.01/1.17 inference(transitivity,[status(thm)],[1775, 1773])).
% 1.01/1.17 tff(1777,plain,
% 1.01/1.17 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(1778,plain,
% 1.01/1.17 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c0_1(a138)) | (~c3_1(a138))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 1.01/1.17 tff(1779,plain,
% 1.01/1.17 (hskp24),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1778, 117, 1363, 1378, 1748, 1747, 1354, 1746, 1772])).
% 1.01/1.17 tff(1780,plain,
% 1.01/1.17 (((~hskp24) | (~c3_1(a147))) <=> ((~hskp24) | (~c3_1(a147)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1781,plain,
% 1.01/1.17 (((~c3_1(a147)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a147)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1782,axiom,((~c3_1(a147)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.01/1.17 tff(1783,plain,
% 1.01/1.17 ((~hskp24) | (~c3_1(a147))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 1.01/1.17 tff(1784,plain,
% 1.01/1.17 ((~hskp24) | (~c3_1(a147))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1783, 1780])).
% 1.01/1.17 tff(1785,plain,
% 1.01/1.17 (~c3_1(a147)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1784, 1779])).
% 1.01/1.17 tff(1786,plain,
% 1.01/1.17 (((~hskp24) | (~c1_1(a147))) <=> ((~hskp24) | (~c1_1(a147)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1787,plain,
% 1.01/1.17 (((~c1_1(a147)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a147)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1788,axiom,((~c1_1(a147)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.01/1.17 tff(1789,plain,
% 1.01/1.17 ((~hskp24) | (~c1_1(a147))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 1.01/1.17 tff(1790,plain,
% 1.01/1.17 ((~hskp24) | (~c1_1(a147))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1789, 1786])).
% 1.01/1.17 tff(1791,plain,
% 1.01/1.17 (~c1_1(a147)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1790, 1779])).
% 1.01/1.17 tff(1792,plain,
% 1.01/1.17 (((~hskp24) | (~c0_1(a147))) <=> ((~hskp24) | (~c0_1(a147)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1793,plain,
% 1.01/1.17 (((~c0_1(a147)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a147)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1794,axiom,((~c0_1(a147)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.01/1.17 tff(1795,plain,
% 1.01/1.17 ((~hskp24) | (~c0_1(a147))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 1.01/1.17 tff(1796,plain,
% 1.01/1.17 ((~hskp24) | (~c0_1(a147))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1795, 1792])).
% 1.01/1.17 tff(1797,plain,
% 1.01/1.17 (~c0_1(a147)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1796, 1779])).
% 1.01/1.17 tff(1798,plain,
% 1.01/1.17 (c3_1(a112)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[986, 1760])).
% 1.01/1.17 tff(1799,assumption,(hskp6), introduced(assumption)).
% 1.01/1.17 tff(1800,plain,
% 1.01/1.17 (~c3_1(a105)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[377, 1799])).
% 1.01/1.17 tff(1801,plain,
% 1.01/1.17 (c1_1(a105)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[393, 1799])).
% 1.01/1.17 tff(1802,plain,
% 1.01/1.17 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | c3_1(a105) | (~ndr1_0) | (~c0_1(a105)) | (~c1_1(a105)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | c3_1(a105) | (~ndr1_0) | (~c0_1(a105)) | (~c1_1(a105)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1803,plain,
% 1.01/1.17 ((hskp0 | (~ndr1_0) | c3_1(a105) | (~c0_1(a105)) | (~c1_1(a105))) <=> (hskp0 | c3_1(a105) | (~ndr1_0) | (~c0_1(a105)) | (~c1_1(a105)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1804,plain,
% 1.01/1.17 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a105) | (~c0_1(a105)) | (~c1_1(a105)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | c3_1(a105) | (~ndr1_0) | (~c0_1(a105)) | (~c1_1(a105))))),
% 1.01/1.17 inference(monotonicity,[status(thm)],[1803])).
