%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN500-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:22 AM UTC 2025
% Result : Unsatisfiable 1.20s 1.40s
% Output : Proof 1.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN500-1 : TPTP v9.0.0. Released v2.1.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:37:03 EDT 2025
% 0.11/0.32 % CPUTime :
% 1.20/1.40 % SZS status Unsatisfiable
% 1.20/1.40 % SZS output start Proof
% 1.20/1.40 tff(c3_1_type, type, (
% 1.20/1.40 c3_1: $i > $o)).
% 1.20/1.40 tff(a5_type, type, (
% 1.20/1.40 a5: $i)).
% 1.20/1.40 tff(a2_type, type, (
% 1.20/1.40 a2: $i)).
% 1.20/1.40 tff(c1_1_type, type, (
% 1.20/1.40 c1_1: $i > $o)).
% 1.20/1.40 tff(c0_1_type, type, (
% 1.20/1.40 c0_1: $i > $o)).
% 1.20/1.40 tff(c2_1_type, type, (
% 1.20/1.40 c2_1: $i > $o)).
% 1.20/1.40 tff(ndr1_0_type, type, (
% 1.20/1.40 ndr1_0: $o)).
% 1.20/1.40 tff(hskp1_type, type, (
% 1.20/1.40 hskp1: $o)).
% 1.20/1.40 tff(hskp5_type, type, (
% 1.20/1.40 hskp5: $o)).
% 1.20/1.40 tff(hskp3_type, type, (
% 1.20/1.40 hskp3: $o)).
% 1.20/1.40 tff(a19_type, type, (
% 1.20/1.40 a19: $i)).
% 1.20/1.40 tff(hskp11_type, type, (
% 1.20/1.40 hskp11: $o)).
% 1.20/1.40 tff(hskp12_type, type, (
% 1.20/1.40 hskp12: $o)).
% 1.20/1.40 tff(a20_type, type, (
% 1.20/1.40 a20: $i)).
% 1.20/1.40 tff(a1_type, type, (
% 1.20/1.40 a1: $i)).
% 1.20/1.40 tff(a47_type, type, (
% 1.20/1.40 a47: $i)).
% 1.20/1.40 tff(hskp21_type, type, (
% 1.20/1.40 hskp21: $o)).
% 1.20/1.40 tff(a23_type, type, (
% 1.20/1.40 a23: $i)).
% 1.20/1.40 tff(hskp28_type, type, (
% 1.20/1.40 hskp28: $o)).
% 1.20/1.40 tff(hskp4_type, type, (
% 1.20/1.40 hskp4: $o)).
% 1.20/1.40 tff(a7_type, type, (
% 1.20/1.40 a7: $i)).
% 1.20/1.40 tff(a8_type, type, (
% 1.20/1.40 a8: $i)).
% 1.20/1.40 tff(hskp19_type, type, (
% 1.20/1.40 hskp19: $o)).
% 1.20/1.40 tff(hskp29_type, type, (
% 1.20/1.40 hskp29: $o)).
% 1.20/1.40 tff(hskp24_type, type, (
% 1.20/1.40 hskp24: $o)).
% 1.20/1.40 tff(hskp0_type, type, (
% 1.20/1.40 hskp0: $o)).
% 1.20/1.40 tff(hskp22_type, type, (
% 1.20/1.40 hskp22: $o)).
% 1.20/1.40 tff(a48_type, type, (
% 1.20/1.40 a48: $i)).
% 1.20/1.40 tff(a18_type, type, (
% 1.20/1.40 a18: $i)).
% 1.20/1.40 tff(hskp10_type, type, (
% 1.20/1.40 hskp10: $o)).
% 1.20/1.40 tff(a40_type, type, (
% 1.20/1.40 a40: $i)).
% 1.20/1.40 tff(a3_type, type, (
% 1.20/1.40 a3: $i)).
% 1.20/1.40 tff(hskp2_type, type, (
% 1.20/1.40 hskp2: $o)).
% 1.20/1.40 tff(a11_type, type, (
% 1.20/1.40 a11: $i)).
% 1.20/1.40 tff(hskp7_type, type, (
% 1.20/1.40 hskp7: $o)).
% 1.20/1.40 tff(hskp6_type, type, (
% 1.20/1.40 hskp6: $o)).
% 1.20/1.40 tff(a13_type, type, (
% 1.20/1.40 a13: $i)).
% 1.20/1.40 tff(hskp27_type, type, (
% 1.20/1.40 hskp27: $o)).
% 1.20/1.40 tff(hskp9_type, type, (
% 1.20/1.40 hskp9: $o)).
% 1.20/1.40 tff(a15_type, type, (
% 1.20/1.40 a15: $i)).
% 1.20/1.40 tff(a43_type, type, (
% 1.20/1.40 a43: $i)).
% 1.20/1.40 tff(a73_type, type, (
% 1.20/1.40 a73: $i)).
% 1.20/1.40 tff(hskp25_type, type, (
% 1.20/1.40 hskp25: $o)).
% 1.20/1.40 tff(a10_type, type, (
% 1.20/1.40 a10: $i)).
% 1.20/1.40 tff(a33_type, type, (
% 1.20/1.40 a33: $i)).
% 1.20/1.40 tff(hskp17_type, type, (
% 1.20/1.40 hskp17: $o)).
% 1.20/1.40 tff(a64_type, type, (
% 1.20/1.40 a64: $i)).
% 1.20/1.40 tff(a28_type, type, (
% 1.20/1.40 a28: $i)).
% 1.20/1.40 tff(hskp15_type, type, (
% 1.20/1.40 hskp15: $o)).
% 1.20/1.40 tff(a77_type, type, (
% 1.20/1.40 a77: $i)).
% 1.20/1.40 tff(hskp20_type, type, (
% 1.20/1.40 hskp20: $o)).
% 1.20/1.40 tff(a22_type, type, (
% 1.20/1.40 a22: $i)).
% 1.20/1.40 tff(hskp13_type, type, (
% 1.20/1.40 hskp13: $o)).
% 1.20/1.40 tff(a25_type, type, (
% 1.20/1.40 a25: $i)).
% 1.20/1.40 tff(hskp14_type, type, (
% 1.20/1.40 hskp14: $o)).
% 1.20/1.40 tff(a4_type, type, (
% 1.20/1.40 a4: $i)).
% 1.20/1.40 tff(hskp26_type, type, (
% 1.20/1.40 hskp26: $o)).
% 1.20/1.40 tff(a32_type, type, (
% 1.20/1.40 a32: $i)).
% 1.20/1.40 tff(hskp16_type, type, (
% 1.20/1.40 hskp16: $o)).
% 1.20/1.40 tff(1,assumption,(~c3_1(a2)), introduced(assumption)).
% 1.20/1.40 tff(2,plain,
% 1.20/1.40 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 1.20/1.40 inference(bind,[status(th)],[])).
% 1.20/1.40 tff(3,plain,
% 1.20/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.20/1.40 inference(quant_intro,[status(thm)],[2])).
% 1.20/1.40 tff(4,plain,
% 1.20/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(5,plain,
% 1.20/1.40 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 1.20/1.40 inference(bind,[status(th)],[])).
% 1.20/1.40 tff(6,plain,
% 1.20/1.40 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.20/1.40 inference(quant_intro,[status(thm)],[5])).
% 1.20/1.40 tff(7,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.20/1.40 tff(8,plain,
% 1.20/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 1.20/1.40 tff(9,plain,
% 1.20/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.20/1.40 tff(10,plain,(
% 1.20/1.40 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.20/1.40 inference(skolemize,[status(sab)],[9])).
% 1.20/1.40 tff(11,plain,
% 1.20/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[10, 3])).
% 1.20/1.40 tff(12,plain,
% 1.20/1.40 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.20/1.40 inference(bind,[status(th)],[])).
% 1.20/1.40 tff(13,plain,
% 1.20/1.40 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.20/1.40 inference(quant_intro,[status(thm)],[12])).
% 1.20/1.40 tff(14,plain,
% 1.20/1.40 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(15,plain,
% 1.20/1.40 (^[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) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.20/1.40 inference(bind,[status(th)],[])).
% 1.20/1.40 tff(16,plain,
% 1.20/1.40 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.20/1.40 inference(quant_intro,[status(thm)],[15])).
% 1.20/1.40 tff(17,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 1.20/1.40 tff(18,plain,
% 1.20/1.40 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.20/1.40 tff(19,plain,
% 1.20/1.40 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.20/1.40 tff(20,plain,(
% 1.20/1.40 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.20/1.40 inference(skolemize,[status(sab)],[19])).
% 1.20/1.40 tff(21,plain,
% 1.20/1.40 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.20/1.40 tff(22,plain,
% 1.20/1.40 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.20/1.40 inference(bind,[status(th)],[])).
% 1.20/1.40 tff(23,plain,
% 1.20/1.40 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.20/1.40 inference(quant_intro,[status(thm)],[22])).
% 1.20/1.40 tff(24,plain,
% 1.20/1.40 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(25,plain,
% 1.20/1.40 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.20/1.41 inference(bind,[status(th)],[])).
% 1.20/1.41 tff(26,plain,
% 1.20/1.41 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.20/1.41 inference(quant_intro,[status(thm)],[25])).
% 1.20/1.41 tff(27,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 1.20/1.41 tff(28,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.20/1.41 tff(29,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.20/1.41 tff(30,plain,(
% 1.20/1.41 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.20/1.41 inference(skolemize,[status(sab)],[29])).
% 1.20/1.41 tff(31,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.20/1.41 tff(32,assumption,(~hskp1), introduced(assumption)).
% 1.20/1.41 tff(33,assumption,(~c0_1(a20)), introduced(assumption)).
% 1.20/1.41 tff(34,plain,
% 1.20/1.41 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.20/1.41 inference(bind,[status(th)],[])).
% 1.20/1.41 tff(35,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.20/1.41 inference(quant_intro,[status(thm)],[34])).
% 1.20/1.41 tff(36,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(37,plain,
% 1.20/1.41 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp12) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp12))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.20/1.41 inference(bind,[status(th)],[])).
% 1.20/1.41 tff(38,plain,
% 1.20/1.41 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.20/1.41 inference(quant_intro,[status(thm)],[37])).
% 1.20/1.41 tff(39,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 1.20/1.41 tff(40,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.20/1.41 tff(41,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.20/1.41 tff(42,plain,(
% 1.20/1.41 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.20/1.41 inference(skolemize,[status(sab)],[41])).
% 1.20/1.41 tff(43,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[42, 35])).
% 1.20/1.41 tff(44,assumption,(~c3_1(a20)), introduced(assumption)).
% 1.20/1.41 tff(45,assumption,(~c0_1(a7)), introduced(assumption)).
% 1.20/1.41 tff(46,assumption,(~hskp12), introduced(assumption)).
% 1.20/1.41 tff(47,plain,
% 1.20/1.41 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.20/1.41 inference(bind,[status(th)],[])).
% 1.20/1.41 tff(48,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.20/1.41 inference(quant_intro,[status(thm)],[47])).
% 1.20/1.41 tff(49,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(50,plain,
% 1.20/1.41 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.20/1.41 inference(bind,[status(th)],[])).
% 1.20/1.41 tff(51,plain,
% 1.20/1.41 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.20/1.41 inference(quant_intro,[status(thm)],[50])).
% 1.20/1.41 tff(52,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 1.20/1.41 tff(53,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.20/1.41 tff(54,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[53, 49])).
% 1.20/1.41 tff(55,plain,(
% 1.20/1.41 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.20/1.41 inference(skolemize,[status(sab)],[54])).
% 1.20/1.41 tff(56,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[55, 48])).
% 1.20/1.41 tff(57,assumption,(~c1_1(a7)), introduced(assumption)).
% 1.20/1.41 tff(58,assumption,(~c3_1(a7)), introduced(assumption)).
% 1.20/1.41 tff(59,assumption,(~ndr1_0), introduced(assumption)).
% 1.20/1.41 tff(60,plain,
% 1.20/1.41 ((ndr1_0 | (~hskp19)) <=> (ndr1_0 | (~hskp19))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(61,plain,
% 1.20/1.41 (((~hskp19) | ndr1_0) <=> (ndr1_0 | (~hskp19))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(62,axiom,((~hskp19) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause12')).
% 1.20/1.41 tff(63,plain,
% 1.20/1.41 (ndr1_0 | (~hskp19)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.20/1.41 tff(64,plain,
% 1.20/1.41 (ndr1_0 | (~hskp19)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[63, 60])).
% 1.20/1.41 tff(65,plain,
% 1.20/1.41 (~hskp19),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[64, 59])).
% 1.20/1.41 tff(66,plain,
% 1.20/1.41 (((~hskp29) | ndr1_0) <=> ((~hskp29) | ndr1_0)),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(67,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 1.20/1.41 tff(68,plain,
% 1.20/1.41 ((~hskp29) | ndr1_0),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.20/1.41 tff(69,plain,
% 1.20/1.41 ((~hskp29) | ndr1_0),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[68, 66])).
% 1.20/1.41 tff(70,plain,
% 1.20/1.41 ((~hskp29) | ndr1_0),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[69, 66])).
% 1.20/1.41 tff(71,plain,
% 1.20/1.41 ((~hskp29) | ndr1_0),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[70, 66])).
% 1.20/1.41 tff(72,plain,
% 1.20/1.41 ((~hskp29) | ndr1_0),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[71, 66])).
% 1.20/1.41 tff(73,plain,
% 1.20/1.41 (~hskp29),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[72, 59])).
% 1.20/1.41 tff(74,plain,
% 1.20/1.41 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(75,plain,
% 1.20/1.41 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(76,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause7')).
% 1.20/1.41 tff(77,plain,
% 1.20/1.41 (ndr1_0 | (~hskp24)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.20/1.41 tff(78,plain,
% 1.20/1.41 (ndr1_0 | (~hskp24)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[77, 74])).
% 1.20/1.41 tff(79,plain,
% 1.20/1.41 (~hskp24),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[78, 59])).
% 1.20/1.41 tff(80,plain,
% 1.20/1.41 ((hskp29 | hskp24 | hskp19) <=> (hskp29 | hskp24 | hskp19)),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(81,plain,
% 1.20/1.41 (((hskp29 | hskp24) | hskp19) <=> (hskp29 | hskp24 | hskp19)),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(82,plain,
% 1.20/1.41 ((hskp29 | hskp24) <=> (hskp29 | hskp24)),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(83,plain,
% 1.20/1.41 (((hskp29 | hskp24) | hskp19) <=> ((hskp29 | hskp24) | hskp19)),
% 1.20/1.41 inference(monotonicity,[status(thm)],[82])).
% 1.20/1.41 tff(84,plain,
% 1.20/1.41 (((hskp29 | hskp24) | hskp19) <=> (hskp29 | hskp24 | hskp19)),
% 1.20/1.41 inference(transitivity,[status(thm)],[83, 81])).
% 1.20/1.41 tff(85,axiom,((hskp29 | hskp24) | hskp19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 1.20/1.41 tff(86,plain,
% 1.20/1.41 (hskp29 | hskp24 | hskp19),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.20/1.41 tff(87,plain,
% 1.20/1.41 (hskp29 | hskp24 | hskp19),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[86, 80])).
% 1.20/1.41 tff(88,plain,
% 1.20/1.41 (hskp29 | hskp24 | hskp19),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[87, 80])).
% 1.20/1.41 tff(89,plain,
% 1.20/1.41 (hskp29 | hskp24 | hskp19),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[88, 80])).
% 1.20/1.41 tff(90,plain,
% 1.20/1.41 (hskp29 | hskp24 | hskp19),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[89, 80])).
% 1.20/1.41 tff(91,plain,
% 1.20/1.41 ($false),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[90, 79, 73, 65])).
% 1.20/1.41 tff(92,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.20/1.41 tff(93,assumption,(hskp11), introduced(assumption)).
% 1.20/1.41 tff(94,plain,
% 1.20/1.41 (((~hskp11) | (~c0_1(a19))) <=> ((~hskp11) | (~c0_1(a19)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(95,plain,
% 1.20/1.41 (((~c0_1(a19)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a19)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(96,axiom,((~c0_1(a19)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.20/1.41 tff(97,plain,
% 1.20/1.41 ((~hskp11) | (~c0_1(a19))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.20/1.41 tff(98,plain,
% 1.20/1.41 ((~hskp11) | (~c0_1(a19))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[97, 94])).
% 1.20/1.41 tff(99,plain,
% 1.20/1.41 (~c0_1(a19)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[98, 93])).
% 1.20/1.41 tff(100,assumption,(ndr1_0), introduced(assumption)).
% 1.20/1.41 tff(101,plain,
% 1.20/1.41 (((~hskp11) | c1_1(a19)) <=> ((~hskp11) | c1_1(a19))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(102,axiom,((~hskp11) | c1_1(a19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.20/1.41 tff(103,plain,
% 1.20/1.41 ((~hskp11) | c1_1(a19)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.20/1.41 tff(104,plain,
% 1.20/1.41 ((~hskp11) | c1_1(a19)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[103, 101])).
% 1.20/1.41 tff(105,plain,
% 1.20/1.41 ((~hskp11) | c1_1(a19)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[104, 101])).
% 1.20/1.41 tff(106,plain,
% 1.20/1.41 ((~hskp11) | c1_1(a19)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[105, 101])).
% 1.20/1.41 tff(107,plain,
% 1.20/1.41 ((~hskp11) | c1_1(a19)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[106, 101])).
% 1.20/1.41 tff(108,plain,
% 1.20/1.41 (c1_1(a19)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[107, 93])).
% 1.20/1.41 tff(109,plain,
% 1.20/1.41 (((~hskp11) | c2_1(a19)) <=> ((~hskp11) | c2_1(a19))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(110,axiom,((~hskp11) | c2_1(a19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.20/1.41 tff(111,plain,
% 1.20/1.41 ((~hskp11) | c2_1(a19)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.20/1.41 tff(112,plain,
% 1.20/1.41 ((~hskp11) | c2_1(a19)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[111, 109])).
% 1.20/1.41 tff(113,plain,
% 1.20/1.41 ((~hskp11) | c2_1(a19)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[112, 109])).
% 1.20/1.41 tff(114,plain,
% 1.20/1.41 ((~hskp11) | c2_1(a19)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[113, 109])).
% 1.20/1.41 tff(115,plain,
% 1.20/1.41 ((~hskp11) | c2_1(a19)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[114, 109])).
% 1.20/1.41 tff(116,plain,
% 1.20/1.41 (c2_1(a19)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[115, 93])).
% 1.20/1.41 tff(117,plain,
% 1.20/1.41 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.20/1.41 inference(bind,[status(th)],[])).
% 1.20/1.41 tff(118,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.20/1.41 inference(quant_intro,[status(thm)],[117])).
% 1.20/1.41 tff(119,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(120,plain,
% 1.20/1.41 (^[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) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.20/1.41 inference(bind,[status(th)],[])).
% 1.20/1.41 tff(121,plain,
% 1.20/1.41 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.20/1.41 inference(quant_intro,[status(thm)],[120])).
% 1.20/1.41 tff(122,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 1.20/1.41 tff(123,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.20/1.41 tff(124,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[123, 119])).
% 1.20/1.41 tff(125,plain,(
% 1.20/1.41 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.20/1.41 inference(skolemize,[status(sab)],[124])).
% 1.20/1.41 tff(126,plain,
% 1.20/1.41 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[125, 118])).
% 1.20/1.41 tff(127,assumption,(~c0_1(a19)), introduced(assumption)).
% 1.20/1.41 tff(128,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a19) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a19) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(129,plain,
% 1.20/1.41 ((hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a7) | c0_1(a7) | c3_1(a7)) <=> (hskp1 | c0_1(a19) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(130,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a19) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[129])).
% 1.20/1.41 tff(131,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a19) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.20/1.41 inference(transitivity,[status(thm)],[130, 128])).
% 1.20/1.41 tff(132,plain,
% 1.20/1.41 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a7) | c0_1(a7) | c3_1(a7))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(133,plain,
% 1.20/1.41 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a19) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[132, 131])).
% 1.20/1.41 tff(134,plain,
% 1.20/1.41 (hskp1 | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[133, 127, 45, 57, 58, 126])).
% 1.20/1.41 tff(135,plain,
% 1.20/1.41 ($false),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[134, 116, 108, 32, 100])).
% 1.20/1.41 tff(136,plain,((~hskp11) | hskp1 | (~ndr1_0) | c0_1(a19) | c0_1(a7) | c1_1(a7) | c3_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.41 tff(137,plain,
% 1.20/1.41 ($false),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[136, 99, 93, 92, 32, 45, 57, 58])).
% 1.20/1.41 tff(138,plain,((~hskp11) | hskp1 | c0_1(a7) | c1_1(a7) | c3_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.41 tff(139,plain,
% 1.20/1.41 (~hskp11),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[138, 58, 45, 57, 32])).
% 1.20/1.41 tff(140,assumption,(hskp22), introduced(assumption)).
% 1.20/1.41 tff(141,plain,
% 1.20/1.41 (((~hskp22) | (~c0_1(a48))) <=> ((~hskp22) | (~c0_1(a48)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(142,plain,
% 1.20/1.41 (((~c0_1(a48)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a48)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(143,axiom,((~c0_1(a48)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.20/1.41 tff(144,plain,
% 1.20/1.41 ((~hskp22) | (~c0_1(a48))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.20/1.41 tff(145,plain,
% 1.20/1.41 ((~hskp22) | (~c0_1(a48))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[144, 141])).
% 1.20/1.41 tff(146,plain,
% 1.20/1.41 (~c0_1(a48)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[145, 140])).
% 1.20/1.41 tff(147,plain,
% 1.20/1.41 (((~hskp22) | c1_1(a48)) <=> ((~hskp22) | c1_1(a48))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(148,axiom,((~hskp22) | c1_1(a48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.20/1.41 tff(149,plain,
% 1.20/1.41 ((~hskp22) | c1_1(a48)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.20/1.41 tff(150,plain,
% 1.20/1.41 ((~hskp22) | c1_1(a48)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[149, 147])).
% 1.20/1.41 tff(151,plain,
% 1.20/1.41 ((~hskp22) | c1_1(a48)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[150, 147])).
% 1.20/1.41 tff(152,plain,
% 1.20/1.41 ((~hskp22) | c1_1(a48)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[151, 147])).
% 1.20/1.41 tff(153,plain,
% 1.20/1.41 ((~hskp22) | c1_1(a48)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[152, 147])).
% 1.20/1.41 tff(154,plain,
% 1.20/1.41 (c1_1(a48)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[153, 140])).
% 1.20/1.41 tff(155,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a48) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a48) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(156,plain,
% 1.20/1.41 ((hskp1 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a7) | c0_1(a7) | c3_1(a7)) <=> (hskp1 | c0_1(a48) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(157,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a48) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[156])).
% 1.20/1.41 tff(158,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a48) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.20/1.42 inference(transitivity,[status(thm)],[157, 155])).
% 1.20/1.42 tff(159,plain,
% 1.20/1.42 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a7) | c0_1(a7) | c3_1(a7))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(160,plain,
% 1.20/1.42 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a48) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[159, 158])).
% 1.20/1.42 tff(161,plain,
% 1.20/1.42 (~c2_1(a48)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[160, 92, 32, 154, 146, 45, 57, 58, 126])).
% 1.20/1.42 tff(162,plain,
% 1.20/1.42 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.20/1.42 inference(bind,[status(th)],[])).
% 1.20/1.42 tff(163,plain,
% 1.20/1.42 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.42 inference(quant_intro,[status(thm)],[162])).
% 1.20/1.42 tff(164,plain,
% 1.20/1.42 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(165,plain,
% 1.20/1.42 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.20/1.42 inference(bind,[status(th)],[])).
% 1.20/1.42 tff(166,plain,
% 1.20/1.42 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.42 inference(quant_intro,[status(thm)],[165])).
% 1.20/1.42 tff(167,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 1.20/1.42 tff(168,plain,
% 1.20/1.42 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.20/1.42 tff(169,plain,
% 1.20/1.42 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[168, 164])).
% 1.20/1.42 tff(170,plain,(
% 1.20/1.42 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.42 inference(skolemize,[status(sab)],[169])).
% 1.20/1.42 tff(171,plain,
% 1.20/1.42 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[170, 163])).
% 1.20/1.42 tff(172,plain,
% 1.20/1.42 (((~hskp22) | (~c3_1(a48))) <=> ((~hskp22) | (~c3_1(a48)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(173,plain,
% 1.20/1.42 (((~c3_1(a48)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a48)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(174,axiom,((~c3_1(a48)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 1.20/1.42 tff(175,plain,
% 1.20/1.42 ((~hskp22) | (~c3_1(a48))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[174, 173])).
% 1.20/1.42 tff(176,plain,
% 1.20/1.42 ((~hskp22) | (~c3_1(a48))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[175, 172])).
% 1.20/1.42 tff(177,plain,
% 1.20/1.42 (~c3_1(a48)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[176, 140])).
% 1.20/1.42 tff(178,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c3_1(a48) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a48)) | c2_1(a48))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c3_1(a48) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a48)) | c2_1(a48))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(179,plain,
% 1.20/1.42 ((hskp1 | (~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7))) <=> (hskp1 | c3_1(a48) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a48)) | c2_1(a48))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(180,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c3_1(a48) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a48)) | c2_1(a48)))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[179])).
% 1.20/1.42 tff(181,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c3_1(a48) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a48)) | c2_1(a48))),
% 1.20/1.42 inference(transitivity,[status(thm)],[180, 178])).
% 1.20/1.42 tff(182,plain,
% 1.20/1.42 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(183,plain,
% 1.20/1.42 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c3_1(a48) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a48)) | c2_1(a48)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[182, 181])).
% 1.20/1.42 tff(184,plain,
% 1.20/1.42 (~c2_1(a7)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[183, 92, 32, 154, 177, 57, 58, 171, 161])).
% 1.20/1.42 tff(185,plain,
% 1.20/1.42 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_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) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.20/1.42 inference(bind,[status(th)],[])).
% 1.20/1.42 tff(186,plain,
% 1.20/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.20/1.42 inference(quant_intro,[status(thm)],[185])).
% 1.20/1.42 tff(187,plain,
% 1.20/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(188,plain,
% 1.20/1.42 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | 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)) | (~ndr1_0)) | c2_1(U)) | c3_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)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | 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)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_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) | c3_1(U) | c2_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) | c3_1(U) | c2_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)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.20/1.42 inference(bind,[status(th)],[])).
% 1.20/1.42 tff(189,plain,
% 1.20/1.42 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.20/1.42 inference(quant_intro,[status(thm)],[188])).
% 1.20/1.42 tff(190,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 1.20/1.42 tff(191,plain,
% 1.20/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[190, 189])).
% 1.20/1.42 tff(192,plain,
% 1.20/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[191, 187])).
% 1.20/1.42 tff(193,plain,(
% 1.20/1.42 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.20/1.42 inference(skolemize,[status(sab)],[192])).
% 1.20/1.42 tff(194,plain,
% 1.20/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[193, 186])).
% 1.20/1.42 tff(195,plain,
% 1.20/1.42 (^[U: $i] : refl((hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.20/1.42 inference(bind,[status(th)],[])).
% 1.20/1.42 tff(196,plain,
% 1.20/1.42 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.20/1.42 inference(quant_intro,[status(thm)],[195])).
% 1.20/1.42 tff(197,plain,
% 1.20/1.42 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(198,plain,
% 1.20/1.42 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | 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) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp10) <=> ((hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp10))), rewrite(((hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp10) <=> (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp10) <=> (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.20/1.42 inference(bind,[status(th)],[])).
% 1.20/1.42 tff(199,plain,
% 1.20/1.42 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp10) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.20/1.42 inference(quant_intro,[status(thm)],[198])).
% 1.20/1.42 tff(200,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.20/1.42 tff(201,plain,
% 1.20/1.42 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.20/1.42 tff(202,plain,
% 1.20/1.42 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[201, 197])).
% 1.20/1.42 tff(203,plain,(
% 1.20/1.42 ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.20/1.42 inference(skolemize,[status(sab)],[202])).
% 1.20/1.42 tff(204,plain,
% 1.20/1.42 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[203, 196])).
% 1.20/1.42 tff(205,plain,
% 1.20/1.42 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | c0_1(a48) | (~ndr1_0) | (~c1_1(a48)) | c2_1(a48))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c0_1(a48) | (~ndr1_0) | (~c1_1(a48)) | c2_1(a48))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(206,plain,
% 1.20/1.42 ((hskp10 | hskp1 | (~ndr1_0) | c0_1(a48) | c2_1(a48) | (~c1_1(a48))) <=> (hskp10 | hskp1 | c0_1(a48) | (~ndr1_0) | (~c1_1(a48)) | c2_1(a48))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(207,plain,
% 1.20/1.42 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a48) | c2_1(a48) | (~c1_1(a48)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | c0_1(a48) | (~ndr1_0) | (~c1_1(a48)) | c2_1(a48)))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[206])).
% 1.20/1.42 tff(208,plain,
% 1.20/1.42 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a48) | c2_1(a48) | (~c1_1(a48)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c0_1(a48) | (~ndr1_0) | (~c1_1(a48)) | c2_1(a48))),
% 1.20/1.42 inference(transitivity,[status(thm)],[207, 205])).
% 1.20/1.42 tff(209,plain,
% 1.20/1.42 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a48) | c2_1(a48) | (~c1_1(a48)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(210,plain,
% 1.20/1.42 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c0_1(a48) | (~ndr1_0) | (~c1_1(a48)) | c2_1(a48)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[209, 208])).
% 1.20/1.42 tff(211,plain,
% 1.20/1.42 (hskp10 | c2_1(a48)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[210, 92, 32, 154, 146, 204])).
% 1.20/1.42 tff(212,plain,
% 1.20/1.42 (hskp10),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[211, 161])).
% 1.20/1.42 tff(213,plain,
% 1.20/1.42 (((~hskp10) | (~c3_1(a18))) <=> ((~hskp10) | (~c3_1(a18)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(214,plain,
% 1.20/1.42 (((~c3_1(a18)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a18)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(215,axiom,((~c3_1(a18)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 1.20/1.42 tff(216,plain,
% 1.20/1.42 ((~hskp10) | (~c3_1(a18))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.20/1.42 tff(217,plain,
% 1.20/1.42 ((~hskp10) | (~c3_1(a18))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[216, 213])).
% 1.20/1.42 tff(218,plain,
% 1.20/1.42 (~c3_1(a18)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[217, 212])).
% 1.20/1.42 tff(219,plain,
% 1.20/1.42 (((~hskp10) | (~c2_1(a18))) <=> ((~hskp10) | (~c2_1(a18)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(220,plain,
% 1.20/1.42 (((~c2_1(a18)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a18)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(221,axiom,((~c2_1(a18)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.20/1.42 tff(222,plain,
% 1.20/1.42 ((~hskp10) | (~c2_1(a18))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[221, 220])).
% 1.20/1.42 tff(223,plain,
% 1.20/1.42 ((~hskp10) | (~c2_1(a18))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[222, 219])).
% 1.20/1.42 tff(224,plain,
% 1.20/1.42 (~c2_1(a18)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[223, 212])).
% 1.20/1.42 tff(225,plain,
% 1.20/1.42 (((~hskp10) | (~c1_1(a18))) <=> ((~hskp10) | (~c1_1(a18)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(226,plain,
% 1.20/1.42 (((~c1_1(a18)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a18)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(227,axiom,((~c1_1(a18)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.20/1.42 tff(228,plain,
% 1.20/1.42 ((~hskp10) | (~c1_1(a18))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.20/1.42 tff(229,plain,
% 1.20/1.42 ((~hskp10) | (~c1_1(a18))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[228, 225])).
% 1.20/1.42 tff(230,plain,
% 1.20/1.42 (~c1_1(a18)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[229, 212])).
% 1.20/1.42 tff(231,plain,
% 1.20/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a48) | c1_1(a18) | c2_1(a18) | c3_1(a18) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a48)) | c2_1(a48))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a48) | c1_1(a18) | c2_1(a18) | c3_1(a18) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a48)) | c2_1(a48))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(232,plain,
% 1.20/1.42 (((~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a18) | c1_1(a18) | c3_1(a18) | c2_1(a7) | c1_1(a7) | c0_1(a7)) <=> (c3_1(a48) | c1_1(a18) | c2_1(a18) | c3_1(a18) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a48)) | c2_1(a48))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(233,plain,
% 1.20/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a18) | c1_1(a18) | c3_1(a18) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a48) | c1_1(a18) | c2_1(a18) | c3_1(a18) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a48)) | c2_1(a48)))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[232])).
% 1.20/1.42 tff(234,plain,
% 1.20/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a18) | c1_1(a18) | c3_1(a18) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a48) | c1_1(a18) | c2_1(a18) | c3_1(a18) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a48)) | c2_1(a48))),
% 1.20/1.42 inference(transitivity,[status(thm)],[233, 231])).
% 1.20/1.42 tff(235,plain,
% 1.20/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a18) | c1_1(a18) | c3_1(a18) | c2_1(a7) | c1_1(a7) | c0_1(a7))),
% 1.20/1.43 inference(quant_inst,[status(thm)],[])).
% 1.20/1.43 tff(236,plain,
% 1.20/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a48) | c1_1(a18) | c2_1(a18) | c3_1(a18) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a48)) | c2_1(a48)),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[235, 234])).
% 1.20/1.43 tff(237,plain,
% 1.20/1.43 ($false),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[236, 92, 154, 177, 230, 224, 218, 45, 57, 194, 184, 161])).
% 1.20/1.43 tff(238,plain,((~hskp22) | c0_1(a7) | c1_1(a7) | hskp1 | c3_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.43 tff(239,plain,
% 1.20/1.43 (~hskp22),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[238, 58, 57, 32, 45])).
% 1.20/1.43 tff(240,plain,
% 1.20/1.43 ((hskp22 | hskp11 | hskp0) <=> (hskp22 | hskp11 | hskp0)),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(241,plain,
% 1.20/1.43 (((hskp11 | hskp0) | hskp22) <=> (hskp22 | hskp11 | hskp0)),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(242,plain,
% 1.20/1.43 ((hskp11 | hskp0) <=> (hskp11 | hskp0)),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(243,plain,
% 1.20/1.43 (((hskp11 | hskp0) | hskp22) <=> ((hskp11 | hskp0) | hskp22)),
% 1.20/1.43 inference(monotonicity,[status(thm)],[242])).
% 1.20/1.43 tff(244,plain,
% 1.20/1.43 (((hskp11 | hskp0) | hskp22) <=> (hskp22 | hskp11 | hskp0)),
% 1.20/1.43 inference(transitivity,[status(thm)],[243, 241])).
% 1.20/1.43 tff(245,axiom,((hskp11 | hskp0) | hskp22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 1.20/1.43 tff(246,plain,
% 1.20/1.43 (hskp22 | hskp11 | hskp0),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[245, 244])).
% 1.20/1.43 tff(247,plain,
% 1.20/1.43 (hskp22 | hskp11 | hskp0),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[246, 240])).
% 1.20/1.43 tff(248,plain,
% 1.20/1.43 (hskp22 | hskp11 | hskp0),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[247, 240])).
% 1.20/1.43 tff(249,plain,
% 1.20/1.43 (hskp22 | hskp11 | hskp0),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[248, 240])).
% 1.20/1.43 tff(250,plain,
% 1.20/1.43 (hskp22 | hskp11 | hskp0),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[249, 240])).
% 1.20/1.43 tff(251,plain,
% 1.20/1.43 (hskp0),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[250, 139, 239])).
% 1.20/1.43 tff(252,plain,
% 1.20/1.43 (((~hskp0) | (~c2_1(a1))) <=> ((~hskp0) | (~c2_1(a1)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(253,plain,
% 1.20/1.43 (((~c2_1(a1)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(254,axiom,((~c2_1(a1)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.20/1.43 tff(255,plain,
% 1.20/1.43 ((~hskp0) | (~c2_1(a1))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[254, 253])).
% 1.20/1.43 tff(256,plain,
% 1.20/1.43 ((~hskp0) | (~c2_1(a1))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[255, 252])).
% 1.20/1.43 tff(257,plain,
% 1.20/1.43 (~c2_1(a1)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[256, 251])).
% 1.20/1.43 tff(258,plain,
% 1.20/1.43 (((~hskp0) | c3_1(a1)) <=> ((~hskp0) | c3_1(a1))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(259,axiom,((~hskp0) | c3_1(a1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.25/1.43 tff(260,plain,
% 1.25/1.43 ((~hskp0) | c3_1(a1)),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[259, 258])).
% 1.25/1.43 tff(261,plain,
% 1.25/1.43 ((~hskp0) | c3_1(a1)),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[260, 258])).
% 1.25/1.43 tff(262,plain,
% 1.25/1.43 ((~hskp0) | c3_1(a1)),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[261, 258])).
% 1.25/1.43 tff(263,plain,
% 1.25/1.43 ((~hskp0) | c3_1(a1)),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[262, 258])).
% 1.25/1.43 tff(264,plain,
% 1.25/1.43 ((~hskp0) | c3_1(a1)),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[263, 258])).
% 1.25/1.43 tff(265,plain,
% 1.25/1.43 (c3_1(a1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[264, 251])).
% 1.25/1.43 tff(266,plain,
% 1.25/1.43 (((~hskp0) | c1_1(a1)) <=> ((~hskp0) | c1_1(a1))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(267,axiom,((~hskp0) | c1_1(a1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.25/1.43 tff(268,plain,
% 1.25/1.43 ((~hskp0) | c1_1(a1)),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[267, 266])).
% 1.25/1.43 tff(269,plain,
% 1.25/1.43 ((~hskp0) | c1_1(a1)),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[268, 266])).
% 1.25/1.43 tff(270,plain,
% 1.25/1.43 ((~hskp0) | c1_1(a1)),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[269, 266])).
% 1.25/1.43 tff(271,plain,
% 1.25/1.43 ((~hskp0) | c1_1(a1)),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[270, 266])).
% 1.25/1.43 tff(272,plain,
% 1.25/1.43 ((~hskp0) | c1_1(a1)),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[271, 266])).
% 1.25/1.43 tff(273,plain,
% 1.25/1.43 (c1_1(a1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[272, 251])).
% 1.25/1.43 tff(274,assumption,(~hskp11), introduced(assumption)).
% 1.25/1.43 tff(275,plain,
% 1.25/1.43 (^[U: $i] : refl((hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))),
% 1.25/1.43 inference(bind,[status(th)],[])).
% 1.25/1.43 tff(276,plain,
% 1.25/1.43 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.25/1.43 inference(quant_intro,[status(thm)],[275])).
% 1.25/1.43 tff(277,plain,
% 1.25/1.43 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(278,plain,
% 1.25/1.43 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> ((hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp12))), rewrite(((hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))))),
% 1.25/1.43 inference(bind,[status(th)],[])).
% 1.25/1.43 tff(279,plain,
% 1.25/1.43 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.25/1.43 inference(quant_intro,[status(thm)],[278])).
% 1.25/1.43 tff(280,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.25/1.43 tff(281,plain,
% 1.25/1.43 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[280, 279])).
% 1.25/1.43 tff(282,plain,
% 1.25/1.43 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[281, 277])).
% 1.25/1.43 tff(283,plain,(
% 1.25/1.43 ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.25/1.43 inference(skolemize,[status(sab)],[282])).
% 1.25/1.43 tff(284,plain,
% 1.25/1.43 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[283, 276])).
% 1.25/1.43 tff(285,plain,
% 1.25/1.43 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp12 | hskp11 | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp12 | hskp11 | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(286,plain,
% 1.25/1.43 ((hskp12 | hskp11 | (~ndr1_0) | c3_1(a7) | c1_1(a7) | c2_1(a7)) <=> (hskp12 | hskp11 | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(287,plain,
% 1.25/1.43 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a7) | c1_1(a7) | c2_1(a7))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp12 | hskp11 | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7)))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[286])).
% 1.25/1.43 tff(288,plain,
% 1.25/1.43 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a7) | c1_1(a7) | c2_1(a7))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp12 | hskp11 | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7))),
% 1.25/1.43 inference(transitivity,[status(thm)],[287, 285])).
% 1.25/1.43 tff(289,plain,
% 1.25/1.43 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a7) | c1_1(a7) | c2_1(a7))),
% 1.25/1.43 inference(quant_inst,[status(thm)],[])).
% 1.25/1.43 tff(290,plain,
% 1.25/1.43 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp12 | hskp11 | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7)),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[289, 288])).
% 1.25/1.43 tff(291,plain,
% 1.25/1.43 (hskp12 | hskp11 | c3_1(a7) | c2_1(a7)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[290, 92, 57, 284])).
% 1.25/1.43 tff(292,plain,
% 1.25/1.43 (c2_1(a7)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[291, 46, 58, 274])).
% 1.25/1.43 tff(293,plain,
% 1.25/1.43 (^[U: $i] : refl((hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.25/1.43 inference(bind,[status(th)],[])).
% 1.25/1.43 tff(294,plain,
% 1.25/1.43 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.25/1.43 inference(quant_intro,[status(thm)],[293])).
% 1.25/1.43 tff(295,plain,
% 1.25/1.43 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(296,plain,
% 1.25/1.43 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | 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) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp11))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) | hskp12) <=> ((hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp12))), rewrite(((hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.25/1.43 inference(bind,[status(th)],[])).
% 1.25/1.43 tff(297,plain,
% 1.25/1.43 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) | hskp12) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.25/1.43 inference(quant_intro,[status(thm)],[296])).
% 1.25/1.43 tff(298,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.25/1.43 tff(299,plain,
% 1.25/1.43 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[298, 297])).
% 1.25/1.43 tff(300,plain,
% 1.25/1.43 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[299, 295])).
% 1.25/1.43 tff(301,plain,(
% 1.25/1.43 ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.25/1.43 inference(skolemize,[status(sab)],[300])).
% 1.25/1.43 tff(302,plain,
% 1.25/1.43 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[301, 294])).
% 1.25/1.43 tff(303,assumption,(~c2_1(a1)), introduced(assumption)).
% 1.25/1.43 tff(304,assumption,(c1_1(a1)), introduced(assumption)).
% 1.25/1.43 tff(305,plain,
% 1.25/1.43 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp12 | hskp11 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(306,plain,
% 1.25/1.43 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a1) | c2_1(a1) | (~c1_1(a1))) <=> (hskp12 | hskp11 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(307,plain,
% 1.25/1.43 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a1) | c2_1(a1) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1)))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[306])).
% 1.25/1.43 tff(308,plain,
% 1.25/1.43 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a1) | c2_1(a1) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp12 | hskp11 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1))),
% 1.25/1.43 inference(transitivity,[status(thm)],[307, 305])).
% 1.25/1.43 tff(309,plain,
% 1.25/1.43 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a1) | c2_1(a1) | (~c1_1(a1)))),
% 1.25/1.43 inference(quant_inst,[status(thm)],[])).
% 1.25/1.43 tff(310,plain,
% 1.25/1.43 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp12 | hskp11 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1)),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[309, 308])).
% 1.25/1.43 tff(311,plain,
% 1.25/1.43 (hskp12 | c0_1(a1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[310, 92, 274, 304, 303, 302])).
% 1.25/1.43 tff(312,plain,
% 1.25/1.43 (c0_1(a1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[311, 46])).
% 1.25/1.43 tff(313,plain,
% 1.25/1.43 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))))),
% 1.25/1.43 inference(bind,[status(th)],[])).
% 1.25/1.43 tff(314,plain,
% 1.25/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.25/1.43 inference(quant_intro,[status(thm)],[313])).
% 1.25/1.43 tff(315,plain,
% 1.25/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(316,plain,
% 1.25/1.43 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))))),
% 1.25/1.43 inference(bind,[status(th)],[])).
% 1.25/1.43 tff(317,plain,
% 1.25/1.43 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.25/1.43 inference(quant_intro,[status(thm)],[316])).
% 1.25/1.43 tff(318,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 1.25/1.43 tff(319,plain,
% 1.25/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[318, 317])).
% 1.25/1.43 tff(320,plain,
% 1.25/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[319, 315])).
% 1.25/1.43 tff(321,plain,(
% 1.25/1.43 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.25/1.43 inference(skolemize,[status(sab)],[320])).
% 1.25/1.43 tff(322,plain,
% 1.25/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[321, 314])).
% 1.25/1.43 tff(323,assumption,(c3_1(a1)), introduced(assumption)).
% 1.25/1.43 tff(324,plain,
% 1.25/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a7) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | (~c2_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a7) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | (~c2_1(a7)))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(325,plain,
% 1.25/1.43 (((~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c2_1(a1) | (~c3_1(a1)) | (~c0_1(a1)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7))) <=> (c1_1(a7) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | (~c2_1(a7)))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(326,plain,
% 1.25/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c2_1(a1) | (~c3_1(a1)) | (~c0_1(a1)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a7) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | (~c2_1(a7))))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[325])).
% 1.25/1.43 tff(327,plain,
% 1.25/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c2_1(a1) | (~c3_1(a1)) | (~c0_1(a1)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a7) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | (~c2_1(a7)))),
% 1.25/1.43 inference(transitivity,[status(thm)],[326, 324])).
% 1.25/1.43 tff(328,plain,
% 1.25/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c2_1(a1) | (~c3_1(a1)) | (~c0_1(a1)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)))),
% 1.25/1.43 inference(quant_inst,[status(thm)],[])).
% 1.25/1.43 tff(329,plain,
% 1.25/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a7) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | (~c2_1(a7))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[328, 327])).
% 1.25/1.43 tff(330,plain,
% 1.25/1.43 ((~c0_1(a1)) | (~c2_1(a7))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[329, 92, 304, 323, 57, 58, 303, 322])).
% 1.25/1.43 tff(331,plain,
% 1.25/1.43 ($false),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[330, 312, 292])).
% 1.25/1.43 tff(332,plain,(hskp12 | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a7) | c3_1(a7) | c2_1(a1) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.25/1.43 tff(333,plain,
% 1.25/1.43 (hskp12),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[332, 273, 265, 57, 58, 257, 139])).
% 1.25/1.43 tff(334,plain,
% 1.25/1.43 (((~hskp12) | (~c0_1(a20))) <=> ((~hskp12) | (~c0_1(a20)))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(335,plain,
% 1.25/1.43 (((~c0_1(a20)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a20)))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(336,axiom,((~c0_1(a20)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.25/1.43 tff(337,plain,
% 1.25/1.43 ((~hskp12) | (~c0_1(a20))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[336, 335])).
% 1.25/1.43 tff(338,plain,
% 1.25/1.43 ((~hskp12) | (~c0_1(a20))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[337, 334])).
% 1.25/1.43 tff(339,plain,
% 1.25/1.43 (~c0_1(a20)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[338, 333])).
% 1.25/1.43 tff(340,plain,
% 1.25/1.43 (((~hskp12) | (~c2_1(a20))) <=> ((~hskp12) | (~c2_1(a20)))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(341,plain,
% 1.25/1.43 (((~c2_1(a20)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a20)))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(342,axiom,((~c2_1(a20)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.25/1.43 tff(343,plain,
% 1.25/1.43 ((~hskp12) | (~c2_1(a20))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[342, 341])).
% 1.25/1.43 tff(344,plain,
% 1.25/1.43 ((~hskp12) | (~c2_1(a20))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[343, 340])).
% 1.25/1.43 tff(345,plain,
% 1.25/1.43 (~c2_1(a20)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[344, 333])).
% 1.25/1.43 tff(346,plain,
% 1.25/1.43 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.25/1.43 inference(bind,[status(th)],[])).
% 1.25/1.43 tff(347,plain,
% 1.25/1.43 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.25/1.44 inference(quant_intro,[status(thm)],[346])).
% 1.25/1.44 tff(348,plain,
% 1.25/1.44 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(349,plain,
% 1.25/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.25/1.44 inference(bind,[status(th)],[])).
% 1.25/1.44 tff(350,plain,
% 1.25/1.44 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.25/1.44 inference(quant_intro,[status(thm)],[349])).
% 1.25/1.44 tff(351,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 1.25/1.44 tff(352,plain,
% 1.25/1.44 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[351, 350])).
% 1.25/1.44 tff(353,plain,
% 1.25/1.44 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[352, 348])).
% 1.25/1.44 tff(354,plain,(
% 1.25/1.44 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.25/1.44 inference(skolemize,[status(sab)],[353])).
% 1.25/1.44 tff(355,plain,
% 1.25/1.44 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[354, 347])).
% 1.25/1.44 tff(356,plain,
% 1.25/1.44 (hskp0),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[250, 274, 239])).
% 1.25/1.44 tff(357,plain,
% 1.25/1.44 (~c2_1(a1)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[256, 356])).
% 1.25/1.44 tff(358,plain,
% 1.25/1.44 (c3_1(a1)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[264, 356])).
% 1.25/1.44 tff(359,plain,
% 1.25/1.44 (c1_1(a1)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[272, 356])).
% 1.25/1.44 tff(360,plain,
% 1.25/1.44 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(361,plain,
% 1.25/1.44 ((hskp2 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a7) | c0_1(a7) | c3_1(a7)) <=> (hskp2 | c0_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(362,plain,
% 1.25/1.44 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1))))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[361])).
% 1.25/1.44 tff(363,plain,
% 1.25/1.44 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)))),
% 1.25/1.44 inference(transitivity,[status(thm)],[362, 360])).
% 1.25/1.44 tff(364,plain,
% 1.25/1.44 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a7) | c0_1(a7) | c3_1(a7))),
% 1.25/1.44 inference(quant_inst,[status(thm)],[])).
% 1.25/1.44 tff(365,plain,
% 1.25/1.44 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[364, 363])).
% 1.25/1.44 tff(366,plain,
% 1.25/1.44 (hskp2),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[365, 92, 359, 358, 45, 57, 58, 357, 355])).
% 1.25/1.44 tff(367,plain,
% 1.25/1.44 (((~hskp2) | c3_1(a3)) <=> ((~hskp2) | c3_1(a3))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(368,axiom,((~hskp2) | c3_1(a3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.25/1.44 tff(369,plain,
% 1.25/1.44 ((~hskp2) | c3_1(a3)),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.25/1.44 tff(370,plain,
% 1.25/1.44 ((~hskp2) | c3_1(a3)),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[369, 367])).
% 1.25/1.44 tff(371,plain,
% 1.25/1.44 ((~hskp2) | c3_1(a3)),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[370, 367])).
% 1.25/1.44 tff(372,plain,
% 1.25/1.44 ((~hskp2) | c3_1(a3)),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[371, 367])).
% 1.25/1.44 tff(373,plain,
% 1.25/1.44 ((~hskp2) | c3_1(a3)),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[372, 367])).
% 1.25/1.44 tff(374,plain,
% 1.25/1.44 (c3_1(a3)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[373, 366])).
% 1.25/1.44 tff(375,assumption,(~c0_1(a15)), introduced(assumption)).
% 1.25/1.44 tff(376,assumption,(~hskp22), introduced(assumption)).
% 1.25/1.44 tff(377,plain,
% 1.25/1.44 (hskp0),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[250, 376, 274])).
% 1.25/1.44 tff(378,plain,
% 1.25/1.44 (~c2_1(a1)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[256, 377])).
% 1.25/1.44 tff(379,plain,
% 1.25/1.44 (c3_1(a1)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[264, 377])).
% 1.25/1.44 tff(380,plain,
% 1.25/1.44 (c1_1(a1)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[272, 377])).
% 1.25/1.44 tff(381,plain,
% 1.25/1.44 (hskp12),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[332, 380, 379, 57, 58, 378, 274])).
% 1.25/1.44 tff(382,plain,
% 1.25/1.44 (~c0_1(a20)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[338, 381])).
% 1.25/1.44 tff(383,plain,
% 1.25/1.44 (~c2_1(a20)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[344, 381])).
% 1.25/1.44 tff(384,plain,
% 1.25/1.44 (((~hskp12) | (~c3_1(a20))) <=> ((~hskp12) | (~c3_1(a20)))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(385,plain,
% 1.25/1.44 (((~c3_1(a20)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a20)))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(386,axiom,((~c3_1(a20)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.25/1.44 tff(387,plain,
% 1.25/1.44 ((~hskp12) | (~c3_1(a20))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[386, 385])).
% 1.25/1.44 tff(388,plain,
% 1.25/1.44 ((~hskp12) | (~c3_1(a20))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[387, 384])).
% 1.25/1.44 tff(389,plain,
% 1.25/1.44 (~c3_1(a20)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[388, 381])).
% 1.25/1.44 tff(390,assumption,(~c2_1(a20)), introduced(assumption)).
% 1.25/1.44 tff(391,assumption,(~c1_1(a18)), introduced(assumption)).
% 1.25/1.44 tff(392,plain,
% 1.25/1.44 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 1.25/1.44 inference(bind,[status(th)],[])).
% 1.25/1.44 tff(393,plain,
% 1.25/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.25/1.44 inference(quant_intro,[status(thm)],[392])).
% 1.25/1.44 tff(394,plain,
% 1.25/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(395,plain,
% 1.25/1.44 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | 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)) | (~c1_1(U))) | (~ndr1_0)) | (~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)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 1.25/1.44 inference(bind,[status(th)],[])).
% 1.25/1.44 tff(396,plain,
% 1.25/1.44 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.25/1.44 inference(quant_intro,[status(thm)],[395])).
% 1.25/1.44 tff(397,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.25/1.44 tff(398,plain,
% 1.25/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[397, 396])).
% 1.25/1.44 tff(399,plain,
% 1.25/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[398, 394])).
% 1.25/1.44 tff(400,plain,(
% 1.25/1.44 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.25/1.44 inference(skolemize,[status(sab)],[399])).
% 1.25/1.44 tff(401,plain,
% 1.25/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[400, 393])).
% 1.25/1.44 tff(402,assumption,(~c2_1(a18)), introduced(assumption)).
% 1.25/1.44 tff(403,plain,
% 1.25/1.44 (^[U: $i] : refl((hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.25/1.44 inference(bind,[status(th)],[])).
% 1.25/1.44 tff(404,plain,
% 1.25/1.44 (![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.25/1.44 inference(quant_intro,[status(thm)],[403])).
% 1.25/1.44 tff(405,plain,
% 1.25/1.44 (![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(406,plain,
% 1.25/1.44 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp9) <=> ((hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp9))), rewrite(((hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp9) <=> (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp9) <=> (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.25/1.44 inference(bind,[status(th)],[])).
% 1.25/1.44 tff(407,plain,
% 1.25/1.44 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp9) <=> ![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.25/1.44 inference(quant_intro,[status(thm)],[406])).
% 1.25/1.44 tff(408,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 1.25/1.44 tff(409,plain,
% 1.25/1.44 (![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[408, 407])).
% 1.25/1.44 tff(410,plain,
% 1.25/1.44 (![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[409, 405])).
% 1.25/1.44 tff(411,plain,(
% 1.25/1.44 ![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.25/1.44 inference(skolemize,[status(sab)],[410])).
% 1.25/1.44 tff(412,plain,
% 1.25/1.44 (![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[411, 404])).
% 1.25/1.44 tff(413,assumption,(~c3_1(a18)), introduced(assumption)).
% 1.25/1.44 tff(414,assumption,(~c1_1(a15)), introduced(assumption)).
% 1.25/1.44 tff(415,plain,
% 1.25/1.44 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.25/1.44 inference(bind,[status(th)],[])).
% 1.25/1.44 tff(416,plain,
% 1.25/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.25/1.44 inference(quant_intro,[status(thm)],[415])).
% 1.25/1.44 tff(417,plain,
% 1.25/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(418,plain,
% 1.25/1.44 (^[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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.25/1.44 inference(bind,[status(th)],[])).
% 1.25/1.44 tff(419,plain,
% 1.25/1.44 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.25/1.44 inference(quant_intro,[status(thm)],[418])).
% 1.25/1.44 tff(420,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 1.25/1.44 tff(421,plain,
% 1.25/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[420, 419])).
% 1.25/1.44 tff(422,plain,
% 1.25/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[421, 417])).
% 1.25/1.44 tff(423,plain,(
% 1.25/1.44 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.25/1.44 inference(skolemize,[status(sab)],[422])).
% 1.25/1.44 tff(424,plain,
% 1.25/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[423, 416])).
% 1.25/1.44 tff(425,plain,
% 1.25/1.44 (hskp2),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[365, 92, 380, 379, 45, 57, 58, 378, 355])).
% 1.25/1.44 tff(426,plain,
% 1.25/1.44 (((~hskp2) | (~c1_1(a3))) <=> ((~hskp2) | (~c1_1(a3)))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(427,plain,
% 1.25/1.44 (((~c1_1(a3)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a3)))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(428,axiom,((~c1_1(a3)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.25/1.45 tff(429,plain,
% 1.25/1.45 ((~hskp2) | (~c1_1(a3))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[428, 427])).
% 1.25/1.45 tff(430,plain,
% 1.25/1.45 ((~hskp2) | (~c1_1(a3))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[429, 426])).
% 1.25/1.45 tff(431,plain,
% 1.25/1.45 (~c1_1(a3)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[430, 425])).
% 1.25/1.45 tff(432,assumption,(~c2_1(a15)), introduced(assumption)).
% 1.25/1.45 tff(433,plain,
% 1.25/1.45 (c3_1(a3)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[373, 425])).
% 1.25/1.45 tff(434,plain,
% 1.25/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a15) | c1_1(a15) | c2_1(a15) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a15) | c1_1(a15) | c2_1(a15) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(435,plain,
% 1.25/1.45 (((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a15) | c1_1(a15) | c0_1(a15)) <=> (c0_1(a15) | c1_1(a15) | c2_1(a15) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(436,plain,
% 1.25/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a15) | c1_1(a15) | c2_1(a15) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3))))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[435])).
% 1.25/1.45 tff(437,plain,
% 1.25/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a15) | c1_1(a15) | c2_1(a15) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)))),
% 1.25/1.45 inference(transitivity,[status(thm)],[436, 434])).
% 1.25/1.45 tff(438,plain,
% 1.25/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a15) | c1_1(a15) | c0_1(a15))),
% 1.25/1.45 inference(quant_inst,[status(thm)],[])).
% 1.25/1.45 tff(439,plain,
% 1.25/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a15) | c1_1(a15) | c2_1(a15) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[438, 437])).
% 1.25/1.45 tff(440,plain,
% 1.25/1.45 (~c0_1(a3)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[439, 92, 433, 380, 379, 375, 414, 432, 431, 378, 424])).
% 1.25/1.45 tff(441,plain,
% 1.25/1.45 (^[U: $i] : refl((hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 1.25/1.45 inference(bind,[status(th)],[])).
% 1.25/1.45 tff(442,plain,
% 1.25/1.45 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.25/1.45 inference(quant_intro,[status(thm)],[441])).
% 1.25/1.45 tff(443,plain,
% 1.25/1.45 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(444,plain,
% 1.25/1.45 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp27) <=> ((hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp27))), rewrite(((hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp27) <=> (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp27) <=> (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 1.25/1.45 inference(bind,[status(th)],[])).
% 1.25/1.45 tff(445,plain,
% 1.25/1.45 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp27) <=> ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.25/1.45 inference(quant_intro,[status(thm)],[444])).
% 1.25/1.45 tff(446,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.25/1.45 tff(447,plain,
% 1.25/1.45 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[446, 445])).
% 1.25/1.45 tff(448,plain,
% 1.25/1.45 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[447, 443])).
% 1.25/1.45 tff(449,plain,(
% 1.25/1.45 ![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.25/1.45 inference(skolemize,[status(sab)],[448])).
% 1.25/1.45 tff(450,plain,
% 1.25/1.45 (![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[449, 442])).
