%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN454-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:10 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.63s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN454-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:40:05 EDT 2025
% 0.19/0.33 % CPUTime :
% 0.48/0.63 % SZS status Unsatisfiable
% 0.48/0.63 % SZS output start Proof
% 0.48/0.63 tff(c2_1_type, type, (
% 0.48/0.63 c2_1: $i > $o)).
% 0.48/0.63 tff(a116_type, type, (
% 0.48/0.63 a116: $i)).
% 0.48/0.63 tff(c1_1_type, type, (
% 0.48/0.63 c1_1: $i > $o)).
% 0.48/0.63 tff(a133_type, type, (
% 0.48/0.63 a133: $i)).
% 0.48/0.63 tff(c0_1_type, type, (
% 0.48/0.63 c0_1: $i > $o)).
% 0.48/0.63 tff(c3_1_type, type, (
% 0.48/0.63 c3_1: $i > $o)).
% 0.48/0.63 tff(ndr1_0_type, type, (
% 0.48/0.63 ndr1_0: $o)).
% 0.48/0.63 tff(hskp20_type, type, (
% 0.48/0.63 hskp20: $o)).
% 0.48/0.63 tff(a101_type, type, (
% 0.48/0.63 a101: $i)).
% 0.48/0.63 tff(a104_type, type, (
% 0.48/0.63 a104: $i)).
% 0.48/0.63 tff(a106_type, type, (
% 0.48/0.63 a106: $i)).
% 0.48/0.63 tff(hskp10_type, type, (
% 0.48/0.63 hskp10: $o)).
% 0.48/0.63 tff(a99_type, type, (
% 0.48/0.63 a99: $i)).
% 0.48/0.63 tff(hskp3_type, type, (
% 0.48/0.63 hskp3: $o)).
% 0.48/0.63 tff(a115_type, type, (
% 0.48/0.63 a115: $i)).
% 0.48/0.63 tff(a165_type, type, (
% 0.48/0.63 a165: $i)).
% 0.48/0.63 tff(hskp14_type, type, (
% 0.48/0.63 hskp14: $o)).
% 0.48/0.63 tff(hskp1_type, type, (
% 0.48/0.63 hskp1: $o)).
% 0.48/0.63 tff(hskp13_type, type, (
% 0.48/0.63 hskp13: $o)).
% 0.48/0.63 tff(a112_type, type, (
% 0.48/0.63 a112: $i)).
% 0.48/0.63 tff(hskp0_type, type, (
% 0.48/0.63 hskp0: $o)).
% 0.48/0.63 tff(hskp29_type, type, (
% 0.48/0.63 hskp29: $o)).
% 0.48/0.63 tff(a97_type, type, (
% 0.48/0.63 a97: $i)).
% 0.48/0.63 tff(a96_type, type, (
% 0.48/0.63 a96: $i)).
% 0.48/0.63 tff(a98_type, type, (
% 0.48/0.63 a98: $i)).
% 0.48/0.63 tff(hskp2_type, type, (
% 0.48/0.63 hskp2: $o)).
% 0.48/0.63 tff(a103_type, type, (
% 0.48/0.63 a103: $i)).
% 0.48/0.63 tff(hskp7_type, type, (
% 0.48/0.63 hskp7: $o)).
% 0.48/0.63 tff(hskp11_type, type, (
% 0.48/0.63 hskp11: $o)).
% 0.48/0.63 tff(hskp8_type, type, (
% 0.48/0.63 hskp8: $o)).
% 0.48/0.63 tff(hskp5_type, type, (
% 0.48/0.63 hskp5: $o)).
% 0.48/0.63 tff(a102_type, type, (
% 0.48/0.63 a102: $i)).
% 0.48/0.63 tff(hskp6_type, type, (
% 0.48/0.63 hskp6: $o)).
% 0.48/0.63 tff(a109_type, type, (
% 0.48/0.63 a109: $i)).
% 0.48/0.63 tff(hskp12_type, type, (
% 0.48/0.63 hskp12: $o)).
% 0.48/0.63 tff(a110_type, type, (
% 0.48/0.63 a110: $i)).
% 0.48/0.63 tff(hskp15_type, type, (
% 0.48/0.63 hskp15: $o)).
% 0.48/0.63 tff(1,assumption,(~c2_1(a116)), introduced(assumption)).
% 0.48/0.63 tff(2,plain,
% 0.48/0.63 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))))),
% 0.48/0.63 inference(bind,[status(th)],[])).
% 0.48/0.63 tff(3,plain,
% 0.48/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.48/0.63 inference(quant_intro,[status(thm)],[2])).
% 0.48/0.63 tff(4,plain,
% 0.48/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(5,plain,
% 0.48/0.63 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~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(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_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(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_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(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_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(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_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(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))))),
% 0.48/0.63 inference(bind,[status(th)],[])).
% 0.48/0.63 tff(6,plain,
% 0.48/0.63 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c2_1(V)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.48/0.63 inference(quant_intro,[status(thm)],[5])).
% 0.48/0.63 tff(7,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c2_1(V)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 0.48/0.63 tff(8,plain,
% 0.48/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.48/0.63 tff(9,plain,
% 0.48/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.48/0.63 tff(10,plain,(
% 0.48/0.63 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.48/0.63 inference(skolemize,[status(sab)],[9])).
% 0.48/0.63 tff(11,plain,
% 0.48/0.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.48/0.63 tff(12,plain,
% 0.48/0.63 (^[V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.48/0.63 inference(bind,[status(th)],[])).
% 0.48/0.63 tff(13,plain,
% 0.48/0.63 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.48/0.63 inference(quant_intro,[status(thm)],[12])).
% 0.48/0.63 tff(14,plain,
% 0.48/0.63 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(15,plain,
% 0.48/0.63 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.48/0.63 inference(bind,[status(th)],[])).
% 0.48/0.63 tff(16,plain,
% 0.48/0.63 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.48/0.63 inference(quant_intro,[status(thm)],[15])).
% 0.48/0.63 tff(17,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 0.48/0.63 tff(18,plain,
% 0.48/0.63 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.48/0.63 tff(19,plain,
% 0.48/0.63 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.48/0.63 tff(20,plain,(
% 0.48/0.63 ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.48/0.63 inference(skolemize,[status(sab)],[19])).
% 0.48/0.63 tff(21,plain,
% 0.48/0.63 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.48/0.63 tff(22,assumption,(~hskp20), introduced(assumption)).
% 0.48/0.63 tff(23,assumption,(~hskp3), introduced(assumption)).
% 0.48/0.63 tff(24,plain,
% 0.48/0.63 (^[U: $i] : refl((hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.48/0.63 inference(bind,[status(th)],[])).
% 0.48/0.63 tff(25,plain,
% 0.48/0.63 (![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.48/0.63 inference(quant_intro,[status(thm)],[24])).
% 0.48/0.63 tff(26,plain,
% 0.48/0.63 (![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(27,plain,
% 0.48/0.63 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp10) <=> ((hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp10))), rewrite(((hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp10) <=> (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp10) <=> (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.48/0.63 inference(bind,[status(th)],[])).
% 0.48/0.63 tff(28,plain,
% 0.48/0.63 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp10) <=> ![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.48/0.63 inference(quant_intro,[status(thm)],[27])).
% 0.48/0.63 tff(29,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.48/0.63 tff(30,plain,
% 0.48/0.63 (![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.48/0.63 tff(31,plain,
% 0.48/0.63 (![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.48/0.63 tff(32,plain,(
% 0.48/0.63 ![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.48/0.63 inference(skolemize,[status(sab)],[31])).
% 0.48/0.63 tff(33,plain,
% 0.48/0.63 (![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.48/0.63 tff(34,assumption,(~hskp10), introduced(assumption)).
% 0.48/0.63 tff(35,assumption,(hskp13), introduced(assumption)).
% 0.48/0.63 tff(36,plain,
% 0.48/0.63 (((~hskp13) | (~c1_1(a112))) <=> ((~hskp13) | (~c1_1(a112)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(37,plain,
% 0.48/0.63 (((~c1_1(a112)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a112)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(38,axiom,((~c1_1(a112)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.48/0.63 tff(39,plain,
% 0.48/0.63 ((~hskp13) | (~c1_1(a112))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.48/0.64 tff(40,plain,
% 0.48/0.64 ((~hskp13) | (~c1_1(a112))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.48/0.64 tff(41,plain,
% 0.48/0.64 (~c1_1(a112)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[40, 35])).
% 0.48/0.64 tff(42,plain,
% 0.48/0.64 (((~hskp13) | c0_1(a112)) <=> ((~hskp13) | c0_1(a112))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(43,axiom,((~hskp13) | c0_1(a112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.48/0.64 tff(44,plain,
% 0.48/0.64 ((~hskp13) | c0_1(a112)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.48/0.64 tff(45,plain,
% 0.48/0.64 ((~hskp13) | c0_1(a112)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[44, 42])).
% 0.48/0.64 tff(46,plain,
% 0.48/0.64 ((~hskp13) | c0_1(a112)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[45, 42])).
% 0.48/0.64 tff(47,plain,
% 0.48/0.64 ((~hskp13) | c0_1(a112)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.48/0.64 tff(48,plain,
% 0.48/0.64 ((~hskp13) | c0_1(a112)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[47, 42])).
% 0.48/0.64 tff(49,plain,
% 0.48/0.64 (c0_1(a112)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[48, 35])).
% 0.48/0.64 tff(50,plain,
% 0.48/0.64 (((~hskp13) | c3_1(a112)) <=> ((~hskp13) | c3_1(a112))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(51,axiom,((~hskp13) | c3_1(a112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.48/0.64 tff(52,plain,
% 0.48/0.64 ((~hskp13) | c3_1(a112)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.48/0.64 tff(53,plain,
% 0.48/0.64 ((~hskp13) | c3_1(a112)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[52, 50])).
% 0.48/0.64 tff(54,plain,
% 0.48/0.64 ((~hskp13) | c3_1(a112)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.48/0.64 tff(55,plain,
% 0.48/0.64 ((~hskp13) | c3_1(a112)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.48/0.64 tff(56,plain,
% 0.48/0.64 ((~hskp13) | c3_1(a112)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[55, 50])).
% 0.48/0.64 tff(57,plain,
% 0.48/0.64 (c3_1(a112)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[56, 35])).
% 0.48/0.64 tff(58,plain,
% 0.48/0.64 (^[U: $i] : refl((hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(59,plain,
% 0.48/0.64 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[58])).
% 0.48/0.64 tff(60,plain,
% 0.48/0.64 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(61,plain,
% 0.48/0.64 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp10) <=> ((hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp10) <=> (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(62,plain,
% 0.48/0.64 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp10) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[61])).
% 0.48/0.64 tff(63,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 0.48/0.64 tff(64,plain,
% 0.48/0.64 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.48/0.64 tff(65,plain,
% 0.48/0.64 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.48/0.64 tff(66,plain,(
% 0.48/0.64 ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.48/0.64 inference(skolemize,[status(sab)],[65])).
% 0.48/0.64 tff(67,plain,
% 0.48/0.64 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.48/0.64 tff(68,assumption,(~c1_1(a112)), introduced(assumption)).
% 0.48/0.64 tff(69,assumption,(c3_1(a112)), introduced(assumption)).
% 0.48/0.64 tff(70,assumption,(c0_1(a112)), introduced(assumption)).
% 0.48/0.64 tff(71,assumption,(~ndr1_0), introduced(assumption)).
% 0.48/0.64 tff(72,plain,
% 0.48/0.64 ((ndr1_0 | (~hskp0)) <=> (ndr1_0 | (~hskp0))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(73,plain,
% 0.48/0.64 (((~hskp0) | ndr1_0) <=> (ndr1_0 | (~hskp0))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(74,axiom,((~hskp0) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause30')).
% 0.48/0.64 tff(75,plain,
% 0.48/0.64 (ndr1_0 | (~hskp0)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.48/0.64 tff(76,plain,
% 0.48/0.64 (ndr1_0 | (~hskp0)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[75, 72])).
% 0.48/0.64 tff(77,plain,
% 0.48/0.64 (~hskp0),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[76, 71])).
% 0.48/0.64 tff(78,plain,
% 0.48/0.64 (((~hskp29) | ndr1_0) <=> ((~hskp29) | ndr1_0)),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(79,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.48/0.64 tff(80,plain,
% 0.48/0.64 ((~hskp29) | ndr1_0),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.48/0.64 tff(81,plain,
% 0.48/0.64 ((~hskp29) | ndr1_0),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[80, 78])).
% 0.48/0.64 tff(82,plain,
% 0.48/0.64 ((~hskp29) | ndr1_0),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.48/0.64 tff(83,plain,
% 0.48/0.64 ((~hskp29) | ndr1_0),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.48/0.64 tff(84,plain,
% 0.48/0.64 ((~hskp29) | ndr1_0),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[83, 78])).
% 0.48/0.64 tff(85,plain,
% 0.48/0.64 (~hskp29),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[84, 71])).
% 0.48/0.64 tff(86,plain,
% 0.48/0.64 ((ndr1_0 | (~hskp20)) <=> (ndr1_0 | (~hskp20))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(87,plain,
% 0.48/0.64 (((~hskp20) | ndr1_0) <=> (ndr1_0 | (~hskp20))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(88,axiom,((~hskp20) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause10')).
% 0.48/0.64 tff(89,plain,
% 0.48/0.64 (ndr1_0 | (~hskp20)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.48/0.64 tff(90,plain,
% 0.48/0.64 (ndr1_0 | (~hskp20)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[89, 86])).
% 0.48/0.64 tff(91,plain,
% 0.48/0.64 (~hskp20),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[90, 71])).
% 0.48/0.64 tff(92,plain,
% 0.48/0.64 ((hskp29 | hskp20 | hskp0) <=> (hskp29 | hskp20 | hskp0)),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(93,plain,
% 0.48/0.64 (((hskp20 | hskp29) | hskp0) <=> (hskp29 | hskp20 | hskp0)),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(94,axiom,((hskp20 | hskp29) | hskp0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 0.48/0.64 tff(95,plain,
% 0.48/0.64 (hskp29 | hskp20 | hskp0),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.48/0.64 tff(96,plain,
% 0.48/0.64 (hskp29 | hskp20 | hskp0),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[95, 92])).
% 0.48/0.64 tff(97,plain,
% 0.48/0.64 (hskp29 | hskp20 | hskp0),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.48/0.64 tff(98,plain,
% 0.48/0.64 (hskp29 | hskp20 | hskp0),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[97, 92])).
% 0.48/0.64 tff(99,plain,
% 0.48/0.64 (hskp29 | hskp20 | hskp0),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[98, 92])).
% 0.48/0.64 tff(100,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[99, 91, 85, 77])).
% 0.48/0.64 tff(101,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(102,plain,
% 0.48/0.64 (((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | c1_1(a112) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp14 | hskp10 | c1_1(a112) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(103,plain,
% 0.48/0.64 ((hskp14 | hskp10 | (~ndr1_0) | c1_1(a112) | (~c3_1(a112)) | (~c0_1(a112))) <=> (hskp14 | hskp10 | c1_1(a112) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(104,plain,
% 0.48/0.64 (((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | c1_1(a112) | (~c3_1(a112)) | (~c0_1(a112)))) <=> ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | c1_1(a112) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[103])).
% 0.48/0.64 tff(105,plain,
% 0.48/0.64 (((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | c1_1(a112) | (~c3_1(a112)) | (~c0_1(a112)))) <=> ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp14 | hskp10 | c1_1(a112) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)))),
% 0.48/0.64 inference(transitivity,[status(thm)],[104, 102])).
% 0.48/0.64 tff(106,plain,
% 0.48/0.64 ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | c1_1(a112) | (~c3_1(a112)) | (~c0_1(a112)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(107,plain,
% 0.48/0.64 ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp14 | hskp10 | c1_1(a112) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.48/0.64 tff(108,plain,
% 0.48/0.64 (hskp14 | hskp10),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[107, 101, 70, 69, 68, 67])).
% 0.48/0.64 tff(109,plain,
% 0.48/0.64 (hskp14),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[108, 34])).
% 0.48/0.64 tff(110,plain,
% 0.48/0.64 (((~hskp14) | (~c3_1(a115))) <=> ((~hskp14) | (~c3_1(a115)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(111,plain,
% 0.48/0.64 (((~c3_1(a115)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a115)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(112,axiom,((~c3_1(a115)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.48/0.64 tff(113,plain,
% 0.48/0.64 ((~hskp14) | (~c3_1(a115))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.48/0.64 tff(114,plain,
% 0.48/0.64 ((~hskp14) | (~c3_1(a115))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.48/0.64 tff(115,plain,
% 0.48/0.64 (~c3_1(a115)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[114, 109])).
% 0.48/0.64 tff(116,plain,
% 0.48/0.64 (((~hskp14) | (~c2_1(a115))) <=> ((~hskp14) | (~c2_1(a115)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(117,plain,
% 0.48/0.64 (((~c2_1(a115)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a115)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(118,axiom,((~c2_1(a115)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.48/0.64 tff(119,plain,
% 0.48/0.64 ((~hskp14) | (~c2_1(a115))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.48/0.64 tff(120,plain,
% 0.48/0.64 ((~hskp14) | (~c2_1(a115))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[119, 116])).
% 0.48/0.64 tff(121,plain,
% 0.48/0.64 (~c2_1(a115)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[120, 109])).