% 1.01/1.17 tff(1805,plain,
% 1.01/1.17 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a105) | (~c0_1(a105)) | (~c1_1(a105)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | c3_1(a105) | (~ndr1_0) | (~c0_1(a105)) | (~c1_1(a105)))),
% 1.01/1.17 inference(transitivity,[status(thm)],[1804, 1802])).
% 1.01/1.17 tff(1806,plain,
% 1.01/1.17 ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a105) | (~c0_1(a105)) | (~c1_1(a105)))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(1807,plain,
% 1.01/1.17 ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | c3_1(a105) | (~ndr1_0) | (~c0_1(a105)) | (~c1_1(a105))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 1.01/1.17 tff(1808,plain,
% 1.01/1.17 (~c0_1(a105)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1807, 117, 88, 1801, 1800, 72])).
% 1.01/1.17 tff(1809,assumption,(~c3_1(a147)), introduced(assumption)).
% 1.01/1.17 tff(1810,assumption,(~c1_1(a147)), introduced(assumption)).
% 1.01/1.17 tff(1811,assumption,(~c0_1(a147)), introduced(assumption)).
% 1.01/1.17 tff(1812,plain,
% 1.01/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c3_1(a105) | (~ndr1_0) | c0_1(a105) | (~c1_1(a105)) | (~c3_1(a112)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c3_1(a105) | (~ndr1_0) | c0_1(a105) | (~c1_1(a105)) | (~c3_1(a112)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1813,plain,
% 1.01/1.17 (((~ndr1_0) | c0_1(a105) | c3_1(a105) | (~c1_1(a105)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147)) <=> (c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c3_1(a105) | (~ndr1_0) | c0_1(a105) | (~c1_1(a105)) | (~c3_1(a112)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1814,plain,
% 1.01/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a105) | c3_1(a105) | (~c1_1(a105)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c3_1(a105) | (~ndr1_0) | c0_1(a105) | (~c1_1(a105)) | (~c3_1(a112))))),
% 1.01/1.17 inference(monotonicity,[status(thm)],[1813])).
% 1.01/1.17 tff(1815,plain,
% 1.01/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a105) | c3_1(a105) | (~c1_1(a105)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c3_1(a105) | (~ndr1_0) | c0_1(a105) | (~c1_1(a105)) | (~c3_1(a112)))),
% 1.01/1.17 inference(transitivity,[status(thm)],[1814, 1812])).
% 1.01/1.17 tff(1816,plain,
% 1.01/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a105) | c3_1(a105) | (~c1_1(a105)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(1817,plain,
% 1.01/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c3_1(a105) | (~ndr1_0) | c0_1(a105) | (~c1_1(a105)) | (~c3_1(a112))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1816, 1815])).
% 1.01/1.17 tff(1818,plain,
% 1.01/1.17 ($false),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1817, 117, 1044, 1801, 1811, 1810, 1809, 1043, 1065, 1800, 1337, 1808])).
% 1.01/1.17 tff(1819,plain,((~hskp6) | (~c3_1(a112)) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.01/1.17 tff(1820,plain,
% 1.01/1.17 (~hskp6),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1819, 1798, 1797, 1791, 1785, 1762, 1761, 1759])).
% 1.01/1.17 tff(1821,plain,
% 1.01/1.17 (^[U: $i] : refl((hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.01/1.17 inference(bind,[status(th)],[])).
% 1.01/1.17 tff(1822,plain,
% 1.01/1.17 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.01/1.17 inference(quant_intro,[status(thm)],[1821])).
% 1.01/1.17 tff(1823,plain,
% 1.01/1.17 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1824,plain,
% 1.01/1.17 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp6) <=> ((hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite(((hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp6) <=> (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.01/1.17 inference(bind,[status(th)],[])).
% 1.01/1.17 tff(1825,plain,
% 1.01/1.17 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp6) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.01/1.17 inference(quant_intro,[status(thm)],[1824])).
% 1.01/1.17 tff(1826,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 1.01/1.17 tff(1827,plain,
% 1.01/1.17 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 1.01/1.17 tff(1828,plain,
% 1.01/1.17 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1827, 1823])).