% 1.25/1.45 tff(451,plain,
% 1.25/1.45 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp1 | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp1 | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(452,plain,
% 1.25/1.45 ((hskp27 | hskp1 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | c2_1(a20)) <=> (hskp27 | hskp1 | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(453,plain,
% 1.25/1.45 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | c2_1(a20))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp1 | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0)))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[452])).
% 1.25/1.45 tff(454,plain,
% 1.25/1.45 (((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | c2_1(a20))) <=> ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp1 | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0))),
% 1.25/1.45 inference(transitivity,[status(thm)],[453, 451])).
% 1.25/1.45 tff(455,plain,
% 1.25/1.45 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp1 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | c2_1(a20))),
% 1.25/1.45 inference(quant_inst,[status(thm)],[])).
% 1.25/1.45 tff(456,plain,
% 1.25/1.45 ((~![U: $i] : (hskp27 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp1 | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[455, 454])).
% 1.25/1.45 tff(457,plain,
% 1.25/1.45 (hskp27 | c2_1(a20) | c3_1(a20)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[456, 92, 32, 33, 450])).
% 1.25/1.45 tff(458,plain,
% 1.25/1.45 (hskp27),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[457, 44, 390])).
% 1.25/1.45 tff(459,plain,
% 1.25/1.45 (((~hskp27) | c1_1(a13)) <=> ((~hskp27) | c1_1(a13))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(460,axiom,((~hskp27) | c1_1(a13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 1.25/1.45 tff(461,plain,
% 1.25/1.45 ((~hskp27) | c1_1(a13)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[460, 459])).
% 1.25/1.45 tff(462,plain,
% 1.25/1.45 ((~hskp27) | c1_1(a13)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[461, 459])).
% 1.25/1.45 tff(463,plain,
% 1.25/1.45 ((~hskp27) | c1_1(a13)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[462, 459])).
% 1.25/1.45 tff(464,plain,
% 1.25/1.45 ((~hskp27) | c1_1(a13)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[463, 459])).
% 1.25/1.45 tff(465,plain,
% 1.25/1.45 ((~hskp27) | c1_1(a13)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[464, 459])).
% 1.25/1.45 tff(466,plain,
% 1.25/1.45 (c1_1(a13)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[465, 458])).
% 1.25/1.45 tff(467,plain,
% 1.25/1.45 (((~hskp27) | c3_1(a13)) <=> ((~hskp27) | c3_1(a13))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(468,axiom,((~hskp27) | c3_1(a13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.25/1.45 tff(469,plain,
% 1.25/1.45 ((~hskp27) | c3_1(a13)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[468, 467])).
% 1.25/1.45 tff(470,plain,
% 1.25/1.45 ((~hskp27) | c3_1(a13)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[469, 467])).
% 1.25/1.45 tff(471,plain,
% 1.25/1.45 ((~hskp27) | c3_1(a13)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[470, 467])).
% 1.25/1.45 tff(472,plain,
% 1.25/1.45 ((~hskp27) | c3_1(a13)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[471, 467])).
% 1.25/1.45 tff(473,plain,
% 1.25/1.45 ((~hskp27) | c3_1(a13)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[472, 467])).
% 1.25/1.45 tff(474,plain,
% 1.25/1.45 (c3_1(a13)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[473, 458])).
% 1.25/1.45 tff(475,plain,
% 1.25/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c1_1(a18) | c2_1(a18) | c3_1(a18) | c0_1(a15) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c1_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c1_1(a18) | c2_1(a18) | c3_1(a18) | c0_1(a15) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c1_1(a20)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(476,plain,
% 1.25/1.45 (((~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a18) | c1_1(a18) | c3_1(a18) | c2_1(a15) | c1_1(a15) | c0_1(a15)) <=> (c2_1(a20) | c3_1(a20) | c1_1(a18) | c2_1(a18) | c3_1(a18) | c0_1(a15) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c1_1(a20)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(477,plain,
% 1.25/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a18) | c1_1(a18) | c3_1(a18) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c1_1(a18) | c2_1(a18) | c3_1(a18) | c0_1(a15) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c1_1(a20))))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[476])).
% 1.25/1.45 tff(478,plain,
% 1.25/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a18) | c1_1(a18) | c3_1(a18) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c1_1(a18) | c2_1(a18) | c3_1(a18) | c0_1(a15) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c1_1(a20)))),
% 1.25/1.45 inference(transitivity,[status(thm)],[477, 475])).
% 1.25/1.45 tff(479,plain,
% 1.25/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a18) | c1_1(a18) | c3_1(a18) | c2_1(a15) | c1_1(a15) | c0_1(a15))),
% 1.25/1.45 inference(quant_inst,[status(thm)],[])).
% 1.25/1.45 tff(480,plain,
% 1.25/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c1_1(a18) | c2_1(a18) | c3_1(a18) | c0_1(a15) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c1_1(a20))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[479, 478])).
% 1.25/1.45 tff(481,plain,
% 1.25/1.45 (~c1_1(a20)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[480, 92, 390, 44, 391, 402, 413, 375, 414, 432, 194])).
% 1.25/1.45 tff(482,assumption,(~c0_1(a3)), introduced(assumption)).
% 1.25/1.45 tff(483,plain,
% 1.25/1.45 (((~hskp2) | (~c2_1(a3))) <=> ((~hskp2) | (~c2_1(a3)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(484,plain,
% 1.25/1.45 (((~c2_1(a3)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a3)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(485,axiom,((~c2_1(a3)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.25/1.45 tff(486,plain,
% 1.25/1.45 ((~hskp2) | (~c2_1(a3))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.25/1.45 tff(487,plain,
% 1.25/1.45 ((~hskp2) | (~c2_1(a3))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[486, 483])).
% 1.25/1.45 tff(488,plain,
% 1.25/1.45 (~c2_1(a3)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[487, 425])).
% 1.25/1.45 tff(489,assumption,(hskp6), introduced(assumption)).
% 1.25/1.45 tff(490,plain,
% 1.25/1.45 (((~hskp6) | c0_1(a10)) <=> ((~hskp6) | c0_1(a10))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(491,axiom,((~hskp6) | c0_1(a10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.25/1.45 tff(492,plain,
% 1.25/1.45 ((~hskp6) | c0_1(a10)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[491, 490])).
% 1.25/1.45 tff(493,plain,
% 1.25/1.45 ((~hskp6) | c0_1(a10)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[492, 490])).
% 1.25/1.45 tff(494,plain,
% 1.25/1.45 ((~hskp6) | c0_1(a10)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[493, 490])).
% 1.25/1.45 tff(495,plain,
% 1.25/1.45 ((~hskp6) | c0_1(a10)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[494, 490])).
% 1.25/1.45 tff(496,plain,
% 1.25/1.45 ((~hskp6) | c0_1(a10)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[495, 490])).
% 1.25/1.45 tff(497,plain,
% 1.25/1.45 (c0_1(a10)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[496, 489])).
% 1.25/1.45 tff(498,assumption,(~c1_1(a20)), introduced(assumption)).
% 1.25/1.45 tff(499,plain,
% 1.25/1.45 (((~hskp6) | (~c2_1(a10))) <=> ((~hskp6) | (~c2_1(a10)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(500,plain,
% 1.25/1.45 (((~c2_1(a10)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a10)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(501,axiom,((~c2_1(a10)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.25/1.45 tff(502,plain,
% 1.25/1.45 ((~hskp6) | (~c2_1(a10))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[501, 500])).
% 1.25/1.45 tff(503,plain,
% 1.25/1.45 ((~hskp6) | (~c2_1(a10))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[502, 499])).
% 1.25/1.45 tff(504,plain,
% 1.25/1.45 (~c2_1(a10)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[503, 489])).
% 1.25/1.45 tff(505,plain,
% 1.25/1.45 (((~hskp6) | c3_1(a10)) <=> ((~hskp6) | c3_1(a10))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(506,axiom,((~hskp6) | c3_1(a10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.25/1.45 tff(507,plain,
% 1.25/1.45 ((~hskp6) | c3_1(a10)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[506, 505])).
% 1.25/1.45 tff(508,plain,
% 1.25/1.45 ((~hskp6) | c3_1(a10)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[507, 505])).
% 1.25/1.45 tff(509,plain,
% 1.25/1.45 ((~hskp6) | c3_1(a10)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[508, 505])).
% 1.25/1.45 tff(510,plain,
% 1.25/1.45 ((~hskp6) | c3_1(a10)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[509, 505])).
% 1.25/1.45 tff(511,plain,
% 1.25/1.45 ((~hskp6) | c3_1(a10)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[510, 505])).
% 1.25/1.45 tff(512,plain,
% 1.25/1.45 (c3_1(a10)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[511, 489])).
% 1.25/1.45 tff(513,plain,
% 1.25/1.45 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.25/1.45 inference(bind,[status(th)],[])).
% 1.25/1.45 tff(514,plain,
% 1.25/1.45 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.25/1.45 inference(quant_intro,[status(thm)],[513])).
% 1.25/1.45 tff(515,plain,
% 1.25/1.45 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(516,plain,
% 1.25/1.45 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp19) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp19))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.25/1.45 inference(bind,[status(th)],[])).
% 1.25/1.45 tff(517,plain,
% 1.25/1.45 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.25/1.45 inference(quant_intro,[status(thm)],[516])).
% 1.25/1.45 tff(518,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 1.25/1.45 tff(519,plain,
% 1.25/1.45 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[518, 517])).
% 1.25/1.45 tff(520,plain,
% 1.25/1.45 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[519, 515])).
% 1.25/1.45 tff(521,plain,(
% 1.25/1.45 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.25/1.45 inference(skolemize,[status(sab)],[520])).
% 1.25/1.45 tff(522,plain,
% 1.25/1.45 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[521, 514])).
% 1.25/1.45 tff(523,assumption,(~c2_1(a3)), introduced(assumption)).
% 1.25/1.45 tff(524,assumption,(c3_1(a3)), introduced(assumption)).
% 1.25/1.45 tff(525,assumption,(~hskp19), introduced(assumption)).
% 1.25/1.45 tff(526,plain,
% 1.25/1.45 ((hskp22 | hskp19 | hskp17) <=> (hskp22 | hskp19 | hskp17)),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(527,plain,
% 1.25/1.45 (((hskp17 | hskp22) | hskp19) <=> (hskp22 | hskp19 | hskp17)),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(528,axiom,((hskp17 | hskp22) | hskp19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 1.25/1.45 tff(529,plain,
% 1.25/1.45 (hskp22 | hskp19 | hskp17),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[528, 527])).
% 1.25/1.45 tff(530,plain,
% 1.25/1.45 (hskp22 | hskp19 | hskp17),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[529, 526])).
% 1.25/1.45 tff(531,plain,
% 1.25/1.45 (hskp22 | hskp19 | hskp17),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[530, 526])).
% 1.25/1.45 tff(532,plain,
% 1.25/1.45 (hskp22 | hskp19 | hskp17),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[531, 526])).
% 1.25/1.45 tff(533,plain,
% 1.25/1.45 (hskp22 | hskp19 | hskp17),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[532, 526])).
% 1.25/1.45 tff(534,plain,
% 1.25/1.45 (hskp17),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[533, 525, 376])).
% 1.25/1.45 tff(535,plain,
% 1.25/1.45 (((~hskp17) | (~c1_1(a33))) <=> ((~hskp17) | (~c1_1(a33)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(536,plain,
% 1.25/1.45 (((~c1_1(a33)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a33)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(537,axiom,((~c1_1(a33)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.25/1.45 tff(538,plain,
% 1.25/1.45 ((~hskp17) | (~c1_1(a33))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[537, 536])).
% 1.25/1.45 tff(539,plain,
% 1.25/1.45 ((~hskp17) | (~c1_1(a33))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[538, 535])).
% 1.25/1.45 tff(540,plain,
% 1.25/1.45 (~c1_1(a33)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[539, 534])).
% 1.25/1.45 tff(541,plain,
% 1.25/1.45 (((~hskp17) | (~c3_1(a33))) <=> ((~hskp17) | (~c3_1(a33)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(542,plain,
% 1.25/1.45 (((~c3_1(a33)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a33)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(543,axiom,((~c3_1(a33)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.25/1.45 tff(544,plain,
% 1.25/1.45 ((~hskp17) | (~c3_1(a33))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[543, 542])).
% 1.25/1.45 tff(545,plain,
% 1.25/1.45 ((~hskp17) | (~c3_1(a33))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[544, 541])).
% 1.25/1.45 tff(546,plain,
% 1.25/1.45 (~c3_1(a33)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[545, 534])).
% 1.25/1.45 tff(547,assumption,(c0_1(a10)), introduced(assumption)).
% 1.25/1.45 tff(548,assumption,(~c2_1(a10)), introduced(assumption)).
% 1.25/1.45 tff(549,assumption,(c3_1(a10)), introduced(assumption)).
% 1.25/1.45 tff(550,plain,
% 1.25/1.45 (((~hskp17) | c0_1(a33)) <=> ((~hskp17) | c0_1(a33))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(551,axiom,((~hskp17) | c0_1(a33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.25/1.45 tff(552,plain,
% 1.25/1.45 ((~hskp17) | c0_1(a33)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[551, 550])).
% 1.25/1.45 tff(553,plain,
% 1.25/1.45 ((~hskp17) | c0_1(a33)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[552, 550])).
% 1.25/1.45 tff(554,plain,
% 1.25/1.45 ((~hskp17) | c0_1(a33)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[553, 550])).
% 1.25/1.45 tff(555,plain,
% 1.25/1.45 ((~hskp17) | c0_1(a33)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[554, 550])).
% 1.25/1.45 tff(556,plain,
% 1.25/1.45 ((~hskp17) | c0_1(a33)),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[555, 550])).
% 1.25/1.45 tff(557,plain,
% 1.25/1.45 (c0_1(a33)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[556, 534])).
% 1.25/1.45 tff(558,plain,
% 1.25/1.45 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_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)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(559,plain,
% 1.28/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[558])).
% 1.28/1.45 tff(560,plain,
% 1.28/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(561,plain,
% 1.28/1.45 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(562,plain,
% 1.28/1.45 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[561])).
% 1.28/1.45 tff(563,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.28/1.45 tff(564,plain,
% 1.28/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[563, 562])).
% 1.28/1.45 tff(565,plain,
% 1.28/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[564, 560])).
% 1.28/1.45 tff(566,plain,(
% 1.28/1.45 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.28/1.45 inference(skolemize,[status(sab)],[565])).
% 1.28/1.45 tff(567,plain,
% 1.28/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[566, 559])).
% 1.28/1.45 tff(568,assumption,(~c1_1(a33)), introduced(assumption)).
% 1.28/1.45 tff(569,assumption,(~c3_1(a33)), introduced(assumption)).
% 1.28/1.45 tff(570,assumption,(hskp24), introduced(assumption)).
% 1.28/1.45 tff(571,plain,
% 1.28/1.45 (((~hskp24) | (~c0_1(a64))) <=> ((~hskp24) | (~c0_1(a64)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(572,plain,
% 1.28/1.45 (((~c0_1(a64)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a64)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(573,axiom,((~c0_1(a64)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.28/1.45 tff(574,plain,
% 1.28/1.45 ((~hskp24) | (~c0_1(a64))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[573, 572])).
% 1.28/1.45 tff(575,plain,
% 1.28/1.45 ((~hskp24) | (~c0_1(a64))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[574, 571])).
% 1.28/1.45 tff(576,plain,
% 1.28/1.45 (~c0_1(a64)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[575, 570])).
% 1.28/1.45 tff(577,assumption,(c0_1(a33)), introduced(assumption)).
% 1.28/1.45 tff(578,plain,
% 1.28/1.45 (((~hskp24) | c3_1(a64)) <=> ((~hskp24) | c3_1(a64))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(579,axiom,((~hskp24) | c3_1(a64)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.28/1.45 tff(580,plain,
% 1.28/1.45 ((~hskp24) | c3_1(a64)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[579, 578])).
% 1.28/1.45 tff(581,plain,
% 1.28/1.45 ((~hskp24) | c3_1(a64)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[580, 578])).
% 1.28/1.45 tff(582,plain,
% 1.28/1.45 ((~hskp24) | c3_1(a64)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[581, 578])).
% 1.28/1.45 tff(583,plain,
% 1.28/1.45 ((~hskp24) | c3_1(a64)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[582, 578])).
% 1.28/1.45 tff(584,plain,
% 1.28/1.45 ((~hskp24) | c3_1(a64)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[583, 578])).
% 1.28/1.46 tff(585,plain,
% 1.28/1.46 (c3_1(a64)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[584, 570])).
% 1.28/1.46 tff(586,plain,
% 1.28/1.46 (((~hskp24) | c1_1(a64)) <=> ((~hskp24) | c1_1(a64))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(587,axiom,((~hskp24) | c1_1(a64)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.28/1.46 tff(588,plain,
% 1.28/1.46 ((~hskp24) | c1_1(a64)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[587, 586])).
% 1.28/1.46 tff(589,plain,
% 1.28/1.46 ((~hskp24) | c1_1(a64)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[588, 586])).
% 1.28/1.46 tff(590,plain,
% 1.28/1.46 ((~hskp24) | c1_1(a64)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[589, 586])).
% 1.28/1.46 tff(591,plain,
% 1.28/1.46 ((~hskp24) | c1_1(a64)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[590, 586])).
% 1.28/1.46 tff(592,plain,
% 1.28/1.46 ((~hskp24) | c1_1(a64)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[591, 586])).
% 1.28/1.46 tff(593,plain,
% 1.28/1.46 (c1_1(a64)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[592, 570])).
% 1.28/1.46 tff(594,assumption,(~hskp3), introduced(assumption)).
% 1.28/1.46 tff(595,plain,
% 1.28/1.46 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(596,plain,
% 1.28/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[595])).
% 1.28/1.46 tff(597,plain,
% 1.28/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(598,plain,
% 1.28/1.46 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(599,plain,
% 1.28/1.46 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[598])).
% 1.28/1.46 tff(600,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.28/1.46 tff(601,plain,
% 1.28/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[600, 599])).
% 1.28/1.46 tff(602,plain,
% 1.28/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[601, 597])).
% 1.28/1.46 tff(603,plain,(
% 1.28/1.46 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.46 inference(skolemize,[status(sab)],[602])).
% 1.28/1.46 tff(604,plain,
% 1.28/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[603, 596])).
% 1.28/1.46 tff(605,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(606,plain,
% 1.28/1.46 ((hskp3 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (hskp3 | c2_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(607,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3)))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[606])).
% 1.28/1.46 tff(608,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 1.28/1.46 inference(transitivity,[status(thm)],[607, 605])).
% 1.28/1.46 tff(609,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(610,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[609, 608])).
% 1.28/1.46 tff(611,plain,
% 1.28/1.46 (hskp3 | (~c0_1(a1)) | c0_1(a3)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[610, 92, 524, 304, 523, 303, 604])).
% 1.28/1.46 tff(612,plain,
% 1.28/1.46 (~c0_1(a1)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[611, 594, 482])).
% 1.28/1.46 tff(613,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a10) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a10)) | (~c0_1(a10)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a10) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a10)) | (~c0_1(a10)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(614,plain,
% 1.28/1.46 ((hskp3 | (~ndr1_0) | c2_1(a10) | (~c1_1(a10)) | (~c0_1(a10)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (hskp3 | c2_1(a10) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a10)) | (~c0_1(a10)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(615,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a10) | (~c1_1(a10)) | (~c0_1(a10)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a10) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a10)) | (~c0_1(a10))))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[614])).
% 1.28/1.46 tff(616,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a10) | (~c1_1(a10)) | (~c0_1(a10)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a10) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a10)) | (~c0_1(a10)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[615, 613])).
% 1.28/1.46 tff(617,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a10) | (~c1_1(a10)) | (~c0_1(a10)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(618,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a10) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a10)) | (~c0_1(a10))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[617, 616])).
% 1.28/1.46 tff(619,plain,
% 1.28/1.46 (hskp3 | (~c1_1(a10))),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[618, 92, 547, 524, 548, 523, 604, 482])).
% 1.28/1.46 tff(620,plain,
% 1.28/1.46 (~c1_1(a10)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[619, 594])).
% 1.28/1.46 tff(621,plain,
% 1.28/1.46 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(622,plain,
% 1.28/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[621])).
% 1.28/1.46 tff(623,plain,
% 1.28/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(624,plain,
% 1.28/1.46 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(625,plain,
% 1.28/1.46 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[624])).
% 1.28/1.46 tff(626,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 1.28/1.46 tff(627,plain,
% 1.28/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[626, 625])).
% 1.28/1.46 tff(628,plain,
% 1.28/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[627, 623])).
% 1.28/1.46 tff(629,plain,(
% 1.28/1.46 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.28/1.46 inference(skolemize,[status(sab)],[628])).
% 1.28/1.46 tff(630,plain,
% 1.28/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[629, 622])).
% 1.28/1.46 tff(631,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a33) | c2_1(a10) | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a33) | c2_1(a10) | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(632,plain,
% 1.28/1.46 (((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a10) | c1_1(a10) | (~c0_1(a10))) <=> (c1_1(a33) | c2_1(a10) | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(633,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a10) | c1_1(a10) | (~c0_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a33) | c2_1(a10) | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a33)) | (~c0_1(a33))))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[632])).
% 1.28/1.46 tff(634,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a10) | c1_1(a10) | (~c0_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a33) | c2_1(a10) | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[633, 631])).
% 1.28/1.46 tff(635,plain,
% 1.28/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a10) | c1_1(a10) | (~c0_1(a10)))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(636,plain,
% 1.28/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a33) | c2_1(a10) | (~ndr1_0) | c1_1(a10) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a33)) | (~c0_1(a33))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[635, 634])).
% 1.28/1.46 tff(637,plain,
% 1.28/1.46 (c1_1(a10) | (~c2_1(a33))),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[636, 92, 577, 547, 549, 568, 548, 630])).
% 1.28/1.46 tff(638,plain,
% 1.28/1.46 (~c2_1(a33)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[637, 620])).
% 1.28/1.46 tff(639,plain,
% 1.28/1.46 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(640,plain,
% 1.28/1.46 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[639])).
% 1.28/1.46 tff(641,plain,
% 1.28/1.46 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(642,plain,
% 1.28/1.46 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(643,plain,
% 1.28/1.46 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.28/1.47 inference(quant_intro,[status(thm)],[642])).
% 1.28/1.47 tff(644,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 1.28/1.47 tff(645,plain,
% 1.28/1.47 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[644, 643])).
% 1.28/1.47 tff(646,plain,
% 1.28/1.47 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[645, 641])).
% 1.28/1.47 tff(647,plain,(
% 1.28/1.47 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.28/1.47 inference(skolemize,[status(sab)],[646])).
% 1.28/1.47 tff(648,plain,
% 1.28/1.47 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[647, 640])).
% 1.28/1.47 tff(649,assumption,(~c0_1(a64)), introduced(assumption)).
% 1.28/1.47 tff(650,assumption,(c3_1(a64)), introduced(assumption)).
% 1.28/1.47 tff(651,assumption,(c1_1(a64)), introduced(assumption)).
% 1.28/1.47 tff(652,plain,
% 1.28/1.47 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a64) | c3_1(a33) | (~ndr1_0) | c2_1(a33) | (~c0_1(a33)) | (~c3_1(a64)) | (~c1_1(a64)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a64) | c3_1(a33) | (~ndr1_0) | c2_1(a33) | (~c0_1(a33)) | (~c3_1(a64)) | (~c1_1(a64)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(653,plain,
% 1.28/1.47 ((hskp15 | (~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)) | c0_1(a64) | (~c1_1(a64)) | (~c3_1(a64))) <=> (hskp15 | c0_1(a64) | c3_1(a33) | (~ndr1_0) | c2_1(a33) | (~c0_1(a33)) | (~c3_1(a64)) | (~c1_1(a64)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(654,plain,
% 1.28/1.47 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)) | c0_1(a64) | (~c1_1(a64)) | (~c3_1(a64)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a64) | c3_1(a33) | (~ndr1_0) | c2_1(a33) | (~c0_1(a33)) | (~c3_1(a64)) | (~c1_1(a64))))),
% 1.28/1.47 inference(monotonicity,[status(thm)],[653])).
% 1.28/1.47 tff(655,plain,
% 1.28/1.47 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)) | c0_1(a64) | (~c1_1(a64)) | (~c3_1(a64)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a64) | c3_1(a33) | (~ndr1_0) | c2_1(a33) | (~c0_1(a33)) | (~c3_1(a64)) | (~c1_1(a64)))),
% 1.28/1.47 inference(transitivity,[status(thm)],[654, 652])).
% 1.28/1.47 tff(656,plain,
% 1.28/1.47 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)) | c0_1(a64) | (~c1_1(a64)) | (~c3_1(a64)))),
% 1.28/1.47 inference(quant_inst,[status(thm)],[])).
% 1.28/1.47 tff(657,plain,
% 1.28/1.47 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a64) | c3_1(a33) | (~ndr1_0) | c2_1(a33) | (~c0_1(a33)) | (~c3_1(a64)) | (~c1_1(a64))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[656, 655])).
% 1.28/1.47 tff(658,plain,
% 1.28/1.47 (hskp15 | c2_1(a33)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[657, 92, 651, 650, 577, 649, 569, 648])).
% 1.28/1.47 tff(659,plain,
% 1.28/1.47 (hskp15),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[658, 638])).
% 1.28/1.47 tff(660,plain,
% 1.28/1.47 (((~hskp15) | (~c1_1(a28))) <=> ((~hskp15) | (~c1_1(a28)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(661,plain,
% 1.28/1.47 (((~c1_1(a28)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a28)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(662,axiom,((~c1_1(a28)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.28/1.47 tff(663,plain,
% 1.28/1.47 ((~hskp15) | (~c1_1(a28))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[662, 661])).
% 1.28/1.47 tff(664,plain,
% 1.28/1.47 ((~hskp15) | (~c1_1(a28))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[663, 660])).
% 1.28/1.47 tff(665,plain,
% 1.28/1.47 (~c1_1(a28)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[664, 659])).
% 1.28/1.47 tff(666,plain,
% 1.28/1.47 (((~hskp15) | c2_1(a28)) <=> ((~hskp15) | c2_1(a28))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(667,axiom,((~hskp15) | c2_1(a28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.28/1.47 tff(668,plain,
% 1.28/1.47 ((~hskp15) | c2_1(a28)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[667, 666])).
% 1.28/1.47 tff(669,plain,
% 1.28/1.47 ((~hskp15) | c2_1(a28)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[668, 666])).
% 1.28/1.47 tff(670,plain,
% 1.28/1.47 ((~hskp15) | c2_1(a28)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[669, 666])).
% 1.28/1.47 tff(671,plain,
% 1.28/1.47 ((~hskp15) | c2_1(a28)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[670, 666])).
% 1.28/1.47 tff(672,plain,
% 1.28/1.47 ((~hskp15) | c2_1(a28)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[671, 666])).
% 1.28/1.47 tff(673,plain,
% 1.28/1.47 (c2_1(a28)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[672, 659])).
% 1.28/1.47 tff(674,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a28) | c2_1(a10) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a28)) | c0_1(a28))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a28) | c2_1(a10) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a28)) | c0_1(a28))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(675,plain,
% 1.28/1.47 (((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a28) | c0_1(a28) | (~c2_1(a28))) <=> (c1_1(a28) | c2_1(a10) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a28)) | c0_1(a28))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(676,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a28) | c0_1(a28) | (~c2_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a28) | c2_1(a10) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a28)) | c0_1(a28)))),
% 1.28/1.47 inference(monotonicity,[status(thm)],[675])).
% 1.28/1.47 tff(677,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a28) | c0_1(a28) | (~c2_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a28) | c2_1(a10) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a28)) | c0_1(a28))),
% 1.28/1.47 inference(transitivity,[status(thm)],[676, 674])).
% 1.28/1.47 tff(678,plain,
% 1.28/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a28) | c0_1(a28) | (~c2_1(a28)))),
% 1.28/1.47 inference(quant_inst,[status(thm)],[])).
% 1.28/1.47 tff(679,plain,
% 1.28/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a28) | c2_1(a10) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c2_1(a28)) | c0_1(a28)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[678, 677])).
% 1.28/1.47 tff(680,plain,
% 1.28/1.47 (c0_1(a28)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[679, 92, 673, 547, 549, 304, 323, 665, 548, 567, 612])).
% 1.28/1.47 tff(681,plain,
% 1.28/1.47 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.28/1.47 inference(bind,[status(th)],[])).
% 1.28/1.47 tff(682,plain,
% 1.28/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_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) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.47 inference(quant_intro,[status(thm)],[681])).
% 1.28/1.47 tff(683,plain,
% 1.28/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_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) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(684,plain,
% 1.28/1.47 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.28/1.47 inference(bind,[status(th)],[])).
% 1.28/1.47 tff(685,plain,
% 1.28/1.47 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.47 inference(quant_intro,[status(thm)],[684])).
% 1.28/1.47 tff(686,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.28/1.47 tff(687,plain,
% 1.28/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[686, 685])).
% 1.28/1.47 tff(688,plain,
% 1.28/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[687, 683])).
% 1.28/1.47 tff(689,plain,(
% 1.28/1.47 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.47 inference(skolemize,[status(sab)],[688])).
% 1.28/1.47 tff(690,plain,
% 1.28/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[689, 682])).
% 1.28/1.47 tff(691,plain,
% 1.28/1.47 (((~hskp15) | c3_1(a28)) <=> ((~hskp15) | c3_1(a28))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(692,axiom,((~hskp15) | c3_1(a28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.28/1.47 tff(693,plain,
% 1.28/1.47 ((~hskp15) | c3_1(a28)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[692, 691])).
% 1.28/1.47 tff(694,plain,
% 1.28/1.47 ((~hskp15) | c3_1(a28)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[693, 691])).
% 1.28/1.47 tff(695,plain,
% 1.28/1.47 ((~hskp15) | c3_1(a28)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[694, 691])).
% 1.28/1.47 tff(696,plain,
% 1.28/1.47 ((~hskp15) | c3_1(a28)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[695, 691])).
% 1.28/1.47 tff(697,plain,
% 1.28/1.47 ((~hskp15) | c3_1(a28)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[696, 691])).
% 1.28/1.47 tff(698,plain,
% 1.28/1.47 (c3_1(a28)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[697, 659])).
% 1.28/1.47 tff(699,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a28) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | c1_1(a20) | (~c3_1(a28)) | (~c0_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a28) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | c1_1(a20) | (~c3_1(a28)) | (~c0_1(a28)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(700,plain,
% 1.28/1.47 (((~ndr1_0) | c1_1(a28) | (~c3_1(a28)) | (~c0_1(a28)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c2_1(a20) | c1_1(a20) | c0_1(a20)) <=> (c1_1(a28) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | c1_1(a20) | (~c3_1(a28)) | (~c0_1(a28)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(701,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a28) | (~c3_1(a28)) | (~c0_1(a28)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a28) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | c1_1(a20) | (~c3_1(a28)) | (~c0_1(a28))))),
% 1.28/1.47 inference(monotonicity,[status(thm)],[700])).
% 1.28/1.47 tff(702,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a28) | (~c3_1(a28)) | (~c0_1(a28)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a28) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | c1_1(a20) | (~c3_1(a28)) | (~c0_1(a28)))),
% 1.28/1.47 inference(transitivity,[status(thm)],[701, 699])).
% 1.28/1.47 tff(703,plain,
% 1.28/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a28) | (~c3_1(a28)) | (~c0_1(a28)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c2_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.28/1.47 inference(quant_inst,[status(thm)],[])).
% 1.28/1.47 tff(704,plain,
% 1.28/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a28) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | c1_1(a20) | (~c3_1(a28)) | (~c0_1(a28))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[703, 702])).
% 1.28/1.47 tff(705,plain,
% 1.28/1.47 ($false),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[704, 92, 698, 304, 323, 665, 33, 390, 690, 612, 498, 680])).
% 1.28/1.47 tff(706,plain,(hskp3 | (~c1_1(a1)) | (~c3_1(a1)) | c0_1(a20) | c2_1(a20) | c1_1(a20) | (~c0_1(a10)) | (~c3_1(a10)) | c2_1(a10) | (~c1_1(a64)) | (~c3_1(a64)) | (~c0_1(a33)) | c0_1(a64) | c3_1(a33) | c1_1(a33) | (~c3_1(a3)) | c2_1(a3) | c0_1(a3) | c2_1(a1)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.47 tff(707,plain,
% 1.28/1.47 (hskp3),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[706, 593, 323, 33, 390, 498, 547, 549, 548, 304, 585, 577, 576, 569, 568, 524, 523, 482, 303])).
% 1.28/1.47 tff(708,plain,
% 1.28/1.47 (((~hskp3) | (~c1_1(a5))) <=> ((~hskp3) | (~c1_1(a5)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(709,plain,
% 1.28/1.47 (((~c1_1(a5)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a5)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(710,axiom,((~c1_1(a5)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.28/1.47 tff(711,plain,
% 1.28/1.47 ((~hskp3) | (~c1_1(a5))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[710, 709])).
% 1.28/1.47 tff(712,plain,
% 1.28/1.47 ((~hskp3) | (~c1_1(a5))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[711, 708])).
% 1.28/1.47 tff(713,plain,
% 1.28/1.47 (~c1_1(a5)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[712, 707])).
% 1.28/1.47 tff(714,plain,
% 1.28/1.47 (((~hskp3) | (~c0_1(a5))) <=> ((~hskp3) | (~c0_1(a5)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(715,plain,
% 1.28/1.47 (((~c0_1(a5)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a5)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(716,axiom,((~c0_1(a5)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.28/1.47 tff(717,plain,
% 1.28/1.47 ((~hskp3) | (~c0_1(a5))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[716, 715])).
% 1.28/1.47 tff(718,plain,
% 1.28/1.47 ((~hskp3) | (~c0_1(a5))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[717, 714])).
% 1.28/1.47 tff(719,plain,
% 1.28/1.47 (~c0_1(a5)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[718, 707])).
% 1.28/1.47 tff(720,plain,
% 1.28/1.47 (((~hskp3) | c2_1(a5)) <=> ((~hskp3) | c2_1(a5))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(721,axiom,((~hskp3) | c2_1(a5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.28/1.47 tff(722,plain,
% 1.28/1.47 ((~hskp3) | c2_1(a5)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[721, 720])).
% 1.28/1.47 tff(723,plain,
% 1.28/1.47 ((~hskp3) | c2_1(a5)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[722, 720])).
% 1.28/1.47 tff(724,plain,
% 1.28/1.47 ((~hskp3) | c2_1(a5)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[723, 720])).
% 1.28/1.47 tff(725,plain,
% 1.28/1.47 ((~hskp3) | c2_1(a5)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[724, 720])).
% 1.28/1.47 tff(726,plain,
% 1.28/1.47 ((~hskp3) | c2_1(a5)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[725, 720])).
% 1.28/1.47 tff(727,plain,
% 1.28/1.47 (c2_1(a5)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[726, 707])).
% 1.28/1.47 tff(728,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a64) | c2_1(a10) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c3_1(a64)) | (~c1_1(a64)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a64) | c2_1(a10) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c3_1(a64)) | (~c1_1(a64)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(729,plain,
% 1.28/1.47 (((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a64) | (~c1_1(a64)) | (~c3_1(a64)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5))) <=> (c0_1(a64) | c2_1(a10) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c3_1(a64)) | (~c1_1(a64)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(730,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a64) | (~c1_1(a64)) | (~c3_1(a64)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a64) | c2_1(a10) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c3_1(a64)) | (~c1_1(a64))))),
% 1.28/1.47 inference(monotonicity,[status(thm)],[729])).
% 1.28/1.47 tff(731,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a64) | (~c1_1(a64)) | (~c3_1(a64)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a64) | c2_1(a10) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c3_1(a64)) | (~c1_1(a64)))),
% 1.28/1.47 inference(transitivity,[status(thm)],[730, 728])).
% 1.28/1.47 tff(732,plain,
% 1.28/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a64) | (~c1_1(a64)) | (~c3_1(a64)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))),
% 1.28/1.47 inference(quant_inst,[status(thm)],[])).
% 1.28/1.47 tff(733,plain,
% 1.28/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a64) | c2_1(a10) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c3_1(a64)) | (~c1_1(a64))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[732, 731])).
% 1.28/1.47 tff(734,plain,
% 1.28/1.47 ($false),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[733, 92, 593, 585, 547, 549, 727, 576, 548, 719, 713, 567])).
% 1.28/1.47 tff(735,plain,((~hskp24) | (~c0_1(a10)) | (~c3_1(a10)) | c2_1(a10) | (~c3_1(a1)) | c0_1(a20) | c2_1(a20) | c1_1(a20) | (~c1_1(a1)) | (~c0_1(a33)) | c3_1(a33) | c1_1(a33) | (~c3_1(a3)) | c2_1(a3) | c0_1(a3) | c2_1(a1)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.48 tff(736,plain,
% 1.28/1.48 (~hskp24),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[735, 557, 549, 548, 379, 33, 390, 498, 380, 547, 546, 540, 524, 523, 482, 378])).
% 1.28/1.48 tff(737,plain,
% 1.28/1.48 (^[U: $i] : refl((hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 1.28/1.48 inference(bind,[status(th)],[])).
% 1.28/1.48 tff(738,plain,
% 1.28/1.48 (![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.28/1.48 inference(quant_intro,[status(thm)],[737])).
% 1.28/1.48 tff(739,plain,
% 1.28/1.48 (![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(740,plain,
% 1.28/1.48 (^[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)) | hskp24) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp24))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) | hskp22) <=> ((hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp22))), rewrite(((hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp22) <=> (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) | hskp22) <=> (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 1.28/1.48 inference(bind,[status(th)],[])).
% 1.28/1.48 tff(741,plain,
% 1.28/1.48 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) | hskp22) <=> ![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.28/1.48 inference(quant_intro,[status(thm)],[740])).
% 1.28/1.48 tff(742,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 1.28/1.48 tff(743,plain,
% 1.28/1.48 (![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[742, 741])).
% 1.28/1.48 tff(744,plain,
% 1.28/1.48 (![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[743, 739])).
% 1.28/1.48 tff(745,plain,(
% 1.28/1.48 ![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.28/1.48 inference(skolemize,[status(sab)],[744])).
% 1.28/1.48 tff(746,plain,
% 1.28/1.48 (![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[745, 738])).
% 1.28/1.48 tff(747,plain,
% 1.28/1.48 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp24 | hskp22 | c3_1(a33) | (~ndr1_0) | c2_1(a33) | (~c0_1(a33)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp24 | hskp22 | c3_1(a33) | (~ndr1_0) | c2_1(a33) | (~c0_1(a33)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(748,plain,
% 1.28/1.48 ((hskp24 | hskp22 | (~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33))) <=> (hskp24 | hskp22 | c3_1(a33) | (~ndr1_0) | c2_1(a33) | (~c0_1(a33)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(749,plain,
% 1.28/1.48 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp24 | hskp22 | c3_1(a33) | (~ndr1_0) | c2_1(a33) | (~c0_1(a33))))),
% 1.28/1.48 inference(monotonicity,[status(thm)],[748])).
% 1.28/1.48 tff(750,plain,
% 1.28/1.48 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp24 | hskp22 | c3_1(a33) | (~ndr1_0) | c2_1(a33) | (~c0_1(a33)))),
% 1.28/1.48 inference(transitivity,[status(thm)],[749, 747])).
% 1.28/1.48 tff(751,plain,
% 1.28/1.48 ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)))),
% 1.28/1.48 inference(quant_inst,[status(thm)],[])).
% 1.28/1.48 tff(752,plain,
% 1.28/1.48 ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp24 | hskp22 | c3_1(a33) | (~ndr1_0) | c2_1(a33) | (~c0_1(a33))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[751, 750])).
% 1.28/1.48 tff(753,plain,
% 1.28/1.48 (hskp24 | c2_1(a33)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[752, 92, 376, 557, 546, 746])).
% 1.28/1.48 tff(754,plain,
% 1.28/1.48 (c2_1(a33)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[753, 736])).
% 1.28/1.48 tff(755,plain,
% 1.28/1.48 (^[U: $i] : refl((hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.28/1.48 inference(bind,[status(th)],[])).
% 1.28/1.48 tff(756,plain,
% 1.28/1.48 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.48 inference(quant_intro,[status(thm)],[755])).
% 1.28/1.48 tff(757,plain,
% 1.28/1.48 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(758,plain,
% 1.28/1.48 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp21) <=> ((hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp21))), rewrite(((hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp21) <=> (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.28/1.48 inference(bind,[status(th)],[])).
% 1.28/1.48 tff(759,plain,
% 1.28/1.48 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp21) <=> ![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.48 inference(quant_intro,[status(thm)],[758])).
% 1.28/1.48 tff(760,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 1.28/1.48 tff(761,plain,
% 1.28/1.48 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[760, 759])).
% 1.28/1.48 tff(762,plain,
% 1.28/1.48 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[761, 757])).
% 1.28/1.48 tff(763,plain,(
% 1.28/1.48 ![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.48 inference(skolemize,[status(sab)],[762])).
% 1.28/1.48 tff(764,plain,
% 1.28/1.48 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[763, 756])).
% 1.28/1.48 tff(765,plain,
% 1.28/1.48 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp21 | hskp11 | c1_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp21 | hskp11 | c1_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(766,plain,
% 1.28/1.48 ((hskp21 | hskp11 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33))) <=> (hskp21 | hskp11 | c1_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(767,plain,
% 1.28/1.48 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp21 | hskp11 | c1_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c0_1(a33))))),
% 1.28/1.48 inference(monotonicity,[status(thm)],[766])).
% 1.28/1.48 tff(768,plain,
% 1.28/1.48 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp21 | hskp11 | c1_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.28/1.48 inference(transitivity,[status(thm)],[767, 765])).
% 1.28/1.48 tff(769,plain,
% 1.28/1.48 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.28/1.48 inference(quant_inst,[status(thm)],[])).
% 1.28/1.48 tff(770,plain,
% 1.28/1.48 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp21 | hskp11 | c1_1(a33) | (~ndr1_0) | (~c2_1(a33)) | (~c0_1(a33))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[769, 768])).
% 1.28/1.48 tff(771,plain,
% 1.28/1.48 (hskp21 | (~c2_1(a33))),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[770, 92, 274, 557, 540, 764])).
% 1.28/1.48 tff(772,plain,
% 1.28/1.48 (hskp21),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[771, 754])).
% 1.28/1.48 tff(773,plain,
% 1.28/1.48 (((~hskp21) | (~c0_1(a47))) <=> ((~hskp21) | (~c0_1(a47)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(774,plain,
% 1.28/1.48 (((~c0_1(a47)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a47)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(775,axiom,((~c0_1(a47)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.28/1.48 tff(776,plain,
% 1.28/1.48 ((~hskp21) | (~c0_1(a47))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[775, 774])).
% 1.28/1.48 tff(777,plain,
% 1.28/1.48 ((~hskp21) | (~c0_1(a47))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[776, 773])).
% 1.28/1.48 tff(778,plain,
% 1.28/1.48 (~c0_1(a47)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[777, 772])).
% 1.28/1.48 tff(779,plain,
% 1.28/1.48 (((~hskp21) | c3_1(a47)) <=> ((~hskp21) | c3_1(a47))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(780,axiom,((~hskp21) | c3_1(a47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.28/1.48 tff(781,plain,
% 1.28/1.48 ((~hskp21) | c3_1(a47)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[780, 779])).
% 1.28/1.48 tff(782,plain,
% 1.28/1.48 ((~hskp21) | c3_1(a47)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[781, 779])).
% 1.28/1.48 tff(783,plain,
% 1.28/1.48 ((~hskp21) | c3_1(a47)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[782, 779])).
% 1.28/1.48 tff(784,plain,
% 1.28/1.48 ((~hskp21) | c3_1(a47)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[783, 779])).
% 1.28/1.48 tff(785,plain,
% 1.28/1.48 ((~hskp21) | c3_1(a47)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[784, 779])).
% 1.28/1.48 tff(786,plain,
% 1.28/1.48 (c3_1(a47)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[785, 772])).
% 1.28/1.48 tff(787,plain,
% 1.28/1.48 (((~hskp21) | c2_1(a47)) <=> ((~hskp21) | c2_1(a47))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(788,axiom,((~hskp21) | c2_1(a47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.28/1.48 tff(789,plain,
% 1.28/1.48 ((~hskp21) | c2_1(a47)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[788, 787])).
% 1.28/1.48 tff(790,plain,
% 1.28/1.48 ((~hskp21) | c2_1(a47)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[789, 787])).
% 1.28/1.48 tff(791,plain,
% 1.28/1.48 ((~hskp21) | c2_1(a47)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[790, 787])).
% 1.28/1.48 tff(792,plain,
% 1.28/1.48 ((~hskp21) | c2_1(a47)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[791, 787])).
% 1.28/1.48 tff(793,plain,
% 1.28/1.48 ((~hskp21) | c2_1(a47)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[792, 787])).
% 1.28/1.48 tff(794,plain,
% 1.28/1.48 (c2_1(a47)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[793, 772])).
% 1.28/1.48 tff(795,plain,
% 1.28/1.48 (hskp29),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[90, 736, 525])).
% 1.28/1.48 tff(796,plain,
% 1.28/1.48 (((~hskp29) | c3_1(a77)) <=> ((~hskp29) | c3_1(a77))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(797,axiom,((~hskp29) | c3_1(a77)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.28/1.48 tff(798,plain,
% 1.28/1.48 ((~hskp29) | c3_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[797, 796])).
% 1.28/1.48 tff(799,plain,
% 1.28/1.48 ((~hskp29) | c3_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[798, 796])).
% 1.28/1.48 tff(800,plain,
% 1.28/1.48 ((~hskp29) | c3_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[799, 796])).
% 1.28/1.48 tff(801,plain,
% 1.28/1.48 ((~hskp29) | c3_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[800, 796])).
% 1.28/1.48 tff(802,plain,
% 1.28/1.48 ((~hskp29) | c3_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[801, 796])).
% 1.28/1.48 tff(803,plain,
% 1.28/1.48 (c3_1(a77)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[802, 795])).
% 1.28/1.48 tff(804,plain,
% 1.28/1.48 (((~hskp29) | c2_1(a77)) <=> ((~hskp29) | c2_1(a77))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(805,axiom,((~hskp29) | c2_1(a77)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.28/1.48 tff(806,plain,
% 1.28/1.48 ((~hskp29) | c2_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[805, 804])).
% 1.28/1.48 tff(807,plain,
% 1.28/1.48 ((~hskp29) | c2_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[806, 804])).
% 1.28/1.48 tff(808,plain,
% 1.28/1.48 ((~hskp29) | c2_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[807, 804])).
% 1.28/1.48 tff(809,plain,
% 1.28/1.48 ((~hskp29) | c2_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[808, 804])).
% 1.28/1.48 tff(810,plain,
% 1.28/1.48 ((~hskp29) | c2_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[809, 804])).
% 1.28/1.48 tff(811,plain,
% 1.28/1.48 (c2_1(a77)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[810, 795])).
% 1.28/1.48 tff(812,plain,
% 1.28/1.48 (((~hskp29) | c0_1(a77)) <=> ((~hskp29) | c0_1(a77))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(813,axiom,((~hskp29) | c0_1(a77)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 1.28/1.48 tff(814,plain,
% 1.28/1.48 ((~hskp29) | c0_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[813, 812])).
% 1.28/1.48 tff(815,plain,
% 1.28/1.48 ((~hskp29) | c0_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[814, 812])).
% 1.28/1.48 tff(816,plain,
% 1.28/1.48 ((~hskp29) | c0_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[815, 812])).
% 1.28/1.48 tff(817,plain,
% 1.28/1.48 ((~hskp29) | c0_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[816, 812])).
% 1.28/1.48 tff(818,plain,
% 1.28/1.48 ((~hskp29) | c0_1(a77)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[817, 812])).
% 1.28/1.48 tff(819,plain,
% 1.28/1.48 (c0_1(a77)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[818, 795])).
% 1.28/1.48 tff(820,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a47) | (~ndr1_0) | (~c0_1(a77)) | (~c2_1(a77)) | (~c3_1(a77)) | (~c3_1(a47)) | (~c2_1(a47)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a47) | (~ndr1_0) | (~c0_1(a77)) | (~c2_1(a77)) | (~c3_1(a77)) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(821,plain,
% 1.28/1.48 ((hskp19 | (~ndr1_0) | (~c2_1(a77)) | (~c3_1(a77)) | (~c0_1(a77)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47))) <=> (hskp19 | c0_1(a47) | (~ndr1_0) | (~c0_1(a77)) | (~c2_1(a77)) | (~c3_1(a77)) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(822,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a77)) | (~c3_1(a77)) | (~c0_1(a77)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a47) | (~ndr1_0) | (~c0_1(a77)) | (~c2_1(a77)) | (~c3_1(a77)) | (~c3_1(a47)) | (~c2_1(a47))))),
% 1.28/1.48 inference(monotonicity,[status(thm)],[821])).
% 1.28/1.48 tff(823,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a77)) | (~c3_1(a77)) | (~c0_1(a77)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a47) | (~ndr1_0) | (~c0_1(a77)) | (~c2_1(a77)) | (~c3_1(a77)) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.28/1.48 inference(transitivity,[status(thm)],[822, 820])).
% 1.28/1.48 tff(824,plain,
% 1.28/1.48 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a77)) | (~c3_1(a77)) | (~c0_1(a77)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)))),
% 1.28/1.48 inference(quant_inst,[status(thm)],[])).
% 1.28/1.48 tff(825,plain,
% 1.28/1.48 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a47) | (~ndr1_0) | (~c0_1(a77)) | (~c2_1(a77)) | (~c3_1(a77)) | (~c3_1(a47)) | (~c2_1(a47))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[824, 823])).
% 1.28/1.48 tff(826,plain,
% 1.28/1.48 ($false),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[825, 92, 525, 819, 811, 803, 794, 786, 778, 522])).
% 1.28/1.48 tff(827,plain,(hskp19 | hskp11 | hskp22 | (~c3_1(a10)) | c2_1(a10) | c0_1(a20) | c2_1(a20) | c1_1(a20) | (~c0_1(a10)) | (~c3_1(a3)) | c2_1(a3) | c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.48 tff(828,plain,
% 1.28/1.48 (hskp19),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[827, 512, 376, 274, 504, 33, 390, 498, 497, 433, 488, 482])).
% 1.28/1.48 tff(829,plain,
% 1.28/1.48 (((~hskp19) | (~c0_1(a40))) <=> ((~hskp19) | (~c0_1(a40)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(830,plain,
% 1.28/1.48 (((~c0_1(a40)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a40)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(831,axiom,((~c0_1(a40)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.28/1.48 tff(832,plain,
% 1.28/1.48 ((~hskp19) | (~c0_1(a40))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[831, 830])).
% 1.28/1.48 tff(833,plain,
% 1.28/1.48 ((~hskp19) | (~c0_1(a40))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[832, 829])).
% 1.28/1.48 tff(834,plain,
% 1.28/1.48 (~c0_1(a40)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[833, 828])).
% 1.28/1.48 tff(835,plain,
% 1.28/1.48 (((~hskp19) | c2_1(a40)) <=> ((~hskp19) | c2_1(a40))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(836,axiom,((~hskp19) | c2_1(a40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.28/1.48 tff(837,plain,
% 1.28/1.48 ((~hskp19) | c2_1(a40)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[836, 835])).
% 1.28/1.48 tff(838,plain,
% 1.28/1.48 ((~hskp19) | c2_1(a40)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[837, 835])).
% 1.28/1.48 tff(839,plain,
% 1.28/1.48 ((~hskp19) | c2_1(a40)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[838, 835])).
% 1.28/1.48 tff(840,plain,
% 1.28/1.48 ((~hskp19) | c2_1(a40)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[839, 835])).
% 1.28/1.48 tff(841,plain,
% 1.28/1.48 ((~hskp19) | c2_1(a40)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[840, 835])).
% 1.28/1.48 tff(842,plain,
% 1.28/1.48 (c2_1(a40)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[841, 828])).
% 1.28/1.48 tff(843,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a40) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c1_1(a40)) | (~c2_1(a40)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a40) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c1_1(a40)) | (~c2_1(a40)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(844,plain,
% 1.28/1.48 ((hskp1 | (~ndr1_0) | c0_1(a40) | (~c1_1(a40)) | (~c2_1(a40)) | c1_1(a7) | c0_1(a7) | c3_1(a7)) <=> (hskp1 | c0_1(a40) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c1_1(a40)) | (~c2_1(a40)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(845,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a40) | (~c1_1(a40)) | (~c2_1(a40)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a40) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c1_1(a40)) | (~c2_1(a40))))),
% 1.28/1.48 inference(monotonicity,[status(thm)],[844])).
% 1.28/1.48 tff(846,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a40) | (~c1_1(a40)) | (~c2_1(a40)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a40) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c1_1(a40)) | (~c2_1(a40)))),
% 1.28/1.48 inference(transitivity,[status(thm)],[845, 843])).
% 1.28/1.48 tff(847,plain,
% 1.28/1.48 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a40) | (~c1_1(a40)) | (~c2_1(a40)) | c1_1(a7) | c0_1(a7) | c3_1(a7))),
% 1.28/1.48 inference(quant_inst,[status(thm)],[])).
% 1.28/1.48 tff(848,plain,
% 1.28/1.48 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a40) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c1_1(a40)) | (~c2_1(a40))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[847, 846])).
% 1.28/1.48 tff(849,plain,
% 1.28/1.48 (~c1_1(a40)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[848, 92, 32, 842, 834, 45, 57, 58, 126])).
% 1.28/1.48 tff(850,plain,
% 1.28/1.48 (((~hskp19) | (~c3_1(a40))) <=> ((~hskp19) | (~c3_1(a40)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(851,plain,
% 1.28/1.48 (((~c3_1(a40)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a40)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(852,axiom,((~c3_1(a40)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 1.28/1.48 tff(853,plain,
% 1.28/1.48 ((~hskp19) | (~c3_1(a40))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[852, 851])).
% 1.28/1.48 tff(854,plain,
% 1.28/1.48 ((~hskp19) | (~c3_1(a40))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[853, 850])).
% 1.28/1.48 tff(855,plain,
% 1.28/1.48 (~c3_1(a40)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[854, 828])).
% 1.28/1.48 tff(856,assumption,(c3_1(a13)), introduced(assumption)).
% 1.28/1.48 tff(857,assumption,(c1_1(a13)), introduced(assumption)).
% 1.28/1.48 tff(858,plain,
% 1.28/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a40) | c2_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a13)) | (~c0_1(a13)) | (~c3_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a40) | c2_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a13)) | (~c0_1(a13)) | (~c3_1(a13)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(859,plain,
% 1.28/1.48 (((~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c0_1(a13)) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c1_1(a40) | c3_1(a40) | (~c2_1(a40))) <=> (c3_1(a40) | c2_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a13)) | (~c0_1(a13)) | (~c3_1(a13)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(860,plain,
% 1.28/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c0_1(a13)) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c1_1(a40) | c3_1(a40) | (~c2_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a40) | c2_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a13)) | (~c0_1(a13)) | (~c3_1(a13))))),
% 1.28/1.48 inference(monotonicity,[status(thm)],[859])).
% 1.28/1.48 tff(861,plain,
% 1.28/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c0_1(a13)) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c1_1(a40) | c3_1(a40) | (~c2_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a40) | c2_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a13)) | (~c0_1(a13)) | (~c3_1(a13)))),
% 1.28/1.49 inference(transitivity,[status(thm)],[860, 858])).
% 1.28/1.49 tff(862,plain,
% 1.28/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c0_1(a13)) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c1_1(a40) | c3_1(a40) | (~c2_1(a40)))),
% 1.28/1.49 inference(quant_inst,[status(thm)],[])).
% 1.28/1.49 tff(863,plain,
% 1.28/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a40) | c2_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a13)) | (~c0_1(a13)) | (~c3_1(a13))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[862, 861])).
% 1.28/1.49 tff(864,plain,
% 1.28/1.49 (~c0_1(a13)),
% 1.28/1.49 inference(unit_resolution,[status(thm)],[863, 92, 857, 856, 842, 497, 512, 855, 504, 322, 849])).
% 1.28/1.49 tff(865,plain,
% 1.28/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a40) | c2_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a13)) | c0_1(a13) | (~c3_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a40) | c2_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a13)) | c0_1(a13) | (~c3_1(a13)))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(866,plain,
% 1.28/1.49 (((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c1_1(a40) | c0_1(a40) | (~c2_1(a40))) <=> (c0_1(a40) | c2_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a13)) | c0_1(a13) | (~c3_1(a13)))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(867,plain,
% 1.28/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c1_1(a40) | c0_1(a40) | (~c2_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a40) | c2_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a13)) | c0_1(a13) | (~c3_1(a13))))),
% 1.28/1.49 inference(monotonicity,[status(thm)],[866])).
% 1.28/1.49 tff(868,plain,
% 1.28/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c1_1(a40) | c0_1(a40) | (~c2_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a40) | c2_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a13)) | c0_1(a13) | (~c3_1(a13)))),
% 1.28/1.49 inference(transitivity,[status(thm)],[867, 865])).
% 1.28/1.49 tff(869,plain,
% 1.28/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a10) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c1_1(a40) | c0_1(a40) | (~c2_1(a40)))),
% 1.28/1.49 inference(quant_inst,[status(thm)],[])).
% 1.28/1.49 tff(870,plain,
% 1.28/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a40) | c2_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c3_1(a10)) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a13)) | c0_1(a13) | (~c3_1(a13))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[869, 868])).
% 1.28/1.49 tff(871,plain,
% 1.28/1.49 ($false),
% 1.28/1.49 inference(unit_resolution,[status(thm)],[870, 92, 857, 856, 842, 497, 512, 834, 504, 567, 864, 849])).
% 1.28/1.49 tff(872,plain,((~hskp6) | (~c1_1(a13)) | (~c3_1(a13)) | hskp1 | c0_1(a7) | c1_1(a7) | c3_1(a7) | hskp22 | hskp11 | c0_1(a20) | c2_1(a20) | c1_1(a20) | c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.49 tff(873,plain,
% 1.28/1.49 (~hskp6),
% 1.28/1.49 inference(unit_resolution,[status(thm)],[872, 481, 474, 32, 45, 57, 58, 376, 274, 33, 390, 466, 440])).
% 1.28/1.49 tff(874,plain,
% 1.28/1.49 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.28/1.49 inference(bind,[status(th)],[])).
% 1.28/1.49 tff(875,plain,
% 1.28/1.49 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.28/1.49 inference(quant_intro,[status(thm)],[874])).
% 1.28/1.49 tff(876,plain,
% 1.28/1.49 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(877,plain,
% 1.28/1.49 (^[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)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.28/1.49 inference(bind,[status(th)],[])).
% 1.28/1.49 tff(878,plain,
% 1.28/1.49 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.28/1.49 inference(quant_intro,[status(thm)],[877])).
% 1.28/1.49 tff(879,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.28/1.49 tff(880,plain,
% 1.28/1.49 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[879, 878])).
% 1.28/1.49 tff(881,plain,
% 1.28/1.49 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[880, 876])).
% 1.28/1.49 tff(882,plain,(
% 1.28/1.49 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.28/1.49 inference(skolemize,[status(sab)],[881])).
% 1.28/1.49 tff(883,plain,
% 1.28/1.49 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[882, 875])).
% 1.28/1.49 tff(884,plain,
% 1.28/1.49 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(885,plain,
% 1.28/1.49 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (hskp7 | hskp6 | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(886,plain,
% 1.28/1.49 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3)))),
% 1.28/1.49 inference(monotonicity,[status(thm)],[885])).
% 1.28/1.49 tff(887,plain,
% 1.28/1.49 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3))),
% 1.28/1.49 inference(transitivity,[status(thm)],[886, 884])).