% 0.48/0.64 tff(122,plain,
% 0.48/0.64 (((~hskp14) | c0_1(a115)) <=> ((~hskp14) | c0_1(a115))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(123,axiom,((~hskp14) | c0_1(a115)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.48/0.64 tff(124,plain,
% 0.48/0.64 ((~hskp14) | c0_1(a115)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.48/0.64 tff(125,plain,
% 0.48/0.64 ((~hskp14) | c0_1(a115)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[124, 122])).
% 0.48/0.64 tff(126,plain,
% 0.48/0.64 ((~hskp14) | c0_1(a115)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[125, 122])).
% 0.48/0.64 tff(127,plain,
% 0.48/0.64 ((~hskp14) | c0_1(a115)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.48/0.64 tff(128,plain,
% 0.48/0.64 ((~hskp14) | c0_1(a115)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[127, 122])).
% 0.48/0.64 tff(129,plain,
% 0.48/0.64 (c0_1(a115)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[128, 109])).
% 0.48/0.64 tff(130,plain,
% 0.48/0.64 (((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp20 | hskp10 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c0_1(a115)))) <=> ((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp20 | hskp10 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c0_1(a115)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(131,plain,
% 0.48/0.64 ((hskp20 | hskp10 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | (~c0_1(a115))) <=> (hskp20 | hskp10 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c0_1(a115)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(132,plain,
% 0.48/0.64 (((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp20 | hskp10 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | (~c0_1(a115)))) <=> ((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp20 | hskp10 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c0_1(a115))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[131])).
% 0.48/0.64 tff(133,plain,
% 0.48/0.64 (((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp20 | hskp10 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | (~c0_1(a115)))) <=> ((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp20 | hskp10 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c0_1(a115)))),
% 0.48/0.64 inference(transitivity,[status(thm)],[132, 130])).
% 0.48/0.64 tff(134,plain,
% 0.48/0.64 ((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp20 | hskp10 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | (~c0_1(a115)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(135,plain,
% 0.48/0.64 ((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp20 | hskp10 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c0_1(a115))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.48/0.64 tff(136,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[135, 101, 22, 34, 129, 121, 115, 33])).
% 0.48/0.64 tff(137,plain,(hskp10 | hskp20 | (~c0_1(a112)) | (~c3_1(a112)) | c1_1(a112)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(138,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[137, 57, 49, 22, 34, 41])).
% 0.48/0.64 tff(139,plain,((~hskp13) | hskp20 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(140,plain,
% 0.48/0.64 (~hskp13),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[139, 34, 22])).
% 0.48/0.64 tff(141,plain,
% 0.48/0.64 (^[U: $i] : refl((hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(142,plain,
% 0.48/0.64 (![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[141])).
% 0.48/0.64 tff(143,plain,
% 0.48/0.64 (![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(144,plain,
% 0.48/0.64 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(145,plain,
% 0.48/0.64 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) <=> ![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[144])).
% 0.48/0.64 tff(146,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.48/0.64 tff(147,plain,
% 0.48/0.64 (![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.48/0.64 tff(148,plain,
% 0.48/0.64 (![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.48/0.64 tff(149,plain,(
% 0.48/0.64 ![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.48/0.64 inference(skolemize,[status(sab)],[148])).
% 0.48/0.64 tff(150,plain,
% 0.48/0.64 (![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.48/0.64 tff(151,assumption,(hskp1), introduced(assumption)).
% 0.48/0.64 tff(152,plain,
% 0.48/0.64 (((~hskp1) | (~c1_1(a97))) <=> ((~hskp1) | (~c1_1(a97)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(153,plain,
% 0.48/0.64 (((~c1_1(a97)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a97)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(154,axiom,((~c1_1(a97)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.48/0.64 tff(155,plain,
% 0.48/0.64 ((~hskp1) | (~c1_1(a97))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.48/0.64 tff(156,plain,
% 0.48/0.64 ((~hskp1) | (~c1_1(a97))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[155, 152])).
% 0.48/0.64 tff(157,plain,
% 0.48/0.64 (~c1_1(a97)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[156, 151])).
% 0.48/0.64 tff(158,plain,
% 0.48/0.64 (((~hskp1) | c3_1(a97)) <=> ((~hskp1) | c3_1(a97))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(159,axiom,((~hskp1) | c3_1(a97)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.48/0.64 tff(160,plain,
% 0.48/0.64 ((~hskp1) | c3_1(a97)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.48/0.64 tff(161,plain,
% 0.48/0.64 ((~hskp1) | c3_1(a97)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[160, 158])).
% 0.48/0.64 tff(162,plain,
% 0.48/0.64 ((~hskp1) | c3_1(a97)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[161, 158])).
% 0.48/0.64 tff(163,plain,
% 0.48/0.64 ((~hskp1) | c3_1(a97)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.48/0.64 tff(164,plain,
% 0.48/0.64 ((~hskp1) | c3_1(a97)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[163, 158])).
% 0.48/0.64 tff(165,plain,
% 0.48/0.64 (c3_1(a97)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[164, 151])).
% 0.48/0.64 tff(166,plain,
% 0.48/0.64 (((~hskp1) | c2_1(a97)) <=> ((~hskp1) | c2_1(a97))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(167,axiom,((~hskp1) | c2_1(a97)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.48/0.64 tff(168,plain,
% 0.48/0.64 ((~hskp1) | c2_1(a97)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.48/0.64 tff(169,plain,
% 0.48/0.64 ((~hskp1) | c2_1(a97)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[168, 166])).
% 0.48/0.64 tff(170,plain,
% 0.48/0.64 ((~hskp1) | c2_1(a97)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[169, 166])).
% 0.48/0.64 tff(171,plain,
% 0.48/0.64 ((~hskp1) | c2_1(a97)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.48/0.64 tff(172,plain,
% 0.48/0.64 ((~hskp1) | c2_1(a97)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[171, 166])).
% 0.48/0.64 tff(173,plain,
% 0.48/0.64 (c2_1(a97)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[172, 151])).
% 0.48/0.64 tff(174,assumption,(~hskp13), introduced(assumption)).
% 0.48/0.64 tff(175,plain,
% 0.48/0.64 (((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | c1_1(a97) | (~ndr1_0) | (~c2_1(a97)) | (~c3_1(a97)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | c1_1(a97) | (~ndr1_0) | (~c2_1(a97)) | (~c3_1(a97)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(176,plain,
% 0.48/0.64 ((hskp13 | (~ndr1_0) | c1_1(a97) | (~c3_1(a97)) | (~c2_1(a97))) <=> (hskp13 | c1_1(a97) | (~ndr1_0) | (~c2_1(a97)) | (~c3_1(a97)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(177,plain,
% 0.48/0.64 (((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | (~ndr1_0) | c1_1(a97) | (~c3_1(a97)) | (~c2_1(a97)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | c1_1(a97) | (~ndr1_0) | (~c2_1(a97)) | (~c3_1(a97))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[176])).
% 0.48/0.64 tff(178,plain,
% 0.48/0.64 (((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | (~ndr1_0) | c1_1(a97) | (~c3_1(a97)) | (~c2_1(a97)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | c1_1(a97) | (~ndr1_0) | (~c2_1(a97)) | (~c3_1(a97)))),
% 0.48/0.64 inference(transitivity,[status(thm)],[177, 175])).
% 0.48/0.64 tff(179,plain,
% 0.48/0.64 ((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | (~ndr1_0) | c1_1(a97) | (~c3_1(a97)) | (~c2_1(a97)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(180,plain,
% 0.48/0.64 ((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | c1_1(a97) | (~ndr1_0) | (~c2_1(a97)) | (~c3_1(a97))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.48/0.64 tff(181,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[180, 101, 174, 173, 165, 157, 150])).
% 0.48/0.64 tff(182,plain,((~hskp1) | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(183,plain,
% 0.48/0.64 (~hskp1),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[182, 140])).
% 0.48/0.64 tff(184,plain,
% 0.48/0.64 ((hskp14 | hskp3 | hskp1) <=> (hskp14 | hskp3 | hskp1)),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(185,plain,
% 0.48/0.64 (((hskp14 | hskp1) | hskp3) <=> (hskp14 | hskp3 | hskp1)),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(186,plain,
% 0.48/0.64 ((hskp14 | hskp1) <=> (hskp14 | hskp1)),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(187,plain,
% 0.48/0.64 (((hskp14 | hskp1) | hskp3) <=> ((hskp14 | hskp1) | hskp3)),
% 0.48/0.64 inference(monotonicity,[status(thm)],[186])).
% 0.48/0.64 tff(188,plain,
% 0.48/0.64 (((hskp14 | hskp1) | hskp3) <=> (hskp14 | hskp3 | hskp1)),
% 0.48/0.64 inference(transitivity,[status(thm)],[187, 185])).
% 0.48/0.64 tff(189,axiom,((hskp14 | hskp1) | hskp3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 0.48/0.64 tff(190,plain,
% 0.48/0.64 (hskp14 | hskp3 | hskp1),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.48/0.64 tff(191,plain,
% 0.48/0.64 (hskp14 | hskp3 | hskp1),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[190, 184])).
% 0.48/0.64 tff(192,plain,
% 0.48/0.64 (hskp14 | hskp3 | hskp1),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.48/0.64 tff(193,plain,
% 0.48/0.64 (hskp14 | hskp3 | hskp1),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[192, 184])).
% 0.48/0.64 tff(194,plain,
% 0.48/0.64 (hskp14 | hskp3 | hskp1),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[193, 184])).
% 0.48/0.64 tff(195,plain,
% 0.48/0.64 (hskp14),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[194, 183, 23])).
% 0.48/0.64 tff(196,plain,
% 0.48/0.64 (~c3_1(a115)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[114, 195])).
% 0.48/0.64 tff(197,plain,
% 0.48/0.64 (~c2_1(a115)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[120, 195])).
% 0.48/0.64 tff(198,plain,
% 0.48/0.64 (c0_1(a115)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[128, 195])).
% 0.48/0.64 tff(199,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[135, 101, 22, 34, 198, 197, 196, 33])).
% 0.48/0.64 tff(200,plain,(hskp10 | hskp20 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64 tff(201,plain,
% 0.48/0.64 (hskp10),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[200, 23, 22])).
% 0.48/0.64 tff(202,plain,
% 0.48/0.64 (((~hskp10) | c1_1(a106)) <=> ((~hskp10) | c1_1(a106))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(203,axiom,((~hskp10) | c1_1(a106)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.48/0.64 tff(204,plain,
% 0.48/0.64 ((~hskp10) | c1_1(a106)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.48/0.64 tff(205,plain,
% 0.48/0.64 ((~hskp10) | c1_1(a106)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[204, 202])).
% 0.48/0.64 tff(206,plain,
% 0.48/0.64 ((~hskp10) | c1_1(a106)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[205, 202])).
% 0.48/0.64 tff(207,plain,
% 0.48/0.64 ((~hskp10) | c1_1(a106)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.48/0.64 tff(208,plain,
% 0.48/0.64 ((~hskp10) | c1_1(a106)),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[207, 202])).
% 0.48/0.64 tff(209,plain,
% 0.48/0.64 (c1_1(a106)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[208, 201])).
% 0.48/0.64 tff(210,plain,
% 0.48/0.64 (((~hskp10) | (~c2_1(a106))) <=> ((~hskp10) | (~c2_1(a106)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(211,plain,
% 0.48/0.64 (((~c2_1(a106)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a106)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(212,axiom,((~c2_1(a106)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 0.48/0.64 tff(213,plain,
% 0.48/0.64 ((~hskp10) | (~c2_1(a106))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.48/0.64 tff(214,plain,
% 0.48/0.64 ((~hskp10) | (~c2_1(a106))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[213, 210])).
% 0.48/0.64 tff(215,plain,
% 0.48/0.64 (~c2_1(a106)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[214, 201])).
% 0.48/0.64 tff(216,plain,
% 0.48/0.64 (^[U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(217,plain,
% 0.48/0.64 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[216])).
% 0.48/0.64 tff(218,plain,
% 0.48/0.64 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(219,plain,
% 0.48/0.64 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(220,plain,
% 0.48/0.64 (![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) <=> ![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[219])).
% 0.48/0.64 tff(221,axiom,(![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.48/0.64 tff(222,plain,
% 0.48/0.64 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.48/0.64 tff(223,plain,
% 0.48/0.64 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[222, 218])).
% 0.48/0.64 tff(224,plain,(
% 0.48/0.64 ![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.48/0.64 inference(skolemize,[status(sab)],[223])).
% 0.48/0.64 tff(225,plain,
% 0.48/0.64 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[224, 217])).
% 0.48/0.64 tff(226,assumption,(hskp0), introduced(assumption)).
% 0.48/0.64 tff(227,plain,
% 0.48/0.64 (((~hskp0) | (~c3_1(a96))) <=> ((~hskp0) | (~c3_1(a96)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(228,plain,
% 0.48/0.64 (((~c3_1(a96)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a96)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(229,axiom,((~c3_1(a96)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.48/0.64 tff(230,plain,
% 0.48/0.64 ((~hskp0) | (~c3_1(a96))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.48/0.64 tff(231,plain,
% 0.48/0.64 ((~hskp0) | (~c3_1(a96))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[230, 227])).
% 0.48/0.64 tff(232,plain,
% 0.48/0.64 (~c3_1(a96)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[231, 226])).
% 0.48/0.64 tff(233,plain,
% 0.48/0.64 (((~hskp0) | (~c2_1(a96))) <=> ((~hskp0) | (~c2_1(a96)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(234,plain,
% 0.48/0.64 (((~c2_1(a96)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a96)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(235,axiom,((~c2_1(a96)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.48/0.64 tff(236,plain,
% 0.48/0.64 ((~hskp0) | (~c2_1(a96))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.48/0.64 tff(237,plain,
% 0.48/0.64 ((~hskp0) | (~c2_1(a96))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[236, 233])).
% 0.48/0.64 tff(238,plain,
% 0.48/0.64 (~c2_1(a96)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[237, 226])).
% 0.48/0.64 tff(239,plain,
% 0.48/0.64 (((~hskp0) | (~c1_1(a96))) <=> ((~hskp0) | (~c1_1(a96)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(240,plain,
% 0.48/0.64 (((~c1_1(a96)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a96)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(241,axiom,((~c1_1(a96)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.48/0.65 tff(242,plain,
% 0.48/0.65 ((~hskp0) | (~c1_1(a96))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.48/0.65 tff(243,plain,
% 0.48/0.65 ((~hskp0) | (~c1_1(a96))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[242, 239])).
% 0.48/0.65 tff(244,plain,
% 0.48/0.65 (~c1_1(a96)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[243, 226])).
% 0.48/0.65 tff(245,plain,
% 0.48/0.65 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp1 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(246,plain,
% 0.48/0.65 ((hskp1 | (~ndr1_0) | c3_1(a96) | c2_1(a96) | c1_1(a96)) <=> (hskp1 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(247,plain,
% 0.48/0.65 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a96) | c2_1(a96) | c1_1(a96))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0)))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[246])).
% 0.48/0.65 tff(248,plain,
% 0.48/0.65 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a96) | c2_1(a96) | c1_1(a96))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp1 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0))),
% 0.48/0.65 inference(transitivity,[status(thm)],[247, 245])).
% 0.48/0.65 tff(249,plain,
% 0.48/0.65 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a96) | c2_1(a96) | c1_1(a96))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(250,plain,
% 0.48/0.65 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp1 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.48/0.65 tff(251,plain,
% 0.48/0.65 (hskp1),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[250, 101, 244, 238, 232, 225])).
% 0.48/0.65 tff(252,plain,
% 0.48/0.65 (~c1_1(a97)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[156, 251])).
% 0.48/0.65 tff(253,plain,
% 0.48/0.65 (c3_1(a97)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[164, 251])).
% 0.48/0.65 tff(254,plain,
% 0.48/0.65 (c2_1(a97)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[172, 251])).
% 0.48/0.65 tff(255,plain,
% 0.48/0.65 (hskp13),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[180, 101, 254, 253, 252, 150])).
% 0.48/0.65 tff(256,plain,
% 0.48/0.65 (~c1_1(a112)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[40, 255])).
% 0.48/0.65 tff(257,plain,
% 0.48/0.65 (c3_1(a112)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[56, 255])).
% 0.48/0.65 tff(258,plain,
% 0.48/0.65 (c0_1(a112)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[48, 255])).
% 0.48/0.65 tff(259,plain,
% 0.48/0.65 (hskp10),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[137, 258, 22, 257, 256])).
% 0.48/0.65 tff(260,plain,
% 0.48/0.65 (~c2_1(a106)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[214, 259])).
% 0.48/0.65 tff(261,plain,
% 0.48/0.65 (((~hskp10) | c3_1(a106)) <=> ((~hskp10) | c3_1(a106))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(262,axiom,((~hskp10) | c3_1(a106)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.48/0.65 tff(263,plain,
% 0.48/0.65 ((~hskp10) | c3_1(a106)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.48/0.65 tff(264,plain,
% 0.48/0.65 ((~hskp10) | c3_1(a106)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[263, 261])).
% 0.48/0.65 tff(265,plain,
% 0.48/0.65 ((~hskp10) | c3_1(a106)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[264, 261])).
% 0.48/0.65 tff(266,plain,
% 0.48/0.65 ((~hskp10) | c3_1(a106)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[265, 261])).
% 0.48/0.65 tff(267,plain,
% 0.48/0.65 ((~hskp10) | c3_1(a106)),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[266, 261])).