% 1.01/1.17 tff(1829,plain,(
% 1.01/1.17 ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.01/1.17 inference(skolemize,[status(sab)],[1828])).
% 1.01/1.17 tff(1830,plain,
% 1.01/1.17 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1829, 1822])).
% 1.01/1.17 tff(1831,plain,
% 1.01/1.17 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp9 | hskp6 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | (~c3_1(a112)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1832,plain,
% 1.01/1.17 ((hskp9 | hskp6 | (~ndr1_0) | c1_1(a112) | c0_1(a112) | (~c3_1(a112))) <=> (hskp9 | hskp6 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | (~c3_1(a112)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1833,plain,
% 1.01/1.17 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | (~c3_1(a112))))),
% 1.01/1.17 inference(monotonicity,[status(thm)],[1832])).
% 1.01/1.17 tff(1834,plain,
% 1.01/1.17 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp9 | hskp6 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | (~c3_1(a112)))),
% 1.01/1.17 inference(transitivity,[status(thm)],[1833, 1831])).
% 1.01/1.17 tff(1835,plain,
% 1.01/1.17 ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(1836,plain,
% 1.01/1.17 ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp9 | hskp6 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | (~c3_1(a112))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 1.01/1.17 tff(1837,plain,
% 1.01/1.17 (hskp9 | hskp6),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1836, 117, 1798, 1762, 1761, 1830])).
% 1.01/1.17 tff(1838,plain,
% 1.01/1.17 (hskp9),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1837, 1820])).
% 1.01/1.17 tff(1839,plain,
% 1.01/1.17 (c2_1(a108)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1007, 1838])).
% 1.01/1.17 tff(1840,plain,
% 1.01/1.17 (c1_1(a108)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1015, 1838])).
% 1.01/1.17 tff(1841,plain,
% 1.01/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c3_1(a108)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c3_1(a108)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1842,plain,
% 1.01/1.17 (((~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129))) <=> (c1_1(a129) | (~ndr1_0) | (~c3_1(a108)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1843,plain,
% 1.01/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c3_1(a108)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)))),
% 1.01/1.17 inference(monotonicity,[status(thm)],[1842])).
% 1.01/1.17 tff(1844,plain,
% 1.01/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c3_1(a108)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 1.01/1.17 inference(transitivity,[status(thm)],[1843, 1841])).
% 1.01/1.17 tff(1845,plain,
% 1.01/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(1846,plain,
% 1.01/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c3_1(a108)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 1.01/1.17 tff(1847,plain,
% 1.01/1.17 (~c3_1(a108)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1846, 117, 1748, 1747, 1840, 1839, 1746, 642, 1749])).
% 1.01/1.17 tff(1848,plain,
% 1.01/1.17 (~c0_1(a108)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[999, 1838])).
% 1.01/1.17 tff(1849,plain,
% 1.01/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c0_1(a108) | (~ndr1_0) | c3_1(a108) | (~c1_1(a108)) | (~c3_1(a112)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c0_1(a108) | (~ndr1_0) | c3_1(a108) | (~c1_1(a108)) | (~c3_1(a112)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1850,plain,
% 1.01/1.17 (((~ndr1_0) | c0_1(a108) | c3_1(a108) | (~c1_1(a108)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147)) <=> (c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c0_1(a108) | (~ndr1_0) | c3_1(a108) | (~c1_1(a108)) | (~c3_1(a112)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(1851,plain,
% 1.01/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a108) | c3_1(a108) | (~c1_1(a108)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c0_1(a108) | (~ndr1_0) | c3_1(a108) | (~c1_1(a108)) | (~c3_1(a112))))),
% 1.01/1.17 inference(monotonicity,[status(thm)],[1850])).
% 1.01/1.17 tff(1852,plain,
% 1.01/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a108) | c3_1(a108) | (~c1_1(a108)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c0_1(a108) | (~ndr1_0) | c3_1(a108) | (~c1_1(a108)) | (~c3_1(a112)))),
% 1.01/1.17 inference(transitivity,[status(thm)],[1851, 1849])).