% 1.28/1.49 tff(888,plain,
% 1.28/1.49 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.28/1.49 inference(quant_inst,[status(thm)],[])).
% 1.28/1.49 tff(889,plain,
% 1.28/1.49 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3)),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[888, 887])).
% 1.28/1.49 tff(890,plain,
% 1.28/1.49 (hskp7 | hskp6 | c0_1(a3)),
% 1.28/1.49 inference(unit_resolution,[status(thm)],[889, 92, 433, 431, 883])).
% 1.28/1.49 tff(891,plain,
% 1.28/1.49 (hskp7),
% 1.28/1.49 inference(unit_resolution,[status(thm)],[890, 873, 440])).
% 1.28/1.49 tff(892,plain,
% 1.28/1.49 (((~hskp7) | (~c2_1(a11))) <=> ((~hskp7) | (~c2_1(a11)))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(893,plain,
% 1.28/1.49 (((~c2_1(a11)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a11)))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(894,axiom,((~c2_1(a11)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.28/1.49 tff(895,plain,
% 1.28/1.49 ((~hskp7) | (~c2_1(a11))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[894, 893])).
% 1.28/1.49 tff(896,plain,
% 1.28/1.49 ((~hskp7) | (~c2_1(a11))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[895, 892])).
% 1.28/1.49 tff(897,plain,
% 1.28/1.49 (~c2_1(a11)),
% 1.28/1.49 inference(unit_resolution,[status(thm)],[896, 891])).
% 1.28/1.49 tff(898,plain,
% 1.28/1.49 (((~hskp7) | (~c0_1(a11))) <=> ((~hskp7) | (~c0_1(a11)))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(899,plain,
% 1.28/1.49 (((~c0_1(a11)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a11)))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(900,axiom,((~c0_1(a11)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.28/1.49 tff(901,plain,
% 1.28/1.49 ((~hskp7) | (~c0_1(a11))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[900, 899])).
% 1.28/1.49 tff(902,plain,
% 1.28/1.49 ((~hskp7) | (~c0_1(a11))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[901, 898])).
% 1.28/1.49 tff(903,plain,
% 1.28/1.49 (~c0_1(a11)),
% 1.28/1.49 inference(unit_resolution,[status(thm)],[902, 891])).
% 1.28/1.49 tff(904,plain,
% 1.28/1.49 (((~hskp7) | c1_1(a11)) <=> ((~hskp7) | c1_1(a11))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(905,axiom,((~hskp7) | c1_1(a11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.28/1.49 tff(906,plain,
% 1.28/1.49 ((~hskp7) | c1_1(a11)),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[905, 904])).
% 1.28/1.49 tff(907,plain,
% 1.28/1.49 ((~hskp7) | c1_1(a11)),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[906, 904])).
% 1.28/1.49 tff(908,plain,
% 1.28/1.49 ((~hskp7) | c1_1(a11)),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[907, 904])).
% 1.28/1.49 tff(909,plain,
% 1.28/1.49 ((~hskp7) | c1_1(a11)),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[908, 904])).
% 1.28/1.49 tff(910,plain,
% 1.28/1.49 ((~hskp7) | c1_1(a11)),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[909, 904])).
% 1.28/1.49 tff(911,plain,
% 1.28/1.49 (c1_1(a11)),
% 1.28/1.49 inference(unit_resolution,[status(thm)],[910, 891])).
% 1.28/1.49 tff(912,plain,
% 1.28/1.49 (((~hskp27) | c2_1(a13)) <=> ((~hskp27) | c2_1(a13))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(913,axiom,((~hskp27) | c2_1(a13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.28/1.49 tff(914,plain,
% 1.28/1.49 ((~hskp27) | c2_1(a13)),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[913, 912])).
% 1.28/1.49 tff(915,plain,
% 1.28/1.49 ((~hskp27) | c2_1(a13)),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[914, 912])).
% 1.28/1.49 tff(916,plain,
% 1.28/1.49 ((~hskp27) | c2_1(a13)),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[915, 912])).
% 1.28/1.49 tff(917,plain,
% 1.28/1.49 ((~hskp27) | c2_1(a13)),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[916, 912])).
% 1.28/1.49 tff(918,plain,
% 1.28/1.49 ((~hskp27) | c2_1(a13)),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[917, 912])).
% 1.28/1.49 tff(919,plain,
% 1.28/1.49 (c2_1(a13)),
% 1.28/1.49 inference(unit_resolution,[status(thm)],[918, 458])).
% 1.28/1.49 tff(920,assumption,(~c1_1(a3)), introduced(assumption)).
% 1.28/1.49 tff(921,plain,
% 1.28/1.49 (^[U: $i] : refl((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.28/1.49 inference(bind,[status(th)],[])).
% 1.28/1.49 tff(922,plain,
% 1.28/1.49 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.28/1.49 inference(quant_intro,[status(thm)],[921])).
% 1.28/1.49 tff(923,plain,
% 1.28/1.49 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(924,plain,
% 1.28/1.49 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.28/1.49 inference(bind,[status(th)],[])).
% 1.28/1.49 tff(925,plain,
% 1.28/1.49 (![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.28/1.49 inference(quant_intro,[status(thm)],[924])).
% 1.28/1.49 tff(926,axiom,(![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.28/1.49 tff(927,plain,
% 1.28/1.49 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[926, 925])).
% 1.28/1.49 tff(928,plain,
% 1.28/1.49 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[927, 923])).
% 1.28/1.49 tff(929,plain,(
% 1.28/1.49 ![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.28/1.49 inference(skolemize,[status(sab)],[928])).
% 1.28/1.49 tff(930,plain,
% 1.28/1.49 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[929, 922])).
% 1.28/1.49 tff(931,assumption,(~c2_1(a11)), introduced(assumption)).
% 1.28/1.49 tff(932,assumption,(c1_1(a11)), introduced(assumption)).
% 1.28/1.49 tff(933,plain,
% 1.28/1.49 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a11) | (~ndr1_0) | (~c1_1(a11)) | c3_1(a11))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a11) | (~ndr1_0) | (~c1_1(a11)) | c3_1(a11))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(934,plain,
% 1.28/1.49 ((hskp19 | (~ndr1_0) | c3_1(a11) | c2_1(a11) | (~c1_1(a11))) <=> (hskp19 | c2_1(a11) | (~ndr1_0) | (~c1_1(a11)) | c3_1(a11))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(935,plain,
% 1.28/1.49 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a11) | c2_1(a11) | (~c1_1(a11)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a11) | (~ndr1_0) | (~c1_1(a11)) | c3_1(a11)))),
% 1.28/1.49 inference(monotonicity,[status(thm)],[934])).
% 1.28/1.49 tff(936,plain,
% 1.28/1.49 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a11) | c2_1(a11) | (~c1_1(a11)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a11) | (~ndr1_0) | (~c1_1(a11)) | c3_1(a11))),
% 1.28/1.49 inference(transitivity,[status(thm)],[935, 933])).
% 1.28/1.49 tff(937,plain,
% 1.28/1.49 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a11) | c2_1(a11) | (~c1_1(a11)))),
% 1.28/1.49 inference(quant_inst,[status(thm)],[])).
% 1.28/1.49 tff(938,plain,
% 1.28/1.49 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a11) | (~ndr1_0) | (~c1_1(a11)) | c3_1(a11)),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[937, 936])).
% 1.28/1.49 tff(939,plain,
% 1.28/1.49 (hskp19 | c3_1(a11)),
% 1.28/1.49 inference(unit_resolution,[status(thm)],[938, 92, 932, 931, 930])).
% 1.28/1.49 tff(940,plain,
% 1.28/1.49 (c3_1(a11)),
% 1.28/1.49 inference(unit_resolution,[status(thm)],[939, 525])).
% 1.28/1.49 tff(941,assumption,(~c0_1(a11)), introduced(assumption)).
% 1.28/1.49 tff(942,assumption,(c2_1(a13)), introduced(assumption)).
% 1.28/1.49 tff(943,assumption,(~c2_1(a33)), introduced(assumption)).
% 1.28/1.49 tff(944,plain,
% 1.28/1.49 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.28/1.49 inference(bind,[status(th)],[])).
% 1.28/1.49 tff(945,plain,
% 1.28/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.49 inference(quant_intro,[status(thm)],[944])).
% 1.28/1.49 tff(946,plain,
% 1.28/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.49 inference(rewrite,[status(thm)],[])).
% 1.28/1.49 tff(947,plain,
% 1.28/1.49 (^[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(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.28/1.49 inference(bind,[status(th)],[])).
% 1.28/1.49 tff(948,plain,
% 1.28/1.49 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.49 inference(quant_intro,[status(thm)],[947])).
% 1.28/1.49 tff(949,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.28/1.49 tff(950,plain,
% 1.28/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[949, 948])).
% 1.28/1.49 tff(951,plain,
% 1.28/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[950, 946])).
% 1.28/1.49 tff(952,plain,(
% 1.28/1.49 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.49 inference(skolemize,[status(sab)],[951])).
% 1.28/1.49 tff(953,plain,
% 1.28/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.49 inference(modus_ponens,[status(thm)],[952, 945])).
% 1.28/1.49 tff(954,plain,
% 1.28/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a33) | c1_1(a7) | c3_1(a7) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c2_1(a7)) | c2_1(a33) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a33) | c1_1(a7) | c3_1(a7) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c2_1(a7)) | c2_1(a33) | (~c0_1(a33)))),
% 1.28/1.50 inference(rewrite,[status(thm)],[])).
% 1.28/1.50 tff(955,plain,
% 1.28/1.50 (((~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c3_1(a33) | c1_1(a7) | c3_1(a7) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c2_1(a7)) | c2_1(a33) | (~c0_1(a33)))),
% 1.28/1.50 inference(rewrite,[status(thm)],[])).
% 1.28/1.50 tff(956,plain,
% 1.28/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a33) | c1_1(a7) | c3_1(a7) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c2_1(a7)) | c2_1(a33) | (~c0_1(a33))))),
% 1.28/1.50 inference(monotonicity,[status(thm)],[955])).
% 1.28/1.50 tff(957,plain,
% 1.28/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a33) | c1_1(a7) | c3_1(a7) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c2_1(a7)) | c2_1(a33) | (~c0_1(a33)))),
% 1.28/1.50 inference(transitivity,[status(thm)],[956, 954])).
% 1.28/1.50 tff(958,plain,
% 1.28/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.28/1.50 inference(quant_inst,[status(thm)],[])).
% 1.28/1.50 tff(959,plain,
% 1.28/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a33) | c1_1(a7) | c3_1(a7) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c2_1(a7)) | c2_1(a33) | (~c0_1(a33))),
% 1.28/1.50 inference(modus_ponens,[status(thm)],[958, 957])).
% 1.28/1.50 tff(960,plain,
% 1.28/1.50 ((~c2_1(a7)) | c2_1(a33)),
% 1.28/1.50 inference(unit_resolution,[status(thm)],[959, 92, 577, 524, 569, 57, 58, 920, 953, 482])).
% 1.28/1.50 tff(961,plain,
% 1.28/1.50 (~c2_1(a7)),
% 1.28/1.50 inference(unit_resolution,[status(thm)],[960, 943])).
% 1.28/1.50 tff(962,plain,
% 1.28/1.50 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.28/1.50 inference(bind,[status(th)],[])).
% 1.28/1.50 tff(963,plain,
% 1.28/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.50 inference(quant_intro,[status(thm)],[962])).
% 1.28/1.50 tff(964,plain,
% 1.28/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.50 inference(rewrite,[status(thm)],[])).
% 1.28/1.50 tff(965,plain,
% 1.28/1.50 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.28/1.50 inference(bind,[status(th)],[])).
% 1.28/1.50 tff(966,plain,
% 1.28/1.50 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.50 inference(quant_intro,[status(thm)],[965])).
% 1.28/1.50 tff(967,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 1.28/1.50 tff(968,plain,
% 1.28/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.50 inference(modus_ponens,[status(thm)],[967, 966])).
% 1.28/1.50 tff(969,plain,
% 1.28/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.50 inference(modus_ponens,[status(thm)],[968, 964])).
% 1.28/1.50 tff(970,plain,(
% 1.28/1.50 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.50 inference(skolemize,[status(sab)],[969])).
% 1.28/1.50 tff(971,plain,
% 1.28/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.28/1.50 inference(modus_ponens,[status(thm)],[970, 963])).
% 1.28/1.50 tff(972,assumption,(c3_1(a11)), introduced(assumption)).
% 1.28/1.50 tff(973,plain,
% 1.28/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a33) | c0_1(a11) | (~ndr1_0) | (~c1_1(a11)) | (~c3_1(a11)) | c2_1(a33) | (~c0_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a33) | c0_1(a11) | (~ndr1_0) | (~c1_1(a11)) | (~c3_1(a11)) | c2_1(a33) | (~c0_1(a33)))),
% 1.28/1.50 inference(rewrite,[status(thm)],[])).
% 1.28/1.50 tff(974,plain,
% 1.28/1.50 ((hskp15 | (~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)) | c0_1(a11) | (~c1_1(a11)) | (~c3_1(a11))) <=> (hskp15 | c3_1(a33) | c0_1(a11) | (~ndr1_0) | (~c1_1(a11)) | (~c3_1(a11)) | c2_1(a33) | (~c0_1(a33)))),
% 1.28/1.50 inference(rewrite,[status(thm)],[])).
% 1.28/1.50 tff(975,plain,
% 1.28/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)) | c0_1(a11) | (~c1_1(a11)) | (~c3_1(a11)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a33) | c0_1(a11) | (~ndr1_0) | (~c1_1(a11)) | (~c3_1(a11)) | c2_1(a33) | (~c0_1(a33))))),
% 1.28/1.50 inference(monotonicity,[status(thm)],[974])).
% 1.28/1.50 tff(976,plain,
% 1.28/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)) | c0_1(a11) | (~c1_1(a11)) | (~c3_1(a11)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a33) | c0_1(a11) | (~ndr1_0) | (~c1_1(a11)) | (~c3_1(a11)) | c2_1(a33) | (~c0_1(a33)))),
% 1.28/1.50 inference(transitivity,[status(thm)],[975, 973])).
% 1.28/1.50 tff(977,plain,
% 1.28/1.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a33) | c2_1(a33) | (~c0_1(a33)) | c0_1(a11) | (~c1_1(a11)) | (~c3_1(a11)))),
% 1.28/1.50 inference(quant_inst,[status(thm)],[])).
% 1.28/1.50 tff(978,plain,
% 1.28/1.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a33) | c0_1(a11) | (~ndr1_0) | (~c1_1(a11)) | (~c3_1(a11)) | c2_1(a33) | (~c0_1(a33))),
% 1.28/1.50 inference(modus_ponens,[status(thm)],[977, 976])).
% 1.28/1.50 tff(979,plain,
% 1.28/1.50 (hskp15 | c2_1(a33)),
% 1.28/1.50 inference(unit_resolution,[status(thm)],[978, 92, 577, 932, 569, 941, 648, 972])).
% 1.28/1.50 tff(980,plain,
% 1.28/1.50 (hskp15),
% 1.28/1.50 inference(unit_resolution,[status(thm)],[979, 943])).
% 1.28/1.50 tff(981,plain,
% 1.28/1.50 (~c1_1(a28)),
% 1.28/1.50 inference(unit_resolution,[status(thm)],[664, 980])).
% 1.28/1.50 tff(982,plain,
% 1.28/1.50 (c3_1(a28)),
% 1.28/1.50 inference(unit_resolution,[status(thm)],[697, 980])).
% 1.28/1.50 tff(983,plain,
% 1.28/1.50 (c2_1(a28)),
% 1.28/1.50 inference(unit_resolution,[status(thm)],[672, 980])).
% 1.28/1.50 tff(984,plain,
% 1.28/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a28) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c2_1(a28)) | (~c3_1(a28)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a28) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c2_1(a28)) | (~c3_1(a28)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.28/1.50 inference(rewrite,[status(thm)],[])).
% 1.28/1.50 tff(985,plain,
% 1.28/1.50 (((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c2_1(a7) | c1_1(a7) | c0_1(a7)) <=> (c1_1(a28) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c2_1(a28)) | (~c3_1(a28)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.28/1.50 inference(rewrite,[status(thm)],[])).
% 1.28/1.50 tff(986,plain,
% 1.28/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a28) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c2_1(a28)) | (~c3_1(a28)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))))),
% 1.28/1.50 inference(monotonicity,[status(thm)],[985])).
% 1.28/1.50 tff(987,plain,
% 1.28/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a28) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c2_1(a28)) | (~c3_1(a28)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.28/1.50 inference(transitivity,[status(thm)],[986, 984])).
% 1.28/1.50 tff(988,plain,
% 1.28/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c2_1(a7) | c1_1(a7) | c0_1(a7))),
% 1.28/1.50 inference(quant_inst,[status(thm)],[])).
% 1.28/1.50 tff(989,plain,
% 1.28/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a28) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c2_1(a28)) | (~c3_1(a28)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))),
% 1.28/1.50 inference(modus_ponens,[status(thm)],[988, 987])).
% 1.28/1.50 tff(990,plain,
% 1.28/1.50 ($false),
% 1.28/1.50 inference(unit_resolution,[status(thm)],[989, 92, 857, 942, 856, 983, 982, 981, 45, 57, 971, 961])).
% 1.28/1.50 tff(991,plain,(c2_1(a33) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a7) | c1_1(a7) | (~c0_1(a33)) | (~c1_1(a11)) | c3_1(a33) | c0_1(a11) | (~c3_1(a11)) | (~c3_1(a3)) | c3_1(a7) | c1_1(a3) | c0_1(a3)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.50 tff(992,plain,
% 1.28/1.50 (c2_1(a33)),
% 1.28/1.50 inference(unit_resolution,[status(thm)],[991, 557, 942, 856, 45, 57, 857, 932, 546, 941, 940, 524, 58, 920, 482])).
% 1.28/1.50 tff(993,plain,
% 1.28/1.50 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.28/1.50 inference(bind,[status(th)],[])).
% 1.28/1.50 tff(994,plain,
% 1.28/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_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)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.50 inference(quant_intro,[status(thm)],[993])).
% 1.28/1.50 tff(995,plain,
% 1.28/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_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)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.50 inference(rewrite,[status(thm)],[])).
% 1.28/1.50 tff(996,plain,
% 1.28/1.50 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | 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)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.28/1.50 inference(bind,[status(th)],[])).
% 1.28/1.50 tff(997,plain,
% 1.28/1.50 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.50 inference(quant_intro,[status(thm)],[996])).
% 1.28/1.50 tff(998,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 1.28/1.50 tff(999,plain,
% 1.28/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.50 inference(modus_ponens,[status(thm)],[998, 997])).
% 1.28/1.50 tff(1000,plain,
% 1.28/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.50 inference(modus_ponens,[status(thm)],[999, 995])).
% 1.28/1.50 tff(1001,plain,(
% 1.28/1.50 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.50 inference(skolemize,[status(sab)],[1000])).
% 1.28/1.50 tff(1002,plain,
% 1.28/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.50 inference(modus_ponens,[status(thm)],[1001, 994])).
% 1.28/1.50 tff(1003,plain,
% 1.28/1.50 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.28/1.50 inference(bind,[status(th)],[])).
% 1.28/1.50 tff(1004,plain,
% 1.28/1.50 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.28/1.50 inference(quant_intro,[status(thm)],[1003])).
% 1.28/1.50 tff(1005,plain,
% 1.28/1.50 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.28/1.50 inference(rewrite,[status(thm)],[])).
% 1.28/1.50 tff(1006,plain,
% 1.28/1.50 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp20) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp20))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.28/1.51 inference(bind,[status(th)],[])).
% 1.28/1.51 tff(1007,plain,
% 1.28/1.51 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.28/1.51 inference(quant_intro,[status(thm)],[1006])).
% 1.28/1.51 tff(1008,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 1.28/1.51 tff(1009,plain,
% 1.28/1.51 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 1.28/1.51 tff(1010,plain,
% 1.28/1.51 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1009, 1005])).
% 1.28/1.51 tff(1011,plain,(
% 1.28/1.51 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.28/1.51 inference(skolemize,[status(sab)],[1010])).
% 1.28/1.51 tff(1012,plain,
% 1.28/1.51 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1011, 1004])).
% 1.28/1.51 tff(1013,plain,
% 1.28/1.51 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | c1_1(a33) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a33) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1014,plain,
% 1.28/1.51 ((hskp20 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a20) | c1_1(a20) | c3_1(a20)) <=> (hskp20 | c1_1(a33) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1015,plain,
% 1.28/1.51 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a20) | c1_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | c1_1(a33) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c2_1(a33)) | (~c0_1(a33))))),
% 1.28/1.51 inference(monotonicity,[status(thm)],[1014])).
% 1.28/1.51 tff(1016,plain,
% 1.28/1.51 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a20) | c1_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a33) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c2_1(a33)) | (~c0_1(a33)))),
% 1.28/1.51 inference(transitivity,[status(thm)],[1015, 1013])).
% 1.28/1.51 tff(1017,plain,
% 1.28/1.51 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp20 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a20) | c1_1(a20) | c3_1(a20))),
% 1.28/1.51 inference(quant_inst,[status(thm)],[])).
% 1.28/1.51 tff(1018,plain,
% 1.28/1.51 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp20 | c1_1(a33) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c2_1(a33)) | (~c0_1(a33))),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 1.28/1.51 tff(1019,plain,
% 1.28/1.51 (hskp20 | (~c2_1(a33))),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[1018, 92, 557, 540, 390, 44, 1012, 498])).
% 1.28/1.51 tff(1020,plain,
% 1.28/1.51 (hskp20),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[1019, 992])).
% 1.28/1.51 tff(1021,plain,
% 1.28/1.51 (((~hskp20) | (~c3_1(a43))) <=> ((~hskp20) | (~c3_1(a43)))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1022,plain,
% 1.28/1.51 (((~c3_1(a43)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a43)))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1023,axiom,((~c3_1(a43)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.28/1.51 tff(1024,plain,
% 1.28/1.51 ((~hskp20) | (~c3_1(a43))),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 1.28/1.51 tff(1025,plain,
% 1.28/1.51 ((~hskp20) | (~c3_1(a43))),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1024, 1021])).
% 1.28/1.51 tff(1026,plain,
% 1.28/1.51 (~c3_1(a43)),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[1025, 1020])).
% 1.28/1.51 tff(1027,plain,
% 1.28/1.51 (((~hskp20) | c1_1(a43)) <=> ((~hskp20) | c1_1(a43))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1028,axiom,((~hskp20) | c1_1(a43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.28/1.51 tff(1029,plain,
% 1.28/1.51 ((~hskp20) | c1_1(a43)),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 1.28/1.51 tff(1030,plain,
% 1.28/1.51 ((~hskp20) | c1_1(a43)),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1029, 1027])).
% 1.28/1.51 tff(1031,plain,
% 1.28/1.51 ((~hskp20) | c1_1(a43)),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1030, 1027])).
% 1.28/1.51 tff(1032,plain,
% 1.28/1.51 ((~hskp20) | c1_1(a43)),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1031, 1027])).
% 1.28/1.51 tff(1033,plain,
% 1.28/1.51 ((~hskp20) | c1_1(a43)),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1032, 1027])).
% 1.28/1.51 tff(1034,plain,
% 1.28/1.51 (c1_1(a43)),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[1033, 1020])).
% 1.28/1.51 tff(1035,plain,
% 1.28/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a43) | c1_1(a33) | c3_1(a33) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a43)) | (~c2_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a43) | c1_1(a33) | c3_1(a33) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a43)) | (~c2_1(a43)))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1036,plain,
% 1.28/1.51 (((~ndr1_0) | c3_1(a43) | (~c1_1(a43)) | (~c2_1(a43)) | c1_1(a33) | c3_1(a33) | (~c2_1(a33)) | c2_1(a20) | c0_1(a20) | c3_1(a20)) <=> (c3_1(a43) | c1_1(a33) | c3_1(a33) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a43)) | (~c2_1(a43)))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1037,plain,
% 1.28/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a43) | (~c1_1(a43)) | (~c2_1(a43)) | c1_1(a33) | c3_1(a33) | (~c2_1(a33)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a43) | c1_1(a33) | c3_1(a33) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a43)) | (~c2_1(a43))))),
% 1.28/1.51 inference(monotonicity,[status(thm)],[1036])).
% 1.28/1.51 tff(1038,plain,
% 1.28/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a43) | (~c1_1(a43)) | (~c2_1(a43)) | c1_1(a33) | c3_1(a33) | (~c2_1(a33)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a43) | c1_1(a33) | c3_1(a33) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a43)) | (~c2_1(a43)))),
% 1.28/1.51 inference(transitivity,[status(thm)],[1037, 1035])).
% 1.28/1.51 tff(1039,plain,
% 1.28/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a43) | (~c1_1(a43)) | (~c2_1(a43)) | c1_1(a33) | c3_1(a33) | (~c2_1(a33)) | c2_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.28/1.51 inference(quant_inst,[status(thm)],[])).
% 1.28/1.51 tff(1040,plain,
% 1.28/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a43) | c1_1(a33) | c3_1(a33) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a33)) | (~c1_1(a43)) | (~c2_1(a43))),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1039, 1038])).
% 1.28/1.51 tff(1041,plain,
% 1.28/1.51 (~c2_1(a43)),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[1040, 92, 1034, 1026, 540, 546, 33, 390, 44, 1002, 992])).
% 1.28/1.51 tff(1042,plain,
% 1.28/1.51 (((~hskp20) | c0_1(a43)) <=> ((~hskp20) | c0_1(a43))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1043,axiom,((~hskp20) | c0_1(a43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 1.28/1.51 tff(1044,plain,
% 1.28/1.51 ((~hskp20) | c0_1(a43)),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 1.28/1.51 tff(1045,plain,
% 1.28/1.51 ((~hskp20) | c0_1(a43)),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1044, 1042])).
% 1.28/1.51 tff(1046,plain,
% 1.28/1.51 ((~hskp20) | c0_1(a43)),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1045, 1042])).
% 1.28/1.51 tff(1047,plain,
% 1.28/1.51 ((~hskp20) | c0_1(a43)),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1046, 1042])).
% 1.28/1.51 tff(1048,plain,
% 1.28/1.51 ((~hskp20) | c0_1(a43)),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1047, 1042])).
% 1.28/1.51 tff(1049,plain,
% 1.28/1.51 (c0_1(a43)),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[1048, 1020])).
% 1.28/1.51 tff(1050,plain,
% 1.28/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a43) | c1_1(a33) | c3_1(a33) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c2_1(a33)) | c2_1(a43) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a43) | c1_1(a33) | c3_1(a33) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c2_1(a33)) | c2_1(a43) | (~c0_1(a43)))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1051,plain,
% 1.28/1.51 (((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c1_1(a33) | c3_1(a33) | (~c2_1(a33)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c3_1(a43) | c1_1(a33) | c3_1(a33) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c2_1(a33)) | c2_1(a43) | (~c0_1(a43)))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1052,plain,
% 1.28/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c1_1(a33) | c3_1(a33) | (~c2_1(a33)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a43) | c1_1(a33) | c3_1(a33) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c2_1(a33)) | c2_1(a43) | (~c0_1(a43))))),
% 1.28/1.51 inference(monotonicity,[status(thm)],[1051])).
% 1.28/1.51 tff(1053,plain,
% 1.28/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c1_1(a33) | c3_1(a33) | (~c2_1(a33)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a43) | c1_1(a33) | c3_1(a33) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c2_1(a33)) | c2_1(a43) | (~c0_1(a43)))),
% 1.28/1.51 inference(transitivity,[status(thm)],[1052, 1050])).
% 1.28/1.51 tff(1054,plain,
% 1.28/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c1_1(a33) | c3_1(a33) | (~c2_1(a33)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.28/1.51 inference(quant_inst,[status(thm)],[])).
% 1.28/1.51 tff(1055,plain,
% 1.28/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a43) | c1_1(a33) | c3_1(a33) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c2_1(a33)) | c2_1(a43) | (~c0_1(a43))),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 1.28/1.51 tff(1056,plain,
% 1.28/1.51 ($false),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[1055, 92, 1049, 524, 1026, 540, 546, 920, 953, 482, 992, 1041])).
% 1.28/1.51 tff(1057,plain,(hskp19 | (~c3_1(a3)) | c1_1(a3) | c0_1(a3) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a20) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a7) | c1_1(a7) | (~c1_1(a13)) | (~c1_1(a11)) | c0_1(a11) | c3_1(a7) | c2_1(a11) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.28/1.51 tff(1058,plain,
% 1.28/1.51 (hskp19),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[1057, 440, 431, 433, 33, 390, 44, 481, 919, 474, 45, 57, 466, 911, 903, 58, 897, 376])).
% 1.28/1.51 tff(1059,plain,
% 1.28/1.51 (~c0_1(a40)),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[833, 1058])).
% 1.28/1.51 tff(1060,plain,
% 1.28/1.51 (c2_1(a40)),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[841, 1058])).
% 1.28/1.51 tff(1061,plain,
% 1.28/1.51 (~c1_1(a40)),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[848, 92, 32, 1060, 1059, 45, 57, 58, 126])).
% 1.28/1.51 tff(1062,plain,
% 1.28/1.51 (~c3_1(a40)),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[854, 1058])).
% 1.28/1.51 tff(1063,assumption,(~c1_1(a40)), introduced(assumption)).
% 1.28/1.51 tff(1064,plain,
% 1.28/1.51 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.28/1.51 inference(bind,[status(th)],[])).
% 1.28/1.51 tff(1065,plain,
% 1.28/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.51 inference(quant_intro,[status(thm)],[1064])).
% 1.28/1.51 tff(1066,plain,
% 1.28/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1067,plain,
% 1.28/1.51 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c2_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) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c2_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) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c2_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) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c2_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) | (~c2_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) | (~c2_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) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_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) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_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)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c2_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)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.28/1.51 inference(bind,[status(th)],[])).
% 1.28/1.51 tff(1068,plain,
% 1.28/1.51 (![W: $i, V: $i, U: $i] : ((((((((((~c2_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)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.51 inference(quant_intro,[status(thm)],[1067])).
% 1.28/1.51 tff(1069,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_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)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 1.28/1.51 tff(1070,plain,
% 1.28/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 1.28/1.51 tff(1071,plain,
% 1.28/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1070, 1066])).
% 1.28/1.51 tff(1072,plain,(
% 1.28/1.51 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.51 inference(skolemize,[status(sab)],[1071])).
% 1.28/1.51 tff(1073,plain,
% 1.28/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1072, 1065])).
% 1.28/1.51 tff(1074,assumption,(~c3_1(a40)), introduced(assumption)).
% 1.28/1.51 tff(1075,assumption,(hskp21), introduced(assumption)).
% 1.28/1.51 tff(1076,plain,
% 1.28/1.51 (~c0_1(a47)),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[777, 1075])).
% 1.28/1.51 tff(1077,assumption,(c2_1(a40)), introduced(assumption)).
% 1.28/1.51 tff(1078,plain,
% 1.28/1.51 (c3_1(a47)),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[785, 1075])).
% 1.28/1.51 tff(1079,plain,
% 1.28/1.51 (c2_1(a47)),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[793, 1075])).
% 1.28/1.51 tff(1080,plain,
% 1.28/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c3_1(a40) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | c1_1(a40) | (~c2_1(a40)) | (~c3_1(a47)) | (~c2_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c3_1(a40) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | c1_1(a40) | (~c2_1(a40)) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1081,plain,
% 1.28/1.51 (((~ndr1_0) | c3_1(a40) | c1_1(a40) | (~c2_1(a40)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c0_1(a47) | c3_1(a40) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | c1_1(a40) | (~c2_1(a40)) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1082,plain,
% 1.28/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a40) | c1_1(a40) | (~c2_1(a40)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c3_1(a40) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | c1_1(a40) | (~c2_1(a40)) | (~c3_1(a47)) | (~c2_1(a47))))),
% 1.28/1.51 inference(monotonicity,[status(thm)],[1081])).
% 1.28/1.51 tff(1083,plain,
% 1.28/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a40) | c1_1(a40) | (~c2_1(a40)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c3_1(a40) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | c1_1(a40) | (~c2_1(a40)) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.28/1.51 inference(transitivity,[status(thm)],[1082, 1080])).
% 1.28/1.51 tff(1084,plain,
% 1.28/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a40) | c1_1(a40) | (~c2_1(a40)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.28/1.51 inference(quant_inst,[status(thm)],[])).
% 1.28/1.51 tff(1085,plain,
% 1.28/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c3_1(a40) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | c1_1(a40) | (~c2_1(a40)) | (~c3_1(a47)) | (~c2_1(a47))),
% 1.28/1.51 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 1.28/1.51 tff(1086,plain,
% 1.28/1.51 ($false),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[1085, 92, 1079, 1078, 1077, 524, 1076, 1074, 920, 1073, 482, 1063])).
% 1.28/1.51 tff(1087,plain,((~hskp21) | (~c2_1(a40)) | (~c3_1(a3)) | c3_1(a40) | c1_1(a3) | c0_1(a3) | c1_1(a40)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.51 tff(1088,plain,
% 1.28/1.51 (~hskp21),
% 1.28/1.51 inference(unit_resolution,[status(thm)],[1087, 1060, 433, 1062, 431, 440, 1061])).
% 1.28/1.51 tff(1089,plain,
% 1.28/1.51 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.28/1.51 inference(bind,[status(th)],[])).
% 1.28/1.51 tff(1090,plain,
% 1.28/1.51 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.28/1.51 inference(quant_intro,[status(thm)],[1089])).
% 1.28/1.51 tff(1091,plain,
% 1.28/1.51 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.28/1.51 inference(rewrite,[status(thm)],[])).
% 1.28/1.51 tff(1092,plain,
% 1.28/1.51 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp21) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp21))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.28/1.52 inference(bind,[status(th)],[])).
% 1.28/1.52 tff(1093,plain,
% 1.28/1.52 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.28/1.52 inference(quant_intro,[status(thm)],[1092])).
% 1.28/1.52 tff(1094,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.28/1.52 tff(1095,plain,
% 1.28/1.52 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.28/1.52 tff(1096,plain,
% 1.28/1.52 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1095, 1091])).
% 1.28/1.52 tff(1097,plain,(
% 1.28/1.52 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.28/1.52 inference(skolemize,[status(sab)],[1096])).
% 1.28/1.52 tff(1098,plain,
% 1.28/1.52 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1097, 1090])).
% 1.28/1.52 tff(1099,plain,
% 1.28/1.52 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1100,plain,
% 1.28/1.52 ((hskp21 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3))) <=> (hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1101,plain,
% 1.28/1.52 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13))))),
% 1.28/1.52 inference(monotonicity,[status(thm)],[1100])).
% 1.28/1.52 tff(1102,plain,
% 1.28/1.52 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)))),
% 1.28/1.52 inference(transitivity,[status(thm)],[1101, 1099])).
% 1.28/1.52 tff(1103,plain,
% 1.28/1.52 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3)))),
% 1.28/1.52 inference(quant_inst,[status(thm)],[])).
% 1.28/1.52 tff(1104,plain,
% 1.28/1.52 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13))),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 1.28/1.52 tff(1105,plain,
% 1.28/1.52 (hskp21 | (~c0_1(a13))),
% 1.28/1.52 inference(unit_resolution,[status(thm)],[1104, 92, 466, 919, 433, 431, 488, 1098])).
% 1.28/1.52 tff(1106,plain,
% 1.28/1.52 (~c0_1(a13)),
% 1.28/1.52 inference(unit_resolution,[status(thm)],[1105, 1088])).
% 1.28/1.52 tff(1107,plain,
% 1.28/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a40) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | c1_1(a40) | (~c2_1(a40)) | (~c2_1(a13)) | c0_1(a13) | (~c3_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a40) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | c1_1(a40) | (~c2_1(a40)) | (~c2_1(a13)) | c0_1(a13) | (~c3_1(a13)))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1108,plain,
% 1.28/1.52 (((~ndr1_0) | c3_1(a40) | c1_1(a40) | (~c2_1(a40)) | c0_1(a13) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c3_1(a40) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | c1_1(a40) | (~c2_1(a40)) | (~c2_1(a13)) | c0_1(a13) | (~c3_1(a13)))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1109,plain,
% 1.28/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a40) | c1_1(a40) | (~c2_1(a40)) | c0_1(a13) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a40) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | c1_1(a40) | (~c2_1(a40)) | (~c2_1(a13)) | c0_1(a13) | (~c3_1(a13))))),
% 1.28/1.52 inference(monotonicity,[status(thm)],[1108])).
% 1.28/1.52 tff(1110,plain,
% 1.28/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a40) | c1_1(a40) | (~c2_1(a40)) | c0_1(a13) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a40) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | c1_1(a40) | (~c2_1(a40)) | (~c2_1(a13)) | c0_1(a13) | (~c3_1(a13)))),
% 1.28/1.52 inference(transitivity,[status(thm)],[1109, 1107])).
% 1.28/1.52 tff(1111,plain,
% 1.28/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a40) | c1_1(a40) | (~c2_1(a40)) | c0_1(a13) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.28/1.52 inference(quant_inst,[status(thm)],[])).
% 1.28/1.52 tff(1112,plain,
% 1.28/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a40) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | c1_1(a40) | (~c2_1(a40)) | (~c2_1(a13)) | c0_1(a13) | (~c3_1(a13))),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 1.28/1.52 tff(1113,plain,
% 1.28/1.52 ($false),
% 1.28/1.52 inference(unit_resolution,[status(thm)],[1112, 92, 919, 474, 1060, 433, 1062, 431, 1073, 440, 1106, 1061])).
% 1.28/1.52 tff(1114,plain,(c2_1(a15) | hskp1 | c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a20) | c2_1(a20) | c3_1(a20) | hskp22 | hskp11 | c1_1(a18) | c2_1(a18) | c3_1(a18) | c0_1(a15) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.52 tff(1115,plain,
% 1.28/1.52 (c2_1(a15)),
% 1.28/1.52 inference(unit_resolution,[status(thm)],[1114, 414, 45, 57, 58, 33, 390, 44, 376, 274, 391, 402, 413, 375, 32])).
% 1.28/1.52 tff(1116,plain,
% 1.28/1.52 (((~hskp9) | (~c2_1(a15))) <=> ((~hskp9) | (~c2_1(a15)))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1117,plain,
% 1.28/1.52 (((~c2_1(a15)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a15)))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1118,axiom,((~c2_1(a15)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.28/1.52 tff(1119,plain,
% 1.28/1.52 ((~hskp9) | (~c2_1(a15))),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 1.28/1.52 tff(1120,plain,
% 1.28/1.52 ((~hskp9) | (~c2_1(a15))),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1119, 1116])).
% 1.28/1.52 tff(1121,plain,
% 1.28/1.52 (~hskp9),
% 1.28/1.52 inference(unit_resolution,[status(thm)],[1120, 1115])).
% 1.28/1.52 tff(1122,plain,
% 1.28/1.52 ((hskp9 | hskp25 | hskp22) <=> (hskp9 | hskp25 | hskp22)),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1123,plain,
% 1.28/1.52 (((hskp25 | hskp22) | hskp9) <=> (hskp9 | hskp25 | hskp22)),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1124,plain,
% 1.28/1.52 ((hskp25 | hskp22) <=> (hskp25 | hskp22)),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1125,plain,
% 1.28/1.52 (((hskp25 | hskp22) | hskp9) <=> ((hskp25 | hskp22) | hskp9)),
% 1.28/1.52 inference(monotonicity,[status(thm)],[1124])).
% 1.28/1.52 tff(1126,plain,
% 1.28/1.52 (((hskp25 | hskp22) | hskp9) <=> (hskp9 | hskp25 | hskp22)),
% 1.28/1.52 inference(transitivity,[status(thm)],[1125, 1123])).
% 1.28/1.52 tff(1127,axiom,((hskp25 | hskp22) | hskp9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 1.28/1.52 tff(1128,plain,
% 1.28/1.52 (hskp9 | hskp25 | hskp22),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 1.28/1.52 tff(1129,plain,
% 1.28/1.52 (hskp9 | hskp25 | hskp22),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1128, 1122])).
% 1.28/1.52 tff(1130,plain,
% 1.28/1.52 (hskp9 | hskp25 | hskp22),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1129, 1122])).
% 1.28/1.52 tff(1131,plain,
% 1.28/1.52 (hskp9 | hskp25 | hskp22),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1130, 1122])).
% 1.28/1.52 tff(1132,plain,
% 1.28/1.52 (hskp9 | hskp25 | hskp22),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1131, 1122])).
% 1.28/1.52 tff(1133,plain,
% 1.28/1.52 (hskp25),
% 1.28/1.52 inference(unit_resolution,[status(thm)],[1132, 1121, 376])).
% 1.28/1.52 tff(1134,plain,
% 1.28/1.52 (((~hskp25) | (~c3_1(a73))) <=> ((~hskp25) | (~c3_1(a73)))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1135,plain,
% 1.28/1.52 (((~c3_1(a73)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a73)))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1136,axiom,((~c3_1(a73)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.28/1.52 tff(1137,plain,
% 1.28/1.52 ((~hskp25) | (~c3_1(a73))),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1136, 1135])).
% 1.28/1.52 tff(1138,plain,
% 1.28/1.52 ((~hskp25) | (~c3_1(a73))),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1137, 1134])).
% 1.28/1.52 tff(1139,plain,
% 1.28/1.52 (~c3_1(a73)),
% 1.28/1.52 inference(unit_resolution,[status(thm)],[1138, 1133])).
% 1.28/1.52 tff(1140,plain,
% 1.28/1.52 (((~hskp25) | c0_1(a73)) <=> ((~hskp25) | c0_1(a73))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1141,axiom,((~hskp25) | c0_1(a73)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.28/1.52 tff(1142,plain,
% 1.28/1.52 ((~hskp25) | c0_1(a73)),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 1.28/1.52 tff(1143,plain,
% 1.28/1.52 ((~hskp25) | c0_1(a73)),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1142, 1140])).
% 1.28/1.52 tff(1144,plain,
% 1.28/1.52 ((~hskp25) | c0_1(a73)),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1143, 1140])).
% 1.28/1.52 tff(1145,plain,
% 1.28/1.52 ((~hskp25) | c0_1(a73)),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1144, 1140])).
% 1.28/1.52 tff(1146,plain,
% 1.28/1.52 ((~hskp25) | c0_1(a73)),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1145, 1140])).
% 1.28/1.52 tff(1147,plain,
% 1.28/1.52 (c0_1(a73)),
% 1.28/1.52 inference(unit_resolution,[status(thm)],[1146, 1133])).
% 1.28/1.52 tff(1148,plain,
% 1.28/1.52 (((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp11 | c3_1(a73) | (~ndr1_0) | c1_1(a73) | (~c0_1(a73)))) <=> ((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp11 | c3_1(a73) | (~ndr1_0) | c1_1(a73) | (~c0_1(a73)))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1149,plain,
% 1.28/1.52 ((hskp9 | hskp11 | (~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c0_1(a73))) <=> (hskp9 | hskp11 | c3_1(a73) | (~ndr1_0) | c1_1(a73) | (~c0_1(a73)))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1150,plain,
% 1.28/1.52 (((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp11 | (~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c0_1(a73)))) <=> ((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp11 | c3_1(a73) | (~ndr1_0) | c1_1(a73) | (~c0_1(a73))))),
% 1.28/1.52 inference(monotonicity,[status(thm)],[1149])).
% 1.28/1.52 tff(1151,plain,
% 1.28/1.52 (((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp11 | (~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c0_1(a73)))) <=> ((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp11 | c3_1(a73) | (~ndr1_0) | c1_1(a73) | (~c0_1(a73)))),
% 1.28/1.52 inference(transitivity,[status(thm)],[1150, 1148])).
% 1.28/1.52 tff(1152,plain,
% 1.28/1.52 ((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp11 | (~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c0_1(a73)))),
% 1.28/1.52 inference(quant_inst,[status(thm)],[])).
% 1.28/1.52 tff(1153,plain,
% 1.28/1.52 ((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp11 | c3_1(a73) | (~ndr1_0) | c1_1(a73) | (~c0_1(a73))),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 1.28/1.52 tff(1154,plain,
% 1.28/1.52 (c1_1(a73)),
% 1.28/1.52 inference(unit_resolution,[status(thm)],[1153, 1121, 92, 274, 1147, 1139, 412])).
% 1.28/1.52 tff(1155,plain,
% 1.28/1.52 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 1.28/1.52 inference(bind,[status(th)],[])).
% 1.28/1.52 tff(1156,plain,
% 1.28/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.52 inference(quant_intro,[status(thm)],[1155])).
% 1.28/1.52 tff(1157,plain,
% 1.28/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1158,plain,
% 1.28/1.52 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 1.28/1.52 inference(bind,[status(th)],[])).
% 1.28/1.52 tff(1159,plain,
% 1.28/1.52 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.52 inference(quant_intro,[status(thm)],[1158])).
% 1.28/1.52 tff(1160,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.28/1.52 tff(1161,plain,
% 1.28/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 1.28/1.52 tff(1162,plain,
% 1.28/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1161, 1157])).
% 1.28/1.52 tff(1163,plain,(
% 1.28/1.52 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.52 inference(skolemize,[status(sab)],[1162])).
% 1.28/1.52 tff(1164,plain,
% 1.28/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.52 inference(modus_ponens,[status(thm)],[1163, 1156])).
% 1.28/1.52 tff(1165,plain,
% 1.28/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a18) | c3_1(a18) | c0_1(a15) | c1_1(a15) | (~c2_1(a15)) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c0_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a18) | c3_1(a18) | c0_1(a15) | c1_1(a15) | (~c2_1(a15)) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c0_1(a18)))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1166,plain,
% 1.28/1.52 (((~ndr1_0) | c3_1(a18) | c2_1(a18) | (~c0_1(a18)) | c1_1(a15) | c0_1(a15) | (~c2_1(a15)) | c1_1(a7) | c0_1(a7) | c3_1(a7)) <=> (c2_1(a18) | c3_1(a18) | c0_1(a15) | c1_1(a15) | (~c2_1(a15)) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c0_1(a18)))),
% 1.28/1.52 inference(rewrite,[status(thm)],[])).
% 1.28/1.52 tff(1167,plain,
% 1.28/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a18) | c2_1(a18) | (~c0_1(a18)) | c1_1(a15) | c0_1(a15) | (~c2_1(a15)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a18) | c3_1(a18) | c0_1(a15) | c1_1(a15) | (~c2_1(a15)) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c0_1(a18))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1166])).
% 1.35/1.53 tff(1168,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a18) | c2_1(a18) | (~c0_1(a18)) | c1_1(a15) | c0_1(a15) | (~c2_1(a15)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a18) | c3_1(a18) | c0_1(a15) | c1_1(a15) | (~c2_1(a15)) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c0_1(a18)))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1167, 1165])).
% 1.35/1.53 tff(1169,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a18) | c2_1(a18) | (~c0_1(a18)) | c1_1(a15) | c0_1(a15) | (~c2_1(a15)) | c1_1(a7) | c0_1(a7) | c3_1(a7))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1170,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a18) | c3_1(a18) | c0_1(a15) | c1_1(a15) | (~c2_1(a15)) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c0_1(a18))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 1.35/1.53 tff(1171,plain,
% 1.35/1.53 ((~c2_1(a15)) | (~c0_1(a18))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1170, 92, 402, 413, 375, 414, 45, 57, 58, 1164])).
% 1.35/1.53 tff(1172,plain,
% 1.35/1.53 (~c0_1(a18)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1171, 1115])).
% 1.35/1.53 tff(1173,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a18) | c2_1(a18) | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | (~c3_1(a15)) | c0_1(a18) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a18) | c2_1(a18) | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | (~c3_1(a15)) | c0_1(a18) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1174,plain,
% 1.35/1.53 (((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a18) | c1_1(a18) | c0_1(a18)) <=> (c1_1(a18) | c2_1(a18) | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | (~c3_1(a15)) | c0_1(a18) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1175,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a18) | c1_1(a18) | c0_1(a18))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a18) | c2_1(a18) | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | (~c3_1(a15)) | c0_1(a18) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1174])).
% 1.35/1.53 tff(1176,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a18) | c1_1(a18) | c0_1(a18))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a18) | c2_1(a18) | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | (~c3_1(a15)) | c0_1(a18) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1175, 1173])).
% 1.35/1.53 tff(1177,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a18) | c1_1(a18) | c0_1(a18))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1178,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a18) | c2_1(a18) | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | (~c3_1(a15)) | c0_1(a18) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 1.35/1.53 tff(1179,plain,
% 1.35/1.53 ((~c2_1(a15)) | (~c3_1(a15)) | c0_1(a18)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1178, 92, 466, 919, 474, 391, 402, 414, 971])).
% 1.35/1.53 tff(1180,plain,
% 1.35/1.53 (~c3_1(a15)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1179, 1172, 1115])).
% 1.35/1.53 tff(1181,plain,
% 1.35/1.53 (((~hskp25) | c2_1(a73)) <=> ((~hskp25) | c2_1(a73))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1182,axiom,((~hskp25) | c2_1(a73)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 1.35/1.53 tff(1183,plain,
% 1.35/1.53 ((~hskp25) | c2_1(a73)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 1.35/1.53 tff(1184,plain,
% 1.35/1.53 ((~hskp25) | c2_1(a73)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1183, 1181])).
% 1.35/1.53 tff(1185,plain,
% 1.35/1.53 ((~hskp25) | c2_1(a73)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1184, 1181])).
% 1.35/1.53 tff(1186,plain,
% 1.35/1.53 ((~hskp25) | c2_1(a73)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1185, 1181])).
% 1.35/1.53 tff(1187,plain,
% 1.35/1.53 ((~hskp25) | c2_1(a73)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1186, 1181])).
% 1.35/1.53 tff(1188,plain,
% 1.35/1.53 (c2_1(a73)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1187, 1133])).
% 1.35/1.53 tff(1189,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a73) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c3_1(a15) | (~c1_1(a73)) | (~c2_1(a73)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a73) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c3_1(a15) | (~c1_1(a73)) | (~c2_1(a73)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1190,plain,
% 1.35/1.53 (((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a15) | c3_1(a15) | (~c2_1(a15)) | c2_1(a20) | c0_1(a20) | c3_1(a20)) <=> (c3_1(a73) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c3_1(a15) | (~c1_1(a73)) | (~c2_1(a73)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1191,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a15) | c3_1(a15) | (~c2_1(a15)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a73) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c3_1(a15) | (~c1_1(a73)) | (~c2_1(a73))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1190])).
% 1.35/1.53 tff(1192,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a15) | c3_1(a15) | (~c2_1(a15)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a73) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c3_1(a15) | (~c1_1(a73)) | (~c2_1(a73)))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1191, 1189])).
% 1.35/1.53 tff(1193,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a15) | c3_1(a15) | (~c2_1(a15)) | c2_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1194,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a73) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c3_1(a15) | (~c1_1(a73)) | (~c2_1(a73))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 1.35/1.53 tff(1195,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1194, 92, 1188, 1139, 33, 390, 44, 414, 1115, 1002, 1180, 1154])).
% 1.35/1.53 tff(1196,plain,(c1_1(a15) | c0_1(a20) | c2_1(a20) | c3_1(a20) | hskp11 | c1_1(a18) | c2_1(a18) | hskp22 | c3_1(a18) | c0_1(a15) | c0_1(a7) | c1_1(a7) | c3_1(a7) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(1197,plain,
% 1.35/1.53 (c1_1(a15)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1196, 413, 390, 44, 274, 391, 402, 376, 33, 375, 45, 57, 58, 32])).
% 1.35/1.53 tff(1198,plain,
% 1.35/1.53 (((~hskp9) | (~c1_1(a15))) <=> ((~hskp9) | (~c1_1(a15)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1199,plain,
% 1.35/1.53 (((~c1_1(a15)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a15)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1200,axiom,((~c1_1(a15)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 1.35/1.53 tff(1201,plain,
% 1.35/1.53 ((~hskp9) | (~c1_1(a15))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 1.35/1.53 tff(1202,plain,
% 1.35/1.53 ((~hskp9) | (~c1_1(a15))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1201, 1198])).
% 1.35/1.53 tff(1203,plain,
% 1.35/1.53 (~hskp9),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1202, 1197])).
% 1.35/1.53 tff(1204,plain,
% 1.35/1.53 (hskp25),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1132, 1203, 376])).
% 1.35/1.53 tff(1205,plain,
% 1.35/1.53 (~c3_1(a73)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1138, 1204])).
% 1.35/1.53 tff(1206,plain,
% 1.35/1.53 (c0_1(a73)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1146, 1204])).
% 1.35/1.53 tff(1207,plain,
% 1.35/1.53 (c1_1(a73)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1153, 1203, 92, 274, 1206, 1205, 412])).
% 1.35/1.53 tff(1208,plain,
% 1.35/1.53 (((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp11 | c1_1(a18) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)))) <=> ((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp11 | c1_1(a18) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1209,plain,
% 1.35/1.53 ((hskp9 | hskp11 | (~ndr1_0) | c3_1(a18) | c1_1(a18) | (~c0_1(a18))) <=> (hskp9 | hskp11 | c1_1(a18) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1210,plain,
% 1.35/1.53 (((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp11 | (~ndr1_0) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)))) <=> ((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp11 | c1_1(a18) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1209])).
% 1.35/1.53 tff(1211,plain,
% 1.35/1.53 (((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp11 | (~ndr1_0) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)))) <=> ((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp11 | c1_1(a18) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1210, 1208])).
% 1.35/1.53 tff(1212,plain,
% 1.35/1.53 ((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp11 | (~ndr1_0) | c3_1(a18) | c1_1(a18) | (~c0_1(a18)))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1213,plain,
% 1.35/1.53 ((~![U: $i] : (hskp9 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp11 | c1_1(a18) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 1.35/1.53 tff(1214,plain,
% 1.35/1.53 (hskp9 | c3_1(a18) | (~c0_1(a18))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1213, 92, 274, 391, 412])).
% 1.35/1.53 tff(1215,plain,
% 1.35/1.53 (~c0_1(a18)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1214, 1203, 413])).
% 1.35/1.53 tff(1216,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c1_1(a18) | c2_1(a18) | c3_1(a18) | (~ndr1_0) | c0_1(a18) | (~c1_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c1_1(a18) | c2_1(a18) | c3_1(a18) | (~ndr1_0) | c0_1(a18) | (~c1_1(a20)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1217,plain,
% 1.35/1.53 (((~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a18) | c1_1(a18) | c3_1(a18) | c2_1(a18) | c1_1(a18) | c0_1(a18)) <=> (c2_1(a20) | c3_1(a20) | c1_1(a18) | c2_1(a18) | c3_1(a18) | (~ndr1_0) | c0_1(a18) | (~c1_1(a20)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1218,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a18) | c1_1(a18) | c3_1(a18) | c2_1(a18) | c1_1(a18) | c0_1(a18))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c1_1(a18) | c2_1(a18) | c3_1(a18) | (~ndr1_0) | c0_1(a18) | (~c1_1(a20))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1217])).
% 1.35/1.53 tff(1219,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a18) | c1_1(a18) | c3_1(a18) | c2_1(a18) | c1_1(a18) | c0_1(a18))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c1_1(a18) | c2_1(a18) | c3_1(a18) | (~ndr1_0) | c0_1(a18) | (~c1_1(a20)))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1218, 1216])).
% 1.35/1.53 tff(1220,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a18) | c1_1(a18) | c3_1(a18) | c2_1(a18) | c1_1(a18) | c0_1(a18))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1221,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c1_1(a18) | c2_1(a18) | c3_1(a18) | (~ndr1_0) | c0_1(a18) | (~c1_1(a20))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 1.35/1.53 tff(1222,plain,
% 1.35/1.53 (c3_1(a18) | c0_1(a18) | (~c1_1(a20))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1221, 92, 390, 44, 391, 402, 194])).
% 1.35/1.53 tff(1223,plain,
% 1.35/1.53 (~c1_1(a20)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1222, 1215, 413])).
% 1.35/1.53 tff(1224,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a18) | c2_1(a18) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c0_1(a18))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a18) | c2_1(a18) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c0_1(a18))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1225,plain,
% 1.35/1.53 (((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a18) | c1_1(a18) | c0_1(a18)) <=> (c1_1(a18) | c2_1(a18) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c0_1(a18))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1226,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a18) | c1_1(a18) | c0_1(a18))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a18) | c2_1(a18) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c0_1(a18)))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[1225])).
% 1.35/1.53 tff(1227,plain,
% 1.35/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a18) | c1_1(a18) | c0_1(a18))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a18) | c2_1(a18) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c0_1(a18))),
% 1.35/1.53 inference(transitivity,[status(thm)],[1226, 1224])).
% 1.35/1.53 tff(1228,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a18) | c1_1(a18) | c0_1(a18))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(1229,plain,
% 1.35/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a18) | c2_1(a18) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c0_1(a18)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 1.35/1.53 tff(1230,plain,
% 1.35/1.53 ((~c0_1(a3)) | c0_1(a18)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1229, 92, 433, 380, 379, 391, 402, 431, 378, 424])).
% 1.35/1.53 tff(1231,plain,
% 1.35/1.53 (~c0_1(a3)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1230, 1215])).
% 1.35/1.53 tff(1232,plain,
% 1.35/1.53 (~hskp6),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[872, 1223, 474, 32, 45, 57, 58, 376, 274, 33, 390, 466, 1231])).
% 1.35/1.53 tff(1233,plain,
% 1.35/1.53 (hskp7),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[890, 1232, 1231])).
% 1.35/1.53 tff(1234,plain,
% 1.35/1.53 (~c2_1(a11)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[896, 1233])).
% 1.35/1.53 tff(1235,plain,
% 1.35/1.53 (~c0_1(a11)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[902, 1233])).
% 1.35/1.53 tff(1236,plain,
% 1.35/1.53 (c1_1(a11)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[910, 1233])).
% 1.35/1.53 tff(1237,plain,
% 1.35/1.53 (hskp19),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1057, 1236, 431, 433, 33, 390, 44, 1223, 919, 474, 45, 57, 466, 1231, 1235, 58, 1234, 376])).
% 1.35/1.53 tff(1238,plain,
% 1.35/1.53 (~c0_1(a40)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[833, 1237])).
% 1.35/1.53 tff(1239,plain,
% 1.35/1.53 (c2_1(a40)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[841, 1237])).
% 1.35/1.53 tff(1240,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a40) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a40)) | (~c2_1(a40)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a40) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a40)) | (~c2_1(a40)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1241,plain,
% 1.35/1.53 ((hskp1 | (~ndr1_0) | c0_1(a40) | (~c1_1(a40)) | (~c2_1(a40)) | c1_1(a20) | c0_1(a20) | c3_1(a20)) <=> (hskp1 | c0_1(a40) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a40)) | (~c2_1(a40)))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(1242,plain,
% 1.35/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a40) | (~c1_1(a40)) | (~c2_1(a40)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a40) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a40)) | (~c2_1(a40))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1241])).
% 1.35/1.54 tff(1243,plain,
% 1.35/1.54 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a40) | (~c1_1(a40)) | (~c2_1(a40)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a40) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a40)) | (~c2_1(a40)))),
% 1.35/1.54 inference(transitivity,[status(thm)],[1242, 1240])).
% 1.35/1.54 tff(1244,plain,
% 1.35/1.54 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a40) | (~c1_1(a40)) | (~c2_1(a40)) | c1_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(1245,plain,
% 1.35/1.54 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a40) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a40)) | (~c2_1(a40))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 1.35/1.54 tff(1246,plain,
% 1.35/1.54 (~c1_1(a40)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1245, 92, 32, 1239, 1238, 33, 44, 126, 1223])).