% 0.48/0.65 tff(268,plain,
% 0.48/0.65 (c3_1(a106)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[267, 259])).
% 0.48/0.65 tff(269,plain,
% 0.48/0.65 (c1_1(a106)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[208, 259])).
% 0.48/0.65 tff(270,plain,
% 0.48/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a106)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(271,plain,
% 0.48/0.65 (((~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a106) | (~c0_1(a106)) | (~c1_1(a106))) <=> (c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a106)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(272,plain,
% 0.48/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a106) | (~c0_1(a106)) | (~c1_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a106))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[271])).
% 0.48/0.65 tff(273,plain,
% 0.48/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a106) | (~c0_1(a106)) | (~c1_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a106)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[272, 270])).
% 0.48/0.65 tff(274,plain,
% 0.48/0.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a106) | (~c0_1(a106)) | (~c1_1(a106)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(275,plain,
% 0.48/0.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a106))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.48/0.65 tff(276,plain,
% 0.48/0.65 (~c0_1(a106)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[275, 101, 269, 268, 260, 11])).
% 0.48/0.65 tff(277,plain,
% 0.48/0.65 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(278,plain,
% 0.48/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[277])).
% 0.48/0.65 tff(279,plain,
% 0.48/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(280,plain,
% 0.48/0.65 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(281,plain,
% 0.48/0.65 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[280])).
% 0.48/0.65 tff(282,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.48/0.65 tff(283,plain,
% 0.48/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.48/0.65 tff(284,plain,
% 0.48/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[283, 279])).
% 0.48/0.65 tff(285,plain,(
% 0.48/0.65 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.48/0.65 inference(skolemize,[status(sab)],[284])).
% 0.48/0.65 tff(286,plain,
% 0.48/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[285, 278])).
% 0.48/0.65 tff(287,plain,
% 0.48/0.65 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(288,plain,
% 0.48/0.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[287])).
% 0.48/0.65 tff(289,plain,
% 0.48/0.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(290,plain,
% 0.48/0.65 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp3))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(291,plain,
% 0.48/0.65 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[290])).
% 0.48/0.65 tff(292,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 0.48/0.65 tff(293,plain,
% 0.48/0.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.48/0.65 tff(294,plain,
% 0.48/0.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.48/0.65 tff(295,plain,(
% 0.48/0.65 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.48/0.65 inference(skolemize,[status(sab)],[294])).
% 0.48/0.65 tff(296,plain,
% 0.48/0.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[295, 288])).
% 0.48/0.65 tff(297,assumption,(~c3_1(a96)), introduced(assumption)).
% 0.48/0.65 tff(298,assumption,(~c2_1(a96)), introduced(assumption)).
% 0.48/0.65 tff(299,assumption,(~c1_1(a96)), introduced(assumption)).
% 0.48/0.65 tff(300,plain,
% 0.48/0.65 (hskp1),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[250, 101, 299, 298, 297, 225])).
% 0.48/0.65 tff(301,plain,
% 0.48/0.65 (~c1_1(a97)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[156, 300])).
% 0.48/0.65 tff(302,plain,
% 0.48/0.65 (c3_1(a97)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[164, 300])).
% 0.48/0.65 tff(303,plain,
% 0.48/0.65 (c2_1(a97)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[172, 300])).
% 0.48/0.65 tff(304,plain,
% 0.48/0.65 (hskp13),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[180, 101, 303, 302, 301, 150])).
% 0.48/0.65 tff(305,plain,
% 0.48/0.65 (c3_1(a112)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[56, 304])).
% 0.48/0.65 tff(306,plain,
% 0.48/0.65 (c0_1(a112)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[48, 304])).
% 0.48/0.65 tff(307,plain,
% 0.48/0.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)) | (~c2_1(a112)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)) | (~c2_1(a112)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(308,plain,
% 0.48/0.65 ((hskp3 | (~ndr1_0) | (~c3_1(a112)) | (~c2_1(a112)) | (~c0_1(a112)) | c3_1(a96) | c2_1(a96) | c1_1(a96)) <=> (hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)) | (~c2_1(a112)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(309,plain,
% 0.48/0.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a112)) | (~c2_1(a112)) | (~c0_1(a112)) | c3_1(a96) | c2_1(a96) | c1_1(a96))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)) | (~c2_1(a112))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[308])).
% 0.48/0.65 tff(310,plain,
% 0.48/0.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a112)) | (~c2_1(a112)) | (~c0_1(a112)) | c3_1(a96) | c2_1(a96) | c1_1(a96))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)) | (~c2_1(a112)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[309, 307])).
% 0.48/0.65 tff(311,plain,
% 0.48/0.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a112)) | (~c2_1(a112)) | (~c0_1(a112)) | c3_1(a96) | c2_1(a96) | c1_1(a96))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(312,plain,
% 0.48/0.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)) | (~c2_1(a112))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.48/0.65 tff(313,plain,
% 0.48/0.65 (hskp3 | (~c2_1(a112))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[312, 101, 306, 305, 299, 298, 297, 296])).
% 0.48/0.65 tff(314,plain,
% 0.48/0.65 (~c2_1(a112)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[313, 23])).
% 0.48/0.65 tff(315,plain,
% 0.48/0.65 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(316,plain,
% 0.48/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[315])).
% 0.48/0.65 tff(317,plain,
% 0.48/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(318,plain,
% 0.48/0.65 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(319,plain,
% 0.48/0.65 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[318])).
% 0.48/0.65 tff(320,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 0.48/0.65 tff(321,plain,
% 0.48/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.48/0.65 tff(322,plain,
% 0.48/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[321, 317])).
% 0.48/0.65 tff(323,plain,(
% 0.48/0.65 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.48/0.65 inference(skolemize,[status(sab)],[322])).
% 0.48/0.65 tff(324,plain,
% 0.48/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[323, 316])).
% 0.48/0.65 tff(325,assumption,(~hskp2), introduced(assumption)).
% 0.48/0.65 tff(326,plain,
% 0.48/0.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(327,plain,
% 0.48/0.66 ((hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c2_1(a96) | c1_1(a96)) <=> (hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(328,plain,
% 0.48/0.66 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c2_1(a96) | c1_1(a96))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[327])).
% 0.48/0.66 tff(329,plain,
% 0.48/0.66 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c2_1(a96) | c1_1(a96))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)))),
% 0.48/0.66 inference(transitivity,[status(thm)],[328, 326])).
% 0.48/0.66 tff(330,plain,
% 0.48/0.66 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c2_1(a96) | c1_1(a96))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(331,plain,
% 0.48/0.66 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.48/0.66 tff(332,plain,
% 0.48/0.66 (hskp3 | (~c0_1(a97))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[331, 101, 303, 302, 299, 298, 297, 296])).
% 0.48/0.66 tff(333,plain,
% 0.48/0.66 (~c0_1(a97)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[332, 23])).
% 0.48/0.66 tff(334,plain,
% 0.48/0.66 (^[U: $i] : refl((hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(335,plain,
% 0.48/0.66 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[334])).
% 0.48/0.66 tff(336,plain,
% 0.48/0.66 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(337,plain,
% 0.48/0.66 (^[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)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3) <=> ((hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp3))), rewrite(((hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(338,plain,
% 0.48/0.66 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[337])).
% 0.48/0.66 tff(339,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 0.48/0.66 tff(340,plain,
% 0.48/0.66 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.48/0.66 tff(341,plain,
% 0.48/0.66 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[340, 336])).
% 0.48/0.66 tff(342,plain,(
% 0.48/0.66 ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.48/0.66 inference(skolemize,[status(sab)],[341])).
% 0.48/0.66 tff(343,plain,
% 0.48/0.66 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[342, 335])).
% 0.48/0.66 tff(344,plain,
% 0.48/0.66 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp3 | hskp2 | c1_1(a97) | (~ndr1_0) | c0_1(a97) | (~c3_1(a97)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp3 | hskp2 | c1_1(a97) | (~ndr1_0) | c0_1(a97) | (~c3_1(a97)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(345,plain,
% 0.48/0.66 ((hskp3 | hskp2 | (~ndr1_0) | c1_1(a97) | c0_1(a97) | (~c3_1(a97))) <=> (hskp3 | hskp2 | c1_1(a97) | (~ndr1_0) | c0_1(a97) | (~c3_1(a97)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(346,plain,
% 0.48/0.66 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a97) | c0_1(a97) | (~c3_1(a97)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp3 | hskp2 | c1_1(a97) | (~ndr1_0) | c0_1(a97) | (~c3_1(a97))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[345])).
% 0.48/0.66 tff(347,plain,
% 0.48/0.66 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a97) | c0_1(a97) | (~c3_1(a97)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp3 | hskp2 | c1_1(a97) | (~ndr1_0) | c0_1(a97) | (~c3_1(a97)))),
% 0.48/0.66 inference(transitivity,[status(thm)],[346, 344])).
% 0.48/0.66 tff(348,plain,
% 0.48/0.66 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a97) | c0_1(a97) | (~c3_1(a97)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(349,plain,
% 0.48/0.66 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp3 | hskp2 | c1_1(a97) | (~ndr1_0) | c0_1(a97) | (~c3_1(a97))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.48/0.66 tff(350,plain,
% 0.48/0.66 (hskp3 | hskp2 | c0_1(a97)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[349, 101, 302, 301, 343])).
% 0.48/0.66 tff(351,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[350, 333, 23, 325])).
% 0.48/0.66 tff(352,plain,(hskp3 | hskp2 | c1_1(a96) | c2_1(a96) | c3_1(a96)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.66 tff(353,plain,
% 0.48/0.66 (hskp2),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[352, 23, 299, 298, 297])).
% 0.48/0.66 tff(354,plain,
% 0.48/0.66 (((~hskp2) | (~c3_1(a98))) <=> ((~hskp2) | (~c3_1(a98)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(355,plain,
% 0.48/0.66 (((~c3_1(a98)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a98)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(356,axiom,((~c3_1(a98)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.48/0.66 tff(357,plain,
% 0.48/0.66 ((~hskp2) | (~c3_1(a98))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.48/0.66 tff(358,plain,
% 0.48/0.66 ((~hskp2) | (~c3_1(a98))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[357, 354])).
% 0.48/0.66 tff(359,plain,
% 0.48/0.66 (~c3_1(a98)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[358, 353])).
% 0.48/0.66 tff(360,plain,
% 0.48/0.66 (((~hskp2) | (~c0_1(a98))) <=> ((~hskp2) | (~c0_1(a98)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(361,plain,
% 0.48/0.66 (((~c0_1(a98)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a98)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(362,axiom,((~c0_1(a98)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.48/0.66 tff(363,plain,
% 0.48/0.66 ((~hskp2) | (~c0_1(a98))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.48/0.66 tff(364,plain,
% 0.48/0.66 ((~hskp2) | (~c0_1(a98))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[363, 360])).
% 0.48/0.66 tff(365,plain,
% 0.48/0.66 (~c0_1(a98)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[364, 353])).
% 0.48/0.66 tff(366,assumption,(~c2_1(a106)), introduced(assumption)).
% 0.48/0.66 tff(367,plain,
% 0.48/0.66 (((~hskp2) | c1_1(a98)) <=> ((~hskp2) | c1_1(a98))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(368,axiom,((~hskp2) | c1_1(a98)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.48/0.66 tff(369,plain,
% 0.48/0.66 ((~hskp2) | c1_1(a98)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.48/0.66 tff(370,plain,
% 0.48/0.66 ((~hskp2) | c1_1(a98)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[369, 367])).
% 0.48/0.66 tff(371,plain,
% 0.48/0.66 ((~hskp2) | c1_1(a98)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[370, 367])).
% 0.48/0.66 tff(372,plain,
% 0.48/0.66 ((~hskp2) | c1_1(a98)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[371, 367])).
% 0.48/0.66 tff(373,plain,
% 0.48/0.66 ((~hskp2) | c1_1(a98)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[372, 367])).
% 0.48/0.66 tff(374,plain,
% 0.48/0.66 (c1_1(a98)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[373, 353])).
% 0.48/0.66 tff(375,assumption,(c3_1(a106)), introduced(assumption)).
% 0.48/0.66 tff(376,assumption,(c1_1(a106)), introduced(assumption)).
% 0.48/0.66 tff(377,plain,
% 0.48/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a106) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a112)) | (~c3_1(a112)) | c2_1(a112))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a106) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a112)) | (~c3_1(a112)) | c2_1(a112))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(378,plain,
% 0.48/0.66 (((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a112) | (~c0_1(a112)) | (~c3_1(a112)) | c3_1(a98) | c0_1(a98) | (~c1_1(a98))) <=> (c2_1(a106) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a112)) | (~c3_1(a112)) | c2_1(a112))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(379,plain,
% 0.48/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a112) | (~c0_1(a112)) | (~c3_1(a112)) | c3_1(a98) | c0_1(a98) | (~c1_1(a98)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a106) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a112)) | (~c3_1(a112)) | c2_1(a112)))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[378])).
% 0.48/0.66 tff(380,plain,
% 0.48/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a112) | (~c0_1(a112)) | (~c3_1(a112)) | c3_1(a98) | c0_1(a98) | (~c1_1(a98)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a106) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a112)) | (~c3_1(a112)) | c2_1(a112))),
% 0.48/0.66 inference(transitivity,[status(thm)],[379, 377])).
% 0.48/0.66 tff(381,plain,
% 0.48/0.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a112) | (~c0_1(a112)) | (~c3_1(a112)) | c3_1(a98) | c0_1(a98) | (~c1_1(a98)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(382,plain,
% 0.48/0.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a106) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a112)) | (~c3_1(a112)) | c2_1(a112)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.48/0.66 tff(383,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[382, 101, 306, 305, 376, 375, 374, 366, 365, 359, 324, 314])).
% 0.48/0.66 tff(384,plain,(hskp3 | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a106) | c1_1(a96) | c2_1(a96) | c3_1(a96)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.66 tff(385,plain,
% 0.48/0.66 (hskp3),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[384, 269, 268, 260, 244, 238, 232])).
% 0.48/0.66 tff(386,plain,
% 0.48/0.66 (((~hskp3) | (~c3_1(a99))) <=> ((~hskp3) | (~c3_1(a99)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(387,plain,
% 0.48/0.66 (((~c3_1(a99)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a99)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(388,axiom,((~c3_1(a99)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.48/0.66 tff(389,plain,
% 0.48/0.66 ((~hskp3) | (~c3_1(a99))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.48/0.66 tff(390,plain,
% 0.48/0.66 ((~hskp3) | (~c3_1(a99))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[389, 386])).
% 0.48/0.66 tff(391,plain,
% 0.48/0.66 (~c3_1(a99)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[390, 385])).
% 0.48/0.66 tff(392,plain,
% 0.48/0.66 (((~hskp3) | (~c1_1(a99))) <=> ((~hskp3) | (~c1_1(a99)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(393,plain,
% 0.48/0.66 (((~c1_1(a99)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a99)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(394,axiom,((~c1_1(a99)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.48/0.66 tff(395,plain,
% 0.48/0.66 ((~hskp3) | (~c1_1(a99))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.48/0.66 tff(396,plain,
% 0.48/0.66 ((~hskp3) | (~c1_1(a99))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[395, 392])).
% 0.48/0.66 tff(397,plain,
% 0.48/0.66 (~c1_1(a99)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[396, 385])).
% 0.48/0.66 tff(398,plain,
% 0.48/0.66 (((~hskp3) | c2_1(a99)) <=> ((~hskp3) | c2_1(a99))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(399,axiom,((~hskp3) | c2_1(a99)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.48/0.66 tff(400,plain,
% 0.48/0.66 ((~hskp3) | c2_1(a99)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.48/0.66 tff(401,plain,
% 0.48/0.66 ((~hskp3) | c2_1(a99)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[400, 398])).
% 0.48/0.66 tff(402,plain,
% 0.48/0.66 ((~hskp3) | c2_1(a99)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[401, 398])).
% 0.48/0.66 tff(403,plain,
% 0.48/0.66 ((~hskp3) | c2_1(a99)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[402, 398])).
% 0.48/0.66 tff(404,plain,
% 0.48/0.66 ((~hskp3) | c2_1(a99)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[403, 398])).
% 0.48/0.66 tff(405,plain,
% 0.48/0.66 (c2_1(a99)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[404, 385])).
% 0.48/0.66 tff(406,plain,
% 0.48/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a99) | c3_1(a99) | c1_1(a96) | c2_1(a96) | (~ndr1_0) | c0_1(a96) | (~c2_1(a99)) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a99) | c3_1(a99) | c1_1(a96) | c2_1(a96) | (~ndr1_0) | c0_1(a96) | (~c2_1(a99)) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(407,plain,
% 0.48/0.66 (((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a96) | c1_1(a96) | c0_1(a96)) <=> (c1_1(a99) | c3_1(a99) | c1_1(a96) | c2_1(a96) | (~ndr1_0) | c0_1(a96) | (~c2_1(a99)) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(408,plain,
% 0.48/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a96) | c1_1(a96) | c0_1(a96))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a99) | c3_1(a99) | c1_1(a96) | c2_1(a96) | (~ndr1_0) | c0_1(a96) | (~c2_1(a99)) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106)))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[407])).
% 0.48/0.66 tff(409,plain,
% 0.48/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a96) | c1_1(a96) | c0_1(a96))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a99) | c3_1(a99) | c1_1(a96) | c2_1(a96) | (~ndr1_0) | c0_1(a96) | (~c2_1(a99)) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.48/0.66 inference(transitivity,[status(thm)],[408, 406])).