% 1.01/1.17 tff(1853,plain,
% 1.01/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a108) | c3_1(a108) | (~c1_1(a108)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(1854,plain,
% 1.01/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c0_1(a108) | (~ndr1_0) | c3_1(a108) | (~c1_1(a108)) | (~c3_1(a112))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 1.01/1.17 tff(1855,plain,
% 1.01/1.17 ($false),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1854, 117, 1798, 1840, 1797, 1791, 1785, 1762, 1761, 1848, 1337, 1847])).
% 1.01/1.17 tff(1856,plain,(c2_1(a97)), inference(lemma,lemma(discharge,[]))).
% 1.01/1.17 tff(1857,plain,
% 1.01/1.17 (~hskp0),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[227, 1856])).
% 1.01/1.17 tff(1858,plain,
% 1.01/1.17 (~hskp4),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[1386, 52, 1857])).
% 1.01/1.17 tff(1859,plain,
% 1.01/1.17 (hskp20),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[764, 52, 1858])).
% 1.01/1.17 tff(1860,plain,
% 1.01/1.17 (~c3_1(a132)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[672, 1859])).
% 1.01/1.17 tff(1861,plain,
% 1.01/1.17 (~c2_1(a132)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[692, 1859])).
% 1.01/1.17 tff(1862,plain,
% 1.01/1.17 (~c1_1(a132)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[678, 1859])).
% 1.01/1.17 tff(1863,plain,
% 1.01/1.17 (hskp19),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[699, 117, 52, 1862, 1861, 1860, 30])).
% 1.01/1.17 tff(1864,plain,
% 1.01/1.17 (~c2_1(a130)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[237, 1863])).
% 1.01/1.17 tff(1865,plain,
% 1.01/1.17 (c3_1(a130)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[245, 1863])).
% 1.01/1.17 tff(1866,plain,
% 1.01/1.17 (c1_1(a130)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[253, 1863])).
% 1.01/1.17 tff(1867,plain,
% 1.01/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a132) | c2_1(a132) | c3_1(a132) | c2_1(a130) | (~ndr1_0) | (~c3_1(a130)) | (~c1_1(a130)) | (~c0_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a132) | c2_1(a132) | c3_1(a132) | c2_1(a130) | (~ndr1_0) | (~c3_1(a130)) | (~c1_1(a130)) | (~c0_1(a132)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(1868,plain,
% 1.01/1.18 (((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132))) <=> (c1_1(a132) | c2_1(a132) | c3_1(a132) | c2_1(a130) | (~ndr1_0) | (~c3_1(a130)) | (~c1_1(a130)) | (~c0_1(a132)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(1869,plain,
% 1.01/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a132) | c2_1(a132) | c3_1(a132) | c2_1(a130) | (~ndr1_0) | (~c3_1(a130)) | (~c1_1(a130)) | (~c0_1(a132))))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[1868])).
% 1.01/1.18 tff(1870,plain,
% 1.01/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a132) | c2_1(a132) | c3_1(a132) | c2_1(a130) | (~ndr1_0) | (~c3_1(a130)) | (~c1_1(a130)) | (~c0_1(a132)))),
% 1.01/1.18 inference(transitivity,[status(thm)],[1869, 1867])).
% 1.01/1.18 tff(1871,plain,
% 1.01/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(1872,plain,
% 1.01/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a132) | c2_1(a132) | c3_1(a132) | c2_1(a130) | (~ndr1_0) | (~c3_1(a130)) | (~c1_1(a130)) | (~c0_1(a132))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 1.01/1.18 tff(1873,plain,
% 1.01/1.18 (~c0_1(a132)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1872, 117, 1866, 1865, 1862, 1861, 1860, 1864, 20])).
% 1.01/1.18 tff(1874,plain,
% 1.01/1.18 (hskp7),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1404, 1858])).