% 1.35/1.54 tff(1247,plain,
% 1.35/1.54 (~c3_1(a40)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[854, 1237])).
% 1.35/1.54 tff(1248,plain,
% 1.35/1.54 (c2_1(a73)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1187, 1204])).
% 1.35/1.54 tff(1249,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a73) | c3_1(a40) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a73)) | (~c2_1(a73)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a73) | c3_1(a40) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a73)) | (~c2_1(a73)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1250,plain,
% 1.35/1.54 (((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a40) | c3_1(a40) | (~c2_1(a40)) | c2_1(a20) | c0_1(a20) | c3_1(a20)) <=> (c3_1(a73) | c3_1(a40) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a73)) | (~c2_1(a73)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1251,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a40) | c3_1(a40) | (~c2_1(a40)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a73) | c3_1(a40) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a73)) | (~c2_1(a73))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1250])).
% 1.35/1.54 tff(1252,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a40) | c3_1(a40) | (~c2_1(a40)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a73) | c3_1(a40) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a73)) | (~c2_1(a73)))),
% 1.35/1.54 inference(transitivity,[status(thm)],[1251, 1249])).
% 1.35/1.54 tff(1253,plain,
% 1.35/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a40) | c3_1(a40) | (~c2_1(a40)) | c2_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(1254,plain,
% 1.35/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a73) | c3_1(a40) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a40) | (~c2_1(a40)) | (~c1_1(a73)) | (~c2_1(a73))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 1.35/1.54 tff(1255,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1254, 92, 1248, 1239, 1205, 1247, 33, 390, 44, 1002, 1246, 1207])).
% 1.35/1.54 tff(1256,plain,(c3_1(a18) | c0_1(a20) | c2_1(a20) | c3_1(a20) | hskp11 | hskp1 | c0_1(a7) | c1_1(a7) | c3_1(a7) | hskp22 | c1_1(a18) | c2_1(a18) | c0_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(1257,plain,
% 1.35/1.54 (c3_1(a18)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1256, 402, 390, 44, 274, 32, 45, 57, 58, 376, 391, 33, 375])).
% 1.35/1.54 tff(1258,plain,
% 1.35/1.54 (~hskp10),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[217, 1257])).
% 1.35/1.54 tff(1259,plain,
% 1.35/1.54 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1260,plain,
% 1.35/1.54 ((hskp10 | hskp1 | (~ndr1_0) | c0_1(a1) | c2_1(a1) | (~c1_1(a1))) <=> (hskp10 | hskp1 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1261,plain,
% 1.35/1.54 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a1) | c2_1(a1) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1)))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1260])).
% 1.35/1.54 tff(1262,plain,
% 1.35/1.54 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a1) | c2_1(a1) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1))),
% 1.35/1.54 inference(transitivity,[status(thm)],[1261, 1259])).
% 1.35/1.54 tff(1263,plain,
% 1.35/1.54 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a1) | c2_1(a1) | (~c1_1(a1)))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(1264,plain,
% 1.35/1.54 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1)),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1263, 1262])).
% 1.35/1.54 tff(1265,plain,
% 1.35/1.54 (hskp10 | c0_1(a1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1264, 92, 32, 380, 378, 204])).
% 1.35/1.54 tff(1266,plain,
% 1.35/1.54 (c0_1(a1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1265, 1258])).
% 1.35/1.54 tff(1267,plain,
% 1.35/1.54 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1268,plain,
% 1.35/1.54 ((hskp10 | hskp1 | (~ndr1_0) | c0_1(a20) | c2_1(a20) | (~c1_1(a20))) <=> (hskp10 | hskp1 | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1269,plain,
% 1.35/1.54 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a20) | c2_1(a20) | (~c1_1(a20)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1268])).
% 1.35/1.54 tff(1270,plain,
% 1.35/1.54 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a20) | c2_1(a20) | (~c1_1(a20)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)))),
% 1.35/1.54 inference(transitivity,[status(thm)],[1269, 1267])).
% 1.35/1.54 tff(1271,plain,
% 1.35/1.54 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a20) | c2_1(a20) | (~c1_1(a20)))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(1272,plain,
% 1.35/1.54 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 1.35/1.54 tff(1273,plain,
% 1.35/1.54 (hskp10 | c2_1(a20) | (~c1_1(a20))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1272, 92, 32, 33, 204])).
% 1.35/1.54 tff(1274,plain,
% 1.35/1.54 (~c1_1(a20)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1273, 1258, 390])).
% 1.35/1.54 tff(1275,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c1_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c1_1(a20))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1276,plain,
% 1.35/1.54 (((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a20) | c1_1(a20) | c0_1(a20)) <=> (c0_1(a20) | c2_1(a20) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c1_1(a20))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1277,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c1_1(a20)))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1276])).
% 1.35/1.54 tff(1278,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c1_1(a20))),
% 1.35/1.54 inference(transitivity,[status(thm)],[1277, 1275])).
% 1.35/1.54 tff(1279,plain,
% 1.35/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(1280,plain,
% 1.35/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c1_1(a20)),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 1.35/1.54 tff(1281,plain,
% 1.35/1.54 ((~c0_1(a3)) | c1_1(a20)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1280, 92, 433, 380, 379, 33, 390, 431, 378, 424])).
% 1.35/1.54 tff(1282,plain,
% 1.35/1.54 (~c0_1(a3)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1281, 1274])).
% 1.35/1.54 tff(1283,plain,
% 1.35/1.54 (hskp3 | (~c0_1(a1)) | c0_1(a3)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[610, 92, 433, 380, 488, 378, 604])).
% 1.35/1.54 tff(1284,plain,
% 1.35/1.54 (hskp3),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1283, 1282, 1266])).
% 1.35/1.54 tff(1285,plain,
% 1.35/1.54 (~c1_1(a5)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[712, 1284])).
% 1.35/1.54 tff(1286,plain,
% 1.35/1.54 (~hskp6),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[872, 1274, 474, 32, 45, 57, 58, 376, 274, 33, 390, 466, 1282])).
% 1.35/1.54 tff(1287,plain,
% 1.35/1.54 (^[U: $i] : refl((hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.35/1.54 inference(bind,[status(th)],[])).
% 1.35/1.54 tff(1288,plain,
% 1.35/1.54 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.35/1.54 inference(quant_intro,[status(thm)],[1287])).
% 1.35/1.54 tff(1289,plain,
% 1.35/1.54 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1290,plain,
% 1.35/1.54 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp6) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp6))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp6) <=> (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.35/1.54 inference(bind,[status(th)],[])).
% 1.35/1.54 tff(1291,plain,
% 1.35/1.54 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp6) <=> ![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.35/1.54 inference(quant_intro,[status(thm)],[1290])).
% 1.35/1.54 tff(1292,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 1.35/1.54 tff(1293,plain,
% 1.35/1.54 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 1.35/1.54 tff(1294,plain,
% 1.35/1.54 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1293, 1289])).
% 1.35/1.54 tff(1295,plain,(
% 1.35/1.54 ![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.35/1.54 inference(skolemize,[status(sab)],[1294])).
% 1.35/1.54 tff(1296,plain,
% 1.35/1.54 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1295, 1288])).
% 1.35/1.54 tff(1297,plain,
% 1.35/1.54 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp6 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp6 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1298,plain,
% 1.35/1.54 ((hskp20 | hskp6 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1))) <=> (hskp20 | hskp6 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1299,plain,
% 1.35/1.54 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp6 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1298])).
% 1.35/1.54 tff(1300,plain,
% 1.35/1.54 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp6 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)))),
% 1.35/1.54 inference(transitivity,[status(thm)],[1299, 1297])).
% 1.35/1.54 tff(1301,plain,
% 1.35/1.54 ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(1302,plain,
% 1.35/1.54 ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp6 | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1301, 1300])).
% 1.35/1.54 tff(1303,plain,
% 1.35/1.54 (hskp20 | hskp6 | (~c0_1(a1))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1302, 92, 380, 378, 1296])).
% 1.35/1.54 tff(1304,plain,
% 1.35/1.54 (hskp20),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1303, 1286, 1266])).
% 1.35/1.54 tff(1305,plain,
% 1.35/1.54 (~c3_1(a43)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1025, 1304])).
% 1.35/1.54 tff(1306,plain,
% 1.35/1.54 (c2_1(a5)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[726, 1284])).
% 1.35/1.54 tff(1307,plain,
% 1.35/1.54 (c1_1(a43)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1033, 1304])).
% 1.35/1.54 tff(1308,plain,
% 1.35/1.54 (c0_1(a43)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1048, 1304])).
% 1.35/1.54 tff(1309,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a43) | c1_1(a18) | c2_1(a18) | (~c3_1(a18)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a43)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a43) | c1_1(a18) | c2_1(a18) | (~c3_1(a18)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a43)) | (~c0_1(a43)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1310,plain,
% 1.35/1.54 (((~ndr1_0) | c3_1(a43) | (~c1_1(a43)) | (~c0_1(a43)) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a18) | c1_1(a18) | (~c3_1(a18))) <=> (c3_1(a43) | c1_1(a18) | c2_1(a18) | (~c3_1(a18)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a43)) | (~c0_1(a43)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1311,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c1_1(a43)) | (~c0_1(a43)) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a18) | c1_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a43) | c1_1(a18) | c2_1(a18) | (~c3_1(a18)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a43)) | (~c0_1(a43))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1310])).
% 1.35/1.54 tff(1312,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c1_1(a43)) | (~c0_1(a43)) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a18) | c1_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a43) | c1_1(a18) | c2_1(a18) | (~c3_1(a18)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a43)) | (~c0_1(a43)))),
% 1.35/1.54 inference(transitivity,[status(thm)],[1311, 1309])).
% 1.35/1.54 tff(1313,plain,
% 1.35/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c1_1(a43)) | (~c0_1(a43)) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a18) | c1_1(a18) | (~c3_1(a18)))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(1314,plain,
% 1.35/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a43) | c1_1(a18) | c2_1(a18) | (~c3_1(a18)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a43)) | (~c0_1(a43))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 1.35/1.54 tff(1315,plain,
% 1.35/1.54 (~c3_1(a5)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1314, 92, 1308, 1307, 1306, 1305, 391, 402, 1257, 1285, 401])).
% 1.35/1.54 tff(1316,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a43) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a43)) | (~c2_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a43) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a43)) | (~c2_1(a43)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1317,plain,
% 1.35/1.54 (((~ndr1_0) | c3_1(a43) | (~c1_1(a43)) | (~c2_1(a43)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20)) <=> (c3_1(a43) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a43)) | (~c2_1(a43)))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1318,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a43) | (~c1_1(a43)) | (~c2_1(a43)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a43) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a43)) | (~c2_1(a43))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1317])).
% 1.35/1.54 tff(1319,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a43) | (~c1_1(a43)) | (~c2_1(a43)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a43) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a43)) | (~c2_1(a43)))),
% 1.35/1.54 inference(transitivity,[status(thm)],[1318, 1316])).
% 1.35/1.54 tff(1320,plain,
% 1.35/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a43) | (~c1_1(a43)) | (~c2_1(a43)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(1321,plain,
% 1.35/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a43) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a43)) | (~c2_1(a43))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 1.35/1.54 tff(1322,plain,
% 1.35/1.54 (~c2_1(a43)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1321, 92, 1307, 1306, 1305, 33, 390, 44, 1285, 1002, 1315])).
% 1.35/1.54 tff(1323,plain,
% 1.35/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | c1_1(a18) | (~c3_1(a18)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | c1_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a18) | (~c3_1(a18)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | c1_1(a20))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(1324,plain,
% 1.35/1.55 (((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a18) | (~c3_1(a18)) | (~c0_1(a18)) | c2_1(a20) | c1_1(a20) | c0_1(a20)) <=> (c0_1(a20) | c2_1(a20) | c1_1(a18) | (~c3_1(a18)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | c1_1(a20))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1325,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a18) | (~c3_1(a18)) | (~c0_1(a18)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | c1_1(a18) | (~c3_1(a18)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | c1_1(a20)))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[1324])).
% 1.35/1.55 tff(1326,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a18) | (~c3_1(a18)) | (~c0_1(a18)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a18) | (~c3_1(a18)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | c1_1(a20))),
% 1.35/1.55 inference(transitivity,[status(thm)],[1325, 1323])).
% 1.35/1.55 tff(1327,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a18) | (~c3_1(a18)) | (~c0_1(a18)) | c2_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(1328,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a18) | (~c3_1(a18)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a18)) | c1_1(a20)),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 1.35/1.55 tff(1329,plain,
% 1.35/1.55 ((~c3_1(a18)) | (~c0_1(a18)) | c1_1(a20)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1328, 92, 380, 379, 33, 390, 391, 378, 424])).
% 1.35/1.55 tff(1330,plain,
% 1.35/1.55 (~c0_1(a18)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1329, 1274, 1257])).
% 1.35/1.55 tff(1331,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a43) | c1_1(a18) | (~c3_1(a18)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c0_1(a18) | c2_1(a43) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a43) | c1_1(a18) | (~c3_1(a18)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c0_1(a18) | c2_1(a43) | (~c0_1(a43)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1332,plain,
% 1.35/1.55 (((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18))) <=> (c3_1(a43) | c1_1(a18) | (~c3_1(a18)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c0_1(a18) | c2_1(a43) | (~c0_1(a43)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1333,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a43) | c1_1(a18) | (~c3_1(a18)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c0_1(a18) | c2_1(a43) | (~c0_1(a43))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[1332])).
% 1.35/1.55 tff(1334,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a43) | c1_1(a18) | (~c3_1(a18)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c0_1(a18) | c2_1(a43) | (~c0_1(a43)))),
% 1.35/1.55 inference(transitivity,[status(thm)],[1333, 1331])).
% 1.35/1.55 tff(1335,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(1336,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a43) | c1_1(a18) | (~c3_1(a18)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c0_1(a18) | c2_1(a43) | (~c0_1(a43))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 1.35/1.55 tff(1337,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1336, 92, 1308, 1306, 1305, 391, 1257, 1285, 953, 1330, 1315, 1322])).
% 1.35/1.55 tff(1338,plain,(c2_1(a18) | c1_1(a18) | c0_1(a20) | c2_1(a20) | c3_1(a20) | hskp1 | c0_1(a7) | c1_1(a7) | c3_1(a7) | hskp22 | hskp11 | c0_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(1339,plain,
% 1.35/1.55 (c2_1(a18)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1338, 391, 33, 390, 44, 32, 45, 57, 58, 376, 274, 375])).
% 1.35/1.55 tff(1340,plain,
% 1.35/1.55 (~hskp10),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[223, 1339])).
% 1.35/1.55 tff(1341,plain,
% 1.35/1.55 (~c1_1(a20)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1273, 1340, 390])).
% 1.35/1.55 tff(1342,plain,
% 1.35/1.55 (c0_1(a1)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1265, 1340])).
% 1.35/1.55 tff(1343,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a18) | (~c2_1(a18)) | c3_1(a18) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a18) | (~c2_1(a18)) | c3_1(a18) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1344,plain,
% 1.35/1.55 (((~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c2_1(a1) | (~c3_1(a1)) | (~c0_1(a1)) | c1_1(a18) | c3_1(a18) | (~c2_1(a18))) <=> (c1_1(a18) | (~c2_1(a18)) | c3_1(a18) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1345,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c2_1(a1) | (~c3_1(a1)) | (~c0_1(a1)) | c1_1(a18) | c3_1(a18) | (~c2_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a18) | (~c2_1(a18)) | c3_1(a18) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[1344])).
% 1.35/1.55 tff(1346,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c2_1(a1) | (~c3_1(a1)) | (~c0_1(a1)) | c1_1(a18) | c3_1(a18) | (~c2_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a18) | (~c2_1(a18)) | c3_1(a18) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)))),
% 1.35/1.55 inference(transitivity,[status(thm)],[1345, 1343])).
% 1.35/1.55 tff(1347,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c2_1(a1) | (~c3_1(a1)) | (~c0_1(a1)) | c1_1(a18) | c3_1(a18) | (~c2_1(a18)))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(1348,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a18) | (~c2_1(a18)) | c3_1(a18) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 1.35/1.55 tff(1349,plain,
% 1.35/1.55 ((~c2_1(a18)) | c3_1(a18) | (~c0_1(a1))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1348, 92, 380, 379, 391, 378, 322])).
% 1.35/1.55 tff(1350,plain,
% 1.35/1.55 (c3_1(a18)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1349, 1342, 1339])).
% 1.35/1.55 tff(1351,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | (~ndr1_0) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | (~ndr1_0) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1352,plain,
% 1.35/1.55 (((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a20) | c1_1(a20) | c0_1(a20)) <=> (c0_1(a20) | c2_1(a20) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | (~ndr1_0) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1353,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | (~ndr1_0) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[1352])).
% 1.35/1.55 tff(1354,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | (~ndr1_0) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.35/1.55 inference(transitivity,[status(thm)],[1353, 1351])).
% 1.35/1.55 tff(1355,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(1356,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | (~ndr1_0) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 1.35/1.55 tff(1357,plain,
% 1.35/1.55 ((~c2_1(a18)) | (~c3_1(a18)) | c1_1(a20)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1356, 92, 466, 919, 474, 33, 390, 391, 971])).
% 1.35/1.55 tff(1358,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1357, 1350, 1341, 1339])).
% 1.35/1.55 tff(1359,plain,(c1_1(a18) | c0_1(a20) | c2_1(a20) | hskp1 | c3_1(a20) | c0_1(a7) | c1_1(a7) | c3_1(a7) | hskp22 | hskp11 | c0_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(1360,plain,
% 1.35/1.55 (c1_1(a18)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1359, 44, 390, 32, 33, 45, 57, 58, 376, 274, 375])).
% 1.35/1.55 tff(1361,plain,
% 1.35/1.55 (~hskp10),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[229, 1360])).
% 1.35/1.55 tff(1362,plain,
% 1.35/1.55 (~c1_1(a20)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1273, 1361, 390])).
% 1.35/1.55 tff(1363,plain,
% 1.35/1.55 (~c0_1(a3)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1281, 1362])).
% 1.35/1.55 tff(1364,plain,
% 1.35/1.55 (~hskp6),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[872, 1362, 474, 32, 45, 57, 58, 376, 274, 33, 390, 466, 1363])).
% 1.35/1.55 tff(1365,plain,
% 1.35/1.55 (hskp7),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[890, 1364, 1363])).
% 1.35/1.55 tff(1366,plain,
% 1.35/1.55 (~c2_1(a11)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[896, 1365])).
% 1.35/1.55 tff(1367,plain,
% 1.35/1.55 (~c0_1(a11)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[902, 1365])).
% 1.35/1.55 tff(1368,plain,
% 1.35/1.55 (c1_1(a11)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[910, 1365])).
% 1.35/1.55 tff(1369,plain,
% 1.35/1.55 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | c0_1(a11) | c2_1(a11) | (~ndr1_0) | (~c1_1(a11)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c0_1(a11) | c2_1(a11) | (~ndr1_0) | (~c1_1(a11)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1370,plain,
% 1.35/1.55 ((hskp10 | hskp1 | (~ndr1_0) | c0_1(a11) | c2_1(a11) | (~c1_1(a11))) <=> (hskp10 | hskp1 | c0_1(a11) | c2_1(a11) | (~ndr1_0) | (~c1_1(a11)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1371,plain,
% 1.35/1.55 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a11) | c2_1(a11) | (~c1_1(a11)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | c0_1(a11) | c2_1(a11) | (~ndr1_0) | (~c1_1(a11))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[1370])).
% 1.35/1.55 tff(1372,plain,
% 1.35/1.55 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a11) | c2_1(a11) | (~c1_1(a11)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c0_1(a11) | c2_1(a11) | (~ndr1_0) | (~c1_1(a11)))),
% 1.35/1.55 inference(transitivity,[status(thm)],[1371, 1369])).
% 1.35/1.55 tff(1373,plain,
% 1.35/1.55 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a11) | c2_1(a11) | (~c1_1(a11)))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(1374,plain,
% 1.35/1.55 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c0_1(a11) | c2_1(a11) | (~ndr1_0) | (~c1_1(a11))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 1.35/1.55 tff(1375,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1374, 92, 1361, 32, 1368, 1367, 1366, 204])).
% 1.35/1.55 tff(1376,plain,(c3_1(a20) | hskp1 | c0_1(a7) | c1_1(a7) | c3_1(a7) | hskp22 | hskp11 | c0_1(a20) | c2_1(a20) | c0_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(1377,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1376, 389, 383, 45, 57, 58, 376, 274, 382, 32, 375])).
% 1.35/1.55 tff(1378,plain,(hskp22 | c0_1(a7) | c1_1(a7) | c3_1(a7) | hskp11 | hskp1 | c0_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(1379,plain,
% 1.35/1.55 (c0_1(a15)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1378, 274, 57, 58, 239, 32, 45])).
% 1.35/1.55 tff(1380,plain,
% 1.35/1.55 (((~hskp9) | (~c0_1(a15))) <=> ((~hskp9) | (~c0_1(a15)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1381,plain,
% 1.35/1.55 (((~c0_1(a15)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a15)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1382,axiom,((~c0_1(a15)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.35/1.55 tff(1383,plain,
% 1.35/1.55 ((~hskp9) | (~c0_1(a15))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1382, 1381])).
% 1.35/1.55 tff(1384,plain,
% 1.35/1.55 ((~hskp9) | (~c0_1(a15))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1383, 1380])).
% 1.35/1.55 tff(1385,plain,
% 1.35/1.55 (~hskp9),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1384, 1379])).
% 1.35/1.55 tff(1386,plain,
% 1.35/1.55 ((hskp27 | hskp9) <=> (hskp27 | hskp9)),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1387,axiom,(hskp27 | hskp9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 1.35/1.55 tff(1388,plain,
% 1.35/1.55 (hskp27 | hskp9),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 1.35/1.55 tff(1389,plain,
% 1.35/1.55 (hskp27),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1388, 1385])).
% 1.35/1.55 tff(1390,plain,
% 1.35/1.55 (c1_1(a13)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[465, 1389])).
% 1.35/1.55 tff(1391,plain,
% 1.35/1.55 (hskp25),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1132, 1385, 239])).
% 1.35/1.55 tff(1392,plain,
% 1.35/1.55 (~c3_1(a73)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1138, 1391])).
% 1.35/1.55 tff(1393,plain,
% 1.35/1.55 (c0_1(a73)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1146, 1391])).
% 1.35/1.55 tff(1394,plain,
% 1.35/1.55 (c1_1(a73)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1153, 1385, 92, 274, 1393, 1392, 412])).
% 1.35/1.55 tff(1395,plain,
% 1.35/1.55 (hskp12),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[332, 359, 358, 57, 58, 357, 274])).
% 1.35/1.55 tff(1396,plain,
% 1.35/1.55 (~c3_1(a20)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[388, 1395])).
% 1.35/1.55 tff(1397,plain,
% 1.35/1.55 (c2_1(a73)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1187, 1391])).
% 1.35/1.55 tff(1398,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a73) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a73)) | (~c2_1(a73)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a73) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a73)) | (~c2_1(a73)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1399,plain,
% 1.35/1.55 (((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c2_1(a20) | c0_1(a20) | c3_1(a20)) <=> (c3_1(a73) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a73)) | (~c2_1(a73)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1400,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a73) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a73)) | (~c2_1(a73))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[1399])).
% 1.35/1.55 tff(1401,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a73) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a73)) | (~c2_1(a73)))),
% 1.35/1.55 inference(transitivity,[status(thm)],[1400, 1398])).
% 1.35/1.55 tff(1402,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c2_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(1403,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a73) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a73)) | (~c2_1(a73))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1402, 1401])).
% 1.35/1.55 tff(1404,plain,
% 1.35/1.55 ((~c2_1(a7)) | (~c1_1(a73))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1403, 92, 1397, 1392, 33, 390, 1396, 57, 58, 1002])).
% 1.35/1.55 tff(1405,plain,
% 1.35/1.55 (~c2_1(a7)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1404, 1394])).
% 1.35/1.55 tff(1406,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a20)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1407,plain,
% 1.35/1.55 (((~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a7) | c1_1(a7) | c0_1(a7)) <=> (c2_1(a20) | c3_1(a20) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a20)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1408,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a20))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[1407])).
% 1.35/1.55 tff(1409,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a20)))),
% 1.35/1.55 inference(transitivity,[status(thm)],[1408, 1406])).
% 1.35/1.55 tff(1410,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a7) | c1_1(a7) | c0_1(a7))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(1411,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a20))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 1.35/1.55 tff(1412,plain,
% 1.35/1.55 (~c1_1(a20)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1411, 92, 390, 1396, 45, 57, 58, 194, 1405])).
% 1.35/1.55 tff(1413,plain,
% 1.35/1.55 (c3_1(a13)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[473, 1389])).
% 1.35/1.55 tff(1414,plain,
% 1.35/1.55 (~c1_1(a3)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[430, 366])).
% 1.35/1.55 tff(1415,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a7) | c1_1(a7) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a7) | c1_1(a7) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1416,plain,
% 1.35/1.55 (((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7) | c1_1(a7) | c0_1(a7)) <=> (c0_1(a7) | c1_1(a7) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1417,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a7) | c1_1(a7) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7)))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[1416])).
% 1.35/1.55 tff(1418,plain,
% 1.35/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a7) | c1_1(a7) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7))),
% 1.35/1.55 inference(transitivity,[status(thm)],[1417, 1415])).
% 1.35/1.55 tff(1419,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7) | c1_1(a7) | c0_1(a7))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(1420,plain,
% 1.35/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a7) | c1_1(a7) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7)),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1419, 1418])).
% 1.35/1.55 tff(1421,plain,
% 1.35/1.55 (~c0_1(a3)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1420, 92, 374, 359, 358, 45, 57, 1414, 357, 424, 1405])).
% 1.35/1.55 tff(1422,plain,
% 1.35/1.55 (~hskp6),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[872, 1421, 1413, 32, 45, 57, 58, 239, 274, 33, 390, 1412, 1390])).
% 1.35/1.55 tff(1423,plain,
% 1.35/1.55 (hskp7 | hskp6),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[889, 92, 374, 1414, 883, 1421])).
% 1.35/1.55 tff(1424,plain,
% 1.35/1.55 (hskp7),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1423, 1422])).
% 1.35/1.55 tff(1425,plain,
% 1.35/1.55 (~c2_1(a11)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[896, 1424])).
% 1.35/1.55 tff(1426,plain,
% 1.35/1.55 (~c0_1(a11)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[902, 1424])).
% 1.35/1.55 tff(1427,plain,
% 1.35/1.55 (c2_1(a13)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[918, 1389])).
% 1.35/1.55 tff(1428,plain,
% 1.35/1.55 (c1_1(a11)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[910, 1424])).
% 1.35/1.55 tff(1429,plain,
% 1.35/1.55 (hskp19),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1057, 1428, 239, 1414, 33, 390, 1396, 1412, 1427, 1413, 45, 57, 1390, 1421, 1426, 58, 1425, 374])).
% 1.35/1.55 tff(1430,plain,
% 1.35/1.55 (c2_1(a40)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[841, 1429])).
% 1.35/1.55 tff(1431,plain,
% 1.35/1.55 (~c2_1(a3)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[487, 366])).
% 1.35/1.55 tff(1432,plain,
% 1.35/1.55 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1433,plain,
% 1.35/1.55 ((hskp21 | (~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3))) <=> (hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(1434,plain,
% 1.35/1.55 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[1433])).
% 1.35/1.56 tff(1435,plain,
% 1.35/1.56 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.35/1.56 inference(transitivity,[status(thm)],[1434, 1432])).
% 1.35/1.56 tff(1436,plain,
% 1.35/1.56 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3)))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(1437,plain,
% 1.35/1.56 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1436, 1435])).
% 1.35/1.56 tff(1438,plain,
% 1.35/1.56 (hskp21),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1437, 92, 1393, 1397, 374, 1414, 1431, 1098, 1394])).
% 1.35/1.56 tff(1439,plain,
% 1.35/1.56 (~c3_1(a40)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[854, 1429])).
% 1.35/1.56 tff(1440,plain,
% 1.35/1.56 (c1_1(a40)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1087, 1439, 374, 1438, 1414, 1421, 1430])).
% 1.35/1.56 tff(1441,plain,
% 1.35/1.56 (~c0_1(a40)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[833, 1429])).
% 1.35/1.56 tff(1442,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[848, 92, 32, 1430, 1441, 45, 57, 58, 126, 1440])).
% 1.35/1.56 tff(1443,plain,(hskp11 | hskp1 | c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a20) | c2_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(1444,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1443, 345, 339, 45, 57, 58, 32, 139])).
% 1.35/1.56 tff(1445,plain,(c3_1(a7) | c0_1(a7) | c1_1(a7) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(1446,plain,
% 1.35/1.56 (c3_1(a7)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1445, 57, 45, 32])).
% 1.35/1.56 tff(1447,plain,
% 1.35/1.56 (((~hskp4) | (~c3_1(a7))) <=> ((~hskp4) | (~c3_1(a7)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1448,plain,
% 1.35/1.56 (((~c3_1(a7)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a7)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1449,axiom,((~c3_1(a7)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.35/1.56 tff(1450,plain,
% 1.35/1.56 ((~hskp4) | (~c3_1(a7))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1449, 1448])).
% 1.35/1.56 tff(1451,plain,
% 1.35/1.56 ((~hskp4) | (~c3_1(a7))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1450, 1447])).
% 1.35/1.56 tff(1452,plain,
% 1.35/1.56 (~hskp4),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1451, 1446])).
% 1.35/1.56 tff(1453,assumption,(hskp0), introduced(assumption)).
% 1.35/1.56 tff(1454,plain,
% 1.35/1.56 (~c2_1(a1)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[256, 1453])).
% 1.35/1.56 tff(1455,plain,
% 1.35/1.56 (c1_1(a1)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[272, 1453])).
% 1.35/1.56 tff(1456,plain,
% 1.35/1.56 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.35/1.56 inference(bind,[status(th)],[])).
% 1.35/1.56 tff(1457,plain,
% 1.35/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.56 inference(quant_intro,[status(thm)],[1456])).
% 1.35/1.56 tff(1458,plain,
% 1.35/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1459,plain,
% 1.35/1.56 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_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) | c2_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) | c2_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)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_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)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.35/1.56 inference(bind,[status(th)],[])).
% 1.35/1.56 tff(1460,plain,
% 1.35/1.56 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.56 inference(quant_intro,[status(thm)],[1459])).
% 1.35/1.56 tff(1461,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 1.35/1.56 tff(1462,plain,
% 1.35/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 1.35/1.56 tff(1463,plain,
% 1.35/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1462, 1458])).
% 1.35/1.56 tff(1464,plain,(
% 1.35/1.56 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.56 inference(skolemize,[status(sab)],[1463])).
% 1.35/1.56 tff(1465,plain,
% 1.35/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1464, 1457])).
% 1.35/1.56 tff(1466,assumption,(c3_1(a7)), introduced(assumption)).
% 1.35/1.56 tff(1467,plain,
% 1.35/1.56 ((hskp21 | hskp12 | hskp11) <=> (hskp21 | hskp12 | hskp11)),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1468,plain,
% 1.35/1.56 (((hskp11 | hskp21) | hskp12) <=> (hskp21 | hskp12 | hskp11)),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1469,axiom,((hskp11 | hskp21) | hskp12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.35/1.56 tff(1470,plain,
% 1.35/1.56 (hskp21 | hskp12 | hskp11),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1469, 1468])).
% 1.35/1.56 tff(1471,plain,
% 1.35/1.56 (hskp21 | hskp12 | hskp11),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1470, 1467])).
% 1.35/1.56 tff(1472,plain,
% 1.35/1.56 (hskp21 | hskp12 | hskp11),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1471, 1467])).
% 1.35/1.56 tff(1473,plain,
% 1.35/1.56 (hskp21 | hskp12 | hskp11),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1472, 1467])).
% 1.35/1.56 tff(1474,plain,
% 1.35/1.56 (hskp21 | hskp12 | hskp11),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1473, 1467])).
% 1.35/1.56 tff(1475,plain,
% 1.35/1.56 (hskp21),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1474, 46, 274])).
% 1.35/1.56 tff(1476,plain,
% 1.35/1.56 (~c0_1(a47)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[777, 1475])).
% 1.35/1.56 tff(1477,plain,
% 1.35/1.56 (c3_1(a47)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[785, 1475])).
% 1.35/1.56 tff(1478,plain,
% 1.35/1.56 (c2_1(a47)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[793, 1475])).
% 1.35/1.56 tff(1479,plain,
% 1.35/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a47)) | (~c2_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1480,plain,
% 1.35/1.56 (((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7))) <=> (c0_1(a47) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1481,plain,
% 1.35/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a47)) | (~c2_1(a47))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[1480])).
% 1.35/1.56 tff(1482,plain,
% 1.35/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.35/1.56 inference(transitivity,[status(thm)],[1481, 1479])).
% 1.35/1.56 tff(1483,plain,
% 1.35/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(1484,plain,
% 1.35/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a47)) | (~c2_1(a47))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 1.35/1.56 tff(1485,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1484, 92, 1478, 1477, 304, 1476, 45, 57, 1466, 303, 1465, 312])).
% 1.35/1.56 tff(1486,plain,(hskp12 | (~c1_1(a1)) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | c2_1(a1) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(1487,plain,
% 1.35/1.56 (hskp12),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1486, 1455, 45, 57, 1446, 1454, 274])).
% 1.35/1.56 tff(1488,plain,
% 1.35/1.56 (~c2_1(a20)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[344, 1487])).
% 1.35/1.56 tff(1489,plain,
% 1.35/1.56 (c3_1(a1)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[264, 1453])).
% 1.35/1.56 tff(1490,plain,
% 1.35/1.56 (~c0_1(a20)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[338, 1487])).
% 1.35/1.56 tff(1491,plain,
% 1.35/1.56 (~c3_1(a20)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[388, 1487])).
% 1.35/1.56 tff(1492,plain,
% 1.35/1.56 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1493,plain,
% 1.35/1.56 ((hskp4 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c1_1(a20)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20))) <=> (hskp4 | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1494,plain,
% 1.35/1.56 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c1_1(a20)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[1493])).
% 1.35/1.56 tff(1495,plain,
% 1.35/1.56 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c1_1(a20)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)))),
% 1.35/1.56 inference(transitivity,[status(thm)],[1494, 1492])).
% 1.35/1.56 tff(1496,plain,
% 1.35/1.56 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c1_1(a20)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(1497,plain,
% 1.35/1.56 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 1.35/1.56 tff(1498,plain,
% 1.35/1.56 (~c1_1(a20)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1497, 92, 1452, 33, 390, 44, 56])).
% 1.35/1.56 tff(1499,plain,
% 1.35/1.56 ((hskp27 | hskp4 | hskp1) <=> (hskp27 | hskp4 | hskp1)),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1500,plain,
% 1.35/1.56 (((hskp1 | hskp27) | hskp4) <=> (hskp27 | hskp4 | hskp1)),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1501,axiom,((hskp1 | hskp27) | hskp4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 1.35/1.56 tff(1502,plain,
% 1.35/1.56 (hskp27 | hskp4 | hskp1),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 1.35/1.56 tff(1503,plain,
% 1.35/1.56 (hskp27 | hskp4 | hskp1),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1502, 1499])).
% 1.35/1.56 tff(1504,plain,
% 1.35/1.56 (hskp27 | hskp4 | hskp1),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1503, 1499])).
% 1.35/1.56 tff(1505,plain,
% 1.35/1.56 (hskp27 | hskp4 | hskp1),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1504, 1499])).
% 1.35/1.56 tff(1506,plain,
% 1.35/1.56 (hskp27 | hskp4 | hskp1),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1505, 1499])).
% 1.35/1.56 tff(1507,plain,
% 1.35/1.56 (hskp27),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1506, 1452, 32])).
% 1.35/1.56 tff(1508,plain,
% 1.35/1.56 (c2_1(a13)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[918, 1507])).
% 1.35/1.56 tff(1509,plain,
% 1.35/1.56 (c1_1(a13)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[465, 1507])).
% 1.35/1.56 tff(1510,assumption,(~c0_1(a13)), introduced(assumption)).
% 1.35/1.56 tff(1511,plain,
% 1.35/1.56 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a13))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a13))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1512,plain,
% 1.35/1.56 ((hskp1 | (~ndr1_0) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)) | c1_1(a20) | c0_1(a20) | c3_1(a20)) <=> (hskp1 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a13))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1513,plain,
% 1.35/1.56 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a13)))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[1512])).
% 1.35/1.56 tff(1514,plain,
% 1.35/1.56 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a13))),
% 1.35/1.56 inference(transitivity,[status(thm)],[1513, 1511])).
% 1.35/1.56 tff(1515,plain,
% 1.35/1.56 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)) | c1_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(1516,plain,
% 1.35/1.56 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a13)),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 1.35/1.56 tff(1517,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1516, 92, 32, 857, 942, 33, 44, 126, 498, 1510])).
% 1.35/1.56 tff(1518,plain,(c0_1(a13) | hskp1 | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a20) | c3_1(a20) | c1_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(1519,plain,
% 1.35/1.56 (c0_1(a13)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1518, 44, 1509, 1508, 33, 32, 1498])).
% 1.35/1.56 tff(1520,plain,
% 1.35/1.56 (c3_1(a13)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[473, 1507])).
% 1.35/1.56 tff(1521,plain,
% 1.35/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a7)) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a7)) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1522,plain,
% 1.35/1.56 (((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a7) | (~c2_1(a7)) | (~c3_1(a7)) | c2_1(a20) | c1_1(a20) | c0_1(a20)) <=> (c0_1(a20) | c2_1(a20) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a7)) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1523,plain,
% 1.35/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a7) | (~c2_1(a7)) | (~c3_1(a7)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a7)) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[1522])).
% 1.35/1.56 tff(1524,plain,
% 1.35/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a7) | (~c2_1(a7)) | (~c3_1(a7)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a7)) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.35/1.56 inference(transitivity,[status(thm)],[1523, 1521])).
% 1.35/1.56 tff(1525,plain,
% 1.35/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a7) | (~c2_1(a7)) | (~c3_1(a7)) | c2_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(1526,plain,
% 1.35/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a7)) | c1_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1525, 1524])).
% 1.35/1.56 tff(1527,plain,
% 1.35/1.56 (c0_1(a20) | (~c2_1(a7)) | c1_1(a20)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1526, 92, 1509, 1508, 1520, 390, 57, 1446, 971])).
% 1.35/1.56 tff(1528,plain,
% 1.35/1.56 (~c2_1(a7)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1527, 1498, 33])).
% 1.35/1.56 tff(1529,plain,
% 1.35/1.56 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | c2_1(a7) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | c2_1(a7) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1530,plain,
% 1.35/1.56 ((hskp21 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7))) <=> (hskp21 | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | c2_1(a7) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1531,plain,
% 1.35/1.56 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | c2_1(a7) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[1530])).
% 1.35/1.56 tff(1532,plain,
% 1.35/1.56 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | c2_1(a7) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)))),
% 1.35/1.56 inference(transitivity,[status(thm)],[1531, 1529])).
% 1.35/1.56 tff(1533,plain,
% 1.35/1.56 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(1534,plain,
% 1.35/1.56 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | c2_1(a7) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 1.35/1.56 tff(1535,plain,
% 1.35/1.56 (hskp21 | (~c0_1(a13))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1534, 92, 1509, 1508, 57, 1446, 1098, 1528])).
% 1.35/1.56 tff(1536,plain,
% 1.35/1.56 (hskp21),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1535, 1519])).
% 1.35/1.56 tff(1537,plain,
% 1.35/1.56 (~c0_1(a47)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[777, 1536])).
% 1.35/1.56 tff(1538,plain,
% 1.35/1.56 (c2_1(a47)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[793, 1536])).
% 1.35/1.56 tff(1539,plain,
% 1.35/1.56 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a47) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a47)) | (~c2_1(a47)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a47) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a47)) | (~c2_1(a47)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1540,plain,
% 1.35/1.56 ((hskp1 | (~ndr1_0) | c0_1(a47) | (~c1_1(a47)) | (~c2_1(a47)) | c1_1(a20) | c0_1(a20) | c3_1(a20)) <=> (hskp1 | c0_1(a47) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a47)) | (~c2_1(a47)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(1541,plain,
% 1.35/1.56 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a47) | (~c1_1(a47)) | (~c2_1(a47)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a47) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a47)) | (~c2_1(a47))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[1540])).
% 1.35/1.57 tff(1542,plain,
% 1.35/1.57 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a47) | (~c1_1(a47)) | (~c2_1(a47)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a47) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a47)) | (~c2_1(a47)))),
% 1.35/1.57 inference(transitivity,[status(thm)],[1541, 1539])).
% 1.35/1.57 tff(1543,plain,
% 1.35/1.57 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a47) | (~c1_1(a47)) | (~c2_1(a47)) | c1_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(1544,plain,
% 1.35/1.57 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a47) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a47)) | (~c2_1(a47))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 1.35/1.57 tff(1545,plain,
% 1.35/1.57 (~c1_1(a47)),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[1544, 92, 32, 1538, 1537, 33, 44, 126, 1498])).
% 1.35/1.57 tff(1546,plain,
% 1.35/1.57 (^[U: $i] : refl((hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 1.35/1.57 inference(bind,[status(th)],[])).
% 1.35/1.57 tff(1547,plain,
% 1.35/1.57 (![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.35/1.57 inference(quant_intro,[status(thm)],[1546])).
% 1.35/1.57 tff(1548,plain,
% 1.35/1.57 (![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(1549,plain,
% 1.35/1.57 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp25))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.35/1.57 inference(bind,[status(th)],[])).
% 1.35/1.57 tff(1550,plain,
% 1.35/1.57 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> ![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.35/1.57 inference(quant_intro,[status(thm)],[1549])).
% 1.35/1.57 tff(1551,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 1.35/1.57 tff(1552,plain,
% 1.35/1.57 (![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 1.35/1.57 tff(1553,plain,
% 1.35/1.57 (![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[1552, 1548])).
% 1.35/1.57 tff(1554,plain,(
% 1.35/1.57 ![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.35/1.57 inference(skolemize,[status(sab)],[1553])).
% 1.35/1.57 tff(1555,plain,
% 1.35/1.57 (![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[1554, 1547])).
% 1.35/1.57 tff(1556,plain,
% 1.35/1.57 (((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a13)) | (~c0_1(a13)) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | (~c1_1(a13)) | (~c0_1(a13)) | (~c3_1(a13)))),
% 1.39/1.57 inference(rewrite,[status(thm)],[])).
% 1.39/1.57 tff(1557,plain,
% 1.39/1.57 ((hskp25 | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c0_1(a13))) <=> (hskp25 | (~ndr1_0) | (~c1_1(a13)) | (~c0_1(a13)) | (~c3_1(a13)))),
% 1.39/1.57 inference(rewrite,[status(thm)],[])).
% 1.39/1.57 tff(1558,plain,
% 1.39/1.57 (((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c0_1(a13)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a13)) | (~c0_1(a13)) | (~c3_1(a13))))),
% 1.39/1.57 inference(monotonicity,[status(thm)],[1557])).
% 1.39/1.57 tff(1559,plain,
% 1.39/1.57 (((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c0_1(a13)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | (~c1_1(a13)) | (~c0_1(a13)) | (~c3_1(a13)))),
% 1.39/1.57 inference(transitivity,[status(thm)],[1558, 1556])).
% 1.39/1.57 tff(1560,plain,
% 1.39/1.57 ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c0_1(a13)))),
% 1.39/1.57 inference(quant_inst,[status(thm)],[])).
% 1.39/1.57 tff(1561,plain,
% 1.39/1.57 ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | (~c1_1(a13)) | (~c0_1(a13)) | (~c3_1(a13))),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 1.39/1.57 tff(1562,plain,
% 1.39/1.57 (hskp25 | (~c0_1(a13))),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[1561, 92, 1509, 1520, 1555])).
% 1.39/1.57 tff(1563,plain,
% 1.39/1.57 (hskp25),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[1562, 1519])).
% 1.39/1.57 tff(1564,plain,
% 1.39/1.57 (~c3_1(a73)),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[1138, 1563])).
% 1.39/1.57 tff(1565,plain,
% 1.39/1.57 (c3_1(a47)),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[785, 1536])).
% 1.39/1.57 tff(1566,plain,
% 1.39/1.57 (c2_1(a73)),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[1187, 1563])).
% 1.39/1.57 tff(1567,plain,
% 1.39/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a73) | c0_1(a47) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c3_1(a47)) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a73) | c0_1(a47) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c3_1(a47)) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73)))),
% 1.39/1.57 inference(rewrite,[status(thm)],[])).
% 1.39/1.57 tff(1568,plain,
% 1.39/1.57 (((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7))) <=> (c3_1(a73) | c0_1(a47) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c3_1(a47)) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73)))),
% 1.39/1.57 inference(rewrite,[status(thm)],[])).
% 1.39/1.57 tff(1569,plain,
% 1.39/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a73) | c0_1(a47) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c3_1(a47)) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73))))),
% 1.39/1.57 inference(monotonicity,[status(thm)],[1568])).
% 1.39/1.57 tff(1570,plain,
% 1.39/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a73) | c0_1(a47) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c3_1(a47)) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73)))),
% 1.39/1.57 inference(transitivity,[status(thm)],[1569, 1567])).
% 1.39/1.57 tff(1571,plain,
% 1.39/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))),
% 1.39/1.57 inference(quant_inst,[status(thm)],[])).
% 1.39/1.57 tff(1572,plain,
% 1.39/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a73) | c0_1(a47) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c3_1(a47)) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73))),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 1.39/1.57 tff(1573,plain,
% 1.39/1.57 (c1_1(a73)),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[1572, 92, 1566, 1538, 1565, 1564, 1537, 45, 57, 1446, 1073])).
% 1.39/1.57 tff(1574,plain,
% 1.39/1.57 (~c0_1(a1)),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[1484, 92, 1538, 1565, 304, 1537, 45, 57, 1446, 303, 1465])).
% 1.39/1.57 tff(1575,plain,
% 1.39/1.57 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 1.39/1.57 inference(bind,[status(th)],[])).
% 1.39/1.57 tff(1576,plain,
% 1.39/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.39/1.57 inference(quant_intro,[status(thm)],[1575])).
% 1.39/1.57 tff(1577,plain,
% 1.39/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.39/1.57 inference(rewrite,[status(thm)],[])).
% 1.39/1.57 tff(1578,plain,
% 1.39/1.57 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 1.39/1.57 inference(bind,[status(th)],[])).
% 1.39/1.57 tff(1579,plain,
% 1.39/1.57 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.39/1.57 inference(quant_intro,[status(thm)],[1578])).
% 1.39/1.57 tff(1580,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 1.39/1.57 tff(1581,plain,
% 1.39/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1580, 1579])).
% 1.39/1.57 tff(1582,plain,
% 1.39/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1581, 1577])).
% 1.39/1.57 tff(1583,plain,(
% 1.39/1.57 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.39/1.57 inference(skolemize,[status(sab)],[1582])).
% 1.39/1.57 tff(1584,plain,
% 1.39/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1583, 1576])).
% 1.39/1.57 tff(1585,plain,
% 1.39/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a73) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | (~c1_1(a73)) | (~c2_1(a73)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a73) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | (~c1_1(a73)) | (~c2_1(a73)))),
% 1.39/1.57 inference(rewrite,[status(thm)],[])).
% 1.39/1.57 tff(1586,plain,
% 1.39/1.57 (((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1))) <=> (c3_1(a73) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | (~c1_1(a73)) | (~c2_1(a73)))),
% 1.39/1.57 inference(rewrite,[status(thm)],[])).
% 1.39/1.57 tff(1587,plain,
% 1.39/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a73) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | (~c1_1(a73)) | (~c2_1(a73))))),
% 1.39/1.57 inference(monotonicity,[status(thm)],[1586])).
% 1.39/1.57 tff(1588,plain,
% 1.39/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a73) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | (~c1_1(a73)) | (~c2_1(a73)))),
% 1.39/1.57 inference(transitivity,[status(thm)],[1587, 1585])).
% 1.39/1.57 tff(1589,plain,
% 1.39/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a73) | (~c1_1(a73)) | (~c2_1(a73)) | c1_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c0_1(a1) | (~c3_1(a1)) | (~c1_1(a1)))),
% 1.39/1.57 inference(quant_inst,[status(thm)],[])).
% 1.39/1.57 tff(1590,plain,
% 1.39/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a73) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | (~c1_1(a73)) | (~c2_1(a73))),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 1.39/1.57 tff(1591,plain,
% 1.39/1.57 ($false),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[1590, 92, 1566, 1538, 1565, 304, 323, 1564, 1584, 1574, 1573, 1545])).
% 1.39/1.57 tff(1592,plain,(c3_1(a20) | (~c1_1(a1)) | (~c3_1(a1)) | hskp1 | c0_1(a20) | c0_1(a7) | c1_1(a7) | c2_1(a1) | c2_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.57 tff(1593,plain,
% 1.39/1.57 ($false),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[1592, 1491, 1490, 1489, 32, 1455, 45, 57, 1454, 1488])).
% 1.39/1.57 tff(1594,plain,((~hskp0) | hskp1 | c0_1(a7) | c1_1(a7) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.39/1.57 tff(1595,plain,
% 1.39/1.57 (~hskp0),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[1594, 274, 45, 57, 32])).
% 1.39/1.57 tff(1596,plain,
% 1.39/1.57 (^[U: $i] : refl((hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.39/1.57 inference(bind,[status(th)],[])).
% 1.39/1.57 tff(1597,plain,
% 1.39/1.57 (![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.39/1.57 inference(quant_intro,[status(thm)],[1596])).
% 1.39/1.57 tff(1598,plain,
% 1.39/1.57 (![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.39/1.57 inference(rewrite,[status(thm)],[])).
% 1.39/1.57 tff(1599,plain,
% 1.39/1.57 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) | hskp4) <=> ((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4))), rewrite(((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) | hskp4) <=> (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.39/1.57 inference(bind,[status(th)],[])).
% 1.39/1.57 tff(1600,plain,
% 1.39/1.57 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) | hskp4) <=> ![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.39/1.57 inference(quant_intro,[status(thm)],[1599])).
% 1.39/1.57 tff(1601,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp0) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.39/1.57 tff(1602,plain,
% 1.39/1.57 (![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1601, 1600])).
% 1.39/1.57 tff(1603,plain,
% 1.39/1.57 (![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1602, 1598])).
% 1.39/1.57 tff(1604,plain,(
% 1.39/1.57 ![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.39/1.57 inference(skolemize,[status(sab)],[1603])).
% 1.39/1.57 tff(1605,plain,
% 1.39/1.57 (![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1604, 1597])).
% 1.39/1.57 tff(1606,plain,
% 1.39/1.57 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a7) | c1_1(a7) | (~ndr1_0) | (~c2_1(a7)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a7) | c1_1(a7) | (~ndr1_0) | (~c2_1(a7)))),
% 1.39/1.57 inference(rewrite,[status(thm)],[])).
% 1.39/1.57 tff(1607,plain,
% 1.39/1.57 ((hskp4 | hskp0 | (~ndr1_0) | c1_1(a7) | c0_1(a7) | (~c2_1(a7))) <=> (hskp4 | hskp0 | c0_1(a7) | c1_1(a7) | (~ndr1_0) | (~c2_1(a7)))),
% 1.39/1.57 inference(rewrite,[status(thm)],[])).
% 1.39/1.57 tff(1608,plain,
% 1.39/1.57 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a7) | c0_1(a7) | (~c2_1(a7)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a7) | c1_1(a7) | (~ndr1_0) | (~c2_1(a7))))),
% 1.39/1.57 inference(monotonicity,[status(thm)],[1607])).
% 1.39/1.57 tff(1609,plain,
% 1.39/1.57 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a7) | c0_1(a7) | (~c2_1(a7)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a7) | c1_1(a7) | (~ndr1_0) | (~c2_1(a7)))),
% 1.39/1.57 inference(transitivity,[status(thm)],[1608, 1606])).
% 1.39/1.57 tff(1610,plain,
% 1.39/1.57 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a7) | c0_1(a7) | (~c2_1(a7)))),
% 1.39/1.57 inference(quant_inst,[status(thm)],[])).
% 1.39/1.57 tff(1611,plain,
% 1.39/1.57 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a7) | c1_1(a7) | (~ndr1_0) | (~c2_1(a7))),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1610, 1609])).
% 1.39/1.57 tff(1612,plain,
% 1.39/1.57 (hskp4 | hskp0 | c1_1(a7) | (~c2_1(a7))),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[1611, 92, 45, 1605])).
% 1.39/1.57 tff(1613,plain,
% 1.39/1.57 (~c2_1(a7)),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[1612, 1595, 57, 1452])).
% 1.39/1.57 tff(1614,plain,
% 1.39/1.57 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.39/1.57 inference(bind,[status(th)],[])).
% 1.39/1.57 tff(1615,plain,
% 1.39/1.57 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.39/1.57 inference(quant_intro,[status(thm)],[1614])).
% 1.39/1.57 tff(1616,plain,
% 1.39/1.57 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.39/1.57 inference(rewrite,[status(thm)],[])).
% 1.39/1.57 tff(1617,plain,
% 1.39/1.57 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.39/1.57 inference(bind,[status(th)],[])).
% 1.39/1.57 tff(1618,plain,
% 1.39/1.57 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.39/1.57 inference(quant_intro,[status(thm)],[1617])).
% 1.39/1.57 tff(1619,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 1.39/1.57 tff(1620,plain,
% 1.39/1.57 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1619, 1618])).
% 1.39/1.57 tff(1621,plain,
% 1.39/1.57 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1620, 1616])).
% 1.39/1.57 tff(1622,plain,(
% 1.39/1.57 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.39/1.57 inference(skolemize,[status(sab)],[1621])).
% 1.39/1.57 tff(1623,plain,
% 1.39/1.57 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1622, 1615])).
% 1.39/1.57 tff(1624,plain,
% 1.39/1.57 (hskp22),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[250, 1595, 274])).
% 1.39/1.57 tff(1625,plain,
% 1.39/1.57 (~c3_1(a48)),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[176, 1624])).
% 1.39/1.57 tff(1626,plain,
% 1.39/1.57 (c1_1(a48)),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[153, 1624])).
% 1.39/1.57 tff(1627,plain,
% 1.39/1.57 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c3_1(a48) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a48)) | c2_1(a48))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a48) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a48)) | c2_1(a48))),
% 1.39/1.57 inference(rewrite,[status(thm)],[])).
% 1.39/1.57 tff(1628,plain,
% 1.39/1.57 ((hskp0 | (~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a7) | c1_1(a7) | c0_1(a7)) <=> (hskp0 | c3_1(a48) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a48)) | c2_1(a48))),
% 1.39/1.57 inference(rewrite,[status(thm)],[])).
% 1.39/1.57 tff(1629,plain,
% 1.39/1.57 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c3_1(a48) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a48)) | c2_1(a48)))),
% 1.39/1.57 inference(monotonicity,[status(thm)],[1628])).
% 1.39/1.57 tff(1630,plain,
% 1.39/1.57 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a48) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a48)) | c2_1(a48))),
% 1.39/1.57 inference(transitivity,[status(thm)],[1629, 1627])).
% 1.39/1.57 tff(1631,plain,
% 1.39/1.57 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a7) | c1_1(a7) | c0_1(a7))),
% 1.39/1.57 inference(quant_inst,[status(thm)],[])).
% 1.39/1.57 tff(1632,plain,
% 1.39/1.57 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a48) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a48)) | c2_1(a48)),
% 1.39/1.57 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 1.39/1.57 tff(1633,plain,
% 1.39/1.57 (c2_1(a48)),
% 1.39/1.57 inference(unit_resolution,[status(thm)],[1632, 92, 1595, 1626, 1625, 45, 57, 1623, 1613])).
% 1.39/1.57 tff(1634,plain,
% 1.39/1.57 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 1.39/1.57 inference(bind,[status(th)],[])).
% 1.39/1.57 tff(1635,plain,
% 1.39/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.39/1.58 inference(quant_intro,[status(thm)],[1634])).
% 1.39/1.58 tff(1636,plain,
% 1.39/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1637,plain,
% 1.39/1.58 (^[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))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 1.39/1.58 inference(bind,[status(th)],[])).
% 1.39/1.58 tff(1638,plain,
% 1.39/1.58 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.39/1.58 inference(quant_intro,[status(thm)],[1637])).
% 1.39/1.58 tff(1639,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 1.39/1.58 tff(1640,plain,
% 1.39/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1639, 1638])).
% 1.39/1.58 tff(1641,plain,
% 1.39/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1640, 1636])).
% 1.39/1.58 tff(1642,plain,(
% 1.39/1.58 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.39/1.58 inference(skolemize,[status(sab)],[1641])).
% 1.39/1.58 tff(1643,plain,
% 1.39/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1642, 1635])).
% 1.39/1.58 tff(1644,plain,
% 1.39/1.58 (~c0_1(a48)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[145, 1624])).
% 1.39/1.58 tff(1645,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a48) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a48) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1646,plain,
% 1.39/1.58 ((hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7))) <=> (hskp5 | c0_1(a48) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1647,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a48) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48))))),
% 1.39/1.58 inference(monotonicity,[status(thm)],[1646])).
% 1.39/1.58 tff(1648,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a48) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.39/1.58 inference(transitivity,[status(thm)],[1647, 1645])).
% 1.39/1.58 tff(1649,plain,
% 1.39/1.58 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))),
% 1.39/1.58 inference(quant_inst,[status(thm)],[])).
% 1.39/1.58 tff(1650,plain,
% 1.39/1.58 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a48) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 1.39/1.58 tff(1651,plain,
% 1.39/1.58 (hskp5),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1650, 92, 1626, 1644, 45, 57, 1446, 21, 1633])).
% 1.39/1.58 tff(1652,plain,
% 1.39/1.58 (((~hskp5) | (~c3_1(a8))) <=> ((~hskp5) | (~c3_1(a8)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1653,plain,
% 1.39/1.58 (((~c3_1(a8)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a8)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1654,axiom,((~c3_1(a8)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.39/1.58 tff(1655,plain,
% 1.39/1.58 ((~hskp5) | (~c3_1(a8))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 1.39/1.58 tff(1656,plain,
% 1.39/1.58 ((~hskp5) | (~c3_1(a8))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1655, 1652])).
% 1.39/1.58 tff(1657,plain,
% 1.39/1.58 (~c3_1(a8)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1656, 1651])).
% 1.39/1.58 tff(1658,plain,
% 1.39/1.58 (((~hskp5) | (~c2_1(a8))) <=> ((~hskp5) | (~c2_1(a8)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1659,plain,
% 1.39/1.58 (((~c2_1(a8)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a8)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1660,axiom,((~c2_1(a8)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.39/1.58 tff(1661,plain,
% 1.39/1.58 ((~hskp5) | (~c2_1(a8))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1660, 1659])).
% 1.39/1.58 tff(1662,plain,
% 1.39/1.58 ((~hskp5) | (~c2_1(a8))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1661, 1658])).
% 1.39/1.58 tff(1663,plain,
% 1.39/1.58 (~c2_1(a8)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1662, 1651])).
% 1.39/1.58 tff(1664,plain,
% 1.39/1.58 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.39/1.58 inference(bind,[status(th)],[])).
% 1.39/1.58 tff(1665,plain,
% 1.39/1.58 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.58 inference(quant_intro,[status(thm)],[1664])).
% 1.39/1.58 tff(1666,plain,
% 1.39/1.58 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1667,plain,
% 1.39/1.58 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.39/1.58 inference(bind,[status(th)],[])).
% 1.39/1.58 tff(1668,plain,
% 1.39/1.58 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.58 inference(quant_intro,[status(thm)],[1667])).