% 0.48/0.66 tff(410,plain,
% 0.48/0.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a96) | c1_1(a96) | c0_1(a96))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(411,plain,
% 0.48/0.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a99) | c3_1(a99) | c1_1(a96) | c2_1(a96) | (~ndr1_0) | c0_1(a96) | (~c2_1(a99)) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.48/0.66 tff(412,plain,
% 0.48/0.66 (c0_1(a96)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[411, 101, 269, 268, 405, 397, 391, 244, 238, 286, 276])).
% 0.48/0.66 tff(413,plain,
% 0.48/0.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (c1_1(a97) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | (~c0_1(a97)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a97) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | (~c0_1(a97)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(414,plain,
% 0.48/0.66 (((~ndr1_0) | c1_1(a97) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c1_1(a96) | (~c0_1(a96))) <=> (c1_1(a97) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | (~c0_1(a97)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(415,plain,
% 0.48/0.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c1_1(a97) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (c1_1(a97) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | (~c0_1(a97))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[414])).
% 0.48/0.66 tff(416,plain,
% 0.48/0.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c1_1(a97) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a97) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | (~c0_1(a97)))),
% 0.48/0.66 inference(transitivity,[status(thm)],[415, 413])).
% 0.48/0.66 tff(417,plain,
% 0.48/0.66 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c1_1(a97) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(418,plain,
% 0.48/0.66 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a97) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | (~c0_1(a97))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.48/0.66 tff(419,plain,
% 0.48/0.66 ((~c0_1(a96)) | (~c0_1(a97))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[418, 101, 254, 252, 244, 232, 21])).
% 0.48/0.66 tff(420,plain,
% 0.48/0.66 (~c0_1(a97)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[419, 412])).
% 0.48/0.66 tff(421,plain,
% 0.48/0.66 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(422,plain,
% 0.48/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_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) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[421])).
% 0.48/0.66 tff(423,plain,
% 0.48/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_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) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(424,plain,
% 0.48/0.66 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.48/0.67 inference(bind,[status(th)],[])).
% 0.48/0.67 tff(425,plain,
% 0.48/0.67 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.48/0.67 inference(quant_intro,[status(thm)],[424])).
% 0.48/0.67 tff(426,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.48/0.67 tff(427,plain,
% 0.48/0.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.48/0.67 tff(428,plain,
% 0.48/0.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[427, 423])).
% 0.48/0.67 tff(429,plain,(
% 0.48/0.67 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.48/0.67 inference(skolemize,[status(sab)],[428])).
% 0.48/0.67 tff(430,plain,
% 0.48/0.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[429, 422])).
% 0.48/0.67 tff(431,plain,
% 0.48/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a106) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | c0_1(a97) | (~c3_1(a97)) | (~c3_1(a106)) | c0_1(a106))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a106) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | c0_1(a97) | (~c3_1(a97)) | (~c3_1(a106)) | c0_1(a106))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(432,plain,
% 0.48/0.67 (((~ndr1_0) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)) | c0_1(a97) | (~c2_1(a97)) | (~c3_1(a97)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106))) <=> (c2_1(a106) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | c0_1(a97) | (~c3_1(a97)) | (~c3_1(a106)) | c0_1(a106))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(433,plain,
% 0.48/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)) | c0_1(a97) | (~c2_1(a97)) | (~c3_1(a97)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a106) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | c0_1(a97) | (~c3_1(a97)) | (~c3_1(a106)) | c0_1(a106)))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[432])).
% 0.48/0.67 tff(434,plain,
% 0.48/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)) | c0_1(a97) | (~c2_1(a97)) | (~c3_1(a97)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a106) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | c0_1(a97) | (~c3_1(a97)) | (~c3_1(a106)) | c0_1(a106))),
% 0.48/0.67 inference(transitivity,[status(thm)],[433, 431])).
% 0.48/0.67 tff(435,plain,
% 0.48/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)) | c0_1(a97) | (~c2_1(a97)) | (~c3_1(a97)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))),
% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
% 0.48/0.67 tff(436,plain,
% 0.48/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a106) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | c0_1(a97) | (~c3_1(a97)) | (~c3_1(a106)) | c0_1(a106)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.48/0.67 tff(437,plain,
% 0.48/0.67 ($false),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[436, 101, 268, 254, 253, 260, 244, 232, 430, 412, 420, 276])).
% 0.48/0.67 tff(438,plain,((~hskp0) | hskp20), inference(lemma,lemma(discharge,[]))).
% 0.48/0.67 tff(439,plain,
% 0.48/0.67 (~hskp0),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[438, 22])).
% 0.48/0.67 tff(440,plain,
% 0.48/0.67 (hskp29),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[99, 439, 22])).
% 0.48/0.67 tff(441,plain,
% 0.48/0.67 (((~hskp29) | c2_1(a165)) <=> ((~hskp29) | c2_1(a165))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(442,axiom,((~hskp29) | c2_1(a165)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.48/0.67 tff(443,plain,
% 0.48/0.67 ((~hskp29) | c2_1(a165)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.48/0.67 tff(444,plain,
% 0.48/0.67 ((~hskp29) | c2_1(a165)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[443, 441])).
% 0.48/0.67 tff(445,plain,
% 0.48/0.67 ((~hskp29) | c2_1(a165)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[444, 441])).
% 0.48/0.67 tff(446,plain,
% 0.48/0.67 ((~hskp29) | c2_1(a165)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[445, 441])).
% 0.48/0.67 tff(447,plain,
% 0.48/0.67 ((~hskp29) | c2_1(a165)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[446, 441])).
% 0.48/0.67 tff(448,plain,
% 0.48/0.67 (c2_1(a165)),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[447, 440])).
% 0.48/0.67 tff(449,plain,
% 0.48/0.67 (((~hskp29) | c3_1(a165)) <=> ((~hskp29) | c3_1(a165))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(450,axiom,((~hskp29) | c3_1(a165)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.48/0.67 tff(451,plain,
% 0.48/0.67 ((~hskp29) | c3_1(a165)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.48/0.67 tff(452,plain,
% 0.48/0.67 ((~hskp29) | c3_1(a165)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[451, 449])).
% 0.48/0.67 tff(453,plain,
% 0.48/0.67 ((~hskp29) | c3_1(a165)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[452, 449])).
% 0.48/0.67 tff(454,plain,
% 0.48/0.67 ((~hskp29) | c3_1(a165)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[453, 449])).
% 0.48/0.67 tff(455,plain,
% 0.48/0.67 ((~hskp29) | c3_1(a165)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[454, 449])).
% 0.48/0.67 tff(456,plain,
% 0.48/0.67 (c3_1(a165)),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[455, 440])).
% 0.48/0.67 tff(457,plain,
% 0.48/0.67 (c3_1(a106)),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[267, 201])).
% 0.48/0.67 tff(458,plain,
% 0.48/0.67 (~c0_1(a106)),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[275, 101, 376, 375, 366, 11])).
% 0.48/0.67 tff(459,assumption,(~c0_1(a165)), introduced(assumption)).
% 0.48/0.67 tff(460,plain,
% 0.48/0.67 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.48/0.67 inference(bind,[status(th)],[])).
% 0.48/0.67 tff(461,plain,
% 0.48/0.67 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.48/0.67 inference(quant_intro,[status(thm)],[460])).
% 0.48/0.67 tff(462,plain,
% 0.48/0.67 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(463,plain,
% 0.48/0.67 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.48/0.67 inference(bind,[status(th)],[])).
% 0.48/0.67 tff(464,plain,
% 0.48/0.67 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.48/0.67 inference(quant_intro,[status(thm)],[463])).
% 0.48/0.67 tff(465,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.48/0.67 tff(466,plain,
% 0.48/0.67 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.48/0.67 tff(467,plain,
% 0.48/0.67 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[466, 462])).
% 0.48/0.67 tff(468,plain,(
% 0.48/0.67 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.48/0.67 inference(skolemize,[status(sab)],[467])).
% 0.48/0.67 tff(469,plain,
% 0.48/0.67 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[468, 461])).
% 0.48/0.67 tff(470,assumption,(c3_1(a165)), introduced(assumption)).
% 0.48/0.67 tff(471,assumption,(c2_1(a165)), introduced(assumption)).
% 0.48/0.67 tff(472,plain,
% 0.48/0.67 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c1_1(a106)) | c0_1(a106))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c1_1(a106)) | c0_1(a106))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(473,plain,
% 0.48/0.67 ((hskp7 | (~ndr1_0) | c0_1(a165) | (~c3_1(a165)) | (~c2_1(a165)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106))) <=> (hskp7 | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c1_1(a106)) | c0_1(a106))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(474,plain,
% 0.48/0.67 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a165) | (~c3_1(a165)) | (~c2_1(a165)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c1_1(a106)) | c0_1(a106)))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[473])).
% 0.48/0.67 tff(475,plain,
% 0.48/0.67 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a165) | (~c3_1(a165)) | (~c2_1(a165)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c1_1(a106)) | c0_1(a106))),
% 0.48/0.67 inference(transitivity,[status(thm)],[474, 472])).
% 0.48/0.67 tff(476,plain,
% 0.48/0.67 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a165) | (~c3_1(a165)) | (~c2_1(a165)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)))),
% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
% 0.48/0.67 tff(477,plain,
% 0.48/0.67 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c1_1(a106)) | c0_1(a106)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.48/0.67 tff(478,plain,
% 0.48/0.67 (hskp7),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[477, 101, 471, 470, 376, 366, 469, 459, 458])).
% 0.48/0.67 tff(479,plain,
% 0.48/0.67 (((~hskp7) | (~c3_1(a103))) <=> ((~hskp7) | (~c3_1(a103)))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(480,plain,
% 0.48/0.67 (((~c3_1(a103)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a103)))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(481,axiom,((~c3_1(a103)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.48/0.67 tff(482,plain,
% 0.48/0.67 ((~hskp7) | (~c3_1(a103))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[481, 480])).
% 0.48/0.67 tff(483,plain,
% 0.48/0.67 ((~hskp7) | (~c3_1(a103))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[482, 479])).
% 0.48/0.67 tff(484,plain,
% 0.48/0.67 (~c3_1(a103)),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[483, 478])).
% 0.48/0.67 tff(485,plain,
% 0.48/0.67 (((~hskp7) | (~c1_1(a103))) <=> ((~hskp7) | (~c1_1(a103)))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(486,plain,
% 0.48/0.67 (((~c1_1(a103)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a103)))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(487,axiom,((~c1_1(a103)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.48/0.67 tff(488,plain,
% 0.48/0.67 ((~hskp7) | (~c1_1(a103))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.48/0.67 tff(489,plain,
% 0.48/0.67 ((~hskp7) | (~c1_1(a103))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[488, 485])).
% 0.48/0.67 tff(490,plain,
% 0.48/0.67 (~c1_1(a103)),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[489, 478])).
% 0.48/0.67 tff(491,plain,
% 0.48/0.67 (((~hskp7) | c0_1(a103)) <=> ((~hskp7) | c0_1(a103))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(492,axiom,((~hskp7) | c0_1(a103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.48/0.67 tff(493,plain,
% 0.48/0.67 ((~hskp7) | c0_1(a103)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.48/0.67 tff(494,plain,
% 0.48/0.67 ((~hskp7) | c0_1(a103)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[493, 491])).
% 0.48/0.67 tff(495,plain,
% 0.48/0.67 ((~hskp7) | c0_1(a103)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[494, 491])).
% 0.48/0.67 tff(496,plain,
% 0.48/0.67 ((~hskp7) | c0_1(a103)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[495, 491])).
% 0.48/0.67 tff(497,plain,
% 0.48/0.67 ((~hskp7) | c0_1(a103)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[496, 491])).
% 0.48/0.67 tff(498,plain,
% 0.48/0.67 (c0_1(a103)),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[497, 478])).
% 0.48/0.67 tff(499,plain,
% 0.48/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(500,plain,
% 0.48/0.67 (((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a165) | (~c2_1(a165)) | (~c3_1(a165)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106))) <=> (c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(501,plain,
% 0.48/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a165) | (~c2_1(a165)) | (~c3_1(a165)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106)))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[500])).
% 0.48/0.67 tff(502,plain,
% 0.48/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a165) | (~c2_1(a165)) | (~c3_1(a165)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106))),
% 0.48/0.67 inference(transitivity,[status(thm)],[501, 499])).
% 0.48/0.67 tff(503,plain,
% 0.48/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a165) | (~c2_1(a165)) | (~c3_1(a165)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))),
% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
% 0.48/0.67 tff(504,plain,
% 0.48/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106)),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.48/0.67 tff(505,plain,
% 0.48/0.67 ($false),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[504, 101, 471, 470, 375, 498, 366, 490, 484, 430, 459, 458])).
% 0.48/0.67 tff(506,plain,(c0_1(a165) | (~c2_1(a165)) | (~c3_1(a165)) | (~c3_1(a106)) | c2_1(a106) | (~c1_1(a106))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.67 tff(507,plain,
% 0.48/0.67 (c0_1(a165)),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[506, 457, 456, 448, 215, 209])).
% 0.48/0.67 tff(508,plain,
% 0.48/0.67 ((hskp20 | hskp8 | hskp3) <=> (hskp20 | hskp8 | hskp3)),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(509,plain,
% 0.48/0.67 (((hskp20 | hskp3) | hskp8) <=> (hskp20 | hskp8 | hskp3)),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(510,axiom,((hskp20 | hskp3) | hskp8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 0.48/0.67 tff(511,plain,
% 0.48/0.67 (hskp20 | hskp8 | hskp3),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.48/0.67 tff(512,plain,
% 0.48/0.67 (hskp20 | hskp8 | hskp3),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[511, 508])).
% 0.48/0.67 tff(513,plain,
% 0.48/0.67 (hskp20 | hskp8 | hskp3),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[512, 508])).
% 0.48/0.67 tff(514,plain,
% 0.48/0.67 (hskp20 | hskp8 | hskp3),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[513, 508])).
% 0.48/0.67 tff(515,plain,
% 0.48/0.67 (hskp20 | hskp8 | hskp3),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[514, 508])).
% 0.48/0.67 tff(516,plain,
% 0.48/0.67 (hskp8),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[515, 23, 22])).
% 0.48/0.67 tff(517,plain,
% 0.48/0.67 (((~hskp8) | (~c3_1(a104))) <=> ((~hskp8) | (~c3_1(a104)))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(518,plain,
% 0.48/0.67 (((~c3_1(a104)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a104)))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(519,axiom,((~c3_1(a104)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.48/0.67 tff(520,plain,
% 0.48/0.67 ((~hskp8) | (~c3_1(a104))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[519, 518])).
% 0.48/0.67 tff(521,plain,
% 0.48/0.67 ((~hskp8) | (~c3_1(a104))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[520, 517])).
% 0.48/0.67 tff(522,plain,
% 0.48/0.67 (~c3_1(a104)),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[521, 516])).
% 0.48/0.67 tff(523,plain,
% 0.48/0.67 (((~hskp8) | (~c2_1(a104))) <=> ((~hskp8) | (~c2_1(a104)))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(524,plain,
% 0.48/0.67 (((~c2_1(a104)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a104)))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(525,axiom,((~c2_1(a104)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 0.48/0.67 tff(526,plain,
% 0.48/0.67 ((~hskp8) | (~c2_1(a104))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.48/0.67 tff(527,plain,
% 0.48/0.67 ((~hskp8) | (~c2_1(a104))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[526, 523])).
% 0.48/0.67 tff(528,plain,
% 0.48/0.67 (~c2_1(a104)),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[527, 516])).
% 0.48/0.67 tff(529,plain,
% 0.48/0.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a104))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a104))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(530,plain,
% 0.48/0.67 ((hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a104) | c2_1(a104) | c1_1(a104)) <=> (hskp3 | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a104))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(531,plain,
% 0.48/0.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a104) | c2_1(a104) | c1_1(a104))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a104)))),
% 0.48/0.68 inference(monotonicity,[status(thm)],[530])).
% 0.48/0.68 tff(532,plain,
% 0.48/0.68 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a104) | c2_1(a104) | c1_1(a104))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a104))),
% 0.48/0.68 inference(transitivity,[status(thm)],[531, 529])).
% 0.48/0.68 tff(533,plain,
% 0.48/0.68 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a104) | c2_1(a104) | c1_1(a104))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(534,plain,
% 0.48/0.68 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a104)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.48/0.68 tff(535,plain,
% 0.48/0.68 ((~c0_1(a165)) | c1_1(a104)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[534, 101, 23, 448, 456, 528, 522, 296])).
% 0.48/0.68 tff(536,plain,
% 0.48/0.68 (c1_1(a104)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[535, 507])).
% 0.48/0.68 tff(537,plain,
% 0.48/0.68 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.48/0.68 inference(bind,[status(th)],[])).
% 0.48/0.68 tff(538,plain,
% 0.48/0.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.68 inference(quant_intro,[status(thm)],[537])).
% 0.48/0.68 tff(539,plain,
% 0.48/0.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(540,plain,
% 0.48/0.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(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)) | c3_1(V) | 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)) | c3_1(V) | 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)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | 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)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.48/0.68 inference(bind,[status(th)],[])).
% 0.48/0.68 tff(541,plain,
% 0.48/0.68 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.68 inference(quant_intro,[status(thm)],[540])).