% 1.01/1.18 tff(1875,plain,
% 1.01/1.18 (~c0_1(a106)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[912, 1874])).
% 1.01/1.18 tff(1876,plain,
% 1.01/1.18 (c3_1(a106)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[865, 1874])).
% 1.01/1.18 tff(1877,plain,
% 1.01/1.18 (c2_1(a106)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[873, 1874])).
% 1.01/1.18 tff(1878,plain,
% 1.01/1.18 (~c0_1(a130)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1740, 117, 1866, 1877, 1876, 1861, 1860, 1864, 1875, 489, 1873])).
% 1.01/1.18 tff(1879,plain,
% 1.01/1.18 ($false),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[708, 117, 1857, 1865, 1862, 1861, 1864, 199, 1873, 1878])).
% 1.01/1.18 tff(1880,plain,(hskp18), inference(lemma,lemma(discharge,[]))).
% 1.01/1.18 tff(1881,plain,
% 1.01/1.18 (~c1_1(a129)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[276, 1880])).
% 1.01/1.18 tff(1882,plain,
% 1.01/1.18 (c2_1(a129)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[284, 1880])).
% 1.01/1.18 tff(1883,plain,
% 1.01/1.18 (c0_1(a129)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[292, 1880])).
% 1.01/1.18 tff(1884,plain,
% 1.01/1.18 (~c3_1(a129)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[840, 117, 1883, 1882, 1881, 10])).
% 1.01/1.18 tff(1885,plain,
% 1.01/1.18 (c1_1(a138)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1488, 117, 1363, 1883, 1882, 1354, 1881, 134, 1884])).
% 1.01/1.18 tff(1886,plain,
% 1.01/1.18 (hskp11),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1505, 117, 1378, 1883, 1882, 1354, 1499, 1885, 1884])).
% 1.01/1.18 tff(1887,plain,
% 1.01/1.18 (~c1_1(a112)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[797, 1886])).
% 1.01/1.18 tff(1888,plain,
% 1.01/1.18 (~c0_1(a112)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[803, 1886])).
% 1.01/1.18 tff(1889,plain,
% 1.01/1.18 (c3_1(a112)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[986, 1886])).
% 1.01/1.18 tff(1890,plain,
% 1.01/1.18 (hskp24),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1778, 117, 1363, 1378, 1883, 1882, 1354, 1881, 1772])).
% 1.01/1.18 tff(1891,plain,
% 1.01/1.18 (~c3_1(a147)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1784, 1890])).
% 1.01/1.18 tff(1892,plain,
% 1.01/1.18 (~c1_1(a147)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1790, 1890])).
% 1.01/1.18 tff(1893,plain,
% 1.01/1.18 (~c0_1(a147)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1796, 1890])).
% 1.01/1.18 tff(1894,plain,
% 1.01/1.18 (~hskp6),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1819, 1889, 1893, 1892, 1891, 1888, 1887, 1857])).
% 1.01/1.18 tff(1895,plain,
% 1.01/1.18 (hskp9),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1836, 117, 1894, 1889, 1888, 1887, 1830])).
% 1.01/1.18 tff(1896,plain,
% 1.01/1.18 (c2_1(a108)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1007, 1895])).
% 1.01/1.18 tff(1897,plain,
% 1.01/1.18 (c1_1(a108)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1015, 1895])).
% 1.01/1.18 tff(1898,plain,
% 1.01/1.18 (~c3_1(a108)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1846, 117, 1883, 1882, 1897, 1896, 1881, 642, 1884])).
% 1.01/1.18 tff(1899,plain,
% 1.01/1.18 (~c0_1(a108)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[999, 1895])).
% 1.01/1.18 tff(1900,plain,
% 1.01/1.18 ($false),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1854, 117, 1889, 1897, 1893, 1892, 1891, 1888, 1887, 1899, 1337, 1898])).
% 1.01/1.18 % SZS output end Proof
% 1.01/1.18 % E exiting
%------------------------------------------------------------------------------