% 1.39/1.58 tff(1669,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.39/1.58 tff(1670,plain,
% 1.39/1.58 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1669, 1668])).
% 1.39/1.58 tff(1671,plain,
% 1.39/1.58 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1670, 1666])).
% 1.39/1.58 tff(1672,plain,(
% 1.39/1.58 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.58 inference(skolemize,[status(sab)],[1671])).
% 1.39/1.58 tff(1673,plain,
% 1.39/1.58 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1672, 1665])).
% 1.39/1.58 tff(1674,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1675,plain,
% 1.39/1.58 ((hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48))) <=> (hskp28 | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1676,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))))),
% 1.39/1.58 inference(monotonicity,[status(thm)],[1675])).
% 1.39/1.58 tff(1677,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.58 inference(transitivity,[status(thm)],[1676, 1674])).
% 1.39/1.58 tff(1678,plain,
% 1.39/1.58 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48)))),
% 1.39/1.58 inference(quant_inst,[status(thm)],[])).
% 1.39/1.58 tff(1679,plain,
% 1.39/1.58 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1678, 1677])).
% 1.39/1.58 tff(1680,plain,
% 1.39/1.58 (hskp28),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1679, 92, 1509, 1508, 1520, 1626, 1644, 1625, 1673])).
% 1.39/1.58 tff(1681,plain,
% 1.39/1.58 (((~hskp28) | c2_1(a23)) <=> ((~hskp28) | c2_1(a23))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1682,axiom,((~hskp28) | c2_1(a23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 1.39/1.58 tff(1683,plain,
% 1.39/1.58 ((~hskp28) | c2_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 1.39/1.58 tff(1684,plain,
% 1.39/1.58 ((~hskp28) | c2_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1683, 1681])).
% 1.39/1.58 tff(1685,plain,
% 1.39/1.58 ((~hskp28) | c2_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1684, 1681])).
% 1.39/1.58 tff(1686,plain,
% 1.39/1.58 ((~hskp28) | c2_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1685, 1681])).
% 1.39/1.58 tff(1687,plain,
% 1.39/1.58 ((~hskp28) | c2_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1686, 1681])).
% 1.39/1.58 tff(1688,plain,
% 1.39/1.58 (c2_1(a23)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1687, 1680])).
% 1.39/1.58 tff(1689,plain,
% 1.39/1.58 (((~hskp28) | c1_1(a23)) <=> ((~hskp28) | c1_1(a23))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1690,axiom,((~hskp28) | c1_1(a23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 1.39/1.58 tff(1691,plain,
% 1.39/1.58 ((~hskp28) | c1_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 1.39/1.58 tff(1692,plain,
% 1.39/1.58 ((~hskp28) | c1_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1691, 1689])).
% 1.39/1.58 tff(1693,plain,
% 1.39/1.58 ((~hskp28) | c1_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1692, 1689])).
% 1.39/1.58 tff(1694,plain,
% 1.39/1.58 ((~hskp28) | c1_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1693, 1689])).
% 1.39/1.58 tff(1695,plain,
% 1.39/1.58 ((~hskp28) | c1_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1694, 1689])).
% 1.39/1.58 tff(1696,plain,
% 1.39/1.58 (c1_1(a23)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1695, 1680])).
% 1.39/1.58 tff(1697,plain,
% 1.39/1.58 (((~hskp28) | c0_1(a23)) <=> ((~hskp28) | c0_1(a23))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1698,axiom,((~hskp28) | c0_1(a23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.39/1.58 tff(1699,plain,
% 1.39/1.58 ((~hskp28) | c0_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 1.39/1.58 tff(1700,plain,
% 1.39/1.58 ((~hskp28) | c0_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1699, 1697])).
% 1.39/1.58 tff(1701,plain,
% 1.39/1.58 ((~hskp28) | c0_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1700, 1697])).
% 1.39/1.58 tff(1702,plain,
% 1.39/1.58 ((~hskp28) | c0_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1701, 1697])).
% 1.39/1.58 tff(1703,plain,
% 1.39/1.58 ((~hskp28) | c0_1(a23)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1702, 1697])).
% 1.39/1.58 tff(1704,plain,
% 1.39/1.58 (c0_1(a23)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1703, 1680])).
% 1.39/1.58 tff(1705,plain,
% 1.39/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a48) | c3_1(a48) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a48)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a48) | c3_1(a48) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a48)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1706,plain,
% 1.39/1.58 (((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a48) | c3_1(a48) | (~c2_1(a48))) <=> (c0_1(a48) | c3_1(a48) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a48)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1707,plain,
% 1.39/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a48) | c3_1(a48) | (~c2_1(a48)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a48) | c3_1(a48) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a48))))),
% 1.39/1.58 inference(monotonicity,[status(thm)],[1706])).
% 1.39/1.58 tff(1708,plain,
% 1.39/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a48) | c3_1(a48) | (~c2_1(a48)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a48) | c3_1(a48) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a48)))),
% 1.39/1.58 inference(transitivity,[status(thm)],[1707, 1705])).
% 1.39/1.58 tff(1709,plain,
% 1.39/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a48) | c3_1(a48) | (~c2_1(a48)))),
% 1.39/1.58 inference(quant_inst,[status(thm)],[])).
% 1.39/1.58 tff(1710,plain,
% 1.39/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a48) | c3_1(a48) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a48))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1709, 1708])).
% 1.39/1.58 tff(1711,plain,
% 1.39/1.58 (~c0_1(a8)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1710, 92, 1704, 1696, 1688, 1644, 1625, 1663, 1657, 1643, 1633])).
% 1.39/1.58 tff(1712,plain,
% 1.39/1.58 (((~hskp5) | c1_1(a8)) <=> ((~hskp5) | c1_1(a8))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1713,axiom,((~hskp5) | c1_1(a8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.39/1.58 tff(1714,plain,
% 1.39/1.58 ((~hskp5) | c1_1(a8)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1713, 1712])).
% 1.39/1.58 tff(1715,plain,
% 1.39/1.58 ((~hskp5) | c1_1(a8)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1714, 1712])).
% 1.39/1.58 tff(1716,plain,
% 1.39/1.58 ((~hskp5) | c1_1(a8)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1715, 1712])).
% 1.39/1.58 tff(1717,plain,
% 1.39/1.58 ((~hskp5) | c1_1(a8)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1716, 1712])).
% 1.39/1.58 tff(1718,plain,
% 1.39/1.58 ((~hskp5) | c1_1(a8)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1717, 1712])).
% 1.39/1.58 tff(1719,plain,
% 1.39/1.58 (c1_1(a8)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1718, 1651])).
% 1.39/1.58 tff(1720,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a48) | c3_1(a48) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c0_1(a8) | (~c1_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a48) | c3_1(a48) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c0_1(a8) | (~c1_1(a48)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1721,plain,
% 1.39/1.58 ((hskp4 | (~ndr1_0) | c3_1(a48) | c0_1(a48) | (~c1_1(a48)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8))) <=> (hskp4 | c0_1(a48) | c3_1(a48) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c0_1(a8) | (~c1_1(a48)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1722,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a48) | c0_1(a48) | (~c1_1(a48)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a48) | c3_1(a48) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c0_1(a8) | (~c1_1(a48))))),
% 1.39/1.58 inference(monotonicity,[status(thm)],[1721])).
% 1.39/1.58 tff(1723,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a48) | c0_1(a48) | (~c1_1(a48)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a48) | c3_1(a48) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c0_1(a8) | (~c1_1(a48)))),
% 1.39/1.58 inference(transitivity,[status(thm)],[1722, 1720])).
% 1.39/1.58 tff(1724,plain,
% 1.39/1.58 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a48) | c0_1(a48) | (~c1_1(a48)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))),
% 1.39/1.58 inference(quant_inst,[status(thm)],[])).
% 1.39/1.58 tff(1725,plain,
% 1.39/1.58 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a48) | c3_1(a48) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c0_1(a8) | (~c1_1(a48))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1724, 1723])).
% 1.39/1.58 tff(1726,plain,
% 1.39/1.58 ($false),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1725, 92, 1452, 1626, 1719, 1644, 1625, 1663, 56, 1711])).
% 1.39/1.58 tff(1727,plain,(hskp11 | c0_1(a7) | c1_1(a7) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.39/1.58 tff(1728,plain,
% 1.39/1.58 (hskp11),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1727, 57, 45, 32])).
% 1.39/1.58 tff(1729,plain,
% 1.39/1.58 (~c0_1(a19)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[98, 1728])).
% 1.39/1.58 tff(1730,plain,
% 1.39/1.58 (c2_1(a19)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[115, 1728])).
% 1.39/1.58 tff(1731,plain,
% 1.39/1.58 (c1_1(a19)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[107, 1728])).
% 1.39/1.58 tff(1732,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a19) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a19) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1733,plain,
% 1.39/1.58 ((hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7))) <=> (hskp5 | c0_1(a19) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1734,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a19) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19))))),
% 1.39/1.58 inference(monotonicity,[status(thm)],[1733])).
% 1.39/1.58 tff(1735,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a19) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.39/1.58 inference(transitivity,[status(thm)],[1734, 1732])).
% 1.39/1.58 tff(1736,plain,
% 1.39/1.58 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))),
% 1.39/1.58 inference(quant_inst,[status(thm)],[])).
% 1.39/1.58 tff(1737,plain,
% 1.39/1.58 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a19) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19))),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 1.39/1.58 tff(1738,plain,
% 1.39/1.58 (hskp5),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1737, 92, 1731, 1730, 1729, 45, 57, 1446, 21])).
% 1.39/1.58 tff(1739,plain,
% 1.39/1.58 (~c3_1(a8)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1656, 1738])).
% 1.39/1.58 tff(1740,plain,
% 1.39/1.58 (~c2_1(a8)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1662, 1738])).
% 1.39/1.58 tff(1741,plain,
% 1.39/1.58 (c1_1(a8)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1718, 1738])).
% 1.39/1.58 tff(1742,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c0_1(a8))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c0_1(a8))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1743,plain,
% 1.39/1.58 ((hskp4 | (~ndr1_0) | c3_1(a8) | c0_1(a8) | (~c1_1(a8)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8))) <=> (hskp4 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c0_1(a8))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1744,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a8) | c0_1(a8) | (~c1_1(a8)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c0_1(a8)))),
% 1.39/1.58 inference(monotonicity,[status(thm)],[1743])).
% 1.39/1.58 tff(1745,plain,
% 1.39/1.58 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a8) | c0_1(a8) | (~c1_1(a8)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c0_1(a8))),
% 1.39/1.58 inference(transitivity,[status(thm)],[1744, 1742])).
% 1.39/1.58 tff(1746,plain,
% 1.39/1.58 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a8) | c0_1(a8) | (~c1_1(a8)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))),
% 1.39/1.58 inference(quant_inst,[status(thm)],[])).
% 1.39/1.58 tff(1747,plain,
% 1.39/1.58 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c0_1(a8)),
% 1.39/1.58 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 1.39/1.58 tff(1748,plain,
% 1.39/1.58 (c0_1(a8)),
% 1.39/1.58 inference(unit_resolution,[status(thm)],[1747, 92, 1452, 1741, 1740, 1739, 56])).
% 1.39/1.58 tff(1749,plain,
% 1.39/1.58 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1750,plain,
% 1.39/1.58 ((hskp19 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8))) <=> (hskp19 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)))),
% 1.39/1.58 inference(rewrite,[status(thm)],[])).
% 1.39/1.58 tff(1751,plain,
% 1.39/1.58 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8))))),
% 1.39/1.58 inference(monotonicity,[status(thm)],[1750])).
% 1.39/1.58 tff(1752,plain,
% 1.39/1.58 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)))),
% 1.39/1.59 inference(transitivity,[status(thm)],[1751, 1749])).
% 1.39/1.59 tff(1753,plain,
% 1.39/1.59 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)))),
% 1.39/1.59 inference(quant_inst,[status(thm)],[])).
% 1.39/1.59 tff(1754,plain,
% 1.39/1.59 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 1.39/1.59 tff(1755,plain,
% 1.39/1.59 (hskp19),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1754, 92, 1741, 1740, 1739, 930])).
% 1.39/1.59 tff(1756,plain,
% 1.39/1.59 (~c3_1(a40)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[854, 1755])).
% 1.39/1.59 tff(1757,plain,
% 1.39/1.59 (~c0_1(a40)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[833, 1755])).
% 1.39/1.59 tff(1758,plain,
% 1.39/1.59 (c2_1(a40)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[841, 1755])).
% 1.39/1.59 tff(1759,plain,
% 1.39/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a19) | c2_1(a8) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)) | (~c2_1(a19)) | (~c3_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a19) | c2_1(a8) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)) | (~c2_1(a19)) | (~c3_1(a19)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1760,plain,
% 1.39/1.59 (((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c0_1(a19) | (~c2_1(a19)) | (~c3_1(a19)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7))) <=> (c0_1(a19) | c2_1(a8) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)) | (~c2_1(a19)) | (~c3_1(a19)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1761,plain,
% 1.39/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c0_1(a19) | (~c2_1(a19)) | (~c3_1(a19)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a19) | c2_1(a8) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)) | (~c2_1(a19)) | (~c3_1(a19))))),
% 1.39/1.59 inference(monotonicity,[status(thm)],[1760])).
% 1.39/1.59 tff(1762,plain,
% 1.39/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c0_1(a19) | (~c2_1(a19)) | (~c3_1(a19)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a19) | c2_1(a8) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)) | (~c2_1(a19)) | (~c3_1(a19)))),
% 1.39/1.59 inference(transitivity,[status(thm)],[1761, 1759])).
% 1.39/1.59 tff(1763,plain,
% 1.39/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c0_1(a19) | (~c2_1(a19)) | (~c3_1(a19)) | c1_1(a7) | c0_1(a7) | (~c3_1(a7)))),
% 1.39/1.59 inference(quant_inst,[status(thm)],[])).
% 1.39/1.59 tff(1764,plain,
% 1.39/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a19) | c2_1(a8) | c0_1(a7) | c1_1(a7) | (~c3_1(a7)) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)) | (~c2_1(a19)) | (~c3_1(a19))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 1.39/1.59 tff(1765,plain,
% 1.39/1.59 ((~c0_1(a8)) | (~c3_1(a19))),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1764, 92, 1730, 1741, 1729, 1740, 45, 57, 1446, 1465])).
% 1.39/1.59 tff(1766,plain,
% 1.39/1.59 (~c3_1(a19)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1765, 1748])).
% 1.39/1.59 tff(1767,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1768,plain,
% 1.39/1.59 ((hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19))) <=> (hskp28 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1769,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))))),
% 1.39/1.59 inference(monotonicity,[status(thm)],[1768])).
% 1.39/1.59 tff(1770,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.59 inference(transitivity,[status(thm)],[1769, 1767])).
% 1.39/1.59 tff(1771,plain,
% 1.39/1.59 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))),
% 1.39/1.59 inference(quant_inst,[status(thm)],[])).
% 1.39/1.59 tff(1772,plain,
% 1.39/1.59 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 1.39/1.59 tff(1773,plain,
% 1.39/1.59 (hskp28 | c3_1(a19)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1772, 92, 1509, 1508, 1520, 1731, 1729, 1673])).
% 1.39/1.59 tff(1774,plain,
% 1.39/1.59 (hskp28),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1773, 1766])).
% 1.39/1.59 tff(1775,plain,
% 1.39/1.59 (c2_1(a23)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1687, 1774])).
% 1.39/1.59 tff(1776,plain,
% 1.39/1.59 (c1_1(a23)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1695, 1774])).
% 1.39/1.59 tff(1777,plain,
% 1.39/1.59 (c0_1(a23)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1703, 1774])).
% 1.39/1.59 tff(1778,plain,
% 1.39/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a40) | c3_1(a40) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a40) | c3_1(a40) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a40)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1779,plain,
% 1.39/1.59 (((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a40) | c3_1(a40) | (~c2_1(a40))) <=> (c0_1(a40) | c3_1(a40) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a40)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1780,plain,
% 1.39/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a40) | c3_1(a40) | (~c2_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a40) | c3_1(a40) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a40))))),
% 1.39/1.59 inference(monotonicity,[status(thm)],[1779])).
% 1.39/1.59 tff(1781,plain,
% 1.39/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a40) | c3_1(a40) | (~c2_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a40) | c3_1(a40) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a40)))),
% 1.39/1.59 inference(transitivity,[status(thm)],[1780, 1778])).
% 1.39/1.59 tff(1782,plain,
% 1.39/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a40) | c3_1(a40) | (~c2_1(a40)))),
% 1.39/1.59 inference(quant_inst,[status(thm)],[])).
% 1.39/1.59 tff(1783,plain,
% 1.39/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a40) | c3_1(a40) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a40))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 1.39/1.59 tff(1784,plain,
% 1.39/1.59 ($false),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1783, 92, 1777, 1776, 1775, 1758, 1757, 1756, 1740, 1739, 1643, 1748])).
% 1.39/1.59 tff(1785,plain,(c1_1(a7) | c0_1(a7) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.39/1.59 tff(1786,plain,
% 1.39/1.59 (c1_1(a7)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1785, 45, 32])).
% 1.39/1.59 tff(1787,plain,
% 1.39/1.59 (((~hskp4) | (~c1_1(a7))) <=> ((~hskp4) | (~c1_1(a7)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1788,plain,
% 1.39/1.59 (((~c1_1(a7)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a7)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1789,axiom,((~c1_1(a7)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.39/1.59 tff(1790,plain,
% 1.39/1.59 ((~hskp4) | (~c1_1(a7))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 1.39/1.59 tff(1791,plain,
% 1.39/1.59 ((~hskp4) | (~c1_1(a7))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1790, 1787])).
% 1.39/1.59 tff(1792,plain,
% 1.39/1.59 (~hskp4),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1791, 1786])).
% 1.39/1.59 tff(1793,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a20) | c2_1(a20) | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a20) | c2_1(a20) | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a20)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1794,plain,
% 1.39/1.59 ((hskp4 | (~ndr1_0) | c3_1(a7) | c0_1(a7) | (~c1_1(a7)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20))) <=> (hskp4 | c0_1(a20) | c2_1(a20) | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a20)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1795,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a7) | c0_1(a7) | (~c1_1(a7)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a20) | c2_1(a20) | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a20))))),
% 1.39/1.59 inference(monotonicity,[status(thm)],[1794])).
% 1.39/1.59 tff(1796,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a7) | c0_1(a7) | (~c1_1(a7)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a20) | c2_1(a20) | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a20)))),
% 1.39/1.59 inference(transitivity,[status(thm)],[1795, 1793])).
% 1.39/1.59 tff(1797,plain,
% 1.39/1.59 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a7) | c0_1(a7) | (~c1_1(a7)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)))),
% 1.39/1.59 inference(quant_inst,[status(thm)],[])).
% 1.39/1.59 tff(1798,plain,
% 1.39/1.59 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a20) | c2_1(a20) | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a20))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1797, 1796])).
% 1.39/1.59 tff(1799,plain,
% 1.39/1.59 (~c1_1(a20)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1798, 92, 1792, 33, 390, 45, 1786, 58, 56])).
% 1.39/1.59 tff(1800,plain,
% 1.39/1.59 (hskp27),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1506, 1792, 32])).
% 1.39/1.59 tff(1801,plain,
% 1.39/1.59 (c3_1(a13)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[473, 1800])).
% 1.39/1.59 tff(1802,plain,
% 1.39/1.59 (c2_1(a13)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[918, 1800])).
% 1.39/1.59 tff(1803,plain,
% 1.39/1.59 (c1_1(a13)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[465, 1800])).
% 1.39/1.59 tff(1804,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1805,plain,
% 1.39/1.59 ((hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a7) | c3_1(a7) | (~c1_1(a7))) <=> (hskp28 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1806,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a7) | c3_1(a7) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))))),
% 1.39/1.59 inference(monotonicity,[status(thm)],[1805])).
% 1.39/1.59 tff(1807,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a7) | c3_1(a7) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.59 inference(transitivity,[status(thm)],[1806, 1804])).
% 1.39/1.59 tff(1808,plain,
% 1.39/1.59 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a7) | c3_1(a7) | (~c1_1(a7)))),
% 1.39/1.59 inference(quant_inst,[status(thm)],[])).
% 1.39/1.59 tff(1809,plain,
% 1.39/1.59 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1808, 1807])).
% 1.39/1.59 tff(1810,plain,
% 1.39/1.59 (hskp28 | c3_1(a7)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1809, 92, 1803, 1802, 1801, 45, 1786, 1673])).
% 1.39/1.59 tff(1811,plain,
% 1.39/1.59 (hskp28),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1810, 58])).
% 1.39/1.59 tff(1812,plain,
% 1.39/1.59 (c2_1(a23)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1687, 1811])).
% 1.39/1.59 tff(1813,plain,
% 1.39/1.59 (c1_1(a23)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1695, 1811])).
% 1.39/1.59 tff(1814,plain,
% 1.39/1.59 (c0_1(a23)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1703, 1811])).
% 1.39/1.59 tff(1815,assumption,(c1_1(a7)), introduced(assumption)).
% 1.39/1.59 tff(1816,plain,
% 1.39/1.59 (~hskp4),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1791, 1815])).
% 1.39/1.59 tff(1817,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1818,plain,
% 1.39/1.59 ((hskp4 | (~ndr1_0) | c3_1(a7) | c0_1(a7) | (~c1_1(a7)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1))) <=> (hskp4 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1819,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a7) | c0_1(a7) | (~c1_1(a7)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1)))),
% 1.39/1.59 inference(monotonicity,[status(thm)],[1818])).
% 1.39/1.59 tff(1820,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a7) | c0_1(a7) | (~c1_1(a7)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1))),
% 1.39/1.59 inference(transitivity,[status(thm)],[1819, 1817])).
% 1.39/1.59 tff(1821,plain,
% 1.39/1.59 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a7) | c0_1(a7) | (~c1_1(a7)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)))),
% 1.39/1.59 inference(quant_inst,[status(thm)],[])).
% 1.39/1.59 tff(1822,plain,
% 1.39/1.59 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1)),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1821, 1820])).
% 1.39/1.59 tff(1823,plain,
% 1.39/1.59 (c0_1(a1)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1822, 92, 1816, 1455, 45, 1815, 58, 1454, 56])).
% 1.39/1.59 tff(1824,plain,
% 1.39/1.59 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.39/1.59 inference(bind,[status(th)],[])).
% 1.39/1.59 tff(1825,plain,
% 1.39/1.59 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.59 inference(quant_intro,[status(thm)],[1824])).
% 1.39/1.59 tff(1826,plain,
% 1.39/1.59 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1827,plain,
% 1.39/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp13))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.39/1.59 inference(bind,[status(th)],[])).
% 1.39/1.59 tff(1828,plain,
% 1.39/1.59 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.59 inference(quant_intro,[status(thm)],[1827])).
% 1.39/1.59 tff(1829,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 1.39/1.59 tff(1830,plain,
% 1.39/1.59 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 1.39/1.59 tff(1831,plain,
% 1.39/1.59 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1830, 1826])).
% 1.39/1.59 tff(1832,plain,(
% 1.39/1.59 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.59 inference(skolemize,[status(sab)],[1831])).
% 1.39/1.59 tff(1833,plain,
% 1.39/1.59 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1832, 1825])).
% 1.39/1.59 tff(1834,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1835,plain,
% 1.39/1.59 ((hskp13 | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c0_1(a7) | c3_1(a7) | (~c1_1(a7))) <=> (hskp13 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1836,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c0_1(a7) | c3_1(a7) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1))))),
% 1.39/1.59 inference(monotonicity,[status(thm)],[1835])).
% 1.39/1.59 tff(1837,plain,
% 1.39/1.59 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c0_1(a7) | c3_1(a7) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)))),
% 1.39/1.59 inference(transitivity,[status(thm)],[1836, 1834])).
% 1.39/1.59 tff(1838,plain,
% 1.39/1.59 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c0_1(a7) | c3_1(a7) | (~c1_1(a7)))),
% 1.39/1.59 inference(quant_inst,[status(thm)],[])).
% 1.39/1.59 tff(1839,plain,
% 1.39/1.59 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1838, 1837])).
% 1.39/1.59 tff(1840,plain,
% 1.39/1.59 (hskp13 | (~c0_1(a1))),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1839, 92, 1455, 1489, 45, 1815, 58, 1833])).
% 1.39/1.59 tff(1841,plain,
% 1.39/1.59 (hskp13),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1840, 1823])).
% 1.39/1.59 tff(1842,plain,
% 1.39/1.59 (((~hskp13) | (~c1_1(a22))) <=> ((~hskp13) | (~c1_1(a22)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1843,plain,
% 1.39/1.59 (((~c1_1(a22)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a22)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1844,axiom,((~c1_1(a22)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.39/1.59 tff(1845,plain,
% 1.39/1.59 ((~hskp13) | (~c1_1(a22))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 1.39/1.59 tff(1846,plain,
% 1.39/1.59 ((~hskp13) | (~c1_1(a22))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1845, 1842])).
% 1.39/1.59 tff(1847,plain,
% 1.39/1.59 (~c1_1(a22)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1846, 1841])).
% 1.39/1.59 tff(1848,plain,
% 1.39/1.59 (((~hskp13) | (~c0_1(a22))) <=> ((~hskp13) | (~c0_1(a22)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1849,plain,
% 1.39/1.59 (((~c0_1(a22)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a22)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1850,axiom,((~c0_1(a22)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 1.39/1.59 tff(1851,plain,
% 1.39/1.59 ((~hskp13) | (~c0_1(a22))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1850, 1849])).
% 1.39/1.59 tff(1852,plain,
% 1.39/1.59 ((~hskp13) | (~c0_1(a22))),
% 1.39/1.59 inference(modus_ponens,[status(thm)],[1851, 1848])).
% 1.39/1.59 tff(1853,plain,
% 1.39/1.59 (~c0_1(a22)),
% 1.39/1.59 inference(unit_resolution,[status(thm)],[1852, 1841])).
% 1.39/1.59 tff(1854,plain,
% 1.39/1.59 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.39/1.59 inference(bind,[status(th)],[])).
% 1.39/1.59 tff(1855,plain,
% 1.39/1.59 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.59 inference(quant_intro,[status(thm)],[1854])).
% 1.39/1.59 tff(1856,plain,
% 1.39/1.59 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.59 inference(rewrite,[status(thm)],[])).
% 1.39/1.59 tff(1857,plain,
% 1.39/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.39/1.60 inference(bind,[status(th)],[])).
% 1.39/1.60 tff(1858,plain,
% 1.39/1.60 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.60 inference(quant_intro,[status(thm)],[1857])).
% 1.39/1.60 tff(1859,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 1.39/1.60 tff(1860,plain,
% 1.39/1.60 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1859, 1858])).
% 1.39/1.60 tff(1861,plain,
% 1.39/1.60 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1860, 1856])).
% 1.39/1.60 tff(1862,plain,(
% 1.39/1.60 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.60 inference(skolemize,[status(sab)],[1861])).
% 1.39/1.60 tff(1863,plain,
% 1.39/1.60 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1862, 1855])).
% 1.39/1.60 tff(1864,plain,
% 1.39/1.60 (((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1865,plain,
% 1.39/1.60 ((hskp25 | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1))) <=> (hskp25 | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1866,plain,
% 1.39/1.60 (((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1))))),
% 1.39/1.60 inference(monotonicity,[status(thm)],[1865])).
% 1.39/1.60 tff(1867,plain,
% 1.39/1.60 (((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)))),
% 1.39/1.60 inference(transitivity,[status(thm)],[1866, 1864])).
% 1.39/1.60 tff(1868,plain,
% 1.39/1.60 ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)))),
% 1.39/1.60 inference(quant_inst,[status(thm)],[])).
% 1.39/1.60 tff(1869,plain,
% 1.39/1.60 ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1))),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1868, 1867])).
% 1.39/1.60 tff(1870,plain,
% 1.39/1.60 (hskp25 | (~c0_1(a1))),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1869, 92, 1455, 1489, 1555])).
% 1.39/1.60 tff(1871,plain,
% 1.39/1.60 (hskp25),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1870, 1823])).
% 1.39/1.60 tff(1872,plain,
% 1.39/1.60 (~c3_1(a73)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1138, 1871])).
% 1.39/1.60 tff(1873,plain,
% 1.39/1.60 (c2_1(a73)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1187, 1871])).
% 1.39/1.60 tff(1874,plain,
% 1.39/1.60 (c0_1(a73)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1146, 1871])).
% 1.39/1.60 tff(1875,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | c3_1(a73) | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c2_1(a73)) | (~c0_1(a73)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a73) | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1876,plain,
% 1.39/1.60 ((hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a7) | c3_1(a7) | (~c1_1(a7))) <=> (hskp14 | c3_1(a73) | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1877,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a7) | c3_1(a7) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | c3_1(a73) | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c2_1(a73)) | (~c0_1(a73))))),
% 1.39/1.60 inference(monotonicity,[status(thm)],[1876])).
% 1.39/1.60 tff(1878,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a7) | c3_1(a7) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a73) | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.39/1.60 inference(transitivity,[status(thm)],[1877, 1875])).
% 1.39/1.60 tff(1879,plain,
% 1.39/1.60 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a7) | c3_1(a7) | (~c1_1(a7)))),
% 1.39/1.60 inference(quant_inst,[status(thm)],[])).
% 1.39/1.60 tff(1880,plain,
% 1.39/1.60 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a73) | c0_1(a7) | (~c1_1(a7)) | c3_1(a7) | (~ndr1_0) | (~c2_1(a73)) | (~c0_1(a73))),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1879, 1878])).
% 1.39/1.60 tff(1881,plain,
% 1.39/1.60 (hskp14),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1880, 92, 1874, 1873, 1872, 45, 1815, 58, 1863])).
% 1.39/1.60 tff(1882,plain,
% 1.39/1.60 (((~hskp14) | (~c2_1(a25))) <=> ((~hskp14) | (~c2_1(a25)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1883,plain,
% 1.39/1.60 (((~c2_1(a25)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a25)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1884,axiom,((~c2_1(a25)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.39/1.60 tff(1885,plain,
% 1.39/1.60 ((~hskp14) | (~c2_1(a25))),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 1.39/1.60 tff(1886,plain,
% 1.39/1.60 ((~hskp14) | (~c2_1(a25))),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1885, 1882])).
% 1.39/1.60 tff(1887,plain,
% 1.39/1.60 (~c2_1(a25)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1886, 1881])).
% 1.39/1.60 tff(1888,plain,
% 1.39/1.60 (((~hskp13) | c3_1(a22)) <=> ((~hskp13) | c3_1(a22))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1889,axiom,((~hskp13) | c3_1(a22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.39/1.60 tff(1890,plain,
% 1.39/1.60 ((~hskp13) | c3_1(a22)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1889, 1888])).
% 1.39/1.60 tff(1891,plain,
% 1.39/1.60 ((~hskp13) | c3_1(a22)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1890, 1888])).
% 1.39/1.60 tff(1892,plain,
% 1.39/1.60 ((~hskp13) | c3_1(a22)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1891, 1888])).
% 1.39/1.60 tff(1893,plain,
% 1.39/1.60 ((~hskp13) | c3_1(a22)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1892, 1888])).
% 1.39/1.60 tff(1894,plain,
% 1.39/1.60 ((~hskp13) | c3_1(a22)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1893, 1888])).
% 1.39/1.60 tff(1895,plain,
% 1.39/1.60 (c3_1(a22)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1894, 1841])).
% 1.39/1.60 tff(1896,plain,
% 1.39/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a22) | c1_1(a22) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c2_1(a22)) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a22) | c1_1(a22) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c2_1(a22)) | (~c3_1(a22)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1897,plain,
% 1.39/1.60 (((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a22) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22))) <=> (c0_1(a22) | c1_1(a22) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c2_1(a22)) | (~c3_1(a22)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1898,plain,
% 1.39/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a22) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a22) | c1_1(a22) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c2_1(a22)) | (~c3_1(a22))))),
% 1.39/1.60 inference(monotonicity,[status(thm)],[1897])).
% 1.39/1.60 tff(1899,plain,
% 1.39/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a22) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a22) | c1_1(a22) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c2_1(a22)) | (~c3_1(a22)))),
% 1.39/1.60 inference(transitivity,[status(thm)],[1898, 1896])).
% 1.39/1.60 tff(1900,plain,
% 1.39/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a22) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))),
% 1.39/1.60 inference(quant_inst,[status(thm)],[])).
% 1.39/1.60 tff(1901,plain,
% 1.39/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a22) | c1_1(a22) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c2_1(a22)) | (~c3_1(a22))),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1900, 1899])).
% 1.39/1.60 tff(1902,plain,
% 1.39/1.60 (~c2_1(a22)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1901, 92, 1895, 1455, 1853, 1847, 1454, 1465, 1823])).
% 1.39/1.60 tff(1903,assumption,(c2_1(a23)), introduced(assumption)).
% 1.39/1.60 tff(1904,assumption,(c1_1(a23)), introduced(assumption)).
% 1.39/1.60 tff(1905,assumption,(c0_1(a23)), introduced(assumption)).
% 1.39/1.60 tff(1906,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a22) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c2_1(a22) | (~c3_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a22) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c2_1(a22) | (~c3_1(a22)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1907,plain,
% 1.39/1.60 ((hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a22) | c1_1(a22) | (~c3_1(a22))) <=> (hskp21 | c1_1(a22) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c2_1(a22) | (~c3_1(a22)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1908,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a22) | c1_1(a22) | (~c3_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a22) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c2_1(a22) | (~c3_1(a22))))),
% 1.39/1.60 inference(monotonicity,[status(thm)],[1907])).
% 1.39/1.60 tff(1909,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a22) | c1_1(a22) | (~c3_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a22) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c2_1(a22) | (~c3_1(a22)))),
% 1.39/1.60 inference(transitivity,[status(thm)],[1908, 1906])).
% 1.39/1.60 tff(1910,plain,
% 1.39/1.60 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a22) | c1_1(a22) | (~c3_1(a22)))),
% 1.39/1.60 inference(quant_inst,[status(thm)],[])).
% 1.39/1.60 tff(1911,plain,
% 1.39/1.60 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a22) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c2_1(a22) | (~c3_1(a22))),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 1.39/1.60 tff(1912,plain,
% 1.39/1.60 (hskp21),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1911, 92, 1905, 1904, 1903, 1895, 1847, 1098, 1902])).
% 1.39/1.60 tff(1913,plain,
% 1.39/1.60 (~c0_1(a47)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[777, 1912])).
% 1.39/1.60 tff(1914,plain,
% 1.39/1.60 (((~hskp14) | c1_1(a25)) <=> ((~hskp14) | c1_1(a25))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1915,axiom,((~hskp14) | c1_1(a25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.39/1.60 tff(1916,plain,
% 1.39/1.60 ((~hskp14) | c1_1(a25)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1915, 1914])).
% 1.39/1.60 tff(1917,plain,
% 1.39/1.60 ((~hskp14) | c1_1(a25)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1916, 1914])).
% 1.39/1.60 tff(1918,plain,
% 1.39/1.60 ((~hskp14) | c1_1(a25)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1917, 1914])).
% 1.39/1.60 tff(1919,plain,
% 1.39/1.60 ((~hskp14) | c1_1(a25)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1918, 1914])).
% 1.39/1.60 tff(1920,plain,
% 1.39/1.60 ((~hskp14) | c1_1(a25)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1919, 1914])).
% 1.39/1.60 tff(1921,plain,
% 1.39/1.60 (c1_1(a25)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1920, 1881])).
% 1.39/1.60 tff(1922,plain,
% 1.39/1.60 (((~hskp14) | c0_1(a25)) <=> ((~hskp14) | c0_1(a25))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1923,axiom,((~hskp14) | c0_1(a25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.39/1.60 tff(1924,plain,
% 1.39/1.60 ((~hskp14) | c0_1(a25)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1923, 1922])).
% 1.39/1.60 tff(1925,plain,
% 1.39/1.60 ((~hskp14) | c0_1(a25)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1924, 1922])).
% 1.39/1.60 tff(1926,plain,
% 1.39/1.60 ((~hskp14) | c0_1(a25)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1925, 1922])).
% 1.39/1.60 tff(1927,plain,
% 1.39/1.60 ((~hskp14) | c0_1(a25)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1926, 1922])).
% 1.39/1.60 tff(1928,plain,
% 1.39/1.60 ((~hskp14) | c0_1(a25)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1927, 1922])).
% 1.39/1.60 tff(1929,plain,
% 1.39/1.60 (c0_1(a25)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1928, 1881])).
% 1.39/1.60 tff(1930,plain,
% 1.39/1.60 (c3_1(a47)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[785, 1912])).
% 1.39/1.60 tff(1931,plain,
% 1.39/1.60 (c2_1(a47)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[793, 1912])).
% 1.39/1.60 tff(1932,plain,
% 1.39/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c2_1(a25) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c3_1(a22)) | (~c1_1(a25)) | (~c0_1(a25)) | (~c3_1(a47)) | (~c2_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c2_1(a25) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c3_1(a22)) | (~c1_1(a25)) | (~c0_1(a25)) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1933,plain,
% 1.39/1.60 (((~ndr1_0) | c2_1(a25) | (~c1_1(a25)) | (~c0_1(a25)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22))) <=> (c0_1(a47) | c2_1(a25) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c3_1(a22)) | (~c1_1(a25)) | (~c0_1(a25)) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1934,plain,
% 1.39/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a25) | (~c1_1(a25)) | (~c0_1(a25)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c2_1(a25) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c3_1(a22)) | (~c1_1(a25)) | (~c0_1(a25)) | (~c3_1(a47)) | (~c2_1(a47))))),
% 1.39/1.60 inference(monotonicity,[status(thm)],[1933])).
% 1.39/1.60 tff(1935,plain,
% 1.39/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a25) | (~c1_1(a25)) | (~c0_1(a25)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c2_1(a25) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c3_1(a22)) | (~c1_1(a25)) | (~c0_1(a25)) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.39/1.60 inference(transitivity,[status(thm)],[1934, 1932])).
% 1.39/1.60 tff(1936,plain,
% 1.39/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a25) | (~c1_1(a25)) | (~c0_1(a25)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))),
% 1.39/1.60 inference(quant_inst,[status(thm)],[])).
% 1.39/1.60 tff(1937,plain,
% 1.39/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c2_1(a25) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c3_1(a22)) | (~c1_1(a25)) | (~c0_1(a25)) | (~c3_1(a47)) | (~c2_1(a47))),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 1.39/1.60 tff(1938,plain,
% 1.39/1.60 ($false),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1937, 92, 1931, 1930, 1929, 1921, 1895, 1913, 1887, 1853, 1847, 1465])).
% 1.39/1.60 tff(1939,plain,((~hskp0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c0_1(a7) | (~c1_1(a7)) | c3_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.60 tff(1940,plain,
% 1.39/1.60 (~hskp0),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1939, 1814, 1813, 1812, 45, 1786, 58])).
% 1.39/1.60 tff(1941,assumption,(~hskp4), introduced(assumption)).
% 1.39/1.60 tff(1942,assumption,(~hskp0), introduced(assumption)).
% 1.39/1.60 tff(1943,plain,
% 1.39/1.60 (hskp22),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[250, 274, 1942])).
% 1.39/1.60 tff(1944,plain,
% 1.39/1.60 (~c3_1(a48)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[176, 1943])).
% 1.39/1.60 tff(1945,plain,
% 1.39/1.60 (~c0_1(a48)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[145, 1943])).
% 1.39/1.60 tff(1946,plain,
% 1.39/1.60 (c1_1(a48)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[153, 1943])).
% 1.39/1.60 tff(1947,plain,
% 1.39/1.60 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a47) | (~ndr1_0) | c1_1(a47) | (~c2_1(a47)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a47) | (~ndr1_0) | c1_1(a47) | (~c2_1(a47)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1948,plain,
% 1.39/1.60 ((hskp4 | hskp0 | (~ndr1_0) | c1_1(a47) | c0_1(a47) | (~c2_1(a47))) <=> (hskp4 | hskp0 | c0_1(a47) | (~ndr1_0) | c1_1(a47) | (~c2_1(a47)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1949,plain,
% 1.39/1.60 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a47) | c0_1(a47) | (~c2_1(a47)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a47) | (~ndr1_0) | c1_1(a47) | (~c2_1(a47))))),
% 1.39/1.60 inference(monotonicity,[status(thm)],[1948])).
% 1.39/1.60 tff(1950,plain,
% 1.39/1.60 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a47) | c0_1(a47) | (~c2_1(a47)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a47) | (~ndr1_0) | c1_1(a47) | (~c2_1(a47)))),
% 1.39/1.60 inference(transitivity,[status(thm)],[1949, 1947])).
% 1.39/1.60 tff(1951,plain,
% 1.39/1.60 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a47) | c0_1(a47) | (~c2_1(a47)))),
% 1.39/1.60 inference(quant_inst,[status(thm)],[])).
% 1.39/1.60 tff(1952,plain,
% 1.39/1.60 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a47) | (~ndr1_0) | c1_1(a47) | (~c2_1(a47))),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 1.39/1.60 tff(1953,plain,
% 1.39/1.60 (c1_1(a47)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1952, 92, 1941, 1942, 1478, 1476, 1605])).
% 1.39/1.60 tff(1954,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | c0_1(a47) | (~ndr1_0) | (~c3_1(a47)) | (~c1_1(a47)) | (~c2_1(a47)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp12 | c0_1(a47) | (~ndr1_0) | (~c3_1(a47)) | (~c1_1(a47)) | (~c2_1(a47)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1955,plain,
% 1.39/1.60 ((hskp12 | (~ndr1_0) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c0_1(a47) | (~c1_1(a47)) | (~c3_1(a47))) <=> (hskp12 | c0_1(a47) | (~ndr1_0) | (~c3_1(a47)) | (~c1_1(a47)) | (~c2_1(a47)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1956,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c0_1(a47) | (~c1_1(a47)) | (~c3_1(a47)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | c0_1(a47) | (~ndr1_0) | (~c3_1(a47)) | (~c1_1(a47)) | (~c2_1(a47))))),
% 1.39/1.60 inference(monotonicity,[status(thm)],[1955])).
% 1.39/1.60 tff(1957,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c0_1(a47) | (~c1_1(a47)) | (~c3_1(a47)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp12 | c0_1(a47) | (~ndr1_0) | (~c3_1(a47)) | (~c1_1(a47)) | (~c2_1(a47)))),
% 1.39/1.60 inference(transitivity,[status(thm)],[1956, 1954])).
% 1.39/1.60 tff(1958,plain,
% 1.39/1.60 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c0_1(a47) | (~c1_1(a47)) | (~c3_1(a47)))),
% 1.39/1.60 inference(quant_inst,[status(thm)],[])).
% 1.39/1.60 tff(1959,plain,
% 1.39/1.60 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp12 | c0_1(a47) | (~ndr1_0) | (~c3_1(a47)) | (~c1_1(a47)) | (~c2_1(a47))),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1958, 1957])).
% 1.39/1.60 tff(1960,plain,
% 1.39/1.60 ($false),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1959, 92, 46, 1478, 1477, 1476, 43, 1953])).
% 1.39/1.60 tff(1961,plain,(hskp12 | hskp4 | hskp0 | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.39/1.60 tff(1962,plain,
% 1.39/1.60 (hskp12),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1961, 274, 1942, 1941])).
% 1.39/1.60 tff(1963,plain,
% 1.39/1.60 (~c0_1(a20)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[338, 1962])).
% 1.39/1.60 tff(1964,plain,
% 1.39/1.60 (~c2_1(a20)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[344, 1962])).
% 1.39/1.60 tff(1965,assumption,(~c3_1(a48)), introduced(assumption)).
% 1.39/1.60 tff(1966,assumption,(~c0_1(a48)), introduced(assumption)).
% 1.39/1.60 tff(1967,assumption,(c1_1(a48)), introduced(assumption)).
% 1.39/1.60 tff(1968,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a48) | c3_1(a48) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c1_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a48) | c3_1(a48) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c1_1(a48)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1969,plain,
% 1.39/1.60 ((hskp4 | (~ndr1_0) | c3_1(a48) | c0_1(a48) | (~c1_1(a48)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20))) <=> (hskp4 | c0_1(a48) | c3_1(a48) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c1_1(a48)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1970,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a48) | c0_1(a48) | (~c1_1(a48)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a48) | c3_1(a48) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c1_1(a48))))),
% 1.39/1.60 inference(monotonicity,[status(thm)],[1969])).
% 1.39/1.60 tff(1971,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a48) | c0_1(a48) | (~c1_1(a48)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a48) | c3_1(a48) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c1_1(a48)))),
% 1.39/1.60 inference(transitivity,[status(thm)],[1970, 1968])).
% 1.39/1.60 tff(1972,plain,
% 1.39/1.60 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a48) | c0_1(a48) | (~c1_1(a48)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)))),
% 1.39/1.60 inference(quant_inst,[status(thm)],[])).
% 1.39/1.60 tff(1973,plain,
% 1.39/1.60 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a48) | c3_1(a48) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c1_1(a48))),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 1.39/1.60 tff(1974,plain,
% 1.39/1.60 (~c1_1(a20)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1973, 92, 1941, 1967, 1966, 1965, 33, 390, 56])).
% 1.39/1.60 tff(1975,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c3_1(a48) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | c2_1(a48))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a48) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | c2_1(a48))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1976,plain,
% 1.39/1.60 ((hskp0 | (~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a20) | c1_1(a20) | c0_1(a20)) <=> (hskp0 | c3_1(a48) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | c2_1(a48))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1977,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c3_1(a48) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | c2_1(a48)))),
% 1.39/1.60 inference(monotonicity,[status(thm)],[1976])).
% 1.39/1.60 tff(1978,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a48) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | c2_1(a48))),
% 1.39/1.60 inference(transitivity,[status(thm)],[1977, 1975])).
% 1.39/1.60 tff(1979,plain,
% 1.39/1.60 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.39/1.60 inference(quant_inst,[status(thm)],[])).
% 1.39/1.60 tff(1980,plain,
% 1.39/1.60 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a48) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | c2_1(a48)),
% 1.39/1.60 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 1.39/1.60 tff(1981,plain,
% 1.39/1.60 (c2_1(a48)),
% 1.39/1.60 inference(unit_resolution,[status(thm)],[1980, 92, 1942, 1967, 1965, 33, 390, 1623, 1974])).
% 1.39/1.60 tff(1982,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a48) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | (~c2_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a48) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1983,plain,
% 1.39/1.60 ((hskp1 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a20) | c0_1(a20) | c3_1(a20)) <=> (hskp1 | c0_1(a48) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.39/1.60 inference(rewrite,[status(thm)],[])).
% 1.39/1.60 tff(1984,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a48) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | (~c2_1(a48))))),
% 1.39/1.60 inference(monotonicity,[status(thm)],[1983])).
% 1.39/1.60 tff(1985,plain,
% 1.39/1.60 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a48) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.39/1.61 inference(transitivity,[status(thm)],[1984, 1982])).
% 1.39/1.61 tff(1986,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.39/1.61 inference(quant_inst,[status(thm)],[])).
% 1.39/1.61 tff(1987,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a48) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | (~c2_1(a48))),
% 1.39/1.61 inference(modus_ponens,[status(thm)],[1986, 1985])).
% 1.39/1.61 tff(1988,plain,
% 1.39/1.61 (c3_1(a20)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[1987, 92, 32, 1967, 1966, 33, 126, 1974, 1981])).
% 1.39/1.61 tff(1989,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a48) | c0_1(a20) | (~c3_1(a20)) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | (~c2_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a48) | c0_1(a20) | (~c3_1(a20)) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(1990,plain,
% 1.39/1.61 ((hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20))) <=> (hskp5 | c0_1(a48) | c0_1(a20) | (~c3_1(a20)) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(1991,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a48) | c0_1(a20) | (~c3_1(a20)) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | (~c2_1(a48))))),
% 1.39/1.61 inference(monotonicity,[status(thm)],[1990])).
% 1.39/1.61 tff(1992,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a48) | c0_1(a20) | (~c3_1(a20)) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.39/1.61 inference(transitivity,[status(thm)],[1991, 1989])).
% 1.39/1.61 tff(1993,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))),
% 1.39/1.61 inference(quant_inst,[status(thm)],[])).
% 1.39/1.61 tff(1994,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a48) | c0_1(a20) | (~c3_1(a20)) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | (~c2_1(a48))),
% 1.39/1.61 inference(modus_ponens,[status(thm)],[1993, 1992])).
% 1.39/1.61 tff(1995,plain,
% 1.39/1.61 (hskp5 | (~c3_1(a20))),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[1994, 92, 1967, 1966, 33, 21, 1974, 1981])).
% 1.39/1.61 tff(1996,plain,
% 1.39/1.61 (hskp5),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[1995, 1988])).
% 1.39/1.61 tff(1997,plain,
% 1.39/1.61 (~c3_1(a8)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[1656, 1996])).
% 1.39/1.61 tff(1998,plain,
% 1.39/1.61 (~c2_1(a8)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[1662, 1996])).
% 1.39/1.61 tff(1999,plain,
% 1.39/1.61 (c1_1(a8)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[1718, 1996])).
% 1.39/1.61 tff(2000,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a20) | c2_1(a20) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c1_1(a20))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a20) | c2_1(a20) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c1_1(a20))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2001,plain,
% 1.39/1.61 ((hskp0 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a20) | c1_1(a20) | c0_1(a20)) <=> (hskp0 | c0_1(a20) | c2_1(a20) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c1_1(a20))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2002,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a20) | c2_1(a20) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c1_1(a20)))),
% 1.39/1.61 inference(monotonicity,[status(thm)],[2001])).
% 1.39/1.61 tff(2003,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a20) | c2_1(a20) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c1_1(a20))),
% 1.39/1.61 inference(transitivity,[status(thm)],[2002, 2000])).
% 1.39/1.61 tff(2004,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.39/1.61 inference(quant_inst,[status(thm)],[])).
% 1.39/1.61 tff(2005,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a20) | c2_1(a20) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c1_1(a20)),
% 1.39/1.61 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 1.39/1.61 tff(2006,plain,
% 1.39/1.61 ($false),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2005, 92, 1942, 1999, 33, 390, 1998, 1997, 1623, 1974])).
% 1.39/1.61 tff(2007,plain,(c2_1(a20) | hskp0 | c0_1(a20) | (~c1_1(a48)) | c0_1(a48) | hskp1 | c3_1(a48) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.39/1.61 tff(2008,plain,
% 1.39/1.61 ($false),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2007, 1964, 1963, 1942, 1946, 1945, 32, 1944, 1941])).
% 1.39/1.61 tff(2009,plain,(hskp11 | hskp0 | hskp1 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.39/1.61 tff(2010,plain,
% 1.39/1.61 (hskp11),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2009, 1940, 32, 1792])).
% 1.39/1.61 tff(2011,plain,
% 1.39/1.61 (~c0_1(a19)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[98, 2010])).
% 1.39/1.61 tff(2012,plain,
% 1.39/1.61 (c2_1(a19)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[115, 2010])).
% 1.39/1.61 tff(2013,plain,
% 1.39/1.61 (c1_1(a19)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[107, 2010])).
% 1.39/1.61 tff(2014,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a20) | c3_1(a20) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a20) | c3_1(a20) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a20))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2015,plain,
% 1.39/1.61 ((hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a20) | c0_1(a20) | c3_1(a20)) <=> (hskp1 | c0_1(a20) | c3_1(a20) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a20))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2016,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a20) | c3_1(a20) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a20)))),
% 1.39/1.61 inference(monotonicity,[status(thm)],[2015])).
% 1.39/1.61 tff(2017,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a20) | c3_1(a20) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a20))),
% 1.39/1.61 inference(transitivity,[status(thm)],[2016, 2014])).
% 1.39/1.61 tff(2018,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.39/1.61 inference(quant_inst,[status(thm)],[])).
% 1.39/1.61 tff(2019,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a20) | c3_1(a20) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a20)),
% 1.39/1.61 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 1.39/1.61 tff(2020,plain,
% 1.39/1.61 (c3_1(a20)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2019, 92, 32, 2013, 2012, 33, 2011, 126, 1799])).
% 1.39/1.61 tff(2021,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a20) | (~c3_1(a20)) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a20))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a20) | (~c3_1(a20)) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a20))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2022,plain,
% 1.39/1.61 ((hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20))) <=> (hskp5 | c0_1(a20) | (~c3_1(a20)) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a20))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2023,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a20) | (~c3_1(a20)) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a20)))),
% 1.39/1.61 inference(monotonicity,[status(thm)],[2022])).
% 1.39/1.61 tff(2024,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a20) | (~c3_1(a20)) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a20))),
% 1.39/1.61 inference(transitivity,[status(thm)],[2023, 2021])).
% 1.39/1.61 tff(2025,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))),
% 1.39/1.61 inference(quant_inst,[status(thm)],[])).
% 1.39/1.61 tff(2026,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a20) | (~c3_1(a20)) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a20)),
% 1.39/1.61 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 1.39/1.61 tff(2027,plain,
% 1.39/1.61 (hskp5 | (~c3_1(a20))),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2026, 92, 2013, 2012, 33, 2011, 21, 1799])).
% 1.39/1.61 tff(2028,plain,
% 1.39/1.61 (hskp5),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2027, 2020])).
% 1.39/1.61 tff(2029,plain,
% 1.39/1.61 (~c3_1(a8)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[1656, 2028])).
% 1.39/1.61 tff(2030,plain,
% 1.39/1.61 (~c2_1(a8)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[1662, 2028])).
% 1.39/1.61 tff(2031,plain,
% 1.39/1.61 (c1_1(a8)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[1718, 2028])).
% 1.39/1.61 tff(2032,plain,
% 1.39/1.61 ($false),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2005, 92, 1940, 2031, 33, 390, 2030, 2029, 1623, 1799])).
% 1.39/1.61 tff(2033,plain,(c2_1(a20) | c0_1(a20) | hskp1 | c0_1(a7) | c3_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.61 tff(2034,plain,
% 1.39/1.61 (c2_1(a20)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2033, 33, 32, 45, 58])).
% 1.39/1.61 tff(2035,plain,
% 1.39/1.61 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a20) | (~c2_1(a20)) | (~ndr1_0) | c1_1(a20))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a20) | (~c2_1(a20)) | (~ndr1_0) | c1_1(a20))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2036,plain,
% 1.39/1.61 ((hskp4 | hskp0 | (~ndr1_0) | c1_1(a20) | c0_1(a20) | (~c2_1(a20))) <=> (hskp4 | hskp0 | c0_1(a20) | (~c2_1(a20)) | (~ndr1_0) | c1_1(a20))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2037,plain,
% 1.39/1.61 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a20) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a20) | (~c2_1(a20)) | (~ndr1_0) | c1_1(a20)))),
% 1.39/1.61 inference(monotonicity,[status(thm)],[2036])).
% 1.39/1.61 tff(2038,plain,
% 1.39/1.61 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a20) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a20) | (~c2_1(a20)) | (~ndr1_0) | c1_1(a20))),
% 1.39/1.61 inference(transitivity,[status(thm)],[2037, 2035])).
% 1.39/1.61 tff(2039,plain,
% 1.39/1.61 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a20) | c0_1(a20) | (~c2_1(a20)))),
% 1.39/1.61 inference(quant_inst,[status(thm)],[])).
% 1.39/1.61 tff(2040,plain,
% 1.39/1.61 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a20) | (~c2_1(a20)) | (~ndr1_0) | c1_1(a20)),
% 1.39/1.61 inference(modus_ponens,[status(thm)],[2039, 2038])).
% 1.39/1.61 tff(2041,plain,
% 1.39/1.61 ((~c2_1(a20)) | c1_1(a20)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2040, 92, 1792, 1940, 33, 1605])).
% 1.39/1.61 tff(2042,plain,
% 1.39/1.61 (c1_1(a20)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2041, 2034])).
% 1.39/1.61 tff(2043,plain,
% 1.39/1.61 (~hskp12),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[344, 2034])).
% 1.39/1.61 tff(2044,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | (~ndr1_0) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp12 | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | (~ndr1_0) | (~c1_1(a20)))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2045,plain,
% 1.39/1.61 ((hskp12 | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c0_1(a20) | (~c1_1(a20)) | (~c3_1(a20))) <=> (hskp12 | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | (~ndr1_0) | (~c1_1(a20)))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2046,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c0_1(a20) | (~c1_1(a20)) | (~c3_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | (~ndr1_0) | (~c1_1(a20))))),
% 1.39/1.61 inference(monotonicity,[status(thm)],[2045])).
% 1.39/1.61 tff(2047,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c0_1(a20) | (~c1_1(a20)) | (~c3_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp12 | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | (~ndr1_0) | (~c1_1(a20)))),
% 1.39/1.61 inference(transitivity,[status(thm)],[2046, 2044])).
% 1.39/1.61 tff(2048,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c0_1(a20) | (~c1_1(a20)) | (~c3_1(a20)))),
% 1.39/1.61 inference(quant_inst,[status(thm)],[])).
% 1.39/1.61 tff(2049,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp12 | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | (~ndr1_0) | (~c1_1(a20))),
% 1.39/1.61 inference(modus_ponens,[status(thm)],[2048, 2047])).
% 1.39/1.61 tff(2050,plain,
% 1.39/1.61 (hskp12 | (~c2_1(a20)) | (~c3_1(a20)) | (~c1_1(a20))),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2049, 92, 33, 43])).
% 1.39/1.61 tff(2051,plain,
% 1.39/1.61 (~c3_1(a20)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2050, 2043, 2034, 2042])).
% 1.39/1.61 tff(2052,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c3_1(a19)) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp12 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c3_1(a19)) | (~c1_1(a19)))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2053,plain,
% 1.39/1.61 ((hskp12 | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c3_1(a19)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19))) <=> (hskp12 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c3_1(a19)) | (~c1_1(a19)))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2054,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c3_1(a19)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c3_1(a19)) | (~c1_1(a19))))),
% 1.39/1.61 inference(monotonicity,[status(thm)],[2053])).
% 1.39/1.61 tff(2055,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c3_1(a19)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp12 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c3_1(a19)) | (~c1_1(a19)))),
% 1.39/1.61 inference(transitivity,[status(thm)],[2054, 2052])).
% 1.39/1.61 tff(2056,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a19) | (~c2_1(a19)) | (~c3_1(a19)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)))),
% 1.39/1.61 inference(quant_inst,[status(thm)],[])).
% 1.39/1.61 tff(2057,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp12 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c3_1(a19)) | (~c1_1(a19))),
% 1.39/1.61 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 1.39/1.61 tff(2058,plain,
% 1.39/1.61 (hskp12 | (~c3_1(a19))),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2057, 92, 2013, 2012, 2011, 43])).
% 1.39/1.61 tff(2059,plain,
% 1.39/1.61 (~c3_1(a19)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2058, 2043])).
% 1.39/1.61 tff(2060,assumption,(~c3_1(a19)), introduced(assumption)).
% 1.39/1.61 tff(2061,assumption,(c1_1(a20)), introduced(assumption)).
% 1.39/1.61 tff(2062,assumption,(~hskp21), introduced(assumption)).
% 1.39/1.61 tff(2063,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c2_1(a10) | (~ndr1_0) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c2_1(a10) | (~ndr1_0) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2064,plain,
% 1.39/1.61 ((hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a10) | c1_1(a10) | (~c3_1(a10))) <=> (hskp21 | c2_1(a10) | (~ndr1_0) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2065,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a10) | c1_1(a10) | (~c3_1(a10)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c2_1(a10) | (~ndr1_0) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23))))),
% 1.39/1.61 inference(monotonicity,[status(thm)],[2064])).