% 0.48/0.68 tff(542,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 0.48/0.68 tff(543,plain,
% 0.48/0.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[542, 541])).
% 0.48/0.68 tff(544,plain,
% 0.48/0.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[543, 539])).
% 0.48/0.68 tff(545,plain,(
% 0.48/0.68 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.68 inference(skolemize,[status(sab)],[544])).
% 0.48/0.68 tff(546,plain,
% 0.48/0.68 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[545, 538])).
% 0.48/0.68 tff(547,plain,
% 0.48/0.68 (~c0_1(a106)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[275, 101, 209, 457, 215, 11])).
% 0.48/0.68 tff(548,plain,
% 0.48/0.68 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 0.48/0.68 inference(bind,[status(th)],[])).
% 0.48/0.68 tff(549,plain,
% 0.48/0.68 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.48/0.68 inference(quant_intro,[status(thm)],[548])).
% 0.48/0.68 tff(550,plain,
% 0.48/0.68 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(551,plain,
% 0.48/0.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | 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))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 0.48/0.68 inference(bind,[status(th)],[])).
% 0.48/0.68 tff(552,plain,
% 0.48/0.68 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.48/0.68 inference(quant_intro,[status(thm)],[551])).
% 0.48/0.68 tff(553,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.48/0.68 tff(554,plain,
% 0.48/0.68 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[553, 552])).
% 0.48/0.68 tff(555,plain,
% 0.48/0.68 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[554, 550])).
% 0.48/0.68 tff(556,plain,(
% 0.48/0.68 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.48/0.68 inference(skolemize,[status(sab)],[555])).
% 0.48/0.68 tff(557,plain,
% 0.48/0.68 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[556, 549])).
% 0.48/0.68 tff(558,plain,
% 0.48/0.68 (((~hskp8) | (~c0_1(a104))) <=> ((~hskp8) | (~c0_1(a104)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(559,plain,
% 0.48/0.68 (((~c0_1(a104)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a104)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(560,axiom,((~c0_1(a104)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.48/0.68 tff(561,plain,
% 0.48/0.68 ((~hskp8) | (~c0_1(a104))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.48/0.68 tff(562,plain,
% 0.48/0.68 ((~hskp8) | (~c0_1(a104))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[561, 558])).
% 0.48/0.68 tff(563,plain,
% 0.48/0.68 (~c0_1(a104)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[562, 516])).
% 0.48/0.68 tff(564,plain,
% 0.48/0.68 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a106) | c0_1(a104) | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a106) | c0_1(a104) | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(565,plain,
% 0.48/0.68 ((hskp6 | (~ndr1_0) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)) | c3_1(a104) | c2_1(a104) | c0_1(a104)) <=> (hskp6 | c2_1(a106) | c0_1(a104) | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(566,plain,
% 0.48/0.68 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)) | c3_1(a104) | c2_1(a104) | c0_1(a104))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a106) | c0_1(a104) | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106)))),
% 0.48/0.68 inference(monotonicity,[status(thm)],[565])).
% 0.48/0.68 tff(567,plain,
% 0.48/0.68 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)) | c3_1(a104) | c2_1(a104) | c0_1(a104))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a106) | c0_1(a104) | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106))),
% 0.48/0.68 inference(transitivity,[status(thm)],[566, 564])).
% 0.48/0.68 tff(568,plain,
% 0.48/0.68 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)) | c3_1(a104) | c2_1(a104) | c0_1(a104))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(569,plain,
% 0.48/0.68 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a106) | c0_1(a104) | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.48/0.68 tff(570,plain,
% 0.48/0.68 (hskp6),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[569, 101, 209, 215, 563, 528, 522, 557, 547])).
% 0.48/0.68 tff(571,plain,
% 0.48/0.68 (((~hskp6) | (~c3_1(a102))) <=> ((~hskp6) | (~c3_1(a102)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(572,plain,
% 0.48/0.68 (((~c3_1(a102)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a102)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(573,axiom,((~c3_1(a102)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.48/0.68 tff(574,plain,
% 0.48/0.68 ((~hskp6) | (~c3_1(a102))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.48/0.68 tff(575,plain,
% 0.48/0.68 ((~hskp6) | (~c3_1(a102))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[574, 571])).
% 0.48/0.68 tff(576,plain,
% 0.48/0.68 (~c3_1(a102)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[575, 570])).
% 0.48/0.68 tff(577,plain,
% 0.48/0.68 (((~hskp6) | c2_1(a102)) <=> ((~hskp6) | c2_1(a102))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(578,axiom,((~hskp6) | c2_1(a102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.48/0.68 tff(579,plain,
% 0.48/0.68 ((~hskp6) | c2_1(a102)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.48/0.68 tff(580,plain,
% 0.48/0.68 ((~hskp6) | c2_1(a102)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[579, 577])).
% 0.48/0.68 tff(581,plain,
% 0.48/0.68 ((~hskp6) | c2_1(a102)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[580, 577])).
% 0.48/0.68 tff(582,plain,
% 0.48/0.68 ((~hskp6) | c2_1(a102)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[581, 577])).
% 0.48/0.68 tff(583,plain,
% 0.48/0.68 ((~hskp6) | c2_1(a102)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[582, 577])).
% 0.48/0.68 tff(584,plain,
% 0.48/0.68 (c2_1(a102)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[583, 570])).
% 0.48/0.68 tff(585,plain,
% 0.48/0.68 (((~hskp6) | c1_1(a102)) <=> ((~hskp6) | c1_1(a102))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(586,axiom,((~hskp6) | c1_1(a102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.48/0.68 tff(587,plain,
% 0.48/0.68 ((~hskp6) | c1_1(a102)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.48/0.68 tff(588,plain,
% 0.48/0.68 ((~hskp6) | c1_1(a102)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[587, 585])).
% 0.48/0.68 tff(589,plain,
% 0.48/0.68 ((~hskp6) | c1_1(a102)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[588, 585])).
% 0.48/0.68 tff(590,plain,
% 0.48/0.68 ((~hskp6) | c1_1(a102)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[589, 585])).
% 0.48/0.68 tff(591,plain,
% 0.48/0.68 ((~hskp6) | c1_1(a102)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[590, 585])).
% 0.48/0.68 tff(592,plain,
% 0.48/0.68 (c1_1(a102)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[591, 570])).
% 0.48/0.68 tff(593,plain,
% 0.48/0.68 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c2_1(a104) | c3_1(a104) | c3_1(a102) | (~ndr1_0) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c2_1(a104) | c3_1(a104) | c3_1(a102) | (~ndr1_0) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a104)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(594,plain,
% 0.48/0.68 ((hskp5 | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c1_1(a102)) | c3_1(a104) | c2_1(a104) | (~c1_1(a104))) <=> (hskp5 | c2_1(a104) | c3_1(a104) | c3_1(a102) | (~ndr1_0) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a104)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(595,plain,
% 0.48/0.68 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c1_1(a102)) | c3_1(a104) | c2_1(a104) | (~c1_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c2_1(a104) | c3_1(a104) | c3_1(a102) | (~ndr1_0) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a104))))),
% 0.48/0.68 inference(monotonicity,[status(thm)],[594])).
% 0.48/0.68 tff(596,plain,
% 0.48/0.68 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c1_1(a102)) | c3_1(a104) | c2_1(a104) | (~c1_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c2_1(a104) | c3_1(a104) | c3_1(a102) | (~ndr1_0) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a104)))),
% 0.48/0.68 inference(transitivity,[status(thm)],[595, 593])).
% 0.48/0.68 tff(597,plain,
% 0.48/0.68 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c1_1(a102)) | c3_1(a104) | c2_1(a104) | (~c1_1(a104)))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(598,plain,
% 0.48/0.68 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c2_1(a104) | c3_1(a104) | c3_1(a102) | (~ndr1_0) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a104))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[597, 596])).
% 0.48/0.68 tff(599,plain,
% 0.48/0.68 (hskp5 | (~c1_1(a104))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[598, 101, 592, 584, 528, 522, 576, 546])).
% 0.48/0.68 tff(600,plain,
% 0.48/0.68 (hskp5),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[599, 536])).
% 0.48/0.68 tff(601,plain,
% 0.48/0.68 (((~hskp5) | (~c2_1(a101))) <=> ((~hskp5) | (~c2_1(a101)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(602,plain,
% 0.48/0.68 (((~c2_1(a101)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a101)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(603,axiom,((~c2_1(a101)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.48/0.68 tff(604,plain,
% 0.48/0.68 ((~hskp5) | (~c2_1(a101))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.48/0.68 tff(605,plain,
% 0.48/0.68 ((~hskp5) | (~c2_1(a101))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[604, 601])).
% 0.48/0.68 tff(606,plain,
% 0.48/0.68 (~c2_1(a101)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[605, 600])).
% 0.48/0.68 tff(607,plain,
% 0.48/0.68 (((~hskp5) | c3_1(a101)) <=> ((~hskp5) | c3_1(a101))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(608,axiom,((~hskp5) | c3_1(a101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.48/0.68 tff(609,plain,
% 0.48/0.68 ((~hskp5) | c3_1(a101)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.48/0.68 tff(610,plain,
% 0.48/0.68 ((~hskp5) | c3_1(a101)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[609, 607])).
% 0.48/0.68 tff(611,plain,
% 0.48/0.68 ((~hskp5) | c3_1(a101)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[610, 607])).
% 0.48/0.68 tff(612,plain,
% 0.48/0.68 ((~hskp5) | c3_1(a101)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[611, 607])).
% 0.48/0.68 tff(613,plain,
% 0.48/0.68 ((~hskp5) | c3_1(a101)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[612, 607])).
% 0.48/0.68 tff(614,plain,
% 0.48/0.68 (c3_1(a101)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[613, 600])).
% 0.48/0.68 tff(615,plain,
% 0.48/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a106) | c0_1(a104) | c3_1(a104) | c2_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a104)) | (~c3_1(a106)) | (~c1_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a106) | c0_1(a104) | c3_1(a104) | c2_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a104)) | (~c3_1(a106)) | (~c1_1(a106)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(616,plain,
% 0.48/0.68 (((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a101) | (~c0_1(a101)) | (~c3_1(a101)) | c3_1(a104) | c0_1(a104) | (~c1_1(a104))) <=> (c2_1(a106) | c0_1(a104) | c3_1(a104) | c2_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a104)) | (~c3_1(a106)) | (~c1_1(a106)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(617,plain,
% 0.48/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a101) | (~c0_1(a101)) | (~c3_1(a101)) | c3_1(a104) | c0_1(a104) | (~c1_1(a104)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a106) | c0_1(a104) | c3_1(a104) | c2_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a104)) | (~c3_1(a106)) | (~c1_1(a106))))),
% 0.48/0.68 inference(monotonicity,[status(thm)],[616])).
% 0.48/0.68 tff(618,plain,
% 0.48/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a101) | (~c0_1(a101)) | (~c3_1(a101)) | c3_1(a104) | c0_1(a104) | (~c1_1(a104)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a106) | c0_1(a104) | c3_1(a104) | c2_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a104)) | (~c3_1(a106)) | (~c1_1(a106)))),
% 0.48/0.68 inference(transitivity,[status(thm)],[617, 615])).
% 0.48/0.68 tff(619,plain,
% 0.48/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a101) | (~c0_1(a101)) | (~c3_1(a101)) | c3_1(a104) | c0_1(a104) | (~c1_1(a104)))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(620,plain,
% 0.48/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a106) | c0_1(a104) | c3_1(a104) | c2_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a104)) | (~c3_1(a106)) | (~c1_1(a106))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.48/0.68 tff(621,plain,
% 0.48/0.68 (~c0_1(a101)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[620, 101, 209, 457, 614, 215, 563, 522, 606, 324, 536])).
% 0.48/0.68 tff(622,plain,
% 0.48/0.68 (((~hskp5) | (~c1_1(a101))) <=> ((~hskp5) | (~c1_1(a101)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(623,plain,
% 0.48/0.68 (((~c1_1(a101)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a101)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(624,axiom,((~c1_1(a101)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.48/0.68 tff(625,plain,
% 0.48/0.68 ((~hskp5) | (~c1_1(a101))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.48/0.68 tff(626,plain,
% 0.48/0.68 ((~hskp5) | (~c1_1(a101))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[625, 622])).
% 0.48/0.68 tff(627,plain,
% 0.48/0.68 (~c1_1(a101)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[626, 600])).
% 0.48/0.68 tff(628,assumption,(~c0_1(a106)), introduced(assumption)).
% 0.48/0.68 tff(629,plain,
% 0.48/0.68 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.48/0.68 inference(bind,[status(th)],[])).
% 0.48/0.68 tff(630,plain,
% 0.48/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.48/0.68 inference(quant_intro,[status(thm)],[629])).
% 0.48/0.68 tff(631,plain,
% 0.48/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(632,plain,
% 0.48/0.68 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.48/0.69 inference(bind,[status(th)],[])).
% 0.48/0.69 tff(633,plain,
% 0.48/0.69 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.48/0.69 inference(quant_intro,[status(thm)],[632])).
% 0.48/0.69 tff(634,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 0.48/0.69 tff(635,plain,
% 0.48/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[634, 633])).
% 0.48/0.69 tff(636,plain,
% 0.48/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[635, 631])).
% 0.48/0.69 tff(637,plain,(
% 0.48/0.69 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.48/0.69 inference(skolemize,[status(sab)],[636])).
% 0.48/0.69 tff(638,plain,
% 0.48/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[637, 630])).
% 0.48/0.69 tff(639,assumption,(hskp11), introduced(assumption)).
% 0.48/0.69 tff(640,plain,
% 0.48/0.69 (((~hskp11) | (~c3_1(a109))) <=> ((~hskp11) | (~c3_1(a109)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(641,plain,
% 0.48/0.69 (((~c3_1(a109)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a109)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(642,axiom,((~c3_1(a109)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 0.48/0.69 tff(643,plain,
% 0.48/0.69 ((~hskp11) | (~c3_1(a109))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[642, 641])).
% 0.48/0.69 tff(644,plain,
% 0.48/0.69 ((~hskp11) | (~c3_1(a109))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[643, 640])).
% 0.48/0.69 tff(645,plain,
% 0.48/0.69 (~c3_1(a109)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[644, 639])).
% 0.48/0.69 tff(646,plain,
% 0.48/0.69 (((~hskp11) | (~c0_1(a109))) <=> ((~hskp11) | (~c0_1(a109)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(647,plain,
% 0.48/0.69 (((~c0_1(a109)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a109)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(648,axiom,((~c0_1(a109)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.48/0.69 tff(649,plain,
% 0.48/0.69 ((~hskp11) | (~c0_1(a109))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[648, 647])).
% 0.48/0.69 tff(650,plain,
% 0.48/0.69 ((~hskp11) | (~c0_1(a109))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[649, 646])).
% 0.48/0.69 tff(651,plain,
% 0.48/0.69 (~c0_1(a109)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[650, 639])).
% 0.48/0.69 tff(652,plain,
% 0.48/0.69 (((~hskp11) | c2_1(a109)) <=> ((~hskp11) | c2_1(a109))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(653,axiom,((~hskp11) | c2_1(a109)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.48/0.69 tff(654,plain,
% 0.48/0.69 ((~hskp11) | c2_1(a109)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[653, 652])).
% 0.48/0.69 tff(655,plain,
% 0.48/0.69 ((~hskp11) | c2_1(a109)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[654, 652])).
% 0.48/0.69 tff(656,plain,
% 0.48/0.69 ((~hskp11) | c2_1(a109)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[655, 652])).
% 0.48/0.69 tff(657,plain,
% 0.48/0.69 ((~hskp11) | c2_1(a109)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[656, 652])).
% 0.48/0.69 tff(658,plain,
% 0.48/0.69 ((~hskp11) | c2_1(a109)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[657, 652])).
% 0.48/0.69 tff(659,plain,
% 0.48/0.69 (c2_1(a109)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[658, 639])).
% 0.48/0.69 tff(660,plain,
% 0.48/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | (~c1_1(a109)) | (~c2_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | (~c1_1(a109)) | (~c2_1(a109)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(661,plain,
% 0.48/0.69 (((~ndr1_0) | c0_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c3_1(a109) | c0_1(a109) | (~c2_1(a109))) <=> (c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | (~c1_1(a109)) | (~c2_1(a109)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(662,plain,
% 0.48/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c3_1(a109) | c0_1(a109) | (~c2_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | (~c1_1(a109)) | (~c2_1(a109))))),
% 0.48/0.69 inference(monotonicity,[status(thm)],[661])).
% 0.48/0.69 tff(663,plain,
% 0.48/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c3_1(a109) | c0_1(a109) | (~c2_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | (~c1_1(a109)) | (~c2_1(a109)))),
% 0.48/0.69 inference(transitivity,[status(thm)],[662, 660])).
% 0.48/0.69 tff(664,plain,
% 0.48/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c3_1(a109) | c0_1(a109) | (~c2_1(a109)))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(665,plain,
% 0.48/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | (~c1_1(a109)) | (~c2_1(a109))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[664, 663])).
% 0.48/0.69 tff(666,plain,
% 0.48/0.69 (~c1_1(a109)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[665, 101, 659, 376, 375, 651, 645, 638, 628])).
% 0.48/0.69 tff(667,assumption,(~c0_1(a101)), introduced(assumption)).
% 0.48/0.69 tff(668,assumption,(~c2_1(a101)), introduced(assumption)).
% 0.48/0.69 tff(669,assumption,(~c1_1(a101)), introduced(assumption)).
% 0.48/0.69 tff(670,plain,
% 0.48/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a109) | c1_1(a101) | c2_1(a101) | (~ndr1_0) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | c1_1(a109) | (~c2_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a109) | c1_1(a101) | c2_1(a101) | (~ndr1_0) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | c1_1(a109) | (~c2_1(a109)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(671,plain,
% 0.48/0.69 (((~ndr1_0) | c3_1(a109) | c1_1(a109) | (~c2_1(a109)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101)) <=> (c3_1(a109) | c1_1(a101) | c2_1(a101) | (~ndr1_0) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | c1_1(a109) | (~c2_1(a109)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(672,plain,
% 0.48/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a109) | c1_1(a109) | (~c2_1(a109)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a109) | c1_1(a101) | c2_1(a101) | (~ndr1_0) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | c1_1(a109) | (~c2_1(a109))))),
% 0.48/0.69 inference(monotonicity,[status(thm)],[671])).
% 0.48/0.69 tff(673,plain,
% 0.48/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a109) | c1_1(a109) | (~c2_1(a109)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a109) | c1_1(a101) | c2_1(a101) | (~ndr1_0) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | c1_1(a109) | (~c2_1(a109)))),
% 0.48/0.69 inference(transitivity,[status(thm)],[672, 670])).
% 0.48/0.69 tff(674,plain,
% 0.48/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a109) | c1_1(a109) | (~c2_1(a109)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(675,plain,
% 0.48/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a109) | c1_1(a101) | c2_1(a101) | (~ndr1_0) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | c1_1(a109) | (~c2_1(a109))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.48/0.69 tff(676,plain,
% 0.48/0.69 ($false),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[675, 101, 659, 376, 375, 645, 669, 668, 286, 628, 667, 666])).
% 0.48/0.69 tff(677,plain,((~hskp11) | (~c1_1(a106)) | (~c3_1(a106)) | c1_1(a101) | c2_1(a101) | c0_1(a106) | c0_1(a101)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.69 tff(678,plain,
% 0.48/0.69 (~hskp11),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[677, 209, 457, 627, 606, 547, 621])).
% 0.48/0.69 tff(679,assumption,(hskp12), introduced(assumption)).
% 0.48/0.69 tff(680,plain,
% 0.48/0.69 (((~hskp12) | (~c0_1(a110))) <=> ((~hskp12) | (~c0_1(a110)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(681,plain,
% 0.48/0.69 (((~c0_1(a110)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a110)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(682,axiom,((~c0_1(a110)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 0.48/0.69 tff(683,plain,
% 0.48/0.69 ((~hskp12) | (~c0_1(a110))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[682, 681])).
% 0.48/0.69 tff(684,plain,
% 0.48/0.69 ((~hskp12) | (~c0_1(a110))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[683, 680])).
% 0.48/0.69 tff(685,plain,
% 0.48/0.69 (~c0_1(a110)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[684, 679])).
% 0.48/0.69 tff(686,plain,
% 0.48/0.69 (((~hskp12) | c3_1(a110)) <=> ((~hskp12) | c3_1(a110))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(687,axiom,((~hskp12) | c3_1(a110)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.48/0.69 tff(688,plain,
% 0.48/0.69 ((~hskp12) | c3_1(a110)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[687, 686])).
% 0.48/0.69 tff(689,plain,
% 0.48/0.69 ((~hskp12) | c3_1(a110)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[688, 686])).
% 0.48/0.69 tff(690,plain,
% 0.48/0.69 ((~hskp12) | c3_1(a110)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[689, 686])).
% 0.48/0.69 tff(691,plain,
% 0.48/0.69 ((~hskp12) | c3_1(a110)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[690, 686])).
% 0.48/0.69 tff(692,plain,
% 0.48/0.69 ((~hskp12) | c3_1(a110)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[691, 686])).
% 0.48/0.69 tff(693,plain,
% 0.48/0.69 (c3_1(a110)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[692, 679])).
% 0.48/0.69 tff(694,plain,
% 0.48/0.69 (((~hskp12) | c2_1(a110)) <=> ((~hskp12) | c2_1(a110))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(695,axiom,((~hskp12) | c2_1(a110)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.48/0.69 tff(696,plain,
% 0.48/0.69 ((~hskp12) | c2_1(a110)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.48/0.69 tff(697,plain,
% 0.48/0.69 ((~hskp12) | c2_1(a110)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[696, 694])).
% 0.48/0.69 tff(698,plain,
% 0.48/0.69 ((~hskp12) | c2_1(a110)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[697, 694])).
% 0.48/0.69 tff(699,plain,
% 0.48/0.69 ((~hskp12) | c2_1(a110)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[698, 694])).
% 0.48/0.69 tff(700,plain,
% 0.48/0.69 ((~hskp12) | c2_1(a110)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[699, 694])).
% 0.48/0.69 tff(701,plain,
% 0.48/0.69 (c2_1(a110)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[700, 679])).
% 0.48/0.69 tff(702,plain,
% 0.48/0.69 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | c0_1(a110) | c2_1(a106) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp7 | c0_1(a110) | c2_1(a106) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(703,plain,
% 0.48/0.69 ((hskp7 | (~ndr1_0) | c0_1(a110) | (~c3_1(a110)) | (~c2_1(a110)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106))) <=> (hskp7 | c0_1(a110) | c2_1(a106) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(704,plain,
% 0.48/0.69 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a110) | (~c3_1(a110)) | (~c2_1(a110)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | c0_1(a110) | c2_1(a106) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110))))),
% 0.48/0.69 inference(monotonicity,[status(thm)],[703])).
% 0.48/0.69 tff(705,plain,
% 0.48/0.69 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a110) | (~c3_1(a110)) | (~c2_1(a110)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp7 | c0_1(a110) | c2_1(a106) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))),
% 0.48/0.69 inference(transitivity,[status(thm)],[704, 702])).
% 0.48/0.69 tff(706,plain,
% 0.48/0.69 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a110) | (~c3_1(a110)) | (~c2_1(a110)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(707,plain,
% 0.48/0.69 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp7 | c0_1(a110) | c2_1(a106) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[706, 705])).
% 0.48/0.69 tff(708,plain,
% 0.48/0.69 (hskp7),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[707, 101, 701, 693, 376, 685, 366, 469, 458])).
% 0.48/0.69 tff(709,plain,
% 0.48/0.69 (~c3_1(a103)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[483, 708])).
% 0.48/0.69 tff(710,plain,
% 0.48/0.69 (~c1_1(a103)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[489, 708])).
% 0.48/0.69 tff(711,plain,
% 0.48/0.69 (c0_1(a103)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[497, 708])).
% 0.48/0.69 tff(712,plain,
% 0.48/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a110) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a110) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(713,plain,
% 0.48/0.69 (((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a110) | (~c2_1(a110)) | (~c3_1(a110)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106))) <=> (c0_1(a110) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(714,plain,
% 0.48/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a110) | (~c2_1(a110)) | (~c3_1(a110)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a110) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110))))),
% 0.48/0.69 inference(monotonicity,[status(thm)],[713])).
% 0.48/0.69 tff(715,plain,
% 0.48/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a110) | (~c2_1(a110)) | (~c3_1(a110)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a110) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))),
% 0.48/0.69 inference(transitivity,[status(thm)],[714, 712])).
% 0.48/0.69 tff(716,plain,
% 0.48/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a110) | (~c2_1(a110)) | (~c3_1(a110)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(717,plain,
% 0.48/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a110) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[716, 715])).
% 0.48/0.69 tff(718,plain,
% 0.48/0.69 ($false),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[717, 101, 701, 693, 375, 711, 685, 366, 710, 709, 430, 458])).
% 0.48/0.69 tff(719,plain,((~hskp12) | (~c3_1(a106)) | c2_1(a106) | (~c1_1(a106))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.69 tff(720,plain,
% 0.48/0.69 (~hskp12),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[719, 457, 215, 209])).
% 0.48/0.69 tff(721,plain,
% 0.48/0.69 ((hskp14 | hskp12 | hskp11) <=> (hskp14 | hskp12 | hskp11)),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(722,plain,
% 0.48/0.69 (((hskp14 | hskp12) | hskp11) <=> (hskp14 | hskp12 | hskp11)),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(723,plain,
% 0.48/0.69 ((hskp14 | hskp12) <=> (hskp14 | hskp12)),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(724,plain,
% 0.48/0.69 (((hskp14 | hskp12) | hskp11) <=> ((hskp14 | hskp12) | hskp11)),
% 0.48/0.70 inference(monotonicity,[status(thm)],[723])).
% 0.48/0.70 tff(725,plain,
% 0.48/0.70 (((hskp14 | hskp12) | hskp11) <=> (hskp14 | hskp12 | hskp11)),
% 0.48/0.70 inference(transitivity,[status(thm)],[724, 722])).
% 0.48/0.70 tff(726,axiom,((hskp14 | hskp12) | hskp11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 0.48/0.70 tff(727,plain,
% 0.48/0.70 (hskp14 | hskp12 | hskp11),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[726, 725])).
% 0.48/0.70 tff(728,plain,
% 0.48/0.70 (hskp14 | hskp12 | hskp11),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[727, 721])).
% 0.48/0.70 tff(729,plain,
% 0.48/0.70 (hskp14 | hskp12 | hskp11),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[728, 721])).
% 0.48/0.70 tff(730,plain,
% 0.48/0.70 (hskp14 | hskp12 | hskp11),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[729, 721])).
% 0.48/0.70 tff(731,plain,
% 0.48/0.70 (hskp14 | hskp12 | hskp11),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[730, 721])).
% 0.48/0.70 tff(732,plain,
% 0.48/0.70 (hskp14),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[731, 720, 678])).
% 0.48/0.70 tff(733,plain,
% 0.48/0.70 (~c3_1(a115)),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[114, 732])).
% 0.48/0.70 tff(734,plain,
% 0.48/0.70 (~c2_1(a115)),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[120, 732])).
% 0.48/0.70 tff(735,plain,
% 0.48/0.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a115))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a115))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(736,plain,
% 0.48/0.70 ((hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a115) | c2_1(a115) | c1_1(a115)) <=> (hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a115))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(737,plain,
% 0.48/0.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a115) | c2_1(a115) | c1_1(a115))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a115)))),
% 0.48/0.70 inference(monotonicity,[status(thm)],[736])).
% 0.48/0.70 tff(738,plain,
% 0.48/0.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a115) | c2_1(a115) | c1_1(a115))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a115))),
% 0.48/0.70 inference(transitivity,[status(thm)],[737, 735])).
% 0.48/0.70 tff(739,plain,
% 0.48/0.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a115) | c2_1(a115) | c1_1(a115))),
% 0.48/0.70 inference(quant_inst,[status(thm)],[])).
% 0.48/0.70 tff(740,plain,
% 0.48/0.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a115)),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[739, 738])).
% 0.48/0.70 tff(741,plain,
% 0.48/0.70 (c1_1(a115)),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[740, 101, 23, 448, 456, 734, 733, 296, 507])).
% 0.48/0.70 tff(742,plain,
% 0.48/0.70 (c0_1(a115)),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[128, 732])).
% 0.48/0.70 tff(743,plain,
% 0.48/0.70 (((~hskp29) | c1_1(a165)) <=> ((~hskp29) | c1_1(a165))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(744,axiom,((~hskp29) | c1_1(a165)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.48/0.70 tff(745,plain,
% 0.48/0.70 ((~hskp29) | c1_1(a165)),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[744, 743])).
% 0.48/0.70 tff(746,plain,
% 0.48/0.70 ((~hskp29) | c1_1(a165)),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[745, 743])).
% 0.48/0.70 tff(747,plain,
% 0.48/0.70 ((~hskp29) | c1_1(a165)),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[746, 743])).
% 0.48/0.70 tff(748,plain,
% 0.48/0.70 ((~hskp29) | c1_1(a165)),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[747, 743])).
% 0.48/0.70 tff(749,plain,
% 0.48/0.70 ((~hskp29) | c1_1(a165)),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[748, 743])).
% 0.48/0.70 tff(750,plain,
% 0.48/0.70 (c1_1(a165)),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[749, 440])).
% 0.48/0.70 tff(751,plain,
% 0.48/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a115) | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c1_1(a165)) | (~c0_1(a165)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c1_1(a115)) | (~c0_1(a115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a115) | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c1_1(a165)) | (~c0_1(a165)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c1_1(a115)) | (~c0_1(a115)))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(752,plain,
% 0.48/0.70 (((~ndr1_0) | (~c3_1(a165)) | (~c0_1(a165)) | (~c1_1(a165)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115))) <=> (c2_1(a115) | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c1_1(a165)) | (~c0_1(a165)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c1_1(a115)) | (~c0_1(a115)))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(753,plain,
% 0.48/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a165)) | (~c0_1(a165)) | (~c1_1(a165)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a115) | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c1_1(a165)) | (~c0_1(a165)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c1_1(a115)) | (~c0_1(a115))))),
% 0.48/0.70 inference(monotonicity,[status(thm)],[752])).
% 0.48/0.70 tff(754,plain,
% 0.48/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a165)) | (~c0_1(a165)) | (~c1_1(a165)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a115) | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c1_1(a165)) | (~c0_1(a165)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c1_1(a115)) | (~c0_1(a115)))),
% 0.48/0.70 inference(transitivity,[status(thm)],[753, 751])).
% 0.48/0.70 tff(755,plain,
% 0.48/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a165)) | (~c0_1(a165)) | (~c1_1(a165)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115)))),
% 0.48/0.70 inference(quant_inst,[status(thm)],[])).
% 0.48/0.70 tff(756,plain,
% 0.48/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a115) | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c1_1(a165)) | (~c0_1(a165)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c1_1(a115)) | (~c0_1(a115))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[755, 754])).
% 0.48/0.70 tff(757,plain,
% 0.48/0.70 ($false),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[756, 101, 750, 456, 742, 209, 457, 734, 215, 11, 507, 741])).
% 0.48/0.70 tff(758,plain,(hskp3 | hskp20), inference(lemma,lemma(discharge,[]))).
% 0.48/0.70 tff(759,plain,
% 0.48/0.70 (hskp3),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[758, 22])).
% 0.48/0.70 tff(760,plain,
% 0.48/0.70 (~c3_1(a99)),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[390, 759])).
% 0.48/0.70 tff(761,plain,
% 0.48/0.70 (~c1_1(a99)),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[396, 759])).
% 0.48/0.70 tff(762,plain,
% 0.48/0.70 (c2_1(a99)),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[404, 759])).
% 0.48/0.70 tff(763,plain,
% 0.48/0.70 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c0_1(a99)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c0_1(a99)))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(764,plain,
% 0.48/0.70 (((~ndr1_0) | c1_1(a99) | (~c2_1(a99)) | (~c0_1(a99)) | c3_1(a99) | c1_1(a99) | (~c0_1(a99))) <=> (c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c0_1(a99)))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(765,plain,
% 0.48/0.70 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c1_1(a99) | (~c2_1(a99)) | (~c0_1(a99)) | c3_1(a99) | c1_1(a99) | (~c0_1(a99)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c0_1(a99))))),
% 0.48/0.70 inference(monotonicity,[status(thm)],[764])).
% 0.48/0.70 tff(766,plain,
% 0.48/0.70 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c1_1(a99) | (~c2_1(a99)) | (~c0_1(a99)) | c3_1(a99) | c1_1(a99) | (~c0_1(a99)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c0_1(a99)))),
% 0.48/0.70 inference(transitivity,[status(thm)],[765, 763])).
% 0.48/0.70 tff(767,plain,
% 0.48/0.70 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c1_1(a99) | (~c2_1(a99)) | (~c0_1(a99)) | c3_1(a99) | c1_1(a99) | (~c0_1(a99)))),
% 0.48/0.70 inference(quant_inst,[status(thm)],[])).
% 0.48/0.70 tff(768,plain,
% 0.48/0.70 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c0_1(a99))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.48/0.70 tff(769,plain,
% 0.48/0.70 (~c0_1(a99)),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[768, 101, 762, 761, 760, 21])).
% 0.48/0.70 tff(770,plain,
% 0.48/0.70 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.48/0.70 inference(bind,[status(th)],[])).
% 0.48/0.70 tff(771,plain,
% 0.48/0.70 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.48/0.70 inference(quant_intro,[status(thm)],[770])).
% 0.48/0.70 tff(772,plain,
% 0.48/0.70 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(773,plain,
% 0.48/0.70 (^[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) | c3_1(U) | 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) | c3_1(U) | c1_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) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_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) | c3_1(U) | c1_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)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_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)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_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)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_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)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.48/0.70 inference(bind,[status(th)],[])).
% 0.48/0.70 tff(774,plain,
% 0.48/0.70 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.48/0.70 inference(quant_intro,[status(thm)],[773])).
% 0.48/0.70 tff(775,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 0.48/0.70 tff(776,plain,
% 0.48/0.70 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.48/0.70 tff(777,plain,
% 0.48/0.70 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[776, 772])).
% 0.48/0.70 tff(778,plain,(
% 0.48/0.70 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.48/0.70 inference(skolemize,[status(sab)],[777])).
% 0.48/0.70 tff(779,plain,
% 0.48/0.70 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[778, 771])).
% 0.48/0.70 tff(780,plain,
% 0.48/0.70 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a99) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a99) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(781,plain,
% 0.48/0.70 ((hskp10 | (~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99))) <=> (hskp10 | c1_1(a99) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(782,plain,
% 0.48/0.70 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a99) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99))))),
% 0.48/0.70 inference(monotonicity,[status(thm)],[781])).