% 1.39/1.61 tff(2066,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a10) | c1_1(a10) | (~c3_1(a10)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c2_1(a10) | (~ndr1_0) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)))),
% 1.39/1.61 inference(transitivity,[status(thm)],[2065, 2063])).
% 1.39/1.61 tff(2067,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a10) | c1_1(a10) | (~c3_1(a10)))),
% 1.39/1.61 inference(quant_inst,[status(thm)],[])).
% 1.39/1.61 tff(2068,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c2_1(a10) | (~ndr1_0) | c1_1(a10) | (~c3_1(a10)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23))),
% 1.39/1.61 inference(modus_ponens,[status(thm)],[2067, 2066])).
% 1.39/1.61 tff(2069,plain,
% 1.39/1.61 (c1_1(a10)),
% 1.39/1.61 inference(unit_resolution,[status(thm)],[2068, 92, 2062, 1905, 1904, 1903, 512, 504, 1098])).
% 1.39/1.61 tff(2070,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a20)))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2071,plain,
% 1.39/1.61 ((hskp13 | (~ndr1_0) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20))) <=> (hskp13 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a20)))),
% 1.39/1.61 inference(rewrite,[status(thm)],[])).
% 1.39/1.61 tff(2072,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a20))))),
% 1.39/1.61 inference(monotonicity,[status(thm)],[2071])).
% 1.39/1.61 tff(2073,plain,
% 1.39/1.61 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a20)))),
% 1.39/1.61 inference(transitivity,[status(thm)],[2072, 2070])).
% 1.39/1.61 tff(2074,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20)))),
% 1.39/1.61 inference(quant_inst,[status(thm)],[])).
% 1.39/1.61 tff(2075,plain,
% 1.39/1.61 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)) | (~c1_1(a20))),
% 1.39/1.62 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 1.39/1.62 tff(2076,plain,
% 1.39/1.62 (hskp13),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2075, 92, 497, 512, 33, 44, 1833, 2061, 2069])).
% 1.39/1.62 tff(2077,plain,
% 1.39/1.62 (~c1_1(a22)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1846, 2076])).
% 1.39/1.62 tff(2078,plain,
% 1.39/1.62 (~c0_1(a22)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1852, 2076])).
% 1.39/1.62 tff(2079,plain,
% 1.39/1.62 (((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | (~c1_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2080,plain,
% 1.39/1.62 ((hskp25 | (~ndr1_0) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10))) <=> (hskp25 | (~ndr1_0) | (~c1_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2081,plain,
% 1.39/1.62 (((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a10)) | (~c0_1(a10)) | (~c3_1(a10))))),
% 1.39/1.62 inference(monotonicity,[status(thm)],[2080])).
% 1.39/1.62 tff(2082,plain,
% 1.39/1.62 (((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | (~c1_1(a10)) | (~c0_1(a10)) | (~c3_1(a10)))),
% 1.39/1.62 inference(transitivity,[status(thm)],[2081, 2079])).
% 1.39/1.62 tff(2083,plain,
% 1.39/1.62 ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)))),
% 1.39/1.62 inference(quant_inst,[status(thm)],[])).
% 1.39/1.62 tff(2084,plain,
% 1.39/1.62 ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | (~c1_1(a10)) | (~c0_1(a10)) | (~c3_1(a10))),
% 1.39/1.62 inference(modus_ponens,[status(thm)],[2083, 2082])).
% 1.39/1.62 tff(2085,plain,
% 1.39/1.62 (hskp25 | (~c1_1(a10))),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2084, 92, 497, 512, 1555])).
% 1.39/1.62 tff(2086,plain,
% 1.39/1.62 (hskp25),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2085, 2069])).
% 1.39/1.62 tff(2087,plain,
% 1.39/1.62 (~c3_1(a73)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1138, 2086])).
% 1.39/1.62 tff(2088,plain,
% 1.39/1.62 (c2_1(a73)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1187, 2086])).
% 1.39/1.62 tff(2089,plain,
% 1.39/1.62 (c0_1(a73)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1146, 2086])).
% 1.39/1.62 tff(2090,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | c3_1(a73) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c2_1(a73)) | (~c0_1(a73)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a73) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2091,plain,
% 1.39/1.62 ((hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20))) <=> (hskp14 | c3_1(a73) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2092,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | c3_1(a73) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c2_1(a73)) | (~c0_1(a73))))),
% 1.39/1.62 inference(monotonicity,[status(thm)],[2091])).
% 1.39/1.62 tff(2093,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a73) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.39/1.62 inference(transitivity,[status(thm)],[2092, 2090])).
% 1.39/1.62 tff(2094,plain,
% 1.39/1.62 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20)))),
% 1.39/1.62 inference(quant_inst,[status(thm)],[])).
% 1.39/1.62 tff(2095,plain,
% 1.39/1.62 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a73) | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c2_1(a73)) | (~c0_1(a73))),
% 1.39/1.62 inference(modus_ponens,[status(thm)],[2094, 2093])).
% 1.39/1.62 tff(2096,plain,
% 1.39/1.62 (hskp14),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2095, 92, 2089, 2088, 2087, 33, 44, 1863, 2061])).
% 1.39/1.62 tff(2097,plain,
% 1.39/1.62 (~c2_1(a25)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1886, 2096])).
% 1.39/1.62 tff(2098,plain,
% 1.39/1.62 (c3_1(a22)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1894, 2076])).
% 1.39/1.62 tff(2099,plain,
% 1.39/1.62 (c1_1(a25)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1920, 2096])).
% 1.39/1.62 tff(2100,plain,
% 1.39/1.62 (c0_1(a25)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1928, 2096])).
% 1.39/1.62 tff(2101,plain,
% 1.39/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a25) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)) | (~c3_1(a22)) | (~c1_1(a25)) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a25) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)) | (~c3_1(a22)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2102,plain,
% 1.39/1.62 (((~ndr1_0) | c2_1(a25) | (~c1_1(a25)) | (~c0_1(a25)) | c0_1(a22) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22))) <=> (c2_1(a25) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)) | (~c3_1(a22)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2103,plain,
% 1.39/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a25) | (~c1_1(a25)) | (~c0_1(a25)) | c0_1(a22) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a25) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)) | (~c3_1(a22)) | (~c1_1(a25)) | (~c0_1(a25))))),
% 1.39/1.62 inference(monotonicity,[status(thm)],[2102])).
% 1.39/1.62 tff(2104,plain,
% 1.39/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a25) | (~c1_1(a25)) | (~c0_1(a25)) | c0_1(a22) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a25) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)) | (~c3_1(a22)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.39/1.62 inference(transitivity,[status(thm)],[2103, 2101])).
% 1.39/1.62 tff(2105,plain,
% 1.39/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a25) | (~c1_1(a25)) | (~c0_1(a25)) | c0_1(a22) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))),
% 1.39/1.62 inference(quant_inst,[status(thm)],[])).
% 1.39/1.62 tff(2106,plain,
% 1.39/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a25) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)) | (~c3_1(a22)) | (~c1_1(a25)) | (~c0_1(a25))),
% 1.39/1.62 inference(modus_ponens,[status(thm)],[2105, 2104])).
% 1.39/1.62 tff(2107,plain,
% 1.39/1.62 (~c2_1(a22)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2106, 92, 2100, 2099, 2098, 2097, 2078, 2077, 1465])).
% 1.39/1.62 tff(2108,plain,
% 1.39/1.62 ($false),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1911, 92, 2062, 1905, 1904, 1903, 2098, 2077, 1098, 2107])).
% 1.39/1.62 tff(2109,plain,((~hskp6) | hskp21 | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20))), inference(lemma,lemma(discharge,[]))).
% 1.39/1.62 tff(2110,plain,
% 1.39/1.62 (~hskp6),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2109, 2062, 1905, 1904, 1903, 33, 44, 2061])).
% 1.39/1.62 tff(2111,plain,
% 1.39/1.62 (^[U: $i] : refl((hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.39/1.62 inference(bind,[status(th)],[])).
% 1.39/1.62 tff(2112,plain,
% 1.39/1.62 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.39/1.62 inference(quant_intro,[status(thm)],[2111])).
% 1.39/1.62 tff(2113,plain,
% 1.39/1.62 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2114,plain,
% 1.39/1.62 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) | hskp2) <=> ((hskp6 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp2))), rewrite(((hskp6 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp2) <=> (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) | hskp2) <=> (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.39/1.62 inference(bind,[status(th)],[])).
% 1.39/1.62 tff(2115,plain,
% 1.39/1.62 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) | hskp2) <=> ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.39/1.62 inference(quant_intro,[status(thm)],[2114])).
% 1.39/1.62 tff(2116,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 1.39/1.62 tff(2117,plain,
% 1.39/1.62 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.39/1.62 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 1.39/1.62 tff(2118,plain,
% 1.39/1.62 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.39/1.62 inference(modus_ponens,[status(thm)],[2117, 2113])).
% 1.39/1.62 tff(2119,plain,(
% 1.39/1.62 ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.39/1.62 inference(skolemize,[status(sab)],[2118])).
% 1.39/1.62 tff(2120,plain,
% 1.39/1.62 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.39/1.62 inference(modus_ponens,[status(thm)],[2119, 2112])).
% 1.39/1.62 tff(2121,assumption,(c2_1(a19)), introduced(assumption)).
% 1.39/1.62 tff(2122,assumption,(c1_1(a19)), introduced(assumption)).
% 1.39/1.62 tff(2123,plain,
% 1.39/1.62 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp6 | hskp2 | (~ndr1_0) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2124,plain,
% 1.39/1.62 ((hskp6 | hskp2 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19))) <=> (hskp6 | hskp2 | (~ndr1_0) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2125,plain,
% 1.39/1.62 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19))))),
% 1.39/1.62 inference(monotonicity,[status(thm)],[2124])).
% 1.39/1.62 tff(2126,plain,
% 1.39/1.62 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp6 | hskp2 | (~ndr1_0) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.39/1.62 inference(transitivity,[status(thm)],[2125, 2123])).
% 1.39/1.62 tff(2127,plain,
% 1.39/1.62 ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))),
% 1.39/1.62 inference(quant_inst,[status(thm)],[])).
% 1.39/1.62 tff(2128,plain,
% 1.39/1.62 ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp6 | hskp2 | (~ndr1_0) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19))),
% 1.39/1.62 inference(modus_ponens,[status(thm)],[2127, 2126])).
% 1.39/1.62 tff(2129,plain,
% 1.39/1.62 (hskp6 | hskp2 | c3_1(a19)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2128, 92, 2122, 2121, 2120])).
% 1.39/1.62 tff(2130,plain,
% 1.39/1.62 (hskp2),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2129, 2110, 2060])).
% 1.39/1.62 tff(2131,plain,
% 1.39/1.62 (~c2_1(a3)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[487, 2130])).
% 1.39/1.62 tff(2132,plain,
% 1.39/1.62 (~c1_1(a3)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[430, 2130])).
% 1.39/1.62 tff(2133,plain,
% 1.39/1.62 (c3_1(a3)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[373, 2130])).
% 1.39/1.62 tff(2134,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2135,plain,
% 1.39/1.62 ((hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3))) <=> (hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2136,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23))))),
% 1.39/1.62 inference(monotonicity,[status(thm)],[2135])).
% 1.39/1.62 tff(2137,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)))),
% 1.39/1.62 inference(transitivity,[status(thm)],[2136, 2134])).
% 1.39/1.62 tff(2138,plain,
% 1.39/1.62 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3)))),
% 1.39/1.62 inference(quant_inst,[status(thm)],[])).
% 1.39/1.62 tff(2139,plain,
% 1.39/1.62 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23))),
% 1.39/1.62 inference(modus_ponens,[status(thm)],[2138, 2137])).
% 1.39/1.62 tff(2140,plain,
% 1.39/1.62 ($false),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2139, 92, 2062, 1905, 1904, 1903, 2133, 2132, 2131, 1098])).
% 1.39/1.62 tff(2141,plain,(hskp21 | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20))), inference(lemma,lemma(discharge,[]))).
% 1.39/1.62 tff(2142,plain,
% 1.39/1.62 (hskp21),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2141, 2059, 1813, 1812, 1814, 2013, 2012, 33, 2051, 2042])).
% 1.39/1.62 tff(2143,plain,
% 1.39/1.62 (~c0_1(a47)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[777, 2142])).
% 1.39/1.62 tff(2144,plain,
% 1.39/1.62 (c2_1(a47)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[793, 2142])).
% 1.39/1.62 tff(2145,plain,
% 1.39/1.62 (c1_1(a47)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1952, 92, 1792, 1940, 2144, 2143, 1605])).
% 1.39/1.62 tff(2146,plain,
% 1.39/1.62 (c3_1(a47)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[785, 2142])).
% 1.39/1.62 tff(2147,plain,
% 1.39/1.62 ($false),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1959, 92, 2043, 2144, 2146, 2143, 43, 2145])).
% 1.39/1.62 tff(2148,plain,(c0_1(a20) | hskp1 | c0_1(a7) | c3_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.62 tff(2149,plain,
% 1.39/1.62 (c0_1(a20)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2148, 58, 45, 32])).
% 1.39/1.62 tff(2150,plain,
% 1.39/1.62 (~hskp12),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[338, 2149])).
% 1.39/1.62 tff(2151,plain,
% 1.39/1.62 (~c3_1(a19)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2058, 2150])).
% 1.39/1.62 tff(2152,assumption,(hskp14), introduced(assumption)).
% 1.39/1.62 tff(2153,plain,
% 1.39/1.62 (~c2_1(a25)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1886, 2152])).
% 1.39/1.62 tff(2154,plain,
% 1.39/1.62 (c0_1(a25)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1928, 2152])).
% 1.39/1.62 tff(2155,plain,
% 1.39/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a25) | c0_1(a19) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a19)) | c3_1(a19) | (~c0_1(a25)) | c3_1(a25))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a25) | c0_1(a19) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a19)) | c3_1(a19) | (~c0_1(a25)) | c3_1(a25))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2156,plain,
% 1.39/1.62 (((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19))) <=> (c2_1(a25) | c0_1(a19) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a19)) | c3_1(a19) | (~c0_1(a25)) | c3_1(a25))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2157,plain,
% 1.39/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a25) | c0_1(a19) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a19)) | c3_1(a19) | (~c0_1(a25)) | c3_1(a25)))),
% 1.39/1.62 inference(monotonicity,[status(thm)],[2156])).
% 1.39/1.62 tff(2158,plain,
% 1.39/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a25) | c0_1(a19) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a19)) | c3_1(a19) | (~c0_1(a25)) | c3_1(a25))),
% 1.39/1.62 inference(transitivity,[status(thm)],[2157, 2155])).
% 1.39/1.62 tff(2159,plain,
% 1.39/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19)))),
% 1.39/1.62 inference(quant_inst,[status(thm)],[])).
% 1.39/1.62 tff(2160,plain,
% 1.39/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a25) | c0_1(a19) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a19)) | c3_1(a19) | (~c0_1(a25)) | c3_1(a25)),
% 1.39/1.62 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 1.39/1.62 tff(2161,plain,
% 1.39/1.62 (c3_1(a25)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2160, 92, 1905, 1904, 1903, 2154, 2121, 2153, 127, 1643, 2060])).
% 1.39/1.62 tff(2162,plain,
% 1.39/1.62 (c1_1(a25)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1920, 2152])).
% 1.39/1.62 tff(2163,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a25)) | (~c0_1(a25)) | (~c3_1(a25)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a25)) | (~c0_1(a25)) | (~c3_1(a25)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2164,plain,
% 1.39/1.62 ((hskp13 | (~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19))) <=> (hskp13 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a25)) | (~c0_1(a25)) | (~c3_1(a25)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2165,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a25)) | (~c0_1(a25)) | (~c3_1(a25))))),
% 1.39/1.62 inference(monotonicity,[status(thm)],[2164])).
% 1.39/1.62 tff(2166,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a25)) | (~c0_1(a25)) | (~c3_1(a25)))),
% 1.39/1.62 inference(transitivity,[status(thm)],[2165, 2163])).
% 1.39/1.62 tff(2167,plain,
% 1.39/1.62 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))),
% 1.39/1.62 inference(quant_inst,[status(thm)],[])).
% 1.39/1.62 tff(2168,plain,
% 1.39/1.62 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a25)) | (~c0_1(a25)) | (~c3_1(a25))),
% 1.39/1.62 inference(modus_ponens,[status(thm)],[2167, 2166])).
% 1.39/1.62 tff(2169,plain,
% 1.39/1.62 (hskp13),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2168, 92, 2154, 2162, 2122, 127, 1833, 2060, 2161])).
% 1.39/1.62 tff(2170,plain,
% 1.39/1.62 (~c1_1(a22)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1846, 2169])).
% 1.39/1.62 tff(2171,plain,
% 1.39/1.62 (~c0_1(a22)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1852, 2169])).
% 1.39/1.62 tff(2172,plain,
% 1.39/1.62 (c3_1(a22)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1894, 2169])).
% 1.39/1.62 tff(2173,plain,
% 1.39/1.62 (~c2_1(a22)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2106, 92, 2154, 2162, 2172, 2153, 2171, 2170, 1465])).
% 1.39/1.62 tff(2174,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a22) | c1_1(a22) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | (~c3_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a22) | c1_1(a22) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | (~c3_1(a22)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2175,plain,
% 1.39/1.62 ((hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22))) <=> (hskp5 | c0_1(a22) | c1_1(a22) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | (~c3_1(a22)))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2176,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a22) | c1_1(a22) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | (~c3_1(a22))))),
% 1.39/1.62 inference(monotonicity,[status(thm)],[2175])).
% 1.39/1.62 tff(2177,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a22) | c1_1(a22) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | (~c3_1(a22)))),
% 1.39/1.62 inference(transitivity,[status(thm)],[2176, 2174])).
% 1.39/1.62 tff(2178,plain,
% 1.39/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))),
% 1.39/1.62 inference(quant_inst,[status(thm)],[])).
% 1.39/1.62 tff(2179,plain,
% 1.39/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a22) | c1_1(a22) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | (~c3_1(a22))),
% 1.39/1.62 inference(modus_ponens,[status(thm)],[2178, 2177])).
% 1.39/1.62 tff(2180,plain,
% 1.39/1.62 (hskp5),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[2179, 92, 2172, 2122, 2121, 2171, 2170, 127, 21])).
% 1.39/1.62 tff(2181,plain,
% 1.39/1.62 (~c3_1(a8)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1656, 2180])).
% 1.39/1.62 tff(2182,plain,
% 1.39/1.62 (~c2_1(a8)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1662, 2180])).
% 1.39/1.62 tff(2183,plain,
% 1.39/1.62 (c1_1(a8)),
% 1.39/1.62 inference(unit_resolution,[status(thm)],[1718, 2180])).
% 1.39/1.62 tff(2184,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a22) | c1_1(a22) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c2_1(a22))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a22) | c1_1(a22) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c2_1(a22))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2185,plain,
% 1.39/1.62 ((hskp0 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a22) | c1_1(a22) | c0_1(a22)) <=> (hskp0 | c0_1(a22) | c1_1(a22) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c2_1(a22))),
% 1.39/1.62 inference(rewrite,[status(thm)],[])).
% 1.39/1.62 tff(2186,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a22) | c1_1(a22) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c2_1(a22)))),
% 1.39/1.62 inference(monotonicity,[status(thm)],[2185])).
% 1.39/1.62 tff(2187,plain,
% 1.39/1.62 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a22) | c1_1(a22) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c2_1(a22))),
% 1.39/1.63 inference(transitivity,[status(thm)],[2186, 2184])).
% 1.39/1.63 tff(2188,plain,
% 1.39/1.63 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a22) | c1_1(a22) | c0_1(a22))),
% 1.39/1.63 inference(quant_inst,[status(thm)],[])).
% 1.39/1.63 tff(2189,plain,
% 1.39/1.63 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a22) | c1_1(a22) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c2_1(a22)),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 1.39/1.63 tff(2190,plain,
% 1.39/1.63 ($false),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2189, 92, 1942, 2183, 2171, 2170, 2182, 2181, 1623, 2173])).
% 1.39/1.63 tff(2191,plain,((~hskp14) | hskp0 | (~c1_1(a19)) | (~c2_1(a19)) | c0_1(a19) | c3_1(a19) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23))), inference(lemma,lemma(discharge,[]))).
% 1.39/1.63 tff(2192,plain,
% 1.39/1.63 (~hskp14),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2191, 1940, 2013, 2012, 2011, 2151, 1814, 1813, 1812])).
% 1.39/1.63 tff(2193,plain,
% 1.39/1.63 ((hskp20 | hskp14 | hskp12) <=> (hskp20 | hskp14 | hskp12)),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2194,plain,
% 1.39/1.63 (((hskp14 | hskp20) | hskp12) <=> (hskp20 | hskp14 | hskp12)),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2195,axiom,((hskp14 | hskp20) | hskp12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 1.39/1.63 tff(2196,plain,
% 1.39/1.63 (hskp20 | hskp14 | hskp12),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 1.39/1.63 tff(2197,plain,
% 1.39/1.63 (hskp20 | hskp14 | hskp12),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2196, 2193])).
% 1.39/1.63 tff(2198,plain,
% 1.39/1.63 (hskp20 | hskp14 | hskp12),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2197, 2193])).
% 1.39/1.63 tff(2199,plain,
% 1.39/1.63 (hskp20 | hskp14 | hskp12),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2198, 2193])).
% 1.39/1.63 tff(2200,plain,
% 1.39/1.63 (hskp20 | hskp14 | hskp12),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2199, 2193])).
% 1.39/1.63 tff(2201,plain,
% 1.39/1.63 (hskp20),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2200, 2192, 2150])).
% 1.39/1.63 tff(2202,plain,
% 1.39/1.63 (~c3_1(a43)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[1025, 2201])).
% 1.39/1.63 tff(2203,plain,
% 1.39/1.63 (c0_1(a43)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[1048, 2201])).
% 1.39/1.63 tff(2204,plain,
% 1.39/1.63 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | c3_1(a43) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a43) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2205,plain,
% 1.39/1.63 ((hskp14 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19))) <=> (hskp14 | c3_1(a43) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2206,plain,
% 1.39/1.63 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | c3_1(a43) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 1.39/1.63 inference(monotonicity,[status(thm)],[2205])).
% 1.39/1.63 tff(2207,plain,
% 1.39/1.63 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a43) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.39/1.63 inference(transitivity,[status(thm)],[2206, 2204])).
% 1.39/1.63 tff(2208,plain,
% 1.39/1.63 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))),
% 1.39/1.63 inference(quant_inst,[status(thm)],[])).
% 1.39/1.63 tff(2209,plain,
% 1.39/1.63 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a43) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a43)) | (~c0_1(a43))),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2208, 2207])).
% 1.39/1.63 tff(2210,plain,
% 1.39/1.63 (~c2_1(a43)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2209, 92, 2192, 2203, 2013, 2202, 2011, 1863, 2151])).
% 1.39/1.63 tff(2211,plain,
% 1.39/1.63 (c1_1(a43)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[1033, 2201])).
% 1.39/1.63 tff(2212,plain,
% 1.39/1.63 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c3_1(a43) | (~ndr1_0) | (~c1_1(a43)) | c2_1(a43))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a43) | (~ndr1_0) | (~c1_1(a43)) | c2_1(a43))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2213,plain,
% 1.39/1.63 ((hskp19 | (~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43))) <=> (hskp19 | c3_1(a43) | (~ndr1_0) | (~c1_1(a43)) | c2_1(a43))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2214,plain,
% 1.39/1.63 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c3_1(a43) | (~ndr1_0) | (~c1_1(a43)) | c2_1(a43)))),
% 1.39/1.63 inference(monotonicity,[status(thm)],[2213])).
% 1.39/1.63 tff(2215,plain,
% 1.39/1.63 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a43) | (~ndr1_0) | (~c1_1(a43)) | c2_1(a43))),
% 1.39/1.63 inference(transitivity,[status(thm)],[2214, 2212])).
% 1.39/1.63 tff(2216,plain,
% 1.39/1.63 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)))),
% 1.39/1.63 inference(quant_inst,[status(thm)],[])).
% 1.39/1.63 tff(2217,plain,
% 1.39/1.63 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a43) | (~ndr1_0) | (~c1_1(a43)) | c2_1(a43)),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2216, 2215])).
% 1.39/1.63 tff(2218,plain,
% 1.39/1.63 (hskp19 | c2_1(a43)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2217, 92, 2211, 2202, 930])).
% 1.39/1.63 tff(2219,plain,
% 1.39/1.63 (hskp19),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2218, 2210])).
% 1.39/1.63 tff(2220,plain,
% 1.39/1.63 (~c3_1(a40)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[854, 2219])).
% 1.39/1.63 tff(2221,plain,
% 1.39/1.63 (~c0_1(a40)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[833, 2219])).
% 1.39/1.63 tff(2222,plain,
% 1.39/1.63 (c2_1(a40)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[841, 2219])).
% 1.39/1.63 tff(2223,plain,
% 1.39/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a43) | c0_1(a40) | c3_1(a40) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a40)) | c2_1(a43) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a43) | c0_1(a40) | c3_1(a40) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a40)) | c2_1(a43) | (~c0_1(a43)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2224,plain,
% 1.39/1.63 (((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a43) | c3_1(a43) | (~c0_1(a43)) | c0_1(a40) | c3_1(a40) | (~c2_1(a40))) <=> (c3_1(a43) | c0_1(a40) | c3_1(a40) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a40)) | c2_1(a43) | (~c0_1(a43)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2225,plain,
% 1.39/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a43) | c3_1(a43) | (~c0_1(a43)) | c0_1(a40) | c3_1(a40) | (~c2_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a43) | c0_1(a40) | c3_1(a40) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a40)) | c2_1(a43) | (~c0_1(a43))))),
% 1.39/1.63 inference(monotonicity,[status(thm)],[2224])).
% 1.39/1.63 tff(2226,plain,
% 1.39/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a43) | c3_1(a43) | (~c0_1(a43)) | c0_1(a40) | c3_1(a40) | (~c2_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a43) | c0_1(a40) | c3_1(a40) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a40)) | c2_1(a43) | (~c0_1(a43)))),
% 1.39/1.63 inference(transitivity,[status(thm)],[2225, 2223])).
% 1.39/1.63 tff(2227,plain,
% 1.39/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a43) | c3_1(a43) | (~c0_1(a43)) | c0_1(a40) | c3_1(a40) | (~c2_1(a40)))),
% 1.39/1.63 inference(quant_inst,[status(thm)],[])).
% 1.39/1.63 tff(2228,plain,
% 1.39/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a43) | c0_1(a40) | c3_1(a40) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a40)) | c2_1(a43) | (~c0_1(a43))),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2227, 2226])).
% 1.39/1.63 tff(2229,plain,
% 1.39/1.63 ($false),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2228, 92, 1814, 1813, 1812, 2203, 2222, 2202, 2221, 2220, 1643, 2210])).
% 1.39/1.63 tff(2230,plain,(c3_1(a7) | c0_1(a7) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.39/1.63 tff(2231,plain,
% 1.39/1.63 (c3_1(a7)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2230, 45, 32])).
% 1.39/1.63 tff(2232,plain,
% 1.39/1.63 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp12 | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a7)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2233,plain,
% 1.39/1.63 ((hskp12 | (~ndr1_0) | c0_1(a7) | (~c2_1(a7)) | (~c3_1(a7)) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7))) <=> (hskp12 | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a7)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2234,plain,
% 1.39/1.63 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a7) | (~c2_1(a7)) | (~c3_1(a7)) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a7))))),
% 1.39/1.63 inference(monotonicity,[status(thm)],[2233])).
% 1.39/1.63 tff(2235,plain,
% 1.39/1.63 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a7) | (~c2_1(a7)) | (~c3_1(a7)) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp12 | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a7)))),
% 1.39/1.63 inference(transitivity,[status(thm)],[2234, 2232])).
% 1.39/1.63 tff(2236,plain,
% 1.39/1.63 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a7) | (~c2_1(a7)) | (~c3_1(a7)) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)))),
% 1.39/1.63 inference(quant_inst,[status(thm)],[])).
% 1.39/1.63 tff(2237,plain,
% 1.39/1.63 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp12 | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | (~ndr1_0) | (~c2_1(a7))),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 1.39/1.63 tff(2238,plain,
% 1.39/1.63 (hskp12 | (~c1_1(a7)) | (~c3_1(a7)) | (~c2_1(a7))),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2237, 92, 45, 43])).
% 1.39/1.63 tff(2239,plain,
% 1.39/1.63 (~c2_1(a7)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2238, 46, 1786, 2231])).
% 1.39/1.63 tff(2240,plain,
% 1.39/1.63 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2241,plain,
% 1.39/1.63 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a7) | c2_1(a7) | (~c1_1(a7))) <=> (hskp12 | hskp11 | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2242,plain,
% 1.39/1.63 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a7) | c2_1(a7) | (~c1_1(a7)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7)))),
% 1.39/1.63 inference(monotonicity,[status(thm)],[2241])).
% 1.39/1.63 tff(2243,plain,
% 1.39/1.63 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a7) | c2_1(a7) | (~c1_1(a7)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7))),
% 1.39/1.63 inference(transitivity,[status(thm)],[2242, 2240])).
% 1.39/1.63 tff(2244,plain,
% 1.39/1.63 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a7) | c2_1(a7) | (~c1_1(a7)))),
% 1.39/1.63 inference(quant_inst,[status(thm)],[])).
% 1.39/1.63 tff(2245,plain,
% 1.39/1.63 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7)),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2244, 2243])).
% 1.39/1.63 tff(2246,plain,
% 1.39/1.63 (hskp12 | hskp11 | (~c1_1(a7)) | c2_1(a7)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2245, 92, 45, 302])).
% 1.39/1.63 tff(2247,plain,
% 1.39/1.63 (hskp11),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2246, 2239, 1786, 46])).
% 1.39/1.63 tff(2248,plain,
% 1.39/1.63 (~c0_1(a19)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[98, 2247])).
% 1.39/1.63 tff(2249,plain,
% 1.39/1.63 (c2_1(a19)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[115, 2247])).
% 1.39/1.63 tff(2250,plain,
% 1.39/1.63 (c1_1(a19)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[107, 2247])).
% 1.39/1.63 tff(2251,plain,
% 1.39/1.63 (~c3_1(a19)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2057, 92, 46, 2250, 2249, 2248, 43])).
% 1.39/1.63 tff(2252,plain,
% 1.39/1.63 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2253,plain,
% 1.39/1.63 ((hskp10 | hskp1 | (~ndr1_0) | c0_1(a7) | c2_1(a7) | (~c1_1(a7))) <=> (hskp10 | hskp1 | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2254,plain,
% 1.39/1.63 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a7) | c2_1(a7) | (~c1_1(a7)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7)))),
% 1.39/1.63 inference(monotonicity,[status(thm)],[2253])).
% 1.39/1.63 tff(2255,plain,
% 1.39/1.63 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a7) | c2_1(a7) | (~c1_1(a7)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7))),
% 1.39/1.63 inference(transitivity,[status(thm)],[2254, 2252])).
% 1.39/1.63 tff(2256,plain,
% 1.39/1.63 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c0_1(a7) | c2_1(a7) | (~c1_1(a7)))),
% 1.39/1.63 inference(quant_inst,[status(thm)],[])).
% 1.39/1.63 tff(2257,plain,
% 1.39/1.63 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp10 | hskp1 | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7)),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2256, 2255])).
% 1.39/1.63 tff(2258,plain,
% 1.39/1.63 (hskp10 | (~c1_1(a7)) | c2_1(a7)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2257, 92, 32, 45, 204])).
% 1.39/1.63 tff(2259,plain,
% 1.39/1.63 (hskp10),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2258, 2239, 1786])).
% 1.39/1.63 tff(2260,plain,
% 1.39/1.63 (~c3_1(a18)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[217, 2259])).
% 1.39/1.63 tff(2261,plain,
% 1.39/1.63 (~c1_1(a18)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[229, 2259])).
% 1.39/1.63 tff(2262,plain,
% 1.39/1.63 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a19) | c1_1(a18) | c3_1(a18) | (~ndr1_0) | c0_1(a18) | (~c2_1(a19)) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a19) | c1_1(a18) | c3_1(a18) | (~ndr1_0) | c0_1(a18) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2263,plain,
% 1.39/1.63 ((hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a18) | c0_1(a18) | c3_1(a18)) <=> (hskp1 | c0_1(a19) | c1_1(a18) | c3_1(a18) | (~ndr1_0) | c0_1(a18) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2264,plain,
% 1.39/1.63 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a18) | c0_1(a18) | c3_1(a18))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a19) | c1_1(a18) | c3_1(a18) | (~ndr1_0) | c0_1(a18) | (~c2_1(a19)) | (~c1_1(a19))))),
% 1.39/1.63 inference(monotonicity,[status(thm)],[2263])).
% 1.39/1.63 tff(2265,plain,
% 1.39/1.63 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a18) | c0_1(a18) | c3_1(a18))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a19) | c1_1(a18) | c3_1(a18) | (~ndr1_0) | c0_1(a18) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.39/1.63 inference(transitivity,[status(thm)],[2264, 2262])).
% 1.39/1.63 tff(2266,plain,
% 1.39/1.63 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a18) | c0_1(a18) | c3_1(a18))),
% 1.39/1.63 inference(quant_inst,[status(thm)],[])).
% 1.39/1.63 tff(2267,plain,
% 1.39/1.63 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a19) | c1_1(a18) | c3_1(a18) | (~ndr1_0) | c0_1(a18) | (~c2_1(a19)) | (~c1_1(a19))),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2266, 2265])).
% 1.39/1.63 tff(2268,plain,
% 1.39/1.63 (c0_1(a18)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2267, 92, 32, 2250, 2249, 2248, 2261, 2260, 126])).
% 1.39/1.63 tff(2269,plain,
% 1.39/1.63 (~c2_1(a18)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[223, 2259])).
% 1.39/1.63 tff(2270,plain,
% 1.39/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a19) | c2_1(a18) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a19) | c2_1(a18) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2271,plain,
% 1.39/1.63 (((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)) | c2_1(a18) | c3_1(a18) | (~c0_1(a18)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19))) <=> (c0_1(a19) | c2_1(a18) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2272,plain,
% 1.39/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)) | c2_1(a18) | c3_1(a18) | (~c0_1(a18)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a19) | c2_1(a18) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13))))),
% 1.39/1.63 inference(monotonicity,[status(thm)],[2271])).
% 1.39/1.63 tff(2273,plain,
% 1.39/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)) | c2_1(a18) | c3_1(a18) | (~c0_1(a18)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a19) | c2_1(a18) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)))),
% 1.39/1.63 inference(transitivity,[status(thm)],[2272, 2270])).
% 1.39/1.63 tff(2274,plain,
% 1.39/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13)) | c2_1(a18) | c3_1(a18) | (~c0_1(a18)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19)))),
% 1.39/1.63 inference(quant_inst,[status(thm)],[])).
% 1.39/1.63 tff(2275,plain,
% 1.39/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a19) | c2_1(a18) | c3_1(a18) | (~ndr1_0) | (~c0_1(a18)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a13)) | (~c2_1(a13)) | (~c0_1(a13))),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2274, 2273])).
% 1.39/1.63 tff(2276,plain,
% 1.39/1.63 (c3_1(a19) | (~c0_1(a13))),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2275, 92, 1803, 1802, 2249, 2248, 2269, 2260, 1643, 2268])).
% 1.39/1.63 tff(2277,plain,
% 1.39/1.63 (~c0_1(a13)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2276, 2251])).
% 1.39/1.63 tff(2278,plain,
% 1.39/1.63 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c2_1(a18) | c3_1(a18) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | (~ndr1_0) | (~c0_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c2_1(a18) | c3_1(a18) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | (~ndr1_0) | (~c0_1(a18)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2279,plain,
% 1.39/1.63 ((hskp15 | (~ndr1_0) | c3_1(a18) | c2_1(a18) | (~c0_1(a18)) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7))) <=> (hskp15 | c2_1(a18) | c3_1(a18) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | (~ndr1_0) | (~c0_1(a18)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2280,plain,
% 1.39/1.63 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a18) | c2_1(a18) | (~c0_1(a18)) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c2_1(a18) | c3_1(a18) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | (~ndr1_0) | (~c0_1(a18))))),
% 1.39/1.63 inference(monotonicity,[status(thm)],[2279])).
% 1.39/1.63 tff(2281,plain,
% 1.39/1.63 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a18) | c2_1(a18) | (~c0_1(a18)) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c2_1(a18) | c3_1(a18) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | (~ndr1_0) | (~c0_1(a18)))),
% 1.39/1.63 inference(transitivity,[status(thm)],[2280, 2278])).
% 1.39/1.63 tff(2282,plain,
% 1.39/1.63 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a18) | c2_1(a18) | (~c0_1(a18)) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)))),
% 1.39/1.63 inference(quant_inst,[status(thm)],[])).
% 1.39/1.63 tff(2283,plain,
% 1.39/1.63 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c2_1(a18) | c3_1(a18) | c0_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | (~ndr1_0) | (~c0_1(a18))),
% 1.39/1.63 inference(modus_ponens,[status(thm)],[2282, 2281])).
% 1.39/1.63 tff(2284,plain,
% 1.39/1.63 (hskp15 | (~c0_1(a18))),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2283, 92, 2269, 2260, 45, 1786, 2231, 648])).
% 1.39/1.63 tff(2285,plain,
% 1.39/1.63 (hskp15),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[2284, 2268])).
% 1.39/1.63 tff(2286,plain,
% 1.39/1.63 (~c1_1(a28)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[664, 2285])).
% 1.39/1.63 tff(2287,plain,
% 1.39/1.63 (c3_1(a28)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[697, 2285])).
% 1.39/1.63 tff(2288,plain,
% 1.39/1.63 (c2_1(a28)),
% 1.39/1.63 inference(unit_resolution,[status(thm)],[672, 2285])).
% 1.39/1.63 tff(2289,plain,
% 1.39/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a28) | (~ndr1_0) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a28)) | (~c3_1(a28)) | (~c1_1(a13)) | c0_1(a13) | (~c3_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a28) | (~ndr1_0) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a28)) | (~c3_1(a28)) | (~c1_1(a13)) | c0_1(a13) | (~c3_1(a13)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2290,plain,
% 1.39/1.63 (((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c0_1(a13) | (~c3_1(a13)) | (~c1_1(a13))) <=> (c1_1(a28) | (~ndr1_0) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a28)) | (~c3_1(a28)) | (~c1_1(a13)) | c0_1(a13) | (~c3_1(a13)))),
% 1.39/1.63 inference(rewrite,[status(thm)],[])).
% 1.39/1.63 tff(2291,plain,
% 1.39/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c0_1(a13) | (~c3_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a28) | (~ndr1_0) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a28)) | (~c3_1(a28)) | (~c1_1(a13)) | c0_1(a13) | (~c3_1(a13))))),
% 1.39/1.63 inference(monotonicity,[status(thm)],[2290])).
% 1.39/1.63 tff(2292,plain,
% 1.39/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c0_1(a13) | (~c3_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a28) | (~ndr1_0) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a28)) | (~c3_1(a28)) | (~c1_1(a13)) | c0_1(a13) | (~c3_1(a13)))),
% 1.39/1.63 inference(transitivity,[status(thm)],[2291, 2289])).
% 1.39/1.63 tff(2293,plain,
% 1.39/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c0_1(a13) | (~c3_1(a13)) | (~c1_1(a13)))),
% 1.39/1.64 inference(quant_inst,[status(thm)],[])).
% 1.39/1.64 tff(2294,plain,
% 1.39/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a28) | (~ndr1_0) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a28)) | (~c3_1(a28)) | (~c1_1(a13)) | c0_1(a13) | (~c3_1(a13))),
% 1.39/1.64 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 1.39/1.64 tff(2295,plain,
% 1.39/1.64 ($false),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2294, 92, 1803, 1801, 2288, 2287, 2250, 2249, 2286, 1584, 2277, 2251])).
% 1.39/1.64 tff(2296,plain,(hskp12 | c0_1(a7) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.39/1.64 tff(2297,plain,
% 1.39/1.64 (hskp12),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2296, 45, 32])).
% 1.39/1.64 tff(2298,plain,
% 1.39/1.64 (~c0_1(a20)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[338, 2297])).
% 1.39/1.64 tff(2299,plain,
% 1.39/1.64 (~c3_1(a20)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[388, 2297])).
% 1.39/1.64 tff(2300,plain,
% 1.39/1.64 (hskp0),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2009, 274, 32, 1792])).
% 1.39/1.64 tff(2301,plain,
% 1.39/1.64 (~c2_1(a1)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[256, 2300])).
% 1.39/1.64 tff(2302,plain,
% 1.39/1.64 (c3_1(a1)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[264, 2300])).
% 1.39/1.64 tff(2303,plain,
% 1.39/1.64 (c1_1(a1)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[272, 2300])).
% 1.39/1.64 tff(2304,plain,
% 1.39/1.64 (~c1_1(a20)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1497, 92, 1792, 33, 390, 44, 56])).
% 1.39/1.64 tff(2305,plain,
% 1.39/1.64 (c0_1(a13)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1518, 2304, 1803, 1802, 33, 44, 32])).
% 1.39/1.64 tff(2306,plain,
% 1.39/1.64 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a20) | c3_1(a20) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a20))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a20) | c3_1(a20) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a20))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2307,plain,
% 1.39/1.64 ((hskp2 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a20) | c0_1(a20) | c3_1(a20)) <=> (hskp2 | c0_1(a20) | c3_1(a20) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a20))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2308,plain,
% 1.39/1.64 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a20) | c3_1(a20) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a20)))),
% 1.39/1.64 inference(monotonicity,[status(thm)],[2307])).
% 1.39/1.64 tff(2309,plain,
% 1.39/1.64 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a20) | c3_1(a20) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a20))),
% 1.39/1.64 inference(transitivity,[status(thm)],[2308, 2306])).
% 1.39/1.64 tff(2310,plain,
% 1.39/1.64 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.39/1.64 inference(quant_inst,[status(thm)],[])).
% 1.39/1.64 tff(2311,plain,
% 1.39/1.64 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a20) | c3_1(a20) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a20)),
% 1.39/1.64 inference(modus_ponens,[status(thm)],[2310, 2309])).
% 1.39/1.64 tff(2312,plain,
% 1.39/1.64 (hskp2),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2311, 92, 304, 323, 33, 44, 303, 355, 2304])).
% 1.39/1.64 tff(2313,plain,
% 1.39/1.64 (~c2_1(a3)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[487, 2312])).
% 1.39/1.64 tff(2314,plain,
% 1.39/1.64 (~c1_1(a3)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[430, 2312])).
% 1.39/1.64 tff(2315,plain,
% 1.39/1.64 (c3_1(a3)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[373, 2312])).
% 1.39/1.64 tff(2316,plain,
% 1.39/1.64 (hskp21),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1104, 92, 1803, 1802, 2315, 2314, 2313, 1098, 2305])).
% 1.39/1.64 tff(2317,plain,
% 1.39/1.64 (~c0_1(a47)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[777, 2316])).
% 1.39/1.64 tff(2318,plain,
% 1.39/1.64 (c2_1(a47)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[793, 2316])).
% 1.39/1.64 tff(2319,plain,
% 1.39/1.64 (~c1_1(a47)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1544, 92, 32, 2318, 2317, 33, 44, 126, 2304])).
% 1.39/1.64 tff(2320,plain,
% 1.39/1.64 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a20) | c3_1(a20) | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | (~c2_1(a7)) | c1_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a20) | c3_1(a20) | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | (~c2_1(a7)) | c1_1(a20))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2321,plain,
% 1.39/1.64 ((hskp1 | (~ndr1_0) | c0_1(a7) | (~c1_1(a7)) | (~c2_1(a7)) | c1_1(a20) | c0_1(a20) | c3_1(a20)) <=> (hskp1 | c0_1(a20) | c3_1(a20) | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | (~c2_1(a7)) | c1_1(a20))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2322,plain,
% 1.39/1.64 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a7) | (~c1_1(a7)) | (~c2_1(a7)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a20) | c3_1(a20) | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | (~c2_1(a7)) | c1_1(a20)))),
% 1.39/1.64 inference(monotonicity,[status(thm)],[2321])).
% 1.39/1.64 tff(2323,plain,
% 1.39/1.64 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a7) | (~c1_1(a7)) | (~c2_1(a7)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a20) | c3_1(a20) | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | (~c2_1(a7)) | c1_1(a20))),
% 1.39/1.64 inference(transitivity,[status(thm)],[2322, 2320])).
% 1.39/1.64 tff(2324,plain,
% 1.39/1.64 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a7) | (~c1_1(a7)) | (~c2_1(a7)) | c1_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.39/1.64 inference(quant_inst,[status(thm)],[])).
% 1.39/1.64 tff(2325,plain,
% 1.39/1.64 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a20) | c3_1(a20) | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | (~c2_1(a7)) | c1_1(a20)),
% 1.39/1.64 inference(modus_ponens,[status(thm)],[2324, 2323])).
% 1.39/1.64 tff(2326,plain,
% 1.39/1.64 (~c2_1(a7)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2325, 92, 32, 33, 44, 45, 1786, 126, 2304])).
% 1.39/1.64 tff(2327,plain,
% 1.39/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | (~c1_1(a7)) | (~c3_1(a7)) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7) | c1_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | (~c1_1(a7)) | (~c3_1(a7)) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7) | c1_1(a20))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2328,plain,
% 1.39/1.64 (((~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a20) | c1_1(a20) | c0_1(a20)) <=> (c0_1(a20) | c2_1(a20) | (~c1_1(a7)) | (~c3_1(a7)) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7) | c1_1(a20))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2329,plain,
% 1.39/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | (~c1_1(a7)) | (~c3_1(a7)) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7) | c1_1(a20)))),
% 1.39/1.64 inference(monotonicity,[status(thm)],[2328])).
% 1.39/1.64 tff(2330,plain,
% 1.39/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | (~c1_1(a7)) | (~c3_1(a7)) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7) | c1_1(a20))),
% 1.39/1.64 inference(transitivity,[status(thm)],[2329, 2327])).
% 1.39/1.64 tff(2331,plain,
% 1.39/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c3_1(a7)) | c1_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.39/1.64 inference(quant_inst,[status(thm)],[])).
% 1.39/1.64 tff(2332,plain,
% 1.39/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | (~c1_1(a7)) | (~c3_1(a7)) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a7) | c1_1(a20)),
% 1.39/1.64 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 1.39/1.64 tff(2333,plain,
% 1.39/1.64 (~c0_1(a3)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2332, 92, 2315, 33, 390, 1786, 2231, 2314, 424, 2326, 2304])).
% 1.39/1.64 tff(2334,plain,
% 1.39/1.64 (hskp25 | (~c0_1(a13))),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1561, 92, 1803, 1801, 1555])).
% 1.39/1.64 tff(2335,plain,
% 1.39/1.64 (hskp25),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2334, 2305])).
% 1.39/1.64 tff(2336,plain,
% 1.39/1.64 (~c3_1(a73)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1138, 2335])).
% 1.39/1.64 tff(2337,plain,
% 1.39/1.64 (c3_1(a47)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[785, 2316])).
% 1.39/1.64 tff(2338,plain,
% 1.39/1.64 (c2_1(a73)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1187, 2335])).
% 1.39/1.64 tff(2339,plain,
% 1.39/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a73) | c0_1(a47) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c3_1(a47)) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a73) | c0_1(a47) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c3_1(a47)) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73)))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2340,plain,
% 1.39/1.64 (((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c3_1(a73) | c0_1(a47) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c3_1(a47)) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73)))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2341,plain,
% 1.39/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a73) | c0_1(a47) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c3_1(a47)) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73))))),
% 1.39/1.64 inference(monotonicity,[status(thm)],[2340])).
% 1.39/1.64 tff(2342,plain,
% 1.39/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a73) | c0_1(a47) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c3_1(a47)) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73)))),
% 1.39/1.64 inference(transitivity,[status(thm)],[2341, 2339])).
% 1.39/1.64 tff(2343,plain,
% 1.39/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.39/1.64 inference(quant_inst,[status(thm)],[])).
% 1.39/1.64 tff(2344,plain,
% 1.39/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a73) | c0_1(a47) | c1_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c3_1(a47)) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73))),
% 1.39/1.64 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 1.39/1.64 tff(2345,plain,
% 1.39/1.64 (c1_1(a73)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2344, 92, 2338, 2318, 2337, 2315, 2336, 2317, 2314, 1073, 2333])).
% 1.39/1.64 tff(2346,plain,
% 1.39/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c3_1(a47)) | (~c2_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2347,plain,
% 1.39/1.64 (((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c0_1(a47) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2348,plain,
% 1.39/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c3_1(a47)) | (~c2_1(a47))))),
% 1.39/1.64 inference(monotonicity,[status(thm)],[2347])).
% 1.39/1.64 tff(2349,plain,
% 1.39/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.39/1.64 inference(transitivity,[status(thm)],[2348, 2346])).
% 1.39/1.64 tff(2350,plain,
% 1.39/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.39/1.64 inference(quant_inst,[status(thm)],[])).
% 1.39/1.64 tff(2351,plain,
% 1.39/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c1_1(a3) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c3_1(a47)) | (~c2_1(a47))),
% 1.39/1.64 inference(modus_ponens,[status(thm)],[2350, 2349])).
% 1.39/1.64 tff(2352,plain,
% 1.39/1.64 (~c0_1(a1)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2351, 92, 2318, 2337, 2315, 304, 2317, 2314, 303, 1465, 2333])).
% 1.39/1.64 tff(2353,plain,
% 1.39/1.64 ($false),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1590, 92, 2338, 2318, 2337, 304, 323, 2336, 1584, 2352, 2345, 2319])).
% 1.39/1.64 tff(2354,plain,(c2_1(a20) | (~c1_1(a1)) | (~c3_1(a1)) | hskp1 | c0_1(a20) | c3_1(a20) | c2_1(a1) | c0_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.64 tff(2355,plain,
% 1.39/1.64 (c2_1(a20)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2354, 2303, 2302, 32, 33, 44, 2301, 45])).
% 1.39/1.64 tff(2356,plain,
% 1.39/1.64 (~hskp12),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[344, 2355])).
% 1.39/1.64 tff(2357,plain,
% 1.39/1.64 (~c2_1(a7)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2238, 2356, 1786, 2231])).
% 1.39/1.64 tff(2358,plain,
% 1.39/1.64 ($false),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2246, 2357, 2356, 1786, 274])).
% 1.39/1.64 tff(2359,plain,(hskp11 | c0_1(a7) | hskp1 | c0_1(a20) | c3_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.64 tff(2360,plain,
% 1.39/1.64 (hskp11),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2359, 44, 32, 33, 45])).
% 1.39/1.64 tff(2361,plain,
% 1.39/1.64 (~c0_1(a19)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[98, 2360])).
% 1.39/1.64 tff(2362,plain,
% 1.39/1.64 (c2_1(a19)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[115, 2360])).
% 1.39/1.64 tff(2363,plain,
% 1.39/1.64 (c1_1(a19)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[107, 2360])).
% 1.39/1.64 tff(2364,plain,
% 1.39/1.64 ($false),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2019, 92, 32, 2122, 2121, 33, 44, 127, 126, 498])).
% 1.39/1.64 tff(2365,plain,(c1_1(a20) | hskp1 | (~c1_1(a19)) | (~c2_1(a19)) | c0_1(a20) | c3_1(a20) | c0_1(a19)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.64 tff(2366,plain,
% 1.39/1.64 (c1_1(a20)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2365, 2363, 32, 2362, 33, 44, 2361])).
% 1.39/1.64 tff(2367,plain,
% 1.39/1.64 ($false),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1497, 92, 1941, 33, 390, 44, 56, 2061])).
% 1.39/1.64 tff(2368,plain,(c2_1(a20) | hskp4 | c0_1(a20) | c3_1(a20) | (~c1_1(a20))), inference(lemma,lemma(discharge,[]))).
% 1.39/1.64 tff(2369,plain,
% 1.39/1.64 (c2_1(a20)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2368, 44, 33, 1792, 2366])).
% 1.39/1.64 tff(2370,plain,
% 1.39/1.64 (~hskp12),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[344, 2369])).
% 1.39/1.64 tff(2371,plain,
% 1.39/1.64 (~c2_1(a7)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2238, 2370, 1786, 2231])).
% 1.39/1.64 tff(2372,plain,
% 1.39/1.64 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a20) | c3_1(a20) | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a20) | c3_1(a20) | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7) | (~c1_1(a20)))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2373,plain,
% 1.39/1.64 ((hskp4 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c1_1(a20)) | c2_1(a7) | c0_1(a7) | (~c1_1(a7))) <=> (hskp4 | c0_1(a20) | c3_1(a20) | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7) | (~c1_1(a20)))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2374,plain,
% 1.39/1.64 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c1_1(a20)) | c2_1(a7) | c0_1(a7) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a20) | c3_1(a20) | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7) | (~c1_1(a20))))),
% 1.39/1.64 inference(monotonicity,[status(thm)],[2373])).
% 1.39/1.64 tff(2375,plain,
% 1.39/1.64 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c1_1(a20)) | c2_1(a7) | c0_1(a7) | (~c1_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a20) | c3_1(a20) | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7) | (~c1_1(a20)))),
% 1.39/1.64 inference(transitivity,[status(thm)],[2374, 2372])).
% 1.39/1.64 tff(2376,plain,
% 1.39/1.64 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c1_1(a20)) | c2_1(a7) | c0_1(a7) | (~c1_1(a7)))),
% 1.39/1.64 inference(quant_inst,[status(thm)],[])).
% 1.39/1.64 tff(2377,plain,
% 1.39/1.64 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a20) | c3_1(a20) | c0_1(a7) | (~c1_1(a7)) | (~ndr1_0) | c2_1(a7) | (~c1_1(a20))),
% 1.39/1.64 inference(modus_ponens,[status(thm)],[2376, 2375])).
% 1.39/1.64 tff(2378,plain,
% 1.39/1.64 ($false),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2377, 92, 1792, 33, 44, 45, 1786, 56, 2371, 2366])).
% 1.39/1.64 tff(2379,plain,(c3_1(a20) | c0_1(a20) | c0_1(a7) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.39/1.64 tff(2380,plain,
% 1.39/1.64 ($false),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2379, 2299, 2298, 45, 32])).
% 1.39/1.64 tff(2381,plain,(c0_1(a7) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.39/1.64 tff(2382,plain,
% 1.39/1.64 (c0_1(a7)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2381, 32])).
% 1.39/1.64 tff(2383,plain,
% 1.39/1.64 (((~hskp4) | (~c0_1(a7))) <=> ((~hskp4) | (~c0_1(a7)))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2384,plain,
% 1.39/1.64 (((~c0_1(a7)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a7)))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2385,axiom,((~c0_1(a7)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.39/1.64 tff(2386,plain,
% 1.39/1.64 ((~hskp4) | (~c0_1(a7))),
% 1.39/1.64 inference(modus_ponens,[status(thm)],[2385, 2384])).
% 1.39/1.64 tff(2387,plain,
% 1.39/1.64 ((~hskp4) | (~c0_1(a7))),
% 1.39/1.64 inference(modus_ponens,[status(thm)],[2386, 2383])).
% 1.39/1.64 tff(2388,plain,
% 1.39/1.64 (~hskp4),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2387, 2382])).
% 1.39/1.64 tff(2389,plain,
% 1.39/1.64 (~c1_1(a20)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2368, 390, 33, 44, 2388])).
% 1.39/1.64 tff(2390,plain,
% 1.39/1.64 (hskp27),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1506, 2388, 32])).
% 1.39/1.64 tff(2391,plain,
% 1.39/1.64 (c2_1(a13)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[918, 2390])).
% 1.39/1.64 tff(2392,plain,
% 1.39/1.64 (c1_1(a13)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[465, 2390])).
% 1.39/1.64 tff(2393,plain,
% 1.39/1.64 (c0_1(a13)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1518, 2389, 2392, 2391, 33, 44, 32])).
% 1.39/1.64 tff(2394,plain,
% 1.39/1.64 (hskp2),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2311, 92, 1455, 1489, 33, 44, 1454, 355, 2389])).
% 1.39/1.64 tff(2395,plain,
% 1.39/1.64 (~c2_1(a3)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[487, 2394])).
% 1.39/1.64 tff(2396,plain,
% 1.39/1.64 (~c1_1(a3)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[430, 2394])).
% 1.39/1.64 tff(2397,plain,
% 1.39/1.64 (c3_1(a3)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[373, 2394])).
% 1.39/1.64 tff(2398,plain,
% 1.39/1.64 (hskp21),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1104, 92, 2392, 2391, 2397, 2396, 2395, 1098, 2393])).
% 1.39/1.64 tff(2399,plain,
% 1.39/1.64 (~c0_1(a47)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[777, 2398])).
% 1.39/1.64 tff(2400,plain,
% 1.39/1.64 (c2_1(a47)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[793, 2398])).
% 1.39/1.64 tff(2401,plain,
% 1.39/1.64 (~c1_1(a47)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1544, 92, 32, 2400, 2399, 33, 44, 126, 2389])).
% 1.39/1.64 tff(2402,plain,
% 1.39/1.64 (~c0_1(a3)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1280, 92, 2397, 1455, 1489, 33, 390, 2396, 1454, 424, 2389])).
% 1.39/1.64 tff(2403,plain,
% 1.39/1.64 (c3_1(a47)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[785, 2398])).
% 1.39/1.64 tff(2404,plain,
% 1.39/1.64 (~c0_1(a1)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2351, 92, 2400, 2403, 2397, 1455, 2399, 2396, 1454, 1465, 2402])).
% 1.39/1.64 tff(2405,plain,
% 1.39/1.64 (c3_1(a13)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[473, 2390])).
% 1.39/1.64 tff(2406,plain,
% 1.39/1.64 (hskp25 | (~c0_1(a13))),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1561, 92, 2392, 2405, 1555])).
% 1.39/1.64 tff(2407,plain,
% 1.39/1.64 (hskp25),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2406, 2393])).
% 1.39/1.64 tff(2408,plain,
% 1.39/1.64 (~c3_1(a73)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1138, 2407])).
% 1.39/1.64 tff(2409,plain,
% 1.39/1.64 (c2_1(a73)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1187, 2407])).
% 1.39/1.64 tff(2410,plain,
% 1.39/1.64 (c1_1(a73)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2344, 92, 2409, 2400, 2403, 2397, 2408, 2399, 2396, 1073, 2402])).
% 1.39/1.64 tff(2411,plain,
% 1.39/1.64 ($false),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1590, 92, 2409, 2400, 2403, 1455, 1489, 2408, 1584, 2410, 2404, 2401])).
% 1.39/1.64 tff(2412,plain,((~hskp0) | hskp1 | c0_1(a20) | c3_1(a20) | c2_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.64 tff(2413,plain,
% 1.39/1.64 (~hskp0),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2412, 390, 33, 44, 32])).
% 1.39/1.64 tff(2414,plain,
% 1.39/1.64 (hskp11),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2009, 2413, 32, 2388])).
% 1.39/1.64 tff(2415,plain,
% 1.39/1.64 (c2_1(a19)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[115, 2414])).
% 1.39/1.64 tff(2416,plain,
% 1.39/1.64 (c1_1(a19)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[107, 2414])).
% 1.39/1.64 tff(2417,plain,
% 1.39/1.64 (~c0_1(a19)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[98, 2414])).
% 1.39/1.64 tff(2418,plain,
% 1.39/1.64 ($false),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2365, 2417, 2416, 2389, 2415, 33, 44, 32])).
% 1.39/1.64 tff(2419,plain,(c2_1(a20) | c0_1(a20) | c3_1(a20) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.39/1.64 tff(2420,plain,
% 1.39/1.64 (c2_1(a20)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2419, 44, 33, 32])).