% 0.55/0.70 tff(783,plain,
% 0.55/0.70 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a99) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)))),
% 0.55/0.70 inference(transitivity,[status(thm)],[782, 780])).
% 0.55/0.70 tff(784,plain,
% 0.55/0.70 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99)))),
% 0.55/0.70 inference(quant_inst,[status(thm)],[])).
% 0.55/0.70 tff(785,plain,
% 0.55/0.70 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a99) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[784, 783])).
% 0.55/0.70 tff(786,plain,
% 0.55/0.70 (hskp10),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[785, 101, 762, 761, 760, 779, 769])).
% 0.55/0.70 tff(787,plain,
% 0.55/0.70 (~c2_1(a106)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[214, 786])).
% 0.55/0.70 tff(788,plain,
% 0.55/0.70 (c3_1(a106)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[267, 786])).
% 0.55/0.70 tff(789,plain,
% 0.55/0.70 (c1_1(a106)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[208, 786])).
% 0.55/0.70 tff(790,plain,
% 0.55/0.70 (~c0_1(a106)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[275, 101, 789, 788, 787, 11])).
% 0.55/0.70 tff(791,plain,
% 0.55/0.70 (~hskp12),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[719, 788, 787, 789])).
% 0.55/0.70 tff(792,plain,
% 0.55/0.70 (^[U: $i] : refl((hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))),
% 0.55/0.70 inference(bind,[status(th)],[])).
% 0.55/0.70 tff(793,plain,
% 0.55/0.70 (![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.55/0.70 inference(quant_intro,[status(thm)],[792])).
% 0.55/0.70 tff(794,plain,
% 0.55/0.70 (![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(795,plain,
% 0.55/0.70 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp12))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp8) <=> ((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp8))), rewrite(((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp8) <=> (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp8) <=> (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.55/0.70 inference(bind,[status(th)],[])).
% 0.55/0.70 tff(796,plain,
% 0.55/0.70 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp8) <=> ![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.55/0.70 inference(quant_intro,[status(thm)],[795])).
% 0.55/0.70 tff(797,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 0.55/0.70 tff(798,plain,
% 0.55/0.70 (![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[797, 796])).
% 0.55/0.70 tff(799,plain,
% 0.55/0.70 (![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[798, 794])).
% 0.55/0.70 tff(800,plain,(
% 0.55/0.70 ![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.55/0.70 inference(skolemize,[status(sab)],[799])).
% 0.55/0.70 tff(801,plain,
% 0.55/0.70 (![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[800, 793])).
% 0.55/0.70 tff(802,plain,
% 0.55/0.70 (((~![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c1_1(a165)))) <=> ((~![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp8 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c1_1(a165)))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(803,plain,
% 0.55/0.70 ((~![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c1_1(a165)))),
% 0.55/0.70 inference(quant_inst,[status(thm)],[])).
% 0.55/0.70 tff(804,plain,
% 0.55/0.70 ((~![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp8 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c1_1(a165))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[803, 802])).
% 0.55/0.70 tff(805,plain,
% 0.55/0.70 (hskp12 | hskp8),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[804, 101, 750, 448, 456, 801])).
% 0.55/0.70 tff(806,plain,
% 0.55/0.70 (hskp8),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[805, 791])).
% 0.55/0.70 tff(807,plain,
% 0.55/0.70 (~c2_1(a104)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[527, 806])).
% 0.55/0.70 tff(808,plain,
% 0.55/0.70 (~c0_1(a104)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[562, 806])).
% 0.55/0.70 tff(809,plain,
% 0.55/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a104) | c2_1(a104) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c1_1(a104) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a104) | c2_1(a104) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c1_1(a104) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(810,plain,
% 0.55/0.70 (((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a104) | c1_1(a104) | c0_1(a104)) <=> (c0_1(a104) | c2_1(a104) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c1_1(a104) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(811,plain,
% 0.55/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a104) | c1_1(a104) | c0_1(a104))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a104) | c2_1(a104) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c1_1(a104) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106)))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[810])).
% 0.55/0.70 tff(812,plain,
% 0.55/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a104) | c1_1(a104) | c0_1(a104))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a104) | c2_1(a104) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c1_1(a104) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.55/0.71 inference(transitivity,[status(thm)],[811, 809])).
% 0.55/0.71 tff(813,plain,
% 0.55/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a104) | c1_1(a104) | c0_1(a104))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(814,plain,
% 0.55/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a104) | c2_1(a104) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c1_1(a104) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[813, 812])).
% 0.55/0.71 tff(815,plain,
% 0.55/0.71 (c1_1(a104)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[814, 101, 789, 788, 762, 808, 807, 761, 760, 286, 790])).
% 0.55/0.71 tff(816,plain,
% 0.55/0.71 (~c3_1(a104)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[521, 806])).
% 0.55/0.71 tff(817,plain,
% 0.55/0.71 (hskp6),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[569, 101, 789, 787, 808, 807, 816, 557, 790])).
% 0.55/0.71 tff(818,plain,
% 0.55/0.71 (~c3_1(a102)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[575, 817])).
% 0.55/0.71 tff(819,plain,
% 0.55/0.71 (c2_1(a102)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[583, 817])).
% 0.55/0.71 tff(820,plain,
% 0.55/0.71 (c1_1(a102)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[591, 817])).
% 0.55/0.71 tff(821,plain,
% 0.55/0.71 (hskp5),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[598, 101, 820, 819, 807, 816, 818, 546, 815])).
% 0.55/0.71 tff(822,plain,
% 0.55/0.71 (~c2_1(a101)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[605, 821])).
% 0.55/0.71 tff(823,plain,
% 0.55/0.71 (c3_1(a101)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[613, 821])).
% 0.55/0.71 tff(824,plain,
% 0.55/0.71 (~c0_1(a101)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[620, 101, 789, 788, 823, 787, 808, 816, 822, 324, 815])).
% 0.55/0.71 tff(825,plain,
% 0.55/0.71 (~c1_1(a101)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[626, 821])).
% 0.55/0.71 tff(826,plain,
% 0.55/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a101) | c2_1(a101) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a101) | c2_1(a101) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(827,plain,
% 0.55/0.71 (((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101)) <=> (c1_1(a101) | c2_1(a101) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(828,plain,
% 0.55/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a101) | c2_1(a101) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106)))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[827])).
% 0.55/0.71 tff(829,plain,
% 0.55/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a101) | c2_1(a101) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.55/0.71 inference(transitivity,[status(thm)],[828, 826])).
% 0.55/0.71 tff(830,plain,
% 0.55/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(831,plain,
% 0.55/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a101) | c2_1(a101) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[830, 829])).
% 0.55/0.71 tff(832,plain,
% 0.55/0.71 ($false),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[831, 101, 789, 788, 762, 825, 822, 761, 760, 286, 790, 824])).
% 0.55/0.71 tff(833,plain,(hskp20), inference(lemma,lemma(discharge,[]))).
% 0.55/0.71 tff(834,plain,
% 0.55/0.71 (((~hskp20) | (~c2_1(a133))) <=> ((~hskp20) | (~c2_1(a133)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(835,plain,
% 0.55/0.71 (((~c2_1(a133)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a133)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(836,axiom,((~c2_1(a133)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.55/0.71 tff(837,plain,
% 0.55/0.71 ((~hskp20) | (~c2_1(a133))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.55/0.71 tff(838,plain,
% 0.55/0.71 ((~hskp20) | (~c2_1(a133))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[837, 834])).
% 0.55/0.71 tff(839,plain,
% 0.55/0.71 (~c2_1(a133)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[838, 833])).
% 0.55/0.71 tff(840,plain,
% 0.55/0.71 (((~hskp20) | c3_1(a133)) <=> ((~hskp20) | c3_1(a133))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(841,axiom,((~hskp20) | c3_1(a133)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 0.55/0.71 tff(842,plain,
% 0.55/0.71 ((~hskp20) | c3_1(a133)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[841, 840])).
% 0.55/0.71 tff(843,plain,
% 0.55/0.71 ((~hskp20) | c3_1(a133)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[842, 840])).
% 0.55/0.71 tff(844,plain,
% 0.55/0.71 ((~hskp20) | c3_1(a133)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[843, 840])).
% 0.55/0.71 tff(845,plain,
% 0.55/0.71 ((~hskp20) | c3_1(a133)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[844, 840])).
% 0.55/0.71 tff(846,plain,
% 0.55/0.71 ((~hskp20) | c3_1(a133)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[845, 840])).
% 0.55/0.71 tff(847,plain,
% 0.55/0.71 (c3_1(a133)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[846, 833])).
% 0.55/0.71 tff(848,plain,
% 0.55/0.71 (((~hskp20) | c0_1(a133)) <=> ((~hskp20) | c0_1(a133))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(849,axiom,((~hskp20) | c0_1(a133)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.55/0.71 tff(850,plain,
% 0.55/0.71 ((~hskp20) | c0_1(a133)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[849, 848])).
% 0.55/0.71 tff(851,plain,
% 0.55/0.71 ((~hskp20) | c0_1(a133)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[850, 848])).
% 0.55/0.71 tff(852,plain,
% 0.55/0.71 ((~hskp20) | c0_1(a133)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[851, 848])).
% 0.55/0.71 tff(853,plain,
% 0.55/0.71 ((~hskp20) | c0_1(a133)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[852, 848])).
% 0.55/0.71 tff(854,plain,
% 0.55/0.71 ((~hskp20) | c0_1(a133)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[853, 848])).
% 0.55/0.71 tff(855,plain,
% 0.55/0.71 (c0_1(a133)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[854, 833])).
% 0.55/0.71 tff(856,plain,
% 0.55/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(857,plain,
% 0.55/0.71 (((~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c1_1(a133)) | c2_1(a133) | (~c1_1(a133)) | (~c3_1(a133)) | c2_1(a133) | (~c0_1(a133)) | (~c1_1(a133))) <=> (c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(858,plain,
% 0.55/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c1_1(a133)) | c2_1(a133) | (~c1_1(a133)) | (~c3_1(a133)) | c2_1(a133) | (~c0_1(a133)) | (~c1_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133))))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[857])).
% 0.55/0.71 tff(859,plain,
% 0.55/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c1_1(a133)) | c2_1(a133) | (~c1_1(a133)) | (~c3_1(a133)) | c2_1(a133) | (~c0_1(a133)) | (~c1_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)))),
% 0.55/0.71 inference(transitivity,[status(thm)],[858, 856])).
% 0.55/0.71 tff(860,plain,
% 0.55/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c1_1(a133)) | c2_1(a133) | (~c1_1(a133)) | (~c3_1(a133)) | c2_1(a133) | (~c0_1(a133)) | (~c1_1(a133)))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(861,plain,
% 0.55/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[860, 859])).
% 0.55/0.71 tff(862,plain,
% 0.55/0.71 (~c1_1(a133)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[861, 101, 855, 847, 839, 11])).
% 0.55/0.71 tff(863,plain,
% 0.55/0.71 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(864,plain,
% 0.55/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[863])).
% 0.55/0.71 tff(865,plain,
% 0.55/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(866,plain,
% 0.55/0.71 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(867,plain,
% 0.55/0.71 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[866])).
% 0.55/0.71 tff(868,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.55/0.71 tff(869,plain,
% 0.55/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[868, 867])).
% 0.55/0.71 tff(870,plain,
% 0.55/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[869, 865])).
% 0.55/0.71 tff(871,plain,(
% 0.55/0.71 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.55/0.71 inference(skolemize,[status(sab)],[870])).
% 0.55/0.71 tff(872,plain,
% 0.55/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[871, 864])).
% 0.55/0.71 tff(873,plain,
% 0.55/0.71 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(874,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[873])).
% 0.55/0.71 tff(875,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(876,plain,
% 0.55/0.71 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(877,plain,
% 0.55/0.71 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[876])).
% 0.55/0.71 tff(878,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 0.55/0.71 tff(879,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[878, 877])).
% 0.55/0.71 tff(880,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[879, 875])).
% 0.55/0.71 tff(881,plain,(
% 0.55/0.71 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.71 inference(skolemize,[status(sab)],[880])).
% 0.55/0.71 tff(882,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[881, 874])).
% 0.55/0.71 tff(883,plain,
% 0.55/0.71 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(884,plain,
% 0.55/0.71 ((hskp15 | (~ndr1_0) | c2_1(a133) | (~c3_1(a133)) | (~c0_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133))) <=> (hskp15 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(885,plain,
% 0.55/0.71 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a133) | (~c3_1(a133)) | (~c0_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133))))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[884])).
% 0.55/0.71 tff(886,plain,
% 0.55/0.71 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a133) | (~c3_1(a133)) | (~c0_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.55/0.71 inference(transitivity,[status(thm)],[885, 883])).
% 0.55/0.71 tff(887,plain,
% 0.55/0.71 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a133) | (~c3_1(a133)) | (~c0_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(888,plain,
% 0.55/0.71 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[887, 886])).
% 0.55/0.71 tff(889,plain,
% 0.55/0.71 (hskp15),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[888, 101, 855, 847, 839, 882, 862])).
% 0.55/0.71 tff(890,plain,
% 0.55/0.71 (((~hskp15) | c3_1(a116)) <=> ((~hskp15) | c3_1(a116))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(891,axiom,((~hskp15) | c3_1(a116)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 0.55/0.71 tff(892,plain,
% 0.55/0.71 ((~hskp15) | c3_1(a116)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[891, 890])).
% 0.55/0.71 tff(893,plain,
% 0.55/0.71 ((~hskp15) | c3_1(a116)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[892, 890])).
% 0.55/0.71 tff(894,plain,
% 0.55/0.71 ((~hskp15) | c3_1(a116)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[893, 890])).
% 0.55/0.71 tff(895,plain,
% 0.55/0.71 ((~hskp15) | c3_1(a116)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[894, 890])).
% 0.55/0.71 tff(896,plain,
% 0.55/0.71 ((~hskp15) | c3_1(a116)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[895, 890])).
% 0.55/0.71 tff(897,plain,
% 0.55/0.71 (c3_1(a116)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[896, 889])).
% 0.55/0.71 tff(898,plain,
% 0.55/0.71 (((~hskp15) | c1_1(a116)) <=> ((~hskp15) | c1_1(a116))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(899,axiom,((~hskp15) | c1_1(a116)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 0.55/0.71 tff(900,plain,
% 0.55/0.71 ((~hskp15) | c1_1(a116)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[899, 898])).
% 0.55/0.71 tff(901,plain,
% 0.55/0.71 ((~hskp15) | c1_1(a116)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[900, 898])).
% 0.55/0.71 tff(902,plain,
% 0.55/0.71 ((~hskp15) | c1_1(a116)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[901, 898])).
% 0.55/0.71 tff(903,plain,
% 0.55/0.71 ((~hskp15) | c1_1(a116)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[902, 898])).
% 0.55/0.71 tff(904,plain,
% 0.55/0.71 ((~hskp15) | c1_1(a116)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[903, 898])).
% 0.55/0.71 tff(905,plain,
% 0.55/0.71 (c1_1(a116)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[904, 889])).
% 0.55/0.71 tff(906,plain,
% 0.55/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a133) | (~ndr1_0) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a116) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a133) | (~ndr1_0) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a116) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(907,plain,
% 0.55/0.71 (((~ndr1_0) | c2_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133))) <=> (c2_1(a133) | (~ndr1_0) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a116) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(908,plain,
% 0.55/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a133) | (~ndr1_0) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a116) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133))))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[907])).
% 0.55/0.71 tff(909,plain,
% 0.55/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a133) | (~ndr1_0) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a116) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.55/0.71 inference(transitivity,[status(thm)],[908, 906])).
% 0.55/0.71 tff(910,plain,
% 0.55/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(911,plain,
% 0.55/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a133) | (~ndr1_0) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a116) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[910, 909])).
% 0.55/0.71 tff(912,plain,
% 0.55/0.71 ($false),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[911, 101, 855, 847, 905, 897, 839, 872, 862, 1])).
% 0.55/0.71 tff(913,plain,(c2_1(a116)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.71 tff(914,assumption,(hskp6), introduced(assumption)).
% 0.55/0.71 tff(915,plain,
% 0.55/0.72 (~c3_1(a102)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[575, 914])).
% 0.55/0.72 tff(916,plain,
% 0.55/0.72 (c1_1(a102)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[591, 914])).
% 0.55/0.72 tff(917,plain,
% 0.55/0.72 (c2_1(a102)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[583, 914])).
% 0.55/0.72 tff(918,assumption,(c2_1(a116)), introduced(assumption)).
% 0.55/0.72 tff(919,assumption,(~c3_1(a102)), introduced(assumption)).
% 0.55/0.72 tff(920,plain,
% 0.55/0.72 (((~hskp15) | (~c0_1(a116))) <=> ((~hskp15) | (~c0_1(a116)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(921,plain,
% 0.55/0.72 (((~c0_1(a116)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a116)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(922,axiom,((~c0_1(a116)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.55/0.72 tff(923,plain,
% 0.55/0.72 ((~hskp15) | (~c0_1(a116))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[922, 921])).
% 0.55/0.72 tff(924,plain,
% 0.55/0.72 ((~hskp15) | (~c0_1(a116))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[923, 920])).
% 0.55/0.72 tff(925,plain,
% 0.55/0.72 (~c0_1(a116)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[924, 889])).
% 0.55/0.72 tff(926,assumption,(c2_1(a102)), introduced(assumption)).
% 0.55/0.72 tff(927,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a116) | c3_1(a102) | (~ndr1_0) | c0_1(a102) | (~c2_1(a102)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c3_1(a102) | (~ndr1_0) | c0_1(a102) | (~c2_1(a102)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(928,plain,
% 0.55/0.72 (((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a102) | c0_1(a102) | (~c2_1(a102))) <=> (c0_1(a116) | c3_1(a102) | (~ndr1_0) | c0_1(a102) | (~c2_1(a102)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(929,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a102) | c0_1(a102) | (~c2_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a116) | c3_1(a102) | (~ndr1_0) | c0_1(a102) | (~c2_1(a102)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[928])).
% 0.55/0.72 tff(930,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a102) | c0_1(a102) | (~c2_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c3_1(a102) | (~ndr1_0) | c0_1(a102) | (~c2_1(a102)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.55/0.72 inference(transitivity,[status(thm)],[929, 927])).
% 0.55/0.72 tff(931,plain,
% 0.55/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a102) | c0_1(a102) | (~c2_1(a102)))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(932,plain,
% 0.55/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c3_1(a102) | (~ndr1_0) | c0_1(a102) | (~c2_1(a102)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[931, 930])).
% 0.55/0.72 tff(933,plain,
% 0.55/0.72 (c0_1(a102) | (~c2_1(a116))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[932, 101, 905, 897, 926, 925, 919, 638])).
% 0.55/0.72 tff(934,plain,
% 0.55/0.72 (c0_1(a102)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[933, 918])).
% 0.55/0.72 tff(935,plain,
% 0.55/0.72 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(936,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[935])).
% 0.55/0.72 tff(937,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(938,plain,
% 0.55/0.72 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_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)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_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)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_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)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_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)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_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)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(939,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_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)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[938])).
% 0.55/0.72 tff(940,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 0.55/0.72 tff(941,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[940, 939])).
% 0.55/0.72 tff(942,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[941, 937])).
% 0.55/0.72 tff(943,plain,(
% 0.55/0.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.72 inference(skolemize,[status(sab)],[942])).
% 0.55/0.72 tff(944,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[943, 936])).
% 0.55/0.72 tff(945,assumption,(c1_1(a102)), introduced(assumption)).
% 0.55/0.72 tff(946,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a133) | c0_1(a116) | (~ndr1_0) | (~c0_1(a102)) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a116)) | (~c2_1(a116)) | (~c3_1(a133)) | (~c0_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a133) | c0_1(a116) | (~ndr1_0) | (~c0_1(a102)) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a116)) | (~c2_1(a116)) | (~c3_1(a133)) | (~c0_1(a133)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(947,plain,
% 0.55/0.72 (((~ndr1_0) | (~c2_1(a102)) | (~c0_1(a102)) | (~c1_1(a102)) | c2_1(a133) | (~c0_1(a133)) | (~c3_1(a133)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116))) <=> (c2_1(a133) | c0_1(a116) | (~ndr1_0) | (~c0_1(a102)) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a116)) | (~c2_1(a116)) | (~c3_1(a133)) | (~c0_1(a133)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(948,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a102)) | (~c0_1(a102)) | (~c1_1(a102)) | c2_1(a133) | (~c0_1(a133)) | (~c3_1(a133)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a133) | c0_1(a116) | (~ndr1_0) | (~c0_1(a102)) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a116)) | (~c2_1(a116)) | (~c3_1(a133)) | (~c0_1(a133))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[947])).
% 0.55/0.72 tff(949,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a102)) | (~c0_1(a102)) | (~c1_1(a102)) | c2_1(a133) | (~c0_1(a133)) | (~c3_1(a133)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a133) | c0_1(a116) | (~ndr1_0) | (~c0_1(a102)) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a116)) | (~c2_1(a116)) | (~c3_1(a133)) | (~c0_1(a133)))),
% 0.55/0.72 inference(transitivity,[status(thm)],[948, 946])).
% 0.55/0.72 tff(950,plain,
% 0.55/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a102)) | (~c0_1(a102)) | (~c1_1(a102)) | c2_1(a133) | (~c0_1(a133)) | (~c3_1(a133)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(951,plain,
% 0.55/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a133) | c0_1(a116) | (~ndr1_0) | (~c0_1(a102)) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a116)) | (~c2_1(a116)) | (~c3_1(a133)) | (~c0_1(a133))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[950, 949])).
% 0.55/0.72 tff(952,plain,
% 0.55/0.72 ((~c0_1(a102)) | (~c2_1(a116))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[951, 101, 855, 847, 905, 945, 926, 839, 925, 944])).
% 0.55/0.72 tff(953,plain,
% 0.55/0.72 ($false),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[952, 934, 918])).
% 0.55/0.72 tff(954,plain,((~c2_1(a116)) | (~c1_1(a102)) | (~c2_1(a102)) | c3_1(a102)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.72 tff(955,plain,
% 0.55/0.72 ($false),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[954, 917, 916, 913, 915])).
% 0.55/0.72 tff(956,plain,(~hskp6), inference(lemma,lemma(discharge,[]))).
% 0.55/0.72 tff(957,plain,
% 0.55/0.72 (^[U: $i] : refl((hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(958,plain,
% 0.55/0.72 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[957])).
% 0.55/0.72 tff(959,plain,
% 0.55/0.72 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(960,plain,
% 0.55/0.72 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp3) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp3))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp3) <=> (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(961,plain,
% 0.55/0.72 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp3) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[960])).
% 0.55/0.72 tff(962,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 0.55/0.72 tff(963,plain,
% 0.55/0.72 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[962, 961])).
% 0.55/0.72 tff(964,plain,
% 0.55/0.72 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[963, 959])).
% 0.55/0.72 tff(965,plain,(
% 0.55/0.72 ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.72 inference(skolemize,[status(sab)],[964])).
% 0.55/0.72 tff(966,plain,
% 0.55/0.72 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[965, 958])).
% 0.55/0.72 tff(967,plain,
% 0.55/0.72 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(968,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[967])).
% 0.55/0.72 tff(969,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(970,plain,
% 0.55/0.72 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(971,plain,
% 0.55/0.72 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[970])).
% 0.55/0.72 tff(972,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 0.55/0.72 tff(973,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[972, 971])).
% 0.55/0.72 tff(974,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[973, 969])).
% 0.55/0.72 tff(975,plain,(
% 0.55/0.72 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.72 inference(skolemize,[status(sab)],[974])).
% 0.55/0.72 tff(976,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[975, 968])).
% 0.55/0.72 tff(977,plain,
% 0.55/0.72 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(978,plain,
% 0.55/0.72 ((hskp14 | (~ndr1_0) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133))) <=> (hskp14 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(979,plain,
% 0.55/0.72 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[978])).
% 0.55/0.72 tff(980,plain,
% 0.55/0.72 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.55/0.72 inference(transitivity,[status(thm)],[979, 977])).
% 0.55/0.72 tff(981,plain,
% 0.55/0.72 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(982,plain,
% 0.55/0.73 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[981, 980])).
% 0.55/0.73 tff(983,plain,
% 0.55/0.73 (hskp14),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[982, 101, 855, 847, 839, 976, 862])).
% 0.55/0.73 tff(984,plain,
% 0.55/0.73 (~c2_1(a115)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[120, 983])).
% 0.55/0.73 tff(985,plain,
% 0.55/0.73 (c0_1(a115)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[128, 983])).
% 0.55/0.73 tff(986,plain,
% 0.55/0.73 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | c2_1(a115) | (~ndr1_0) | (~c1_1(a115)) | (~c0_1(a115)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c2_1(a115) | (~ndr1_0) | (~c1_1(a115)) | (~c0_1(a115)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(987,plain,
% 0.55/0.73 ((hskp6 | hskp3 | (~ndr1_0) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115))) <=> (hskp6 | hskp3 | c2_1(a115) | (~ndr1_0) | (~c1_1(a115)) | (~c0_1(a115)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(988,plain,
% 0.55/0.73 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | c2_1(a115) | (~ndr1_0) | (~c1_1(a115)) | (~c0_1(a115))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[987])).
% 0.55/0.73 tff(989,plain,
% 0.55/0.73 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c2_1(a115) | (~ndr1_0) | (~c1_1(a115)) | (~c0_1(a115)))),
% 0.55/0.73 inference(transitivity,[status(thm)],[988, 986])).
% 0.55/0.73 tff(990,plain,
% 0.55/0.73 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(991,plain,
% 0.55/0.73 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c2_1(a115) | (~ndr1_0) | (~c1_1(a115)) | (~c0_1(a115))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[990, 989])).
% 0.55/0.73 tff(992,plain,
% 0.55/0.73 (hskp6 | hskp3 | (~c1_1(a115))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[991, 101, 985, 984, 966])).
% 0.55/0.73 tff(993,plain,
% 0.55/0.73 (~c1_1(a115)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[992, 23, 956])).
% 0.55/0.73 tff(994,plain,
% 0.55/0.73 (~c3_1(a115)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[114, 983])).
% 0.55/0.73 tff(995,plain,
% 0.55/0.73 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | c1_1(a115))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp1 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | c1_1(a115))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(996,plain,
% 0.55/0.73 ((hskp1 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | c1_1(a115)) <=> (hskp1 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | c1_1(a115))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(997,plain,
% 0.55/0.73 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | c1_1(a115))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | c1_1(a115)))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[996])).
% 0.55/0.73 tff(998,plain,
% 0.55/0.73 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | c1_1(a115))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp1 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | c1_1(a115))),
% 0.55/0.73 inference(transitivity,[status(thm)],[997, 995])).
% 0.55/0.73 tff(999,plain,
% 0.55/0.73 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | c1_1(a115))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1000,plain,
% 0.55/0.73 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp1 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | c1_1(a115)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[999, 998])).
% 0.55/0.73 tff(1001,plain,
% 0.55/0.73 (hskp1 | c1_1(a115)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1000, 101, 984, 994, 225])).
% 0.55/0.73 tff(1002,plain,
% 0.55/0.73 (hskp1),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1001, 993])).
% 0.55/0.73 tff(1003,plain,
% 0.55/0.73 (c2_1(a97)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[172, 1002])).
% 0.55/0.73 tff(1004,plain,
% 0.55/0.73 (c3_1(a97)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[164, 1002])).
% 0.55/0.73 tff(1005,plain,
% 0.55/0.73 (~c1_1(a97)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[156, 1002])).
% 0.55/0.73 tff(1006,assumption,(~hskp6), introduced(assumption)).
% 0.55/0.73 tff(1007,plain,
% 0.55/0.73 (~c1_1(a115)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[992, 1006, 23])).
% 0.55/0.73 tff(1008,assumption,(c3_1(a97)), introduced(assumption)).
% 0.55/0.73 tff(1009,assumption,(c2_1(a97)), introduced(assumption)).
% 0.55/0.73 tff(1010,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)) | c1_1(a115))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)) | c1_1(a115))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1011,plain,
% 0.55/0.73 ((hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a115) | c2_1(a115) | c1_1(a115)) <=> (hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)) | c1_1(a115))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1012,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a115) | c2_1(a115) | c1_1(a115))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)) | c1_1(a115)))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1011])).
% 0.55/0.73 tff(1013,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a115) | c2_1(a115) | c1_1(a115))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)) | c1_1(a115))),
% 0.55/0.73 inference(transitivity,[status(thm)],[1012, 1010])).
% 0.55/0.73 tff(1014,plain,
% 0.55/0.73 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a115) | c2_1(a115) | c1_1(a115))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1015,plain,
% 0.55/0.73 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)) | c1_1(a115)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 0.55/0.73 tff(1016,plain,
% 0.55/0.73 (hskp3 | (~c0_1(a97)) | c1_1(a115)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1015, 101, 1009, 1008, 984, 994, 296])).
% 0.55/0.73 tff(1017,plain,
% 0.55/0.73 (~c0_1(a97)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1016, 1007, 23])).
% 0.55/0.73 tff(1018,assumption,(~c1_1(a97)), introduced(assumption)).
% 0.55/0.73 tff(1019,plain,
% 0.55/0.73 (hskp3 | hskp2 | c0_1(a97)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[349, 101, 1008, 1018, 343])).
% 0.55/0.73 tff(1020,plain,
% 0.55/0.73 (hskp2),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1019, 1017, 23])).
% 0.55/0.73 tff(1021,plain,
% 0.55/0.73 (~c3_1(a98)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[358, 1020])).
% 0.55/0.73 tff(1022,plain,
% 0.55/0.73 (~c0_1(a98)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[364, 1020])).
% 0.55/0.73 tff(1023,plain,
% 0.55/0.73 (c1_1(a98)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[373, 1020])).
% 0.55/0.73 tff(1024,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a116) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c2_1(a98)) | (~c3_1(a116)) | (~c1_1(a116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c2_1(a98)) | (~c3_1(a116)) | (~c1_1(a116)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1025,plain,
% 0.55/0.73 (((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a98) | (~c1_1(a98)) | (~c2_1(a98)) | c3_1(a98) | c0_1(a98) | (~c2_1(a98))) <=> (c0_1(a116) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c2_1(a98)) | (~c3_1(a116)) | (~c1_1(a116)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1026,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a98) | (~c1_1(a98)) | (~c2_1(a98)) | c3_1(a98) | c0_1(a98) | (~c2_1(a98)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a116) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c2_1(a98)) | (~c3_1(a116)) | (~c1_1(a116))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1025])).
% 0.55/0.73 tff(1027,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a98) | (~c1_1(a98)) | (~c2_1(a98)) | c3_1(a98) | c0_1(a98) | (~c2_1(a98)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c2_1(a98)) | (~c3_1(a116)) | (~c1_1(a116)))),
% 0.55/0.73 inference(transitivity,[status(thm)],[1026, 1024])).
% 0.55/0.73 tff(1028,plain,
% 0.55/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a98) | (~c1_1(a98)) | (~c2_1(a98)) | c3_1(a98) | c0_1(a98) | (~c2_1(a98)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1029,plain,
% 0.55/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c2_1(a98)) | (~c3_1(a116)) | (~c1_1(a116))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 0.55/0.73 tff(1030,plain,
% 0.55/0.73 (~c2_1(a98)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1029, 101, 905, 897, 1023, 925, 1022, 1021, 638])).
% 0.55/0.73 tff(1031,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c0_1(a98) | c3_1(a98) | (~ndr1_0) | c2_1(a98) | (~c1_1(a98)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a98) | c3_1(a98) | (~ndr1_0) | c2_1(a98) | (~c1_1(a98)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1032,plain,
% 0.55/0.73 ((hskp6 | (~ndr1_0) | c2_1(a98) | c0_1(a98) | (~c1_1(a98)) | c3_1(a98) | c2_1(a98) | c0_1(a98)) <=> (hskp6 | c0_1(a98) | c3_1(a98) | (~ndr1_0) | c2_1(a98) | (~c1_1(a98)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1033,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a98) | c0_1(a98) | (~c1_1(a98)) | c3_1(a98) | c2_1(a98) | c0_1(a98))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c0_1(a98) | c3_1(a98) | (~ndr1_0) | c2_1(a98) | (~c1_1(a98))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1032])).
% 0.55/0.73 tff(1034,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a98) | c0_1(a98) | (~c1_1(a98)) | c3_1(a98) | c2_1(a98) | c0_1(a98))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a98) | c3_1(a98) | (~ndr1_0) | c2_1(a98) | (~c1_1(a98)))),
% 0.55/0.73 inference(transitivity,[status(thm)],[1033, 1031])).
% 0.55/0.73 tff(1035,plain,
% 0.55/0.73 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a98) | c0_1(a98) | (~c1_1(a98)) | c3_1(a98) | c2_1(a98) | c0_1(a98))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1036,plain,
% 0.55/0.73 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a98) | c3_1(a98) | (~ndr1_0) | c2_1(a98) | (~c1_1(a98))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 0.55/0.73 tff(1037,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1036, 101, 1006, 1023, 1022, 1021, 557, 1030])).
% 0.55/0.73 tff(1038,plain,(hskp6 | hskp3 | (~c3_1(a97)) | c1_1(a97) | (~c2_1(a97))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1039,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1038, 1005, 1004, 956, 23, 1003])).
% 0.55/0.73 tff(1040,plain,(hskp3), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1041,plain,
% 0.55/0.73 (~c3_1(a99)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[390, 1040])).
% 0.55/0.73 tff(1042,plain,
% 0.55/0.73 (~c1_1(a99)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[396, 1040])).
% 0.55/0.73 tff(1043,plain,
% 0.55/0.73 (c2_1(a99)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[404, 1040])).
% 0.55/0.73 tff(1044,plain,
% 0.55/0.73 (~c0_1(a99)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[768, 101, 1043, 1042, 1041, 21])).
% 0.55/0.73 tff(1045,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a116) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1046,plain,
% 0.55/0.73 (((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99))) <=> (c0_1(a116) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1047,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a116) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1046])).
% 0.55/0.73 tff(1048,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.55/0.74 inference(transitivity,[status(thm)],[1047, 1045])).
% 0.55/0.74 tff(1049,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99)))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(1050,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 0.55/0.74 tff(1051,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1050, 101, 905, 897, 1043, 925, 1041, 638, 1044, 913])).
% 0.55/0.74 % SZS output end Proof
% 0.55/0.74 % E exiting
%------------------------------------------------------------------------------