% 1.39/1.64 tff(2421,plain,
% 1.39/1.64 (~hskp12),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[344, 2420])).
% 1.39/1.64 tff(2422,plain,
% 1.39/1.64 (hskp21),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1474, 274, 46])).
% 1.39/1.64 tff(2423,plain,
% 1.39/1.64 (~c0_1(a47)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[777, 2422])).
% 1.39/1.64 tff(2424,plain,
% 1.39/1.64 (c3_1(a47)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[785, 2422])).
% 1.39/1.64 tff(2425,plain,
% 1.39/1.64 (c2_1(a47)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[793, 2422])).
% 1.39/1.64 tff(2426,plain,
% 1.39/1.64 (~c1_1(a47)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[1959, 92, 46, 2425, 2424, 2423, 43])).
% 1.39/1.64 tff(2427,plain,
% 1.39/1.64 (hskp0),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2009, 274, 32, 2388])).
% 1.39/1.64 tff(2428,plain,
% 1.39/1.64 (~c2_1(a1)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[256, 2427])).
% 1.39/1.64 tff(2429,plain,
% 1.39/1.64 (c1_1(a1)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[272, 2427])).
% 1.39/1.64 tff(2430,plain,
% 1.39/1.64 (c0_1(a1)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[310, 92, 46, 274, 2429, 2428, 302])).
% 1.39/1.64 tff(2431,plain,
% 1.39/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2432,plain,
% 1.39/1.64 (((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47))) <=> (c0_1(a47) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2433,plain,
% 1.39/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47))))),
% 1.39/1.64 inference(monotonicity,[status(thm)],[2432])).
% 1.39/1.64 tff(2434,plain,
% 1.39/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))),
% 1.39/1.64 inference(transitivity,[status(thm)],[2433, 2431])).
% 1.39/1.64 tff(2435,plain,
% 1.39/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))),
% 1.39/1.64 inference(quant_inst,[status(thm)],[])).
% 1.39/1.64 tff(2436,plain,
% 1.39/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47))),
% 1.39/1.64 inference(modus_ponens,[status(thm)],[2435, 2434])).
% 1.39/1.64 tff(2437,plain,
% 1.39/1.64 ($false),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2436, 92, 2425, 2424, 2429, 2423, 2428, 1465, 2430, 2426])).
% 1.39/1.64 tff(2438,plain,(hskp11 | hskp12 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.39/1.64 tff(2439,plain,
% 1.39/1.64 (hskp11),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2438, 2421, 32])).
% 1.39/1.64 tff(2440,plain,
% 1.39/1.64 (c2_1(a19)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[115, 2439])).
% 1.39/1.64 tff(2441,plain,
% 1.39/1.64 (c1_1(a19)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[107, 2439])).
% 1.39/1.64 tff(2442,plain,
% 1.39/1.64 (~c0_1(a19)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[98, 2439])).
% 1.39/1.64 tff(2443,plain,
% 1.39/1.64 (c1_1(a20)),
% 1.39/1.64 inference(unit_resolution,[status(thm)],[2365, 2442, 2441, 2440, 33, 44, 32])).
% 1.39/1.64 tff(2444,plain,
% 1.39/1.64 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.64 inference(rewrite,[status(thm)],[])).
% 1.39/1.64 tff(2445,plain,
% 1.39/1.65 ((hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20))) <=> (hskp28 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2446,plain,
% 1.39/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))))),
% 1.39/1.65 inference(monotonicity,[status(thm)],[2445])).
% 1.39/1.65 tff(2447,plain,
% 1.39/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.65 inference(transitivity,[status(thm)],[2446, 2444])).
% 1.39/1.65 tff(2448,plain,
% 1.39/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20)))),
% 1.39/1.65 inference(quant_inst,[status(thm)],[])).
% 1.39/1.65 tff(2449,plain,
% 1.39/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))),
% 1.39/1.65 inference(modus_ponens,[status(thm)],[2448, 2447])).
% 1.39/1.65 tff(2450,plain,
% 1.39/1.65 (hskp28 | c3_1(a20) | (~c1_1(a20))),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2449, 92, 2392, 2391, 2405, 33, 1673])).
% 1.39/1.65 tff(2451,plain,
% 1.39/1.65 (hskp28),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2450, 2443, 44])).
% 1.39/1.65 tff(2452,plain,
% 1.39/1.65 (c0_1(a23)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[1703, 2451])).
% 1.39/1.65 tff(2453,plain,
% 1.39/1.65 (c1_1(a23)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[1695, 2451])).
% 1.39/1.65 tff(2454,plain,
% 1.39/1.65 (c2_1(a23)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[1687, 2451])).
% 1.39/1.65 tff(2455,plain,
% 1.39/1.65 (~c3_1(a19)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2057, 92, 2421, 2441, 2440, 2442, 43])).
% 1.39/1.65 tff(2456,plain,
% 1.39/1.65 (hskp21),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2141, 2455, 2443, 2454, 2453, 2441, 2440, 33, 44, 2452])).
% 1.39/1.65 tff(2457,plain,
% 1.39/1.65 (~c0_1(a47)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[777, 2456])).
% 1.39/1.65 tff(2458,plain,
% 1.39/1.65 (c3_1(a47)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[785, 2456])).
% 1.39/1.65 tff(2459,plain,
% 1.39/1.65 (c2_1(a47)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[793, 2456])).
% 1.39/1.65 tff(2460,plain,
% 1.39/1.65 (~c1_1(a47)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[1959, 92, 2421, 2459, 2458, 2457, 43])).
% 1.39/1.65 tff(2461,plain,
% 1.39/1.65 (hskp0 | c1_1(a47)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[1952, 92, 2388, 2459, 2457, 1605])).
% 1.39/1.65 tff(2462,plain,
% 1.39/1.65 (hskp0),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2461, 2460])).
% 1.39/1.65 tff(2463,plain,
% 1.39/1.65 (~c2_1(a1)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[256, 2462])).
% 1.39/1.65 tff(2464,plain,
% 1.39/1.65 (c1_1(a1)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[272, 2462])).
% 1.39/1.65 tff(2465,plain,
% 1.39/1.65 (~c0_1(a1)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2436, 92, 2459, 2458, 2464, 2457, 2463, 1465, 2460])).
% 1.39/1.65 tff(2466,plain,
% 1.39/1.65 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.39/1.65 inference(bind,[status(th)],[])).
% 1.39/1.65 tff(2467,plain,
% 1.39/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.39/1.65 inference(quant_intro,[status(thm)],[2466])).
% 1.39/1.65 tff(2468,plain,
% 1.39/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2469,plain,
% 1.39/1.65 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.39/1.65 inference(bind,[status(th)],[])).
% 1.39/1.65 tff(2470,plain,
% 1.39/1.65 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.39/1.65 inference(quant_intro,[status(thm)],[2469])).
% 1.39/1.65 tff(2471,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 1.39/1.65 tff(2472,plain,
% 1.39/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.39/1.65 inference(modus_ponens,[status(thm)],[2471, 2470])).
% 1.39/1.65 tff(2473,plain,
% 1.39/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.39/1.65 inference(modus_ponens,[status(thm)],[2472, 2468])).
% 1.39/1.65 tff(2474,plain,(
% 1.39/1.65 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.39/1.65 inference(skolemize,[status(sab)],[2473])).
% 1.39/1.65 tff(2475,plain,
% 1.39/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.39/1.65 inference(modus_ponens,[status(thm)],[2474, 2467])).
% 1.39/1.65 tff(2476,plain,
% 1.39/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2477,plain,
% 1.39/1.65 (((~ndr1_0) | c1_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47))) <=> (c0_1(a47) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2478,plain,
% 1.39/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47))))),
% 1.39/1.65 inference(monotonicity,[status(thm)],[2477])).
% 1.39/1.65 tff(2479,plain,
% 1.39/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))),
% 1.39/1.65 inference(transitivity,[status(thm)],[2478, 2476])).
% 1.39/1.65 tff(2480,plain,
% 1.39/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))),
% 1.39/1.65 inference(quant_inst,[status(thm)],[])).
% 1.39/1.65 tff(2481,plain,
% 1.39/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47))),
% 1.39/1.65 inference(modus_ponens,[status(thm)],[2480, 2479])).
% 1.39/1.65 tff(2482,plain,
% 1.39/1.65 ($false),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2481, 92, 2459, 2458, 2464, 2457, 2463, 2475, 2460, 2465])).
% 1.39/1.65 tff(2483,plain,(c3_1(a20) | c0_1(a20) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.39/1.65 tff(2484,plain,
% 1.39/1.65 (c3_1(a20)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2483, 33, 32])).
% 1.39/1.65 tff(2485,plain,
% 1.39/1.65 (~hskp12),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[388, 2484])).
% 1.39/1.65 tff(2486,plain,
% 1.39/1.65 (hskp11),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2438, 2485, 32])).
% 1.39/1.65 tff(2487,plain,
% 1.39/1.65 (~c0_1(a19)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[98, 2486])).
% 1.39/1.65 tff(2488,plain,
% 1.39/1.65 (c2_1(a19)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[115, 2486])).
% 1.39/1.65 tff(2489,plain,
% 1.39/1.65 (c1_1(a19)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[107, 2486])).
% 1.39/1.65 tff(2490,plain,
% 1.39/1.65 (~c3_1(a19)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2057, 92, 2485, 2489, 2488, 2487, 43])).
% 1.39/1.65 tff(2491,plain,
% 1.39/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a20) | c2_1(a20) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a20) | c2_1(a20) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a20)))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2492,plain,
% 1.39/1.65 ((hskp4 | (~ndr1_0) | c3_1(a19) | c0_1(a19) | (~c1_1(a19)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20))) <=> (hskp4 | c0_1(a20) | c2_1(a20) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a20)))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2493,plain,
% 1.39/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a19) | c0_1(a19) | (~c1_1(a19)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a20) | c2_1(a20) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a20))))),
% 1.39/1.65 inference(monotonicity,[status(thm)],[2492])).
% 1.39/1.65 tff(2494,plain,
% 1.39/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a19) | c0_1(a19) | (~c1_1(a19)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a20) | c2_1(a20) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a20)))),
% 1.39/1.65 inference(transitivity,[status(thm)],[2493, 2491])).
% 1.39/1.65 tff(2495,plain,
% 1.39/1.65 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a19) | c0_1(a19) | (~c1_1(a19)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)))),
% 1.39/1.65 inference(quant_inst,[status(thm)],[])).
% 1.39/1.65 tff(2496,plain,
% 1.39/1.65 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a20) | c2_1(a20) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a20))),
% 1.39/1.65 inference(modus_ponens,[status(thm)],[2495, 2494])).
% 1.39/1.65 tff(2497,plain,
% 1.39/1.65 (~c1_1(a20)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2496, 92, 1941, 2122, 33, 390, 127, 56, 2060])).
% 1.39/1.65 tff(2498,assumption,(c3_1(a20)), introduced(assumption)).
% 1.39/1.65 tff(2499,plain,
% 1.39/1.65 (hskp28),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[1772, 92, 857, 942, 856, 2122, 127, 1673, 2060])).
% 1.39/1.65 tff(2500,plain,
% 1.39/1.65 (c2_1(a23)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[1687, 2499])).
% 1.39/1.65 tff(2501,plain,
% 1.39/1.65 (c1_1(a23)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[1695, 2499])).
% 1.39/1.65 tff(2502,plain,
% 1.39/1.65 (c0_1(a23)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[1703, 2499])).
% 1.39/1.65 tff(2503,plain,
% 1.39/1.65 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c2_1(a20) | (~c3_1(a20)) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c1_1(a20))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c2_1(a20) | (~c3_1(a20)) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c1_1(a20))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2504,plain,
% 1.39/1.65 ((hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a20) | c1_1(a20) | (~c3_1(a20))) <=> (hskp21 | c2_1(a20) | (~c3_1(a20)) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c1_1(a20))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2505,plain,
% 1.39/1.65 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a20) | c1_1(a20) | (~c3_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c2_1(a20) | (~c3_1(a20)) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c1_1(a20)))),
% 1.39/1.65 inference(monotonicity,[status(thm)],[2504])).
% 1.39/1.65 tff(2506,plain,
% 1.39/1.65 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a20) | c1_1(a20) | (~c3_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c2_1(a20) | (~c3_1(a20)) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c1_1(a20))),
% 1.39/1.65 inference(transitivity,[status(thm)],[2505, 2503])).
% 1.39/1.65 tff(2507,plain,
% 1.39/1.65 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a20) | c1_1(a20) | (~c3_1(a20)))),
% 1.39/1.65 inference(quant_inst,[status(thm)],[])).
% 1.39/1.65 tff(2508,plain,
% 1.39/1.65 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c2_1(a20) | (~c3_1(a20)) | (~ndr1_0) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | c1_1(a20)),
% 1.39/1.65 inference(modus_ponens,[status(thm)],[2507, 2506])).
% 1.39/1.65 tff(2509,plain,
% 1.39/1.65 (hskp21 | c1_1(a20)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2508, 92, 2502, 2501, 2500, 390, 2498, 1098])).
% 1.39/1.65 tff(2510,plain,
% 1.39/1.65 (hskp21),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2509, 2497])).
% 1.39/1.65 tff(2511,plain,
% 1.39/1.65 (~c0_1(a47)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[777, 2510])).
% 1.39/1.65 tff(2512,plain,
% 1.39/1.65 (c3_1(a47)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[785, 2510])).
% 1.39/1.65 tff(2513,plain,
% 1.39/1.65 (c2_1(a47)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[793, 2510])).
% 1.39/1.65 tff(2514,plain,
% 1.39/1.65 (~hskp12),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[388, 2498])).
% 1.39/1.65 tff(2515,plain,
% 1.39/1.65 (~c1_1(a47)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[1959, 92, 2514, 2513, 2512, 2511, 43])).
% 1.39/1.65 tff(2516,plain,
% 1.39/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | (~ndr1_0) | c1_1(a20) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | c1_1(a20) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2517,plain,
% 1.39/1.65 (((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c2_1(a20) | c1_1(a20) | c0_1(a20)) <=> (c0_1(a20) | c2_1(a20) | (~ndr1_0) | c1_1(a20) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2518,plain,
% 1.39/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | (~ndr1_0) | c1_1(a20) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))))),
% 1.39/1.65 inference(monotonicity,[status(thm)],[2517])).
% 1.39/1.65 tff(2519,plain,
% 1.39/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | c1_1(a20) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)))),
% 1.39/1.65 inference(transitivity,[status(thm)],[2518, 2516])).
% 1.39/1.65 tff(2520,plain,
% 1.39/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c1_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c2_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.39/1.65 inference(quant_inst,[status(thm)],[])).
% 1.39/1.65 tff(2521,plain,
% 1.39/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | (~ndr1_0) | c1_1(a20) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13))),
% 1.39/1.65 inference(modus_ponens,[status(thm)],[2520, 2519])).
% 1.39/1.65 tff(2522,plain,
% 1.39/1.65 ($false),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2521, 92, 857, 942, 856, 2513, 2512, 33, 390, 971, 2497, 2515])).
% 1.39/1.65 tff(2523,plain,(c2_1(a20) | (~c1_1(a13)) | (~c2_1(a13)) | (~c3_1(a13)) | c0_1(a20) | (~c3_1(a20)) | hskp4 | (~c1_1(a19)) | c0_1(a19) | c3_1(a19)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.65 tff(2524,plain,
% 1.39/1.65 (c2_1(a20)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2523, 33, 2391, 2405, 2392, 2484, 2388, 2489, 2487, 2490])).
% 1.39/1.65 tff(2525,plain,
% 1.39/1.65 (~c1_1(a20)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2050, 2524, 2484, 2485])).
% 1.39/1.65 tff(2526,plain,
% 1.39/1.65 (hskp0 | (~c2_1(a20)) | c1_1(a20)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2040, 92, 2388, 33, 1605])).
% 1.39/1.65 tff(2527,plain,
% 1.39/1.65 (hskp0),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2526, 2524, 2525])).
% 1.39/1.65 tff(2528,plain,
% 1.39/1.65 (~c2_1(a1)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[256, 2527])).
% 1.39/1.65 tff(2529,plain,
% 1.39/1.65 (c1_1(a1)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[272, 2527])).
% 1.39/1.65 tff(2530,plain,
% 1.39/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | c1_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | c1_1(a20))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2531,plain,
% 1.39/1.65 (((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20))) <=> (c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | c1_1(a20))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2532,plain,
% 1.39/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | c1_1(a20)))),
% 1.39/1.65 inference(monotonicity,[status(thm)],[2531])).
% 1.39/1.65 tff(2533,plain,
% 1.39/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | c1_1(a20))),
% 1.39/1.65 inference(transitivity,[status(thm)],[2532, 2530])).
% 1.39/1.65 tff(2534,plain,
% 1.39/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))),
% 1.39/1.65 inference(quant_inst,[status(thm)],[])).
% 1.39/1.65 tff(2535,plain,
% 1.39/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | c1_1(a20)),
% 1.39/1.65 inference(modus_ponens,[status(thm)],[2534, 2533])).
% 1.39/1.65 tff(2536,plain,
% 1.39/1.65 (~c0_1(a1)),
% 1.39/1.65 inference(unit_resolution,[status(thm)],[2535, 92, 2529, 33, 2524, 2484, 2528, 1465, 2525])).
% 1.39/1.65 tff(2537,plain,
% 1.39/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | c1_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | c1_1(a20))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2538,plain,
% 1.39/1.65 (((~ndr1_0) | c1_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20))) <=> (c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | c1_1(a20))),
% 1.39/1.65 inference(rewrite,[status(thm)],[])).
% 1.39/1.65 tff(2539,plain,
% 1.39/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | c1_1(a20)))),
% 1.39/1.65 inference(monotonicity,[status(thm)],[2538])).
% 1.39/1.65 tff(2540,plain,
% 1.39/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | c1_1(a20))),
% 1.48/1.65 inference(transitivity,[status(thm)],[2539, 2537])).
% 1.48/1.65 tff(2541,plain,
% 1.48/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))),
% 1.48/1.65 inference(quant_inst,[status(thm)],[])).
% 1.48/1.65 tff(2542,plain,
% 1.48/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a20) | (~c2_1(a20)) | (~c3_1(a20)) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | c1_1(a20)),
% 1.48/1.65 inference(modus_ponens,[status(thm)],[2541, 2540])).
% 1.48/1.65 tff(2543,plain,
% 1.48/1.65 ($false),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[2542, 92, 2529, 33, 2524, 2484, 2528, 2475, 2525, 2536])).
% 1.48/1.65 tff(2544,plain,(c0_1(a20) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.48/1.65 tff(2545,plain,
% 1.48/1.65 (c0_1(a20)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[2544, 32])).
% 1.48/1.65 tff(2546,plain,
% 1.48/1.65 (~hskp12),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[338, 2545])).
% 1.48/1.65 tff(2547,plain,
% 1.48/1.65 (hskp11),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[2438, 2546, 32])).
% 1.48/1.65 tff(2548,plain,
% 1.48/1.65 (~c0_1(a19)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[98, 2547])).
% 1.48/1.65 tff(2549,plain,
% 1.48/1.65 (c2_1(a19)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[115, 2547])).
% 1.48/1.65 tff(2550,plain,
% 1.48/1.65 (c1_1(a19)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[107, 2547])).
% 1.48/1.65 tff(2551,plain,
% 1.48/1.65 (~c3_1(a19)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[2057, 92, 2546, 2550, 2549, 2548, 43])).
% 1.48/1.65 tff(2552,plain,
% 1.48/1.65 (hskp28),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[1772, 92, 2392, 2391, 2405, 2550, 2548, 1673, 2551])).
% 1.48/1.65 tff(2553,plain,
% 1.48/1.65 (c2_1(a23)),
% 1.48/1.65 inference(unit_resolution,[status(thm)],[1687, 2552])).
% 1.48/1.65 tff(2554,plain,
% 1.48/1.66 (c1_1(a23)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1695, 2552])).
% 1.48/1.66 tff(2555,plain,
% 1.48/1.66 (c0_1(a23)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1703, 2552])).
% 1.48/1.66 tff(2556,assumption,(hskp5), introduced(assumption)).
% 1.48/1.66 tff(2557,plain,
% 1.48/1.66 (~c3_1(a8)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1656, 2556])).
% 1.48/1.66 tff(2558,plain,
% 1.48/1.66 (~c2_1(a8)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1662, 2556])).
% 1.48/1.66 tff(2559,plain,
% 1.48/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a19) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a19)) | c3_1(a19))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a19) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a19)) | c3_1(a19))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2560,plain,
% 1.48/1.66 (((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19))) <=> (c0_1(a19) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a19)) | c3_1(a19))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2561,plain,
% 1.48/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a19) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a19)) | c3_1(a19)))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[2560])).
% 1.48/1.66 tff(2562,plain,
% 1.48/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a19) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a19)) | c3_1(a19))),
% 1.48/1.66 inference(transitivity,[status(thm)],[2561, 2559])).
% 1.48/1.66 tff(2563,plain,
% 1.48/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a23)) | (~c2_1(a23)) | (~c0_1(a23)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19)))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(2564,plain,
% 1.48/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a19) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a19)) | c3_1(a19)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2563, 2562])).
% 1.48/1.66 tff(2565,plain,
% 1.48/1.66 (~c0_1(a8)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2564, 92, 1905, 1904, 1903, 2121, 127, 2558, 2557, 1643, 2060])).
% 1.48/1.66 tff(2566,plain,
% 1.48/1.66 (c1_1(a8)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1718, 2556])).
% 1.48/1.66 tff(2567,plain,
% 1.48/1.66 ($false),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1747, 92, 1941, 2566, 2558, 2557, 56, 2565])).
% 1.48/1.66 tff(2568,plain,((~hskp5) | hskp4 | (~c0_1(a23)) | (~c1_1(a23)) | (~c2_1(a23)) | (~c2_1(a19)) | c0_1(a19) | c3_1(a19)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.66 tff(2569,plain,
% 1.48/1.66 (~hskp5),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2568, 2388, 2555, 2554, 2553, 2549, 2548, 2551])).
% 1.48/1.66 tff(2570,plain,
% 1.48/1.66 (^[U: $i] : refl((hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.48/1.66 inference(bind,[status(th)],[])).
% 1.48/1.66 tff(2571,plain,
% 1.48/1.66 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.48/1.66 inference(quant_intro,[status(thm)],[2570])).
% 1.48/1.66 tff(2572,plain,
% 1.48/1.66 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2573,plain,
% 1.48/1.66 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp5) <=> ((hskp17 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp5))), rewrite(((hskp17 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp5) <=> (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp5) <=> (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.48/1.66 inference(bind,[status(th)],[])).
% 1.48/1.66 tff(2574,plain,
% 1.48/1.66 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp5) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.48/1.66 inference(quant_intro,[status(thm)],[2573])).
% 1.48/1.66 tff(2575,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 1.48/1.66 tff(2576,plain,
% 1.48/1.66 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2575, 2574])).
% 1.48/1.66 tff(2577,plain,
% 1.48/1.66 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2576, 2572])).
% 1.48/1.66 tff(2578,plain,(
% 1.48/1.66 ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.48/1.66 inference(skolemize,[status(sab)],[2577])).
% 1.48/1.66 tff(2579,plain,
% 1.48/1.66 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2578, 2571])).
% 1.48/1.66 tff(2580,plain,
% 1.48/1.66 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp5 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | hskp5 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2581,plain,
% 1.48/1.66 ((hskp17 | hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19))) <=> (hskp17 | hskp5 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2582,plain,
% 1.48/1.66 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp5 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19))))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[2581])).
% 1.48/1.66 tff(2583,plain,
% 1.48/1.66 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | hskp5 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.48/1.66 inference(transitivity,[status(thm)],[2582, 2580])).
% 1.48/1.66 tff(2584,plain,
% 1.48/1.66 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(2585,plain,
% 1.48/1.66 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | hskp5 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2584, 2583])).
% 1.48/1.66 tff(2586,plain,
% 1.48/1.66 (hskp17 | hskp5),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2585, 92, 2550, 2549, 2548, 2579])).
% 1.48/1.66 tff(2587,plain,
% 1.48/1.66 (hskp17),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2586, 2569])).
% 1.48/1.66 tff(2588,plain,
% 1.48/1.66 (~c3_1(a33)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[545, 2587])).
% 1.48/1.66 tff(2589,plain,
% 1.48/1.66 (~c1_1(a33)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[539, 2587])).
% 1.48/1.66 tff(2590,plain,
% 1.48/1.66 (c0_1(a33)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[556, 2587])).
% 1.48/1.66 tff(2591,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | c1_1(a33) | c3_1(a33) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | (~c0_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c1_1(a33) | c3_1(a33) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | (~c0_1(a33)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2592,plain,
% 1.48/1.66 ((hskp3 | (~ndr1_0) | c3_1(a33) | c1_1(a33) | (~c0_1(a33)) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19))) <=> (hskp3 | c1_1(a33) | c3_1(a33) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | (~c0_1(a33)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2593,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a33) | c1_1(a33) | (~c0_1(a33)) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | c1_1(a33) | c3_1(a33) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | (~c0_1(a33))))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[2592])).
% 1.48/1.66 tff(2594,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a33) | c1_1(a33) | (~c0_1(a33)) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c1_1(a33) | c3_1(a33) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | (~c0_1(a33)))),
% 1.48/1.66 inference(transitivity,[status(thm)],[2593, 2591])).
% 1.48/1.66 tff(2595,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a33) | c1_1(a33) | (~c0_1(a33)) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(2596,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c1_1(a33) | c3_1(a33) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | (~c0_1(a33))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2595, 2594])).
% 1.48/1.66 tff(2597,plain,
% 1.48/1.66 (hskp3),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2596, 92, 2590, 2550, 2549, 2589, 2588, 2548, 31])).
% 1.48/1.66 tff(2598,plain,
% 1.48/1.66 (~c1_1(a5)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[712, 2597])).
% 1.48/1.66 tff(2599,plain,
% 1.48/1.66 (~c0_1(a5)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[718, 2597])).
% 1.48/1.66 tff(2600,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a19) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c2_1(a19)) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a19) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2601,plain,
% 1.48/1.66 ((hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5))) <=> (hskp5 | c0_1(a19) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2602,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a19) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c2_1(a19)) | (~c1_1(a19))))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[2601])).
% 1.48/1.66 tff(2603,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a19) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.48/1.66 inference(transitivity,[status(thm)],[2602, 2600])).
% 1.48/1.66 tff(2604,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(2605,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a19) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c2_1(a19)) | (~c1_1(a19))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2604, 2603])).
% 1.48/1.66 tff(2606,plain,
% 1.48/1.66 (~c3_1(a5)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2605, 92, 2569, 2550, 2549, 2548, 2599, 2598, 21])).
% 1.48/1.66 tff(2607,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a19) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | c3_1(a5) | (~c2_1(a19)) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a19) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | c3_1(a5) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2608,plain,
% 1.48/1.66 ((hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c0_1(a5) | c3_1(a5)) <=> (hskp1 | c0_1(a19) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | c3_1(a5) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2609,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c0_1(a5) | c3_1(a5))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a19) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | c3_1(a5) | (~c2_1(a19)) | (~c1_1(a19))))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[2608])).
% 1.48/1.66 tff(2610,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c0_1(a5) | c3_1(a5))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a19) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | c3_1(a5) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.48/1.66 inference(transitivity,[status(thm)],[2609, 2607])).
% 1.48/1.66 tff(2611,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c0_1(a5) | c3_1(a5))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(2612,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a19) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | c3_1(a5) | (~c2_1(a19)) | (~c1_1(a19))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2611, 2610])).
% 1.48/1.66 tff(2613,plain,
% 1.48/1.66 ($false),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2612, 92, 32, 2550, 2549, 2548, 2599, 2598, 126, 2606])).
% 1.48/1.66 tff(2614,plain,(hskp1), inference(lemma,lemma(discharge,[]))).
% 1.48/1.66 tff(2615,plain,
% 1.48/1.66 (((~hskp1) | (~c1_1(a2))) <=> ((~hskp1) | (~c1_1(a2)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2616,plain,
% 1.48/1.66 (((~c1_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a2)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2617,axiom,((~c1_1(a2)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.48/1.66 tff(2618,plain,
% 1.48/1.66 ((~hskp1) | (~c1_1(a2))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2617, 2616])).
% 1.48/1.66 tff(2619,plain,
% 1.48/1.66 ((~hskp1) | (~c1_1(a2))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2618, 2615])).
% 1.48/1.66 tff(2620,plain,
% 1.48/1.66 (~c1_1(a2)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2619, 2614])).
% 1.48/1.66 tff(2621,plain,
% 1.48/1.66 (((~hskp1) | (~c2_1(a2))) <=> ((~hskp1) | (~c2_1(a2)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2622,plain,
% 1.48/1.66 (((~c2_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a2)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2623,axiom,((~c2_1(a2)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.48/1.66 tff(2624,plain,
% 1.48/1.66 ((~hskp1) | (~c2_1(a2))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2623, 2622])).
% 1.48/1.66 tff(2625,plain,
% 1.48/1.66 ((~hskp1) | (~c2_1(a2))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2624, 2621])).
% 1.48/1.66 tff(2626,plain,
% 1.48/1.66 (~c2_1(a2)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2625, 2614])).
% 1.48/1.66 tff(2627,assumption,(hskp4), introduced(assumption)).
% 1.48/1.66 tff(2628,plain,
% 1.48/1.66 (~c0_1(a7)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2387, 2627])).
% 1.48/1.66 tff(2629,plain,
% 1.48/1.66 (~c1_1(a7)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1791, 2627])).
% 1.48/1.66 tff(2630,plain,
% 1.48/1.66 (~c3_1(a7)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1451, 2627])).
% 1.48/1.66 tff(2631,plain,
% 1.48/1.66 (~c1_1(a20)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2368, 390, 33, 44, 1941])).
% 1.48/1.66 tff(2632,plain,
% 1.48/1.66 (^[U: $i] : refl((hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.48/1.66 inference(bind,[status(th)],[])).
% 1.48/1.66 tff(2633,plain,
% 1.48/1.66 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.48/1.66 inference(quant_intro,[status(thm)],[2632])).
% 1.48/1.66 tff(2634,plain,
% 1.48/1.66 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2635,plain,
% 1.48/1.66 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp26) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp26))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp26) | hskp3) <=> ((hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite(((hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp26) | hskp3) <=> (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.48/1.66 inference(bind,[status(th)],[])).
% 1.48/1.66 tff(2636,plain,
% 1.48/1.66 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp26) | hskp3) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.48/1.66 inference(quant_intro,[status(thm)],[2635])).
% 1.48/1.66 tff(2637,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp26) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.48/1.66 tff(2638,plain,
% 1.48/1.66 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2637, 2636])).
% 1.48/1.66 tff(2639,plain,
% 1.48/1.66 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2638, 2634])).
% 1.48/1.66 tff(2640,plain,(
% 1.48/1.66 ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.48/1.66 inference(skolemize,[status(sab)],[2639])).
% 1.48/1.66 tff(2641,plain,
% 1.48/1.66 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2640, 2633])).
% 1.48/1.66 tff(2642,plain,
% 1.48/1.66 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp3 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2643,plain,
% 1.48/1.66 ((hskp26 | hskp3 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | c0_1(a20)) <=> (hskp26 | hskp3 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2644,plain,
% 1.48/1.66 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20)))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[2643])).
% 1.48/1.66 tff(2645,plain,
% 1.48/1.66 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp3 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20))),
% 1.48/1.66 inference(transitivity,[status(thm)],[2644, 2642])).
% 1.48/1.66 tff(2646,plain,
% 1.48/1.66 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(2647,plain,
% 1.48/1.66 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp3 | c0_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2646, 2645])).
% 1.48/1.66 tff(2648,plain,
% 1.48/1.66 (hskp26 | hskp3 | c3_1(a20) | c1_1(a20)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2647, 92, 33, 2641])).
% 1.48/1.66 tff(2649,plain,
% 1.48/1.66 (hskp26),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2648, 2631, 44, 594])).
% 1.48/1.66 tff(2650,plain,
% 1.48/1.66 (((~hskp26) | c3_1(a4)) <=> ((~hskp26) | c3_1(a4))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2651,axiom,((~hskp26) | c3_1(a4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 1.48/1.66 tff(2652,plain,
% 1.48/1.66 ((~hskp26) | c3_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2651, 2650])).
% 1.48/1.66 tff(2653,plain,
% 1.48/1.66 ((~hskp26) | c3_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2652, 2650])).
% 1.48/1.66 tff(2654,plain,
% 1.48/1.66 ((~hskp26) | c3_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2653, 2650])).
% 1.48/1.66 tff(2655,plain,
% 1.48/1.66 ((~hskp26) | c3_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2654, 2650])).
% 1.48/1.66 tff(2656,plain,
% 1.48/1.66 ((~hskp26) | c3_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2655, 2650])).
% 1.48/1.66 tff(2657,plain,
% 1.48/1.66 (c3_1(a4)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2656, 2649])).
% 1.48/1.66 tff(2658,plain,
% 1.48/1.66 (((~hskp26) | c1_1(a4)) <=> ((~hskp26) | c1_1(a4))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2659,axiom,((~hskp26) | c1_1(a4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.48/1.66 tff(2660,plain,
% 1.48/1.66 ((~hskp26) | c1_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2659, 2658])).
% 1.48/1.66 tff(2661,plain,
% 1.48/1.66 ((~hskp26) | c1_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2660, 2658])).
% 1.48/1.66 tff(2662,plain,
% 1.48/1.66 ((~hskp26) | c1_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2661, 2658])).
% 1.48/1.66 tff(2663,plain,
% 1.48/1.66 ((~hskp26) | c1_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2662, 2658])).
% 1.48/1.66 tff(2664,plain,
% 1.48/1.66 ((~hskp26) | c1_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2663, 2658])).
% 1.48/1.66 tff(2665,plain,
% 1.48/1.66 (c1_1(a4)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2664, 2649])).
% 1.48/1.66 tff(2666,plain,
% 1.48/1.66 (((~hskp26) | c0_1(a4)) <=> ((~hskp26) | c0_1(a4))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2667,axiom,((~hskp26) | c0_1(a4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.48/1.66 tff(2668,plain,
% 1.48/1.66 ((~hskp26) | c0_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2667, 2666])).
% 1.48/1.66 tff(2669,plain,
% 1.48/1.66 ((~hskp26) | c0_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2668, 2666])).
% 1.48/1.66 tff(2670,plain,
% 1.48/1.66 ((~hskp26) | c0_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2669, 2666])).
% 1.48/1.66 tff(2671,plain,
% 1.48/1.66 ((~hskp26) | c0_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2670, 2666])).
% 1.48/1.66 tff(2672,plain,
% 1.48/1.66 ((~hskp26) | c0_1(a4)),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2671, 2666])).
% 1.48/1.66 tff(2673,plain,
% 1.48/1.66 (c0_1(a4)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2672, 2649])).
% 1.48/1.66 tff(2674,plain,
% 1.48/1.66 (~c1_1(a47)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1959, 92, 46, 1478, 1477, 1476, 43])).
% 1.48/1.66 tff(2675,plain,
% 1.48/1.66 (hskp0),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[1961, 46, 274, 1941])).
% 1.48/1.66 tff(2676,plain,
% 1.48/1.66 (~c2_1(a1)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[256, 2675])).
% 1.48/1.66 tff(2677,plain,
% 1.48/1.66 (c1_1(a1)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[272, 2675])).
% 1.48/1.66 tff(2678,plain,
% 1.48/1.66 (c0_1(a1)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[310, 92, 46, 274, 2677, 2676, 302])).
% 1.48/1.66 tff(2679,plain,
% 1.48/1.66 ($false),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2436, 92, 1478, 1477, 2677, 1476, 2676, 1465, 2678, 2674])).
% 1.48/1.66 tff(2680,plain,(hskp12 | hskp11 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.48/1.66 tff(2681,plain,
% 1.48/1.66 (hskp12),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2680, 274, 1941])).
% 1.48/1.66 tff(2682,plain,
% 1.48/1.66 (~c2_1(a20)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[344, 2681])).
% 1.48/1.66 tff(2683,plain,
% 1.48/1.66 (~c1_1(a20)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2368, 2682, 33, 44, 1941])).
% 1.48/1.66 tff(2684,plain,
% 1.48/1.66 (hskp22),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[250, 1942, 274])).
% 1.48/1.66 tff(2685,plain,
% 1.48/1.66 (~c3_1(a48)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[176, 2684])).
% 1.48/1.66 tff(2686,plain,
% 1.48/1.66 (~c0_1(a48)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[145, 2684])).
% 1.48/1.66 tff(2687,plain,
% 1.48/1.66 (c1_1(a48)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[153, 2684])).
% 1.48/1.66 tff(2688,assumption,(hskp3), introduced(assumption)).
% 1.48/1.66 tff(2689,plain,
% 1.48/1.66 (~c1_1(a5)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[712, 2688])).
% 1.48/1.66 tff(2690,plain,
% 1.48/1.66 (~c0_1(a5)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[718, 2688])).
% 1.48/1.66 tff(2691,plain,
% 1.48/1.66 (c2_1(a5)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[726, 2688])).
% 1.48/1.66 tff(2692,plain,
% 1.48/1.66 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2693,plain,
% 1.48/1.66 ((hskp4 | hskp0 | (~ndr1_0) | c1_1(a5) | c0_1(a5) | (~c2_1(a5))) <=> (hskp4 | hskp0 | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2694,plain,
% 1.48/1.66 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5))))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[2693])).
% 1.48/1.66 tff(2695,plain,
% 1.48/1.66 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)))),
% 1.48/1.66 inference(transitivity,[status(thm)],[2694, 2692])).
% 1.48/1.66 tff(2696,plain,
% 1.48/1.66 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(2697,plain,
% 1.48/1.66 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2696, 2695])).
% 1.48/1.66 tff(2698,plain,
% 1.48/1.66 ($false),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2697, 92, 1941, 1942, 2691, 2690, 2689, 1605])).
% 1.48/1.66 tff(2699,plain,((~hskp3) | hskp4 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.48/1.66 tff(2700,plain,
% 1.48/1.66 (~hskp3),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2699, 1942, 1941])).
% 1.48/1.66 tff(2701,plain,
% 1.48/1.66 (hskp26),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2648, 2700, 44, 2683])).
% 1.48/1.66 tff(2702,plain,
% 1.48/1.66 (c3_1(a4)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2656, 2701])).
% 1.48/1.66 tff(2703,plain,
% 1.48/1.66 (c1_1(a4)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2664, 2701])).
% 1.48/1.66 tff(2704,plain,
% 1.48/1.66 (c0_1(a4)),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2672, 2701])).
% 1.48/1.66 tff(2705,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2706,plain,
% 1.48/1.66 ((hskp13 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48))) <=> (hskp13 | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.48/1.66 inference(rewrite,[status(thm)],[])).
% 1.48/1.66 tff(2707,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4))))),
% 1.48/1.66 inference(monotonicity,[status(thm)],[2706])).
% 1.48/1.66 tff(2708,plain,
% 1.48/1.66 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.48/1.66 inference(transitivity,[status(thm)],[2707, 2705])).
% 1.48/1.66 tff(2709,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48)))),
% 1.48/1.66 inference(quant_inst,[status(thm)],[])).
% 1.48/1.66 tff(2710,plain,
% 1.48/1.66 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4))),
% 1.48/1.66 inference(modus_ponens,[status(thm)],[2709, 2708])).
% 1.48/1.66 tff(2711,plain,
% 1.48/1.66 (hskp13),
% 1.48/1.66 inference(unit_resolution,[status(thm)],[2710, 92, 2704, 2703, 2702, 2687, 2686, 2685, 1833])).
% 1.48/1.67 tff(2712,plain,
% 1.48/1.67 (~c1_1(a22)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[1846, 2711])).
% 1.48/1.67 tff(2713,plain,
% 1.48/1.67 (~c0_1(a22)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[1852, 2711])).
% 1.48/1.67 tff(2714,plain,
% 1.48/1.67 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2715,plain,
% 1.48/1.67 ((hskp4 | hskp0 | (~ndr1_0) | c1_1(a22) | c0_1(a22) | (~c2_1(a22))) <=> (hskp4 | hskp0 | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2716,plain,
% 1.48/1.67 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a22) | c0_1(a22) | (~c2_1(a22)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22))))),
% 1.48/1.67 inference(monotonicity,[status(thm)],[2715])).
% 1.48/1.67 tff(2717,plain,
% 1.48/1.67 (((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a22) | c0_1(a22) | (~c2_1(a22)))) <=> ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)))),
% 1.48/1.67 inference(transitivity,[status(thm)],[2716, 2714])).
% 1.48/1.67 tff(2718,plain,
% 1.48/1.67 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp0 | (~ndr1_0) | c1_1(a22) | c0_1(a22) | (~c2_1(a22)))),
% 1.48/1.67 inference(quant_inst,[status(thm)],[])).
% 1.48/1.67 tff(2719,plain,
% 1.48/1.67 ((~![U: $i] : (hskp4 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp0 | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2718, 2717])).
% 1.48/1.67 tff(2720,plain,
% 1.48/1.67 (~c2_1(a22)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2719, 92, 1941, 1942, 2713, 2712, 1605])).
% 1.48/1.67 tff(2721,plain,
% 1.48/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | c2_1(a48))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | c2_1(a48))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2722,plain,
% 1.48/1.67 (((~ndr1_0) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a20) | c1_1(a20) | c3_1(a20) | c2_1(a20) | c1_1(a20) | c0_1(a20)) <=> (c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | c2_1(a48))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2723,plain,
% 1.48/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a20) | c1_1(a20) | c3_1(a20) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | c2_1(a48)))),
% 1.48/1.67 inference(monotonicity,[status(thm)],[2722])).
% 1.48/1.67 tff(2724,plain,
% 1.48/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a20) | c1_1(a20) | c3_1(a20) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | c2_1(a48))),
% 1.48/1.67 inference(transitivity,[status(thm)],[2723, 2721])).
% 1.48/1.67 tff(2725,plain,
% 1.48/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a48) | c2_1(a48) | (~c1_1(a48)) | c2_1(a20) | c1_1(a20) | c3_1(a20) | c2_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.48/1.67 inference(quant_inst,[status(thm)],[])).
% 1.48/1.67 tff(2726,plain,
% 1.48/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c1_1(a48)) | c2_1(a48)),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2725, 2724])).
% 1.48/1.67 tff(2727,plain,
% 1.48/1.67 (c2_1(a48)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2726, 92, 2687, 2685, 33, 2682, 44, 194, 2683])).
% 1.48/1.67 tff(2728,plain,
% 1.48/1.67 (c3_1(a22)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[1894, 2711])).
% 1.48/1.67 tff(2729,plain,
% 1.48/1.67 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a48) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c3_1(a22)) | (~c1_1(a48)) | (~c2_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a48) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c3_1(a22)) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2730,plain,
% 1.48/1.67 ((hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22))) <=> (hskp5 | c0_1(a48) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c3_1(a22)) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2731,plain,
% 1.48/1.67 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a48) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c3_1(a22)) | (~c1_1(a48)) | (~c2_1(a48))))),
% 1.48/1.67 inference(monotonicity,[status(thm)],[2730])).
% 1.48/1.67 tff(2732,plain,
% 1.48/1.67 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a48) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c3_1(a22)) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.48/1.67 inference(transitivity,[status(thm)],[2731, 2729])).
% 1.48/1.67 tff(2733,plain,
% 1.48/1.67 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))),
% 1.48/1.67 inference(quant_inst,[status(thm)],[])).
% 1.48/1.67 tff(2734,plain,
% 1.48/1.67 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a48) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c3_1(a22)) | (~c1_1(a48)) | (~c2_1(a48))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2733, 2732])).
% 1.48/1.67 tff(2735,plain,
% 1.48/1.67 (hskp5),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2734, 92, 2687, 2728, 2686, 2713, 2712, 21, 2727])).
% 1.48/1.67 tff(2736,plain,
% 1.48/1.67 (~c3_1(a8)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[1656, 2735])).
% 1.48/1.67 tff(2737,plain,
% 1.48/1.67 (~c2_1(a8)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[1662, 2735])).
% 1.48/1.67 tff(2738,plain,
% 1.48/1.67 (c1_1(a8)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[1718, 2735])).
% 1.48/1.67 tff(2739,plain,
% 1.48/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a22) | c1_1(a22) | c2_1(a20) | c3_1(a20) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c1_1(a20) | c2_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c1_1(a22) | c2_1(a20) | c3_1(a20) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c1_1(a20) | c2_1(a22))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2740,plain,
% 1.48/1.67 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a20) | c1_1(a20) | c3_1(a20) | c2_1(a22) | c1_1(a22) | c0_1(a22)) <=> (c0_1(a22) | c1_1(a22) | c2_1(a20) | c3_1(a20) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c1_1(a20) | c2_1(a22))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2741,plain,
% 1.48/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a20) | c1_1(a20) | c3_1(a20) | c2_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a22) | c1_1(a22) | c2_1(a20) | c3_1(a20) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c1_1(a20) | c2_1(a22)))),
% 1.48/1.67 inference(monotonicity,[status(thm)],[2740])).
% 1.48/1.67 tff(2742,plain,
% 1.48/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a20) | c1_1(a20) | c3_1(a20) | c2_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c1_1(a22) | c2_1(a20) | c3_1(a20) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c1_1(a20) | c2_1(a22))),
% 1.48/1.67 inference(transitivity,[status(thm)],[2741, 2739])).
% 1.48/1.67 tff(2743,plain,
% 1.48/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a20) | c1_1(a20) | c3_1(a20) | c2_1(a22) | c1_1(a22) | c0_1(a22))),
% 1.48/1.67 inference(quant_inst,[status(thm)],[])).
% 1.48/1.67 tff(2744,plain,
% 1.48/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c1_1(a22) | c2_1(a20) | c3_1(a20) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | c1_1(a20) | c2_1(a22)),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2743, 2742])).
% 1.48/1.67 tff(2745,plain,
% 1.48/1.67 ($false),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2744, 92, 2738, 2713, 2712, 2682, 44, 2737, 2736, 194, 2683, 2720])).
% 1.48/1.67 tff(2746,plain,(hskp0 | c3_1(a20) | hskp4 | c0_1(a20) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.48/1.67 tff(2747,plain,
% 1.48/1.67 (hskp0),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2746, 274, 1941, 33, 44])).
% 1.48/1.67 tff(2748,plain,
% 1.48/1.67 (~c2_1(a1)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[256, 2747])).
% 1.48/1.67 tff(2749,plain,
% 1.48/1.67 (c3_1(a1)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[264, 2747])).
% 1.48/1.67 tff(2750,plain,
% 1.48/1.67 (c1_1(a1)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[272, 2747])).
% 1.48/1.67 tff(2751,plain,
% 1.48/1.67 (((~hskp1) | c0_1(a2)) <=> ((~hskp1) | c0_1(a2))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2752,axiom,((~hskp1) | c0_1(a2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.48/1.67 tff(2753,plain,
% 1.48/1.67 ((~hskp1) | c0_1(a2)),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2752, 2751])).
% 1.48/1.67 tff(2754,plain,
% 1.48/1.67 ((~hskp1) | c0_1(a2)),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2753, 2751])).
% 1.48/1.67 tff(2755,plain,
% 1.48/1.67 ((~hskp1) | c0_1(a2)),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2754, 2751])).
% 1.48/1.67 tff(2756,plain,
% 1.48/1.67 ((~hskp1) | c0_1(a2)),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2755, 2751])).
% 1.48/1.67 tff(2757,plain,
% 1.48/1.67 ((~hskp1) | c0_1(a2)),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2756, 2751])).
% 1.48/1.67 tff(2758,plain,
% 1.48/1.67 (c0_1(a2)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2757, 2614])).
% 1.48/1.67 tff(2759,plain,
% 1.48/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | c1_1(a2) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | c1_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a2) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | c1_1(a20))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2760,plain,
% 1.48/1.67 (((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a20) | c1_1(a20) | c0_1(a20)) <=> (c0_1(a20) | c2_1(a20) | c1_1(a2) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | c1_1(a20))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2761,plain,
% 1.48/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | c1_1(a2) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | c1_1(a20)))),
% 1.48/1.67 inference(monotonicity,[status(thm)],[2760])).
% 1.48/1.67 tff(2762,plain,
% 1.48/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a2) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | c1_1(a20))),
% 1.48/1.67 inference(transitivity,[status(thm)],[2761, 2759])).
% 1.48/1.67 tff(2763,plain,
% 1.48/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.48/1.67 inference(quant_inst,[status(thm)],[])).
% 1.48/1.67 tff(2764,plain,
% 1.48/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c1_1(a2) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | c1_1(a20)),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2763, 2762])).
% 1.48/1.67 tff(2765,plain,
% 1.48/1.67 (~c3_1(a2)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2764, 92, 2758, 2750, 2749, 33, 2682, 2620, 2748, 424, 2683])).
% 1.48/1.67 tff(2766,plain,
% 1.48/1.67 (hskp2),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2311, 92, 2750, 2749, 33, 44, 2748, 355, 2683])).
% 1.48/1.67 tff(2767,plain,
% 1.48/1.67 (~c1_1(a3)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[430, 2766])).
% 1.48/1.67 tff(2768,plain,
% 1.48/1.67 (c3_1(a3)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[373, 2766])).
% 1.48/1.67 tff(2769,plain,
% 1.48/1.67 (~c0_1(a3)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[1280, 92, 2768, 2750, 2749, 33, 2682, 2767, 2748, 424, 2683])).
% 1.48/1.67 tff(2770,plain,
% 1.48/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a20) | c3_1(a20) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | c1_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a20) | c3_1(a20) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | c1_1(a20))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2771,plain,
% 1.48/1.67 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a20) | c0_1(a20) | c3_1(a20)) <=> (c0_1(a20) | c3_1(a20) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | c1_1(a20))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2772,plain,
% 1.48/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a20) | c3_1(a20) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | c1_1(a20)))),
% 1.48/1.67 inference(monotonicity,[status(thm)],[2771])).
% 1.48/1.67 tff(2773,plain,
% 1.48/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a20) | c3_1(a20) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | c1_1(a20))),
% 1.48/1.67 inference(transitivity,[status(thm)],[2772, 2770])).
% 1.48/1.67 tff(2774,plain,
% 1.48/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.48/1.67 inference(quant_inst,[status(thm)],[])).
% 1.48/1.67 tff(2775,plain,
% 1.48/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a20) | c3_1(a20) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | c1_1(a20)),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2774, 2773])).
% 1.48/1.67 tff(2776,plain,
% 1.48/1.67 ($false),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2775, 92, 2691, 2758, 33, 44, 2690, 2689, 2626, 1164, 498, 1])).
% 1.48/1.67 tff(2777,plain,((~hskp3) | c0_1(a20) | c3_1(a20) | c1_1(a20) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.67 tff(2778,plain,
% 1.48/1.67 (~hskp3),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2777, 2683, 44, 33, 2765])).
% 1.48/1.67 tff(2779,plain,
% 1.48/1.67 (hskp2),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2311, 92, 304, 323, 33, 44, 303, 355, 498])).
% 1.48/1.67 tff(2780,plain,
% 1.48/1.67 (~c2_1(a3)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[487, 2779])).
% 1.48/1.67 tff(2781,plain,
% 1.48/1.67 (~c1_1(a3)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[430, 2779])).
% 1.48/1.67 tff(2782,plain,
% 1.48/1.67 (c3_1(a3)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[373, 2779])).
% 1.48/1.67 tff(2783,plain,
% 1.48/1.67 (hskp26),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2648, 594, 44, 498])).
% 1.48/1.67 tff(2784,plain,
% 1.48/1.67 (c1_1(a4)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2664, 2783])).
% 1.48/1.67 tff(2785,plain,
% 1.48/1.67 (c0_1(a4)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2672, 2783])).
% 1.48/1.67 tff(2786,plain,
% 1.48/1.67 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c2_1(a4)) | (~c0_1(a4)) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c2_1(a4)) | (~c0_1(a4)) | (~c1_1(a4)))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2787,plain,
% 1.48/1.67 ((hskp21 | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a4)) | (~c0_1(a4)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3))) <=> (hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c2_1(a4)) | (~c0_1(a4)) | (~c1_1(a4)))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2788,plain,
% 1.48/1.67 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a4)) | (~c0_1(a4)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c2_1(a4)) | (~c0_1(a4)) | (~c1_1(a4))))),
% 1.48/1.67 inference(monotonicity,[status(thm)],[2787])).
% 1.48/1.67 tff(2789,plain,
% 1.48/1.67 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a4)) | (~c0_1(a4)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c2_1(a4)) | (~c0_1(a4)) | (~c1_1(a4)))),
% 1.48/1.67 inference(transitivity,[status(thm)],[2788, 2786])).
% 1.48/1.67 tff(2790,plain,
% 1.48/1.67 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a4)) | (~c0_1(a4)) | c2_1(a3) | c1_1(a3) | (~c3_1(a3)))),
% 1.48/1.67 inference(quant_inst,[status(thm)],[])).
% 1.48/1.67 tff(2791,plain,
% 1.48/1.67 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a3) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c2_1(a4)) | (~c0_1(a4)) | (~c1_1(a4))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2790, 2789])).
% 1.48/1.67 tff(2792,plain,
% 1.48/1.67 (~c2_1(a4)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2791, 92, 2062, 2785, 2784, 2782, 2781, 2780, 1098])).
% 1.48/1.67 tff(2793,plain,
% 1.48/1.67 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))))),
% 1.48/1.67 inference(bind,[status(th)],[])).
% 1.48/1.67 tff(2794,plain,
% 1.48/1.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.48/1.67 inference(quant_intro,[status(thm)],[2793])).
% 1.48/1.67 tff(2795,plain,
% 1.48/1.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2796,plain,
% 1.48/1.67 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))))),
% 1.48/1.67 inference(bind,[status(th)],[])).
% 1.48/1.67 tff(2797,plain,
% 1.48/1.67 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.48/1.67 inference(quant_intro,[status(thm)],[2796])).
% 1.48/1.67 tff(2798,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 1.48/1.67 tff(2799,plain,
% 1.48/1.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2798, 2797])).
% 1.48/1.67 tff(2800,plain,
% 1.48/1.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2799, 2795])).
% 1.48/1.67 tff(2801,plain,(
% 1.48/1.67 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.48/1.67 inference(skolemize,[status(sab)],[2800])).
% 1.48/1.67 tff(2802,plain,
% 1.48/1.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.48/1.67 inference(modus_ponens,[status(thm)],[2801, 2794])).
% 1.48/1.67 tff(2803,plain,
% 1.48/1.67 (hskp3 | (~c0_1(a1))),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[610, 92, 2782, 304, 2780, 303, 604, 482])).
% 1.48/1.67 tff(2804,plain,
% 1.48/1.67 (~c0_1(a1)),
% 1.48/1.67 inference(unit_resolution,[status(thm)],[2803, 594])).
% 1.48/1.67 tff(2805,plain,
% 1.48/1.67 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a2)) | c3_1(a2))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a2)) | c3_1(a2))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2806,plain,
% 1.48/1.67 ((hskp15 | (~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1))) <=> (hskp15 | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a2)) | c3_1(a2))),
% 1.48/1.67 inference(rewrite,[status(thm)],[])).
% 1.48/1.67 tff(2807,plain,
% 1.48/1.67 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a2)) | c3_1(a2)))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[2806])).
% 1.48/1.68 tff(2808,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a2)) | c3_1(a2))),
% 1.48/1.68 inference(transitivity,[status(thm)],[2807, 2805])).
% 1.48/1.68 tff(2809,plain,
% 1.48/1.68 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(2810,plain,
% 1.48/1.68 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a2)) | c3_1(a2)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[2809, 2808])).
% 1.48/1.68 tff(2811,plain,
% 1.48/1.68 (hskp15),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2810, 92, 2758, 304, 323, 2626, 648, 1, 2804])).
% 1.48/1.68 tff(2812,plain,
% 1.48/1.68 (~c1_1(a28)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[664, 2811])).
% 1.48/1.68 tff(2813,plain,
% 1.48/1.68 (c3_1(a28)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[697, 2811])).
% 1.48/1.68 tff(2814,plain,
% 1.48/1.68 (c2_1(a28)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[672, 2811])).
% 1.48/1.68 tff(2815,plain,
% 1.48/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a28) | (~ndr1_0) | (~c2_1(a28)) | (~c3_1(a28)) | (~c0_1(a28)) | (~c0_1(a4)) | (~c1_1(a4)) | c2_1(a4))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a28) | (~ndr1_0) | (~c2_1(a28)) | (~c3_1(a28)) | (~c0_1(a28)) | (~c0_1(a4)) | (~c1_1(a4)) | c2_1(a4))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2816,plain,
% 1.48/1.68 (((~ndr1_0) | c2_1(a4) | (~c1_1(a4)) | (~c0_1(a4)) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c1_1(a28) | (~c2_1(a28)) | (~c0_1(a28))) <=> (c1_1(a28) | (~ndr1_0) | (~c2_1(a28)) | (~c3_1(a28)) | (~c0_1(a28)) | (~c0_1(a4)) | (~c1_1(a4)) | c2_1(a4))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2817,plain,
% 1.48/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a4) | (~c1_1(a4)) | (~c0_1(a4)) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c1_1(a28) | (~c2_1(a28)) | (~c0_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a28) | (~ndr1_0) | (~c2_1(a28)) | (~c3_1(a28)) | (~c0_1(a28)) | (~c0_1(a4)) | (~c1_1(a4)) | c2_1(a4)))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[2816])).
% 1.48/1.68 tff(2818,plain,
% 1.48/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a4) | (~c1_1(a4)) | (~c0_1(a4)) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c1_1(a28) | (~c2_1(a28)) | (~c0_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a28) | (~ndr1_0) | (~c2_1(a28)) | (~c3_1(a28)) | (~c0_1(a28)) | (~c0_1(a4)) | (~c1_1(a4)) | c2_1(a4))),
% 1.48/1.68 inference(transitivity,[status(thm)],[2817, 2815])).
% 1.48/1.68 tff(2819,plain,
% 1.48/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a4) | (~c1_1(a4)) | (~c0_1(a4)) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c1_1(a28) | (~c2_1(a28)) | (~c0_1(a28)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(2820,plain,
% 1.48/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a28) | (~ndr1_0) | (~c2_1(a28)) | (~c3_1(a28)) | (~c0_1(a28)) | (~c0_1(a4)) | (~c1_1(a4)) | c2_1(a4)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[2819, 2818])).
% 1.48/1.68 tff(2821,plain,
% 1.48/1.68 (~c0_1(a28)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2820, 92, 2785, 2784, 2814, 2813, 2812, 2802, 2792])).
% 1.48/1.68 tff(2822,plain,
% 1.48/1.68 (c3_1(a4)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2656, 2783])).
% 1.48/1.68 tff(2823,plain,
% 1.48/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a28) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c2_1(a28)) | c0_1(a28) | (~c0_1(a4)) | c2_1(a4) | (~c3_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a28) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c2_1(a28)) | c0_1(a28) | (~c0_1(a4)) | c2_1(a4) | (~c3_1(a4)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2824,plain,
% 1.48/1.68 (((~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a4)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a28) | c0_1(a28) | (~c2_1(a28))) <=> (c1_1(a28) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c2_1(a28)) | c0_1(a28) | (~c0_1(a4)) | c2_1(a4) | (~c3_1(a4)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2825,plain,
% 1.48/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a4)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a28) | c0_1(a28) | (~c2_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a28) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c2_1(a28)) | c0_1(a28) | (~c0_1(a4)) | c2_1(a4) | (~c3_1(a4))))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[2824])).
% 1.48/1.68 tff(2826,plain,
% 1.48/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a4)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a28) | c0_1(a28) | (~c2_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a28) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c2_1(a28)) | c0_1(a28) | (~c0_1(a4)) | c2_1(a4) | (~c3_1(a4)))),
% 1.48/1.68 inference(transitivity,[status(thm)],[2825, 2823])).
% 1.48/1.68 tff(2827,plain,
% 1.48/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a4)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a28) | c0_1(a28) | (~c2_1(a28)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(2828,plain,
% 1.48/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a28) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c2_1(a28)) | c0_1(a28) | (~c0_1(a4)) | c2_1(a4) | (~c3_1(a4))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[2827, 2826])).
% 1.48/1.68 tff(2829,plain,
% 1.48/1.68 ($false),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2828, 92, 2785, 2822, 2814, 304, 323, 2812, 567, 2804, 2792, 2821])).
% 1.48/1.68 tff(2830,plain,(hskp3 | (~c1_1(a1)) | (~c3_1(a1)) | hskp21 | c3_1(a2) | c2_1(a1) | c0_1(a3) | c3_1(a20) | c1_1(a20) | c0_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.68 tff(2831,plain,
% 1.48/1.68 (hskp21),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2830, 2778, 2749, 2750, 2765, 2748, 2769, 44, 2683, 33])).
% 1.48/1.68 tff(2832,plain,
% 1.48/1.68 (~c0_1(a47)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[777, 2831])).
% 1.48/1.68 tff(2833,plain,
% 1.48/1.68 (c2_1(a47)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[793, 2831])).
% 1.48/1.68 tff(2834,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | c0_1(a47) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a47)) | (~c2_1(a47)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c0_1(a47) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a47)) | (~c2_1(a47)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2835,plain,
% 1.48/1.68 ((hskp3 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c0_1(a47) | (~c1_1(a47)) | (~c2_1(a47))) <=> (hskp3 | c0_1(a47) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a47)) | (~c2_1(a47)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2836,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c0_1(a47) | (~c1_1(a47)) | (~c2_1(a47)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | c0_1(a47) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a47)) | (~c2_1(a47))))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[2835])).
% 1.48/1.68 tff(2837,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c0_1(a47) | (~c1_1(a47)) | (~c2_1(a47)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c0_1(a47) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a47)) | (~c2_1(a47)))),
% 1.48/1.68 inference(transitivity,[status(thm)],[2836, 2834])).
% 1.48/1.68 tff(2838,plain,
% 1.48/1.68 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c0_1(a47) | (~c1_1(a47)) | (~c2_1(a47)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(2839,plain,
% 1.48/1.68 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c0_1(a47) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a47)) | (~c2_1(a47))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 1.48/1.68 tff(2840,plain,
% 1.48/1.68 (~c1_1(a47)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2839, 92, 2778, 2833, 2758, 2832, 2620, 31, 2765])).
% 1.48/1.68 tff(2841,plain,
% 1.48/1.68 (~c2_1(a3)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[487, 2766])).
% 1.48/1.68 tff(2842,plain,
% 1.48/1.68 (hskp3 | (~c0_1(a1))),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[610, 92, 2768, 2750, 2841, 2748, 604, 2769])).
% 1.48/1.68 tff(2843,plain,
% 1.48/1.68 (~c0_1(a1)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2842, 2778])).
% 1.48/1.68 tff(2844,plain,
% 1.48/1.68 (hskp26),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2648, 2778, 44, 2683])).
% 1.48/1.68 tff(2845,plain,
% 1.48/1.68 (c3_1(a4)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2656, 2844])).
% 1.48/1.68 tff(2846,plain,
% 1.48/1.68 (c1_1(a4)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2664, 2844])).
% 1.48/1.68 tff(2847,plain,
% 1.48/1.68 (c0_1(a4)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2672, 2844])).
% 1.48/1.68 tff(2848,plain,
% 1.48/1.68 (((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2849,plain,
% 1.48/1.68 ((hskp25 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4))) <=> (hskp25 | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2850,plain,
% 1.48/1.68 (((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4))))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[2849])).
% 1.48/1.68 tff(2851,plain,
% 1.48/1.68 (((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.48/1.68 inference(transitivity,[status(thm)],[2850, 2848])).
% 1.48/1.68 tff(2852,plain,
% 1.48/1.68 ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(2853,plain,
% 1.48/1.68 ((~![U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[2852, 2851])).
% 1.48/1.68 tff(2854,plain,
% 1.48/1.68 (hskp25),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2853, 92, 2847, 2846, 2845, 1555])).
% 1.48/1.68 tff(2855,plain,
% 1.48/1.68 (~c3_1(a73)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[1138, 2854])).
% 1.48/1.68 tff(2856,plain,
% 1.48/1.68 (c3_1(a47)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[785, 2831])).
% 1.48/1.68 tff(2857,plain,
% 1.48/1.68 (c2_1(a73)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[1187, 2854])).
% 1.48/1.68 tff(2858,plain,
% 1.48/1.68 (~c1_1(a73)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[1590, 92, 2857, 2833, 2856, 2750, 2749, 2855, 1584, 2843, 2840])).
% 1.48/1.68 tff(2859,plain,
% 1.48/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a73) | c0_1(a47) | (~ndr1_0) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a73) | c0_1(a47) | (~ndr1_0) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2860,plain,
% 1.48/1.68 (((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47))) <=> (c3_1(a73) | c0_1(a47) | (~ndr1_0) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2861,plain,
% 1.48/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a73) | c0_1(a47) | (~ndr1_0) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73))))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[2860])).
% 1.48/1.68 tff(2862,plain,
% 1.48/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a73) | c0_1(a47) | (~ndr1_0) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73)))),
% 1.48/1.68 inference(transitivity,[status(thm)],[2861, 2859])).
% 1.48/1.68 tff(2863,plain,
% 1.48/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(2864,plain,
% 1.48/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a73) | c0_1(a47) | (~ndr1_0) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)) | c1_1(a73) | (~c2_1(a73))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[2863, 2862])).
% 1.48/1.68 tff(2865,plain,
% 1.48/1.68 ($false),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2864, 92, 2857, 2833, 2856, 2855, 2832, 1073, 2840, 2858])).
% 1.48/1.68 tff(2866,plain,(hskp11 | c3_1(a20) | c0_1(a20) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.48/1.68 tff(2867,plain,
% 1.48/1.68 (hskp11),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2866, 44, 33, 1941])).
% 1.48/1.68 tff(2868,plain,
% 1.48/1.68 (c1_1(a19)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[107, 2867])).
% 1.48/1.68 tff(2869,plain,
% 1.48/1.68 (~c0_1(a19)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[98, 2867])).
% 1.48/1.68 tff(2870,plain,
% 1.48/1.68 (c2_1(a19)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[115, 2867])).
% 1.48/1.68 tff(2871,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a19)) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2872,plain,
% 1.48/1.68 ((hskp3 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19))) <=> (hskp3 | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2873,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a19)) | (~c1_1(a19))))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[2872])).
% 1.48/1.68 tff(2874,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.48/1.68 inference(transitivity,[status(thm)],[2873, 2871])).
% 1.48/1.68 tff(2875,plain,
% 1.48/1.68 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(2876,plain,
% 1.48/1.68 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a19)) | (~c1_1(a19))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[2875, 2874])).
% 1.48/1.68 tff(2877,plain,
% 1.48/1.68 ($false),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2876, 92, 594, 2122, 2121, 2758, 127, 2620, 31, 1])).
% 1.48/1.68 tff(2878,plain,(c3_1(a2) | hskp3 | (~c1_1(a19)) | (~c2_1(a19)) | c0_1(a19)), inference(lemma,lemma(discharge,[]))).
% 1.48/1.68 tff(2879,plain,
% 1.48/1.68 (c3_1(a2)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2878, 594, 2868, 2870, 2869])).
% 1.48/1.68 tff(2880,plain,
% 1.48/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c3_1(a19)) | (~c1_1(a19)) | c1_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c3_1(a19)) | (~c1_1(a19)) | c1_1(a20))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2881,plain,
% 1.48/1.68 (((~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)) | c2_1(a20) | c1_1(a20) | c0_1(a20)) <=> (c0_1(a20) | c2_1(a20) | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c3_1(a19)) | (~c1_1(a19)) | c1_1(a20))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2882,plain,
% 1.48/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a20) | c2_1(a20) | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c3_1(a19)) | (~c1_1(a19)) | c1_1(a20)))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[2881])).
% 1.48/1.68 tff(2883,plain,
% 1.48/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c3_1(a19)) | (~c1_1(a19)) | c1_1(a20))),
% 1.48/1.68 inference(transitivity,[status(thm)],[2882, 2880])).
% 1.48/1.68 tff(2884,plain,
% 1.48/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)) | c2_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(2885,plain,
% 1.48/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a20) | c2_1(a20) | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c3_1(a19)) | (~c1_1(a19)) | c1_1(a20)),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[2884, 2883])).
% 1.48/1.68 tff(2886,plain,
% 1.48/1.68 (~c3_1(a19)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2885, 92, 2868, 2758, 33, 390, 2869, 2620, 690, 2631, 2879])).
% 1.48/1.68 tff(2887,assumption,(c3_1(a4)), introduced(assumption)).
% 1.48/1.68 tff(2888,assumption,(c1_1(a4)), introduced(assumption)).
% 1.48/1.68 tff(2889,assumption,(c0_1(a4)), introduced(assumption)).
% 1.48/1.68 tff(2890,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2891,plain,
% 1.48/1.68 ((hskp13 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19))) <=> (hskp13 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2892,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4))))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[2891])).
% 1.48/1.68 tff(2893,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.48/1.68 inference(transitivity,[status(thm)],[2892, 2890])).
% 1.48/1.68 tff(2894,plain,
% 1.48/1.68 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))),
% 1.48/1.68 inference(quant_inst,[status(thm)],[])).
% 1.48/1.68 tff(2895,plain,
% 1.48/1.68 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4))),
% 1.48/1.68 inference(modus_ponens,[status(thm)],[2894, 2893])).
% 1.48/1.68 tff(2896,plain,
% 1.48/1.68 (hskp13 | c3_1(a19)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2895, 92, 2889, 2888, 2887, 2122, 127, 1833])).
% 1.48/1.68 tff(2897,plain,
% 1.48/1.68 (hskp13),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2896, 2060])).
% 1.48/1.68 tff(2898,plain,
% 1.48/1.68 (~c1_1(a22)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[1846, 2897])).
% 1.48/1.68 tff(2899,plain,
% 1.48/1.68 (~c0_1(a22)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[1852, 2897])).
% 1.48/1.68 tff(2900,plain,
% 1.48/1.68 (hskp25),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[2853, 92, 2889, 2888, 2887, 1555])).
% 1.48/1.68 tff(2901,plain,
% 1.48/1.68 (~c3_1(a73)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[1138, 2900])).
% 1.48/1.68 tff(2902,plain,
% 1.48/1.68 (c2_1(a73)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[1187, 2900])).
% 1.48/1.68 tff(2903,plain,
% 1.48/1.68 (c0_1(a73)),
% 1.48/1.68 inference(unit_resolution,[status(thm)],[1146, 2900])).
% 1.48/1.68 tff(2904,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | c3_1(a73) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a73)) | (~c0_1(a73)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a73) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2905,plain,
% 1.48/1.68 ((hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19))) <=> (hskp14 | c3_1(a73) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.48/1.68 inference(rewrite,[status(thm)],[])).
% 1.48/1.68 tff(2906,plain,
% 1.48/1.68 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | c3_1(a73) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a73)) | (~c0_1(a73))))),
% 1.48/1.68 inference(monotonicity,[status(thm)],[2905])).
% 1.48/1.68 tff(2907,plain,
% 1.51/1.68 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a73) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.68 inference(transitivity,[status(thm)],[2906, 2904])).
% 1.51/1.68 tff(2908,plain,
% 1.51/1.68 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.68 inference(quant_inst,[status(thm)],[])).
% 1.51/1.68 tff(2909,plain,
% 1.51/1.68 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a73) | c0_1(a19) | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a73)) | (~c0_1(a73))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[2908, 2907])).
% 1.51/1.69 tff(2910,plain,
% 1.51/1.69 (hskp14 | c3_1(a19)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2909, 92, 2903, 2902, 2122, 2901, 127, 1863])).
% 1.51/1.69 tff(2911,plain,
% 1.51/1.69 (hskp14),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2910, 2060])).
% 1.51/1.69 tff(2912,plain,
% 1.51/1.69 (~c2_1(a25)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[1886, 2911])).
% 1.51/1.69 tff(2913,assumption,(c1_1(a73)), introduced(assumption)).
% 1.51/1.69 tff(2914,plain,
% 1.51/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a19) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a19) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(2915,plain,
% 1.51/1.69 (((~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19))) <=> (c0_1(a19) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(2916,plain,
% 1.51/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a19) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73))))),
% 1.51/1.69 inference(monotonicity,[status(thm)],[2915])).
% 1.51/1.69 tff(2917,plain,
% 1.51/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a19) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.69 inference(transitivity,[status(thm)],[2916, 2914])).
% 1.51/1.69 tff(2918,plain,
% 1.51/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a19) | c3_1(a19) | (~c2_1(a19)))),
% 1.51/1.69 inference(quant_inst,[status(thm)],[])).
% 1.51/1.69 tff(2919,plain,
% 1.51/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a19) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[2918, 2917])).
% 1.51/1.69 tff(2920,plain,
% 1.51/1.69 (c3_1(a2) | c3_1(a19)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2919, 92, 2903, 2902, 2121, 2758, 127, 2626, 1643, 2913])).
% 1.51/1.69 tff(2921,plain,
% 1.51/1.69 (c3_1(a2)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2920, 2060])).
% 1.51/1.69 tff(2922,plain,
% 1.51/1.69 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(2923,plain,
% 1.51/1.69 ((hskp21 | (~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2))) <=> (hskp21 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(2924,plain,
% 1.51/1.69 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73))))),
% 1.51/1.69 inference(monotonicity,[status(thm)],[2923])).
% 1.51/1.69 tff(2925,plain,
% 1.51/1.69 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.69 inference(transitivity,[status(thm)],[2924, 2922])).
% 1.51/1.69 tff(2926,plain,
% 1.51/1.69 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))),
% 1.51/1.69 inference(quant_inst,[status(thm)],[])).
% 1.51/1.69 tff(2927,plain,
% 1.51/1.69 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[2926, 2925])).
% 1.51/1.69 tff(2928,plain,
% 1.51/1.69 (hskp21 | (~c3_1(a2))),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2927, 92, 2903, 2902, 2620, 2626, 1098, 2913])).
% 1.51/1.69 tff(2929,plain,
% 1.51/1.69 (hskp21),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2928, 2921])).
% 1.51/1.69 tff(2930,plain,
% 1.51/1.69 (~c0_1(a47)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[777, 2929])).
% 1.51/1.69 tff(2931,plain,
% 1.51/1.69 (c3_1(a22)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[1894, 2897])).
% 1.51/1.69 tff(2932,plain,
% 1.51/1.69 (c1_1(a25)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[1920, 2911])).
% 1.51/1.69 tff(2933,plain,
% 1.51/1.69 (c0_1(a25)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[1928, 2911])).
% 1.51/1.69 tff(2934,plain,
% 1.51/1.69 (c3_1(a47)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[785, 2929])).
% 1.51/1.69 tff(2935,plain,
% 1.51/1.69 (c2_1(a47)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[793, 2929])).
% 1.51/1.69 tff(2936,plain,
% 1.51/1.69 ($false),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[1937, 92, 2935, 2934, 2933, 2932, 2931, 2930, 2912, 2899, 2898, 1465])).
% 1.51/1.69 tff(2937,plain,(c3_1(a19) | (~c1_1(a73)) | (~c2_1(a19)) | c0_1(a19) | (~c1_1(a19)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4))), inference(lemma,lemma(discharge,[]))).
% 1.51/1.69 tff(2938,plain,
% 1.51/1.69 (~c1_1(a73)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2937, 2886, 2870, 2869, 2868, 2673, 2665, 2657])).
% 1.51/1.69 tff(2939,plain,
% 1.51/1.69 (hskp25),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2853, 92, 2673, 2665, 2657, 1555])).
% 1.51/1.69 tff(2940,plain,
% 1.51/1.69 (~c3_1(a73)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[1138, 2939])).
% 1.51/1.69 tff(2941,plain,
% 1.51/1.69 (c0_1(a73)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[1146, 2939])).
% 1.51/1.69 tff(2942,plain,
% 1.51/1.69 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | c3_1(a73) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a73) | (~c0_1(a73)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c3_1(a73) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a73) | (~c0_1(a73)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(2943,plain,
% 1.51/1.69 ((hskp3 | (~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c0_1(a73)) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19))) <=> (hskp3 | c3_1(a73) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a73) | (~c0_1(a73)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(2944,plain,
% 1.51/1.69 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c0_1(a73)) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | c3_1(a73) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a73) | (~c0_1(a73))))),
% 1.51/1.69 inference(monotonicity,[status(thm)],[2943])).
% 1.51/1.69 tff(2945,plain,
% 1.51/1.69 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c0_1(a73)) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c3_1(a73) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a73) | (~c0_1(a73)))),
% 1.51/1.69 inference(transitivity,[status(thm)],[2944, 2942])).
% 1.51/1.69 tff(2946,plain,
% 1.51/1.69 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c0_1(a73)) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))),
% 1.51/1.69 inference(quant_inst,[status(thm)],[])).
% 1.51/1.69 tff(2947,plain,
% 1.51/1.69 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c3_1(a73) | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)) | c1_1(a73) | (~c0_1(a73))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[2946, 2945])).
% 1.51/1.69 tff(2948,plain,
% 1.51/1.69 ($false),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2947, 92, 594, 2941, 2868, 2870, 2940, 2869, 31, 2938])).
% 1.51/1.69 tff(2949,plain,(c2_1(a20) | hskp3 | c0_1(a20) | c3_1(a20) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.51/1.69 tff(2950,plain,
% 1.51/1.69 (hskp3),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2949, 390, 33, 44, 1941])).
% 1.51/1.69 tff(2951,plain,
% 1.51/1.69 (c3_1(a2)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2777, 2950, 44, 33, 2631])).
% 1.51/1.69 tff(2952,plain,
% 1.51/1.69 (c2_1(a20)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2949, 2700, 33, 44, 1941])).
% 1.51/1.69 tff(2953,plain,
% 1.51/1.69 (hskp4 | hskp0 | (~c2_1(a20)) | c1_1(a20)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2040, 92, 33, 1605])).
% 1.51/1.69 tff(2954,plain,
% 1.51/1.69 (c1_1(a20)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2953, 2952, 1941, 1942])).
% 1.51/1.69 tff(2955,plain,
% 1.51/1.69 (c2_1(a20)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2949, 594, 33, 44, 1941])).
% 1.51/1.69 tff(2956,assumption,(c3_1(a2)), introduced(assumption)).
% 1.51/1.69 tff(2957,assumption,(hskp9), introduced(assumption)).
% 1.51/1.69 tff(2958,plain,
% 1.51/1.69 (~c1_1(a15)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[1202, 2957])).
% 1.51/1.69 tff(2959,assumption,(c2_1(a20)), introduced(assumption)).
% 1.51/1.69 tff(2960,plain,
% 1.51/1.69 (~c0_1(a15)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[1384, 2957])).
% 1.51/1.69 tff(2961,plain,
% 1.51/1.69 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.51/1.69 inference(bind,[status(th)],[])).
% 1.51/1.69 tff(2962,plain,
% 1.51/1.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.51/1.69 inference(quant_intro,[status(thm)],[2961])).
% 1.51/1.69 tff(2963,plain,
% 1.51/1.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(2964,plain,
% 1.51/1.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.51/1.69 inference(bind,[status(th)],[])).
% 1.51/1.69 tff(2965,plain,
% 1.51/1.69 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.51/1.69 inference(quant_intro,[status(thm)],[2964])).
% 1.51/1.69 tff(2966,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.51/1.69 tff(2967,plain,
% 1.51/1.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[2966, 2965])).
% 1.51/1.69 tff(2968,plain,
% 1.51/1.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[2967, 2963])).
% 1.51/1.69 tff(2969,plain,(
% 1.51/1.69 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.51/1.69 inference(skolemize,[status(sab)],[2968])).
% 1.51/1.69 tff(2970,plain,
% 1.51/1.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[2969, 2962])).
% 1.51/1.69 tff(2971,assumption,(~hskp26), introduced(assumption)).
% 1.51/1.69 tff(2972,plain,
% 1.51/1.69 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | c0_1(a15) | c1_1(a15) | (~ndr1_0) | c3_1(a15))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp3 | c0_1(a15) | c1_1(a15) | (~ndr1_0) | c3_1(a15))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(2973,plain,
% 1.51/1.69 ((hskp26 | hskp3 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15)) <=> (hskp26 | hskp3 | c0_1(a15) | c1_1(a15) | (~ndr1_0) | c3_1(a15))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(2974,plain,
% 1.51/1.69 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | c0_1(a15) | c1_1(a15) | (~ndr1_0) | c3_1(a15)))),
% 1.51/1.69 inference(monotonicity,[status(thm)],[2973])).
% 1.51/1.69 tff(2975,plain,
% 1.51/1.69 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp3 | c0_1(a15) | c1_1(a15) | (~ndr1_0) | c3_1(a15))),
% 1.51/1.69 inference(transitivity,[status(thm)],[2974, 2972])).
% 1.51/1.69 tff(2976,plain,
% 1.51/1.69 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))),
% 1.51/1.69 inference(quant_inst,[status(thm)],[])).
% 1.51/1.69 tff(2977,plain,
% 1.51/1.69 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp3 | c0_1(a15) | c1_1(a15) | (~ndr1_0) | c3_1(a15)),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[2976, 2975])).
% 1.51/1.69 tff(2978,plain,
% 1.51/1.69 (hskp26 | c3_1(a15)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2977, 92, 594, 375, 414, 2641])).
% 1.51/1.69 tff(2979,plain,
% 1.51/1.69 (c3_1(a15)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2978, 2971])).
% 1.51/1.69 tff(2980,plain,
% 1.51/1.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a20) | (~c2_1(a20)) | c0_1(a15) | c1_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a20) | (~c2_1(a20)) | c0_1(a15) | c1_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c1_1(a20)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(2981,plain,
% 1.51/1.69 ((hskp5 | (~ndr1_0) | c0_1(a20) | (~c1_1(a20)) | (~c2_1(a20)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (hskp5 | c0_1(a20) | (~c2_1(a20)) | c0_1(a15) | c1_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c1_1(a20)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(2982,plain,
% 1.51/1.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a20) | (~c1_1(a20)) | (~c2_1(a20)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a20) | (~c2_1(a20)) | c0_1(a15) | c1_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c1_1(a20))))),
% 1.51/1.69 inference(monotonicity,[status(thm)],[2981])).
% 1.51/1.69 tff(2983,plain,
% 1.51/1.69 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a20) | (~c1_1(a20)) | (~c2_1(a20)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a20) | (~c2_1(a20)) | c0_1(a15) | c1_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c1_1(a20)))),
% 1.51/1.69 inference(transitivity,[status(thm)],[2982, 2980])).
% 1.51/1.69 tff(2984,plain,
% 1.51/1.69 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a20) | (~c1_1(a20)) | (~c2_1(a20)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 1.51/1.69 inference(quant_inst,[status(thm)],[])).
% 1.51/1.69 tff(2985,plain,
% 1.51/1.69 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a20) | (~c2_1(a20)) | c0_1(a15) | c1_1(a15) | (~ndr1_0) | (~c3_1(a15)) | (~c1_1(a20))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[2984, 2983])).
% 1.51/1.69 tff(2986,plain,
% 1.51/1.69 (hskp5 | (~c3_1(a15))),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2985, 92, 33, 2959, 375, 414, 21, 2061])).
% 1.51/1.69 tff(2987,plain,
% 1.51/1.69 (hskp5),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2986, 2979])).
% 1.51/1.69 tff(2988,plain,
% 1.51/1.69 (~c3_1(a8)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[1656, 2987])).
% 1.51/1.69 tff(2989,plain,
% 1.51/1.69 (^[U: $i] : refl((hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.51/1.69 inference(bind,[status(th)],[])).
% 1.51/1.69 tff(2990,plain,
% 1.51/1.69 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.51/1.69 inference(quant_intro,[status(thm)],[2989])).
% 1.51/1.69 tff(2991,plain,
% 1.51/1.69 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(2992,plain,
% 1.51/1.69 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp26) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp26))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp26) | hskp16) <=> ((hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp16))), rewrite(((hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp16) <=> (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp26) | hskp16) <=> (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.51/1.69 inference(bind,[status(th)],[])).
% 1.51/1.69 tff(2993,plain,
% 1.51/1.69 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp26) | hskp16) <=> ![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.51/1.69 inference(quant_intro,[status(thm)],[2992])).
% 1.51/1.69 tff(2994,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp26) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 1.51/1.69 tff(2995,plain,
% 1.51/1.69 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[2994, 2993])).
% 1.51/1.69 tff(2996,plain,
% 1.51/1.69 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[2995, 2991])).
% 1.51/1.69 tff(2997,plain,(
% 1.51/1.69 ![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.51/1.69 inference(skolemize,[status(sab)],[2996])).
% 1.51/1.69 tff(2998,plain,
% 1.51/1.69 (![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[2997, 2990])).
% 1.51/1.69 tff(2999,plain,
% 1.51/1.69 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp26 | hskp16 | c0_1(a20) | (~c2_1(a20)) | (~ndr1_0) | (~c1_1(a20)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp26 | hskp16 | c0_1(a20) | (~c2_1(a20)) | (~ndr1_0) | (~c1_1(a20)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(3000,plain,
% 1.51/1.69 ((hskp26 | hskp16 | (~ndr1_0) | c0_1(a20) | (~c1_1(a20)) | (~c2_1(a20))) <=> (hskp26 | hskp16 | c0_1(a20) | (~c2_1(a20)) | (~ndr1_0) | (~c1_1(a20)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(3001,plain,
% 1.51/1.69 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c0_1(a20) | (~c1_1(a20)) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp26 | hskp16 | c0_1(a20) | (~c2_1(a20)) | (~ndr1_0) | (~c1_1(a20))))),
% 1.51/1.69 inference(monotonicity,[status(thm)],[3000])).
% 1.51/1.69 tff(3002,plain,
% 1.51/1.69 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c0_1(a20) | (~c1_1(a20)) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp26 | hskp16 | c0_1(a20) | (~c2_1(a20)) | (~ndr1_0) | (~c1_1(a20)))),
% 1.51/1.69 inference(transitivity,[status(thm)],[3001, 2999])).
% 1.51/1.69 tff(3003,plain,
% 1.51/1.69 ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c0_1(a20) | (~c1_1(a20)) | (~c2_1(a20)))),
% 1.51/1.69 inference(quant_inst,[status(thm)],[])).
% 1.51/1.69 tff(3004,plain,
% 1.51/1.69 ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp26 | hskp16 | c0_1(a20) | (~c2_1(a20)) | (~ndr1_0) | (~c1_1(a20))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3003, 3002])).
% 1.51/1.69 tff(3005,plain,
% 1.51/1.69 (hskp26 | hskp16 | (~c2_1(a20)) | (~c1_1(a20))),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[3004, 92, 33, 2998])).
% 1.51/1.69 tff(3006,plain,
% 1.51/1.69 (hskp16),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[3005, 2971, 2959, 2061])).
% 1.51/1.69 tff(3007,plain,
% 1.51/1.69 (((~hskp16) | (~c1_1(a32))) <=> ((~hskp16) | (~c1_1(a32)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(3008,plain,
% 1.51/1.69 (((~c1_1(a32)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a32)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(3009,axiom,((~c1_1(a32)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 1.51/1.69 tff(3010,plain,
% 1.51/1.69 ((~hskp16) | (~c1_1(a32))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3009, 3008])).
% 1.51/1.69 tff(3011,plain,
% 1.51/1.69 ((~hskp16) | (~c1_1(a32))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3010, 3007])).
% 1.51/1.69 tff(3012,plain,
% 1.51/1.69 (~c1_1(a32)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[3011, 3006])).
% 1.51/1.69 tff(3013,plain,
% 1.51/1.69 (c1_1(a8)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[1718, 2987])).
% 1.51/1.69 tff(3014,plain,
% 1.51/1.69 (((~hskp16) | c2_1(a32)) <=> ((~hskp16) | c2_1(a32))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(3015,axiom,((~hskp16) | c2_1(a32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.51/1.69 tff(3016,plain,
% 1.51/1.69 ((~hskp16) | c2_1(a32)),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3015, 3014])).
% 1.51/1.69 tff(3017,plain,
% 1.51/1.69 ((~hskp16) | c2_1(a32)),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3016, 3014])).
% 1.51/1.69 tff(3018,plain,
% 1.51/1.69 ((~hskp16) | c2_1(a32)),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3017, 3014])).
% 1.51/1.69 tff(3019,plain,
% 1.51/1.69 ((~hskp16) | c2_1(a32)),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3018, 3014])).
% 1.51/1.69 tff(3020,plain,
% 1.51/1.69 ((~hskp16) | c2_1(a32)),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3019, 3014])).
% 1.51/1.69 tff(3021,plain,
% 1.51/1.69 (c2_1(a32)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[3020, 3006])).
% 1.51/1.69 tff(3022,plain,
% 1.51/1.69 (((~hskp16) | c0_1(a32)) <=> ((~hskp16) | c0_1(a32))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(3023,axiom,((~hskp16) | c0_1(a32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.51/1.69 tff(3024,plain,
% 1.51/1.69 ((~hskp16) | c0_1(a32)),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3023, 3022])).
% 1.51/1.69 tff(3025,plain,
% 1.51/1.69 ((~hskp16) | c0_1(a32)),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3024, 3022])).
% 1.51/1.69 tff(3026,plain,
% 1.51/1.69 ((~hskp16) | c0_1(a32)),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3025, 3022])).
% 1.51/1.69 tff(3027,plain,
% 1.51/1.69 ((~hskp16) | c0_1(a32)),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3026, 3022])).
% 1.51/1.69 tff(3028,plain,
% 1.51/1.69 ((~hskp16) | c0_1(a32)),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3027, 3022])).
% 1.51/1.69 tff(3029,plain,
% 1.51/1.69 (c0_1(a32)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[3028, 3006])).
% 1.51/1.69 tff(3030,plain,
% 1.51/1.69 (~hskp12),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[344, 2959])).
% 1.51/1.69 tff(3031,plain,
% 1.51/1.69 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c1_1(a32) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)) | (~c2_1(a32)) | (~c0_1(a32)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a32) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)) | (~c2_1(a32)) | (~c0_1(a32)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(3032,plain,
% 1.51/1.69 ((hskp12 | (~ndr1_0) | c3_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32))) <=> (hskp12 | c1_1(a32) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)) | (~c2_1(a32)) | (~c0_1(a32)))),
% 1.51/1.69 inference(rewrite,[status(thm)],[])).
% 1.51/1.69 tff(3033,plain,
% 1.51/1.69 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c1_1(a32) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)) | (~c2_1(a32)) | (~c0_1(a32))))),
% 1.51/1.69 inference(monotonicity,[status(thm)],[3032])).
% 1.51/1.69 tff(3034,plain,
% 1.51/1.69 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a32) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)) | (~c2_1(a32)) | (~c0_1(a32)))),
% 1.51/1.69 inference(transitivity,[status(thm)],[3033, 3031])).
% 1.51/1.69 tff(3035,plain,
% 1.51/1.69 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)))),
% 1.51/1.69 inference(quant_inst,[status(thm)],[])).
% 1.51/1.69 tff(3036,plain,
% 1.51/1.69 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a32) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)) | (~c2_1(a32)) | (~c0_1(a32))),
% 1.51/1.69 inference(modus_ponens,[status(thm)],[3035, 3034])).
% 1.51/1.69 tff(3037,plain,
% 1.51/1.69 (~c0_1(a8)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[3036, 92, 3030, 3029, 3021, 3013, 3012, 2988, 2970])).
% 1.51/1.69 tff(3038,plain,
% 1.51/1.69 (~c2_1(a8)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[1662, 2987])).
% 1.51/1.69 tff(3039,plain,
% 1.51/1.69 ($false),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[1747, 92, 1941, 3013, 3038, 2988, 56, 3037])).
% 1.51/1.69 tff(3040,plain,(hskp26 | hskp4 | c0_1(a20) | (~c2_1(a20)) | c0_1(a15) | c1_1(a15) | (~c1_1(a20)) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.51/1.69 tff(3041,plain,
% 1.51/1.69 (hskp26),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[3040, 2960, 33, 2959, 1941, 2958, 2061, 594])).
% 1.51/1.69 tff(3042,plain,
% 1.51/1.69 (c1_1(a4)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2664, 3041])).
% 1.51/1.69 tff(3043,plain,
% 1.51/1.69 (c0_1(a4)),
% 1.51/1.69 inference(unit_resolution,[status(thm)],[2672, 3041])).
% 1.51/1.69 tff(3044,plain,
% 1.51/1.69 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c2_1(a4)) | (~c0_1(a4)) | (~c1_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c2_1(a4)) | (~c0_1(a4)) | (~c1_1(a4)))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3045,plain,
% 1.51/1.70 ((hskp21 | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a4)) | (~c0_1(a4)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2))) <=> (hskp21 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c2_1(a4)) | (~c0_1(a4)) | (~c1_1(a4)))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3046,plain,
% 1.51/1.70 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a4)) | (~c0_1(a4)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c2_1(a4)) | (~c0_1(a4)) | (~c1_1(a4))))),
% 1.51/1.70 inference(monotonicity,[status(thm)],[3045])).
% 1.51/1.70 tff(3047,plain,
% 1.51/1.70 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a4)) | (~c0_1(a4)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c2_1(a4)) | (~c0_1(a4)) | (~c1_1(a4)))),
% 1.51/1.70 inference(transitivity,[status(thm)],[3046, 3044])).
% 1.51/1.70 tff(3048,plain,
% 1.51/1.70 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a4)) | (~c2_1(a4)) | (~c0_1(a4)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))),
% 1.51/1.70 inference(quant_inst,[status(thm)],[])).
% 1.51/1.70 tff(3049,plain,
% 1.51/1.70 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c2_1(a4)) | (~c0_1(a4)) | (~c1_1(a4))),
% 1.51/1.70 inference(modus_ponens,[status(thm)],[3048, 3047])).
% 1.51/1.70 tff(3050,plain,
% 1.51/1.70 (~c2_1(a4)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3049, 92, 2062, 3043, 3042, 2620, 2626, 1098, 2956])).
% 1.51/1.70 tff(3051,plain,
% 1.51/1.70 (~c2_1(a15)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1120, 2957])).
% 1.51/1.70 tff(3052,plain,
% 1.51/1.70 (c3_1(a4)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[2656, 3041])).
% 1.51/1.70 tff(3053,plain,
% 1.51/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a15) | c1_1(a15) | c2_1(a15) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c1_1(a4)) | c2_1(a4) | (~c3_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a15) | c1_1(a15) | c2_1(a15) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c1_1(a4)) | c2_1(a4) | (~c3_1(a4)))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3054,plain,
% 1.51/1.70 (((~ndr1_0) | c2_1(a4) | (~c1_1(a4)) | (~c3_1(a4)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a15) | c1_1(a15) | c0_1(a15)) <=> (c0_1(a15) | c1_1(a15) | c2_1(a15) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c1_1(a4)) | c2_1(a4) | (~c3_1(a4)))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3055,plain,
% 1.51/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a4) | (~c1_1(a4)) | (~c3_1(a4)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a15) | c1_1(a15) | c2_1(a15) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c1_1(a4)) | c2_1(a4) | (~c3_1(a4))))),
% 1.51/1.70 inference(monotonicity,[status(thm)],[3054])).
% 1.51/1.70 tff(3056,plain,
% 1.51/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a4) | (~c1_1(a4)) | (~c3_1(a4)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a15) | c1_1(a15) | c2_1(a15) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c1_1(a4)) | c2_1(a4) | (~c3_1(a4)))),
% 1.51/1.70 inference(transitivity,[status(thm)],[3055, 3053])).
% 1.51/1.70 tff(3057,plain,
% 1.51/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a4) | (~c1_1(a4)) | (~c3_1(a4)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a15) | c1_1(a15) | c0_1(a15))),
% 1.51/1.70 inference(quant_inst,[status(thm)],[])).
% 1.51/1.70 tff(3058,plain,
% 1.51/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a15) | c1_1(a15) | c2_1(a15) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c1_1(a4)) | c2_1(a4) | (~c3_1(a4))),
% 1.51/1.70 inference(modus_ponens,[status(thm)],[3057, 3056])).
% 1.51/1.70 tff(3059,plain,
% 1.51/1.70 ($false),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3058, 92, 3042, 3052, 2758, 2960, 2958, 3051, 2620, 424, 2956, 3050])).
% 1.51/1.70 tff(3060,plain,((~hskp9) | (~c3_1(a2)) | hskp21 | c0_1(a20) | (~c2_1(a20)) | hskp4 | (~c1_1(a20)) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.51/1.70 tff(3061,plain,
% 1.51/1.70 (~hskp9),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3060, 2062, 2879, 33, 2955, 1941, 2061, 594])).
% 1.51/1.70 tff(3062,plain,
% 1.51/1.70 (hskp27),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1388, 3061])).
% 1.51/1.70 tff(3063,plain,
% 1.51/1.70 (c3_1(a13)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[473, 3062])).
% 1.51/1.70 tff(3064,plain,
% 1.51/1.70 (c2_1(a13)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[918, 3062])).
% 1.51/1.70 tff(3065,plain,
% 1.51/1.70 (c1_1(a13)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[465, 3062])).
% 1.51/1.70 tff(3066,plain,
% 1.51/1.70 (hskp28),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[2449, 92, 3065, 3064, 3063, 33, 44, 1673, 2061])).
% 1.51/1.70 tff(3067,plain,
% 1.51/1.70 (c0_1(a23)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1703, 3066])).
% 1.51/1.70 tff(3068,plain,
% 1.51/1.70 (~hskp12),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[344, 2955])).
% 1.51/1.70 tff(3069,plain,
% 1.51/1.70 (hskp12 | (~c3_1(a19))),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[2057, 92, 2868, 2870, 2869, 43])).
% 1.51/1.70 tff(3070,plain,
% 1.51/1.70 (~c3_1(a19)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3069, 3068])).
% 1.51/1.70 tff(3071,plain,
% 1.51/1.70 (c1_1(a23)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1695, 3066])).
% 1.51/1.70 tff(3072,plain,
% 1.51/1.70 (c2_1(a23)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1687, 3066])).
% 1.51/1.70 tff(3073,plain,
% 1.51/1.70 ($false),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[2141, 3072, 3071, 2061, 2062, 3070, 2868, 2870, 33, 44, 3067])).
% 1.51/1.70 tff(3074,plain,(hskp21 | (~c1_1(a20)) | c0_1(a20) | c3_1(a20) | hskp4 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.51/1.70 tff(3075,plain,
% 1.51/1.70 (hskp21),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3074, 2954, 33, 44, 1941, 2700])).
% 1.51/1.70 tff(3076,plain,
% 1.51/1.70 (~c0_1(a47)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[777, 3075])).
% 1.51/1.70 tff(3077,plain,
% 1.51/1.70 (c2_1(a47)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[793, 3075])).
% 1.51/1.70 tff(3078,plain,
% 1.51/1.70 (c1_1(a47)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1952, 92, 1941, 1942, 3077, 3076, 1605])).
% 1.51/1.70 tff(3079,plain,
% 1.51/1.70 (c3_1(a47)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[785, 3075])).
% 1.51/1.70 tff(3080,plain,
% 1.51/1.70 (~hskp12),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[344, 2952])).
% 1.51/1.70 tff(3081,plain,
% 1.51/1.70 ($false),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1959, 92, 3080, 3077, 3079, 3076, 43, 3078])).
% 1.51/1.70 tff(3082,plain,(hskp0 | hskp4 | c0_1(a20) | c3_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.70 tff(3083,plain,
% 1.51/1.70 (hskp0),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3082, 44, 33, 1941])).
% 1.51/1.70 tff(3084,plain,
% 1.51/1.70 (~c2_1(a1)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[256, 3083])).
% 1.51/1.70 tff(3085,plain,
% 1.51/1.70 (c3_1(a1)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[264, 3083])).
% 1.51/1.70 tff(3086,plain,
% 1.51/1.70 (c1_1(a1)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[272, 3083])).
% 1.51/1.70 tff(3087,plain,
% 1.51/1.70 ($false),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[2764, 92, 2758, 3086, 3085, 33, 390, 2620, 3084, 424, 2631, 2951])).
% 1.51/1.70 tff(3088,plain,(c2_1(a20) | c0_1(a20) | c3_1(a20) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.51/1.70 tff(3089,plain,
% 1.51/1.70 (c2_1(a20)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3088, 44, 33, 1941])).
% 1.51/1.70 tff(3090,plain,
% 1.51/1.70 (~hskp12),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[344, 3089])).
% 1.51/1.70 tff(3091,plain,
% 1.51/1.70 (~c3_1(a19)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3069, 3090])).
% 1.51/1.70 tff(3092,plain,
% 1.51/1.70 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a19) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a19) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3093,plain,
% 1.51/1.70 ((hskp4 | (~ndr1_0) | c3_1(a19) | c0_1(a19) | (~c1_1(a19)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1))) <=> (hskp4 | c0_1(a19) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3094,plain,
% 1.51/1.70 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a19) | c0_1(a19) | (~c1_1(a19)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a19) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | c3_1(a19) | (~c1_1(a19))))),
% 1.51/1.70 inference(monotonicity,[status(thm)],[3093])).
% 1.51/1.70 tff(3095,plain,
% 1.51/1.70 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a19) | c0_1(a19) | (~c1_1(a19)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a19) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.70 inference(transitivity,[status(thm)],[3094, 3092])).
% 1.51/1.70 tff(3096,plain,
% 1.51/1.70 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a19) | c0_1(a19) | (~c1_1(a19)) | c2_1(a1) | c0_1(a1) | (~c1_1(a1)))),
% 1.51/1.70 inference(quant_inst,[status(thm)],[])).
% 1.51/1.70 tff(3097,plain,
% 1.51/1.70 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a19) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | c3_1(a19) | (~c1_1(a19))),
% 1.51/1.70 inference(modus_ponens,[status(thm)],[3096, 3095])).
% 1.51/1.70 tff(3098,plain,
% 1.51/1.70 (c0_1(a1)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3097, 92, 1941, 2868, 3086, 2869, 3084, 56, 3091])).
% 1.51/1.70 tff(3099,plain,
% 1.51/1.70 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a19) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a19) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3100,plain,
% 1.51/1.70 ((hskp13 | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19))) <=> (hskp13 | c0_1(a19) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3101,plain,
% 1.51/1.70 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a19) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | c3_1(a19) | (~c1_1(a19))))),
% 1.51/1.70 inference(monotonicity,[status(thm)],[3100])).
% 1.51/1.70 tff(3102,plain,
% 1.51/1.70 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a19) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.70 inference(transitivity,[status(thm)],[3101, 3099])).
% 1.51/1.70 tff(3103,plain,
% 1.51/1.70 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.70 inference(quant_inst,[status(thm)],[])).
% 1.51/1.70 tff(3104,plain,
% 1.51/1.70 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a19) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | c3_1(a19) | (~c1_1(a19))),
% 1.51/1.70 inference(modus_ponens,[status(thm)],[3103, 3102])).
% 1.51/1.70 tff(3105,plain,
% 1.51/1.70 (hskp13 | (~c0_1(a1)) | c3_1(a19)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3104, 92, 2868, 3086, 3085, 2869, 1833])).
% 1.51/1.70 tff(3106,plain,
% 1.51/1.70 (hskp13),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3105, 3098, 3091])).
% 1.51/1.70 tff(3107,plain,
% 1.51/1.70 (~c1_1(a22)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1846, 3106])).
% 1.51/1.70 tff(3108,plain,
% 1.51/1.70 (~c0_1(a22)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1852, 3106])).
% 1.51/1.70 tff(3109,plain,
% 1.51/1.70 (c3_1(a22)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1894, 3106])).
% 1.51/1.70 tff(3110,plain,
% 1.51/1.70 (~c2_1(a22)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1901, 92, 3109, 3086, 3108, 3107, 3084, 1465, 3098])).
% 1.51/1.70 tff(3111,plain,
% 1.51/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a22) | c1_1(a22) | c1_1(a2) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | c2_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c1_1(a22) | c1_1(a2) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | c2_1(a22))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3112,plain,
% 1.51/1.70 (((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a22) | c1_1(a22) | c0_1(a22)) <=> (c0_1(a22) | c1_1(a22) | c1_1(a2) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | c2_1(a22))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3113,plain,
% 1.51/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a22) | c1_1(a22) | c1_1(a2) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | c2_1(a22)))),
% 1.51/1.70 inference(monotonicity,[status(thm)],[3112])).
% 1.51/1.70 tff(3114,plain,
% 1.51/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c1_1(a22) | c1_1(a2) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | c2_1(a22))),
% 1.51/1.70 inference(transitivity,[status(thm)],[3113, 3111])).
% 1.51/1.70 tff(3115,plain,
% 1.51/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a22) | c1_1(a22) | c0_1(a22))),
% 1.51/1.70 inference(quant_inst,[status(thm)],[])).
% 1.51/1.70 tff(3116,plain,
% 1.51/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c1_1(a22) | c1_1(a2) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | c2_1(a22)),
% 1.51/1.70 inference(modus_ponens,[status(thm)],[3115, 3114])).
% 1.51/1.70 tff(3117,plain,
% 1.51/1.70 (~c3_1(a2)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3116, 92, 2758, 3086, 3085, 3108, 3107, 2620, 3084, 424, 3110])).
% 1.51/1.70 tff(3118,plain,
% 1.51/1.70 (hskp5),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[2179, 92, 3109, 2868, 2870, 3108, 3107, 2869, 21])).
% 1.51/1.70 tff(3119,plain,
% 1.51/1.70 (~c3_1(a8)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1656, 3118])).
% 1.51/1.70 tff(3120,plain,
% 1.51/1.70 (~c2_1(a8)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1662, 3118])).
% 1.51/1.70 tff(3121,plain,
% 1.51/1.70 (c1_1(a8)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1718, 3118])).
% 1.51/1.70 tff(3122,plain,
% 1.51/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a22) | c1_1(a22) | c2_1(a8) | c3_1(a8) | c1_1(a2) | c2_1(a2) | (~ndr1_0) | c3_1(a2) | (~c1_1(a8)) | c2_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c1_1(a22) | c2_1(a8) | c3_1(a8) | c1_1(a2) | c2_1(a2) | (~ndr1_0) | c3_1(a2) | (~c1_1(a8)) | c2_1(a22))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3123,plain,
% 1.51/1.70 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a2) | c1_1(a2) | c3_1(a2) | c2_1(a22) | c1_1(a22) | c0_1(a22)) <=> (c0_1(a22) | c1_1(a22) | c2_1(a8) | c3_1(a8) | c1_1(a2) | c2_1(a2) | (~ndr1_0) | c3_1(a2) | (~c1_1(a8)) | c2_1(a22))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3124,plain,
% 1.51/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a2) | c1_1(a2) | c3_1(a2) | c2_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a22) | c1_1(a22) | c2_1(a8) | c3_1(a8) | c1_1(a2) | c2_1(a2) | (~ndr1_0) | c3_1(a2) | (~c1_1(a8)) | c2_1(a22)))),
% 1.51/1.70 inference(monotonicity,[status(thm)],[3123])).
% 1.51/1.70 tff(3125,plain,
% 1.51/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a2) | c1_1(a2) | c3_1(a2) | c2_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c1_1(a22) | c2_1(a8) | c3_1(a8) | c1_1(a2) | c2_1(a2) | (~ndr1_0) | c3_1(a2) | (~c1_1(a8)) | c2_1(a22))),
% 1.51/1.70 inference(transitivity,[status(thm)],[3124, 3122])).
% 1.51/1.70 tff(3126,plain,
% 1.51/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a2) | c1_1(a2) | c3_1(a2) | c2_1(a22) | c1_1(a22) | c0_1(a22))),
% 1.51/1.70 inference(quant_inst,[status(thm)],[])).
% 1.51/1.70 tff(3127,plain,
% 1.51/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a22) | c1_1(a22) | c2_1(a8) | c3_1(a8) | c1_1(a2) | c2_1(a2) | (~ndr1_0) | c3_1(a2) | (~c1_1(a8)) | c2_1(a22)),
% 1.51/1.70 inference(modus_ponens,[status(thm)],[3126, 3125])).
% 1.51/1.70 tff(3128,plain,
% 1.51/1.70 ($false),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3127, 92, 3121, 3108, 3107, 3120, 3119, 2620, 2626, 194, 3117, 3110])).
% 1.51/1.70 tff(3129,plain,(c3_1(a20) | hskp4 | c0_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.70 tff(3130,plain,
% 1.51/1.70 (c3_1(a20)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3129, 1941, 33])).
% 1.51/1.70 tff(3131,plain,
% 1.51/1.70 (~hskp12),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[388, 3130])).
% 1.51/1.70 tff(3132,plain,
% 1.51/1.70 (hskp11),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[2680, 3131, 1941])).
% 1.51/1.70 tff(3133,plain,
% 1.51/1.70 (~c0_1(a19)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[98, 3132])).
% 1.51/1.70 tff(3134,plain,
% 1.51/1.70 (c2_1(a19)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[115, 3132])).
% 1.51/1.70 tff(3135,plain,
% 1.51/1.70 (c1_1(a19)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[107, 3132])).
% 1.51/1.70 tff(3136,plain,
% 1.51/1.70 (~c3_1(a19)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[2057, 92, 3131, 3135, 3134, 3133, 43])).
% 1.51/1.70 tff(3137,plain,
% 1.51/1.70 (~c1_1(a20)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[2496, 92, 1941, 3135, 33, 390, 3133, 56, 3136])).
% 1.51/1.70 tff(3138,plain,
% 1.51/1.70 (hskp5),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[2026, 92, 3135, 3134, 33, 3130, 3133, 21, 3137])).
% 1.51/1.70 tff(3139,plain,
% 1.51/1.70 (~c3_1(a8)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1656, 3138])).
% 1.51/1.70 tff(3140,plain,
% 1.51/1.70 (~c2_1(a8)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1662, 3138])).
% 1.51/1.70 tff(3141,plain,
% 1.51/1.70 (c1_1(a8)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1718, 3138])).
% 1.51/1.70 tff(3142,plain,
% 1.51/1.70 (c0_1(a8)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1747, 92, 1941, 3141, 3140, 3139, 56])).
% 1.51/1.70 tff(3143,plain,
% 1.51/1.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a20) | c2_1(a20) | (~c3_1(a20)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a20) | c2_1(a20) | (~c3_1(a20)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3144,plain,
% 1.51/1.70 ((hskp3 | (~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c2_1(a20) | c0_1(a20) | (~c3_1(a20))) <=> (hskp3 | c0_1(a20) | c2_1(a20) | (~c3_1(a20)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3145,plain,
% 1.51/1.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c2_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a20) | c2_1(a20) | (~c3_1(a20)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8))))),
% 1.51/1.70 inference(monotonicity,[status(thm)],[3144])).
% 1.51/1.70 tff(3146,plain,
% 1.51/1.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c2_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a20) | c2_1(a20) | (~c3_1(a20)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8)))),
% 1.51/1.70 inference(transitivity,[status(thm)],[3145, 3143])).
% 1.51/1.70 tff(3147,plain,
% 1.51/1.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c2_1(a20) | c0_1(a20) | (~c3_1(a20)))),
% 1.51/1.70 inference(quant_inst,[status(thm)],[])).
% 1.51/1.70 tff(3148,plain,
% 1.51/1.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a20) | c2_1(a20) | (~c3_1(a20)) | c2_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c0_1(a8))),
% 1.51/1.70 inference(modus_ponens,[status(thm)],[3147, 3146])).
% 1.51/1.70 tff(3149,plain,
% 1.51/1.70 (hskp3 | (~c0_1(a8))),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3148, 92, 3141, 33, 390, 3130, 3140, 604])).
% 1.51/1.70 tff(3150,plain,
% 1.51/1.70 (hskp3),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3149, 3142])).
% 1.51/1.70 tff(3151,plain,
% 1.51/1.70 (~c1_1(a5)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[712, 3150])).
% 1.51/1.70 tff(3152,plain,
% 1.51/1.70 (~c0_1(a5)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[718, 3150])).
% 1.51/1.70 tff(3153,plain,
% 1.51/1.70 (c2_1(a5)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[726, 3150])).
% 1.51/1.70 tff(3154,plain,
% 1.51/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a8) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a8)) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a8) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a8)) | (~c0_1(a8)))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3155,plain,
% 1.51/1.70 (((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5))) <=> (c2_1(a8) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a8)) | (~c0_1(a8)))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3156,plain,
% 1.51/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a8) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a8)) | (~c0_1(a8))))),
% 1.51/1.70 inference(monotonicity,[status(thm)],[3155])).
% 1.51/1.70 tff(3157,plain,
% 1.51/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a8) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a8)) | (~c0_1(a8)))),
% 1.51/1.70 inference(transitivity,[status(thm)],[3156, 3154])).
% 1.51/1.70 tff(3158,plain,
% 1.51/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))),
% 1.51/1.70 inference(quant_inst,[status(thm)],[])).
% 1.51/1.70 tff(3159,plain,
% 1.51/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a8) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a8)) | (~c0_1(a8))),
% 1.51/1.70 inference(modus_ponens,[status(thm)],[3158, 3157])).
% 1.51/1.70 tff(3160,plain,
% 1.51/1.70 (~c3_1(a5)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[3159, 92, 3141, 3153, 3140, 3152, 3151, 1465, 3142])).
% 1.51/1.70 tff(3161,plain,
% 1.51/1.70 (hskp19),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[1754, 92, 3141, 3140, 3139, 930])).
% 1.51/1.70 tff(3162,plain,
% 1.51/1.70 (~c3_1(a40)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[854, 3161])).
% 1.51/1.70 tff(3163,plain,
% 1.51/1.70 (~c0_1(a40)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[833, 3161])).
% 1.51/1.70 tff(3164,plain,
% 1.51/1.70 (c2_1(a40)),
% 1.51/1.70 inference(unit_resolution,[status(thm)],[841, 3161])).
% 1.51/1.70 tff(3165,plain,
% 1.51/1.70 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.51/1.70 inference(bind,[status(th)],[])).
% 1.51/1.70 tff(3166,plain,
% 1.51/1.70 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.70 inference(quant_intro,[status(thm)],[3165])).
% 1.51/1.70 tff(3167,plain,
% 1.51/1.70 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.70 inference(rewrite,[status(thm)],[])).
% 1.51/1.70 tff(3168,plain,
% 1.51/1.70 (^[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) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.51/1.70 inference(bind,[status(th)],[])).
% 1.51/1.70 tff(3169,plain,
% 1.51/1.70 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.70 inference(quant_intro,[status(thm)],[3168])).
% 1.51/1.70 tff(3170,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.51/1.70 tff(3171,plain,
% 1.51/1.70 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.70 inference(modus_ponens,[status(thm)],[3170, 3169])).
% 1.51/1.70 tff(3172,plain,
% 1.51/1.70 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.70 inference(modus_ponens,[status(thm)],[3171, 3167])).
% 1.51/1.70 tff(3173,plain,(
% 1.51/1.70 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.70 inference(skolemize,[status(sab)],[3172])).
% 1.51/1.70 tff(3174,plain,
% 1.51/1.70 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.70 inference(modus_ponens,[status(thm)],[3173, 3166])).
% 1.51/1.71 tff(3175,plain,
% 1.51/1.71 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp20 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp20 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3176,plain,
% 1.51/1.71 ((hskp20 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (hskp20 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3177,plain,
% 1.51/1.71 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp20 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19))))),
% 1.51/1.71 inference(monotonicity,[status(thm)],[3176])).
% 1.51/1.71 tff(3178,plain,
% 1.51/1.71 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp20 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.71 inference(transitivity,[status(thm)],[3177, 3175])).
% 1.51/1.71 tff(3179,plain,
% 1.51/1.71 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 1.51/1.71 inference(quant_inst,[status(thm)],[])).
% 1.51/1.71 tff(3180,plain,
% 1.51/1.71 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp20 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19))),
% 1.51/1.71 inference(modus_ponens,[status(thm)],[3179, 3178])).
% 1.51/1.71 tff(3181,plain,
% 1.51/1.71 (hskp20 | (~c0_1(a8))),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3180, 92, 3135, 3134, 3140, 3139, 3174, 3136])).
% 1.51/1.71 tff(3182,plain,
% 1.51/1.71 (hskp20),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3181, 3142])).
% 1.51/1.71 tff(3183,plain,
% 1.51/1.71 (c1_1(a43)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[1033, 3182])).
% 1.51/1.71 tff(3184,plain,
% 1.51/1.71 (c0_1(a43)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[1048, 3182])).
% 1.51/1.71 tff(3185,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a40) | c3_1(a40) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c2_1(a40)) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a40) | c3_1(a40) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c2_1(a40)) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3186,plain,
% 1.51/1.71 (((~ndr1_0) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a40) | c3_1(a40) | (~c2_1(a40))) <=> (c0_1(a40) | c3_1(a40) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c2_1(a40)) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3187,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a40) | c3_1(a40) | (~c2_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a40) | c3_1(a40) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c2_1(a40)) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 1.51/1.71 inference(monotonicity,[status(thm)],[3186])).
% 1.51/1.71 tff(3188,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a40) | c3_1(a40) | (~c2_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a40) | c3_1(a40) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c2_1(a40)) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.51/1.71 inference(transitivity,[status(thm)],[3187, 3185])).
% 1.51/1.71 tff(3189,plain,
% 1.51/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)) | c0_1(a40) | c3_1(a40) | (~c2_1(a40)))),
% 1.51/1.71 inference(quant_inst,[status(thm)],[])).
% 1.51/1.71 tff(3190,plain,
% 1.51/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a40) | c3_1(a40) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c2_1(a40)) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43))),
% 1.51/1.71 inference(modus_ponens,[status(thm)],[3189, 3188])).
% 1.51/1.71 tff(3191,plain,
% 1.51/1.71 (~c2_1(a43)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3190, 92, 3184, 3183, 3164, 3163, 3162, 3140, 3139, 1643, 3142])).
% 1.51/1.71 tff(3192,plain,
% 1.51/1.71 (~c3_1(a43)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[1025, 3182])).
% 1.51/1.71 tff(3193,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a43) | c0_1(a20) | (~c3_1(a20)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c1_1(a20) | c2_1(a43) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a43) | c0_1(a20) | (~c3_1(a20)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c1_1(a20) | c2_1(a43) | (~c0_1(a43)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3194,plain,
% 1.51/1.71 (((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20))) <=> (c3_1(a43) | c0_1(a20) | (~c3_1(a20)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c1_1(a20) | c2_1(a43) | (~c0_1(a43)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3195,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a43) | c0_1(a20) | (~c3_1(a20)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c1_1(a20) | c2_1(a43) | (~c0_1(a43))))),
% 1.51/1.71 inference(monotonicity,[status(thm)],[3194])).
% 1.51/1.71 tff(3196,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a43) | c0_1(a20) | (~c3_1(a20)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c1_1(a20) | c2_1(a43) | (~c0_1(a43)))),
% 1.51/1.71 inference(transitivity,[status(thm)],[3195, 3193])).
% 1.51/1.71 tff(3197,plain,
% 1.51/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))),
% 1.51/1.71 inference(quant_inst,[status(thm)],[])).
% 1.51/1.71 tff(3198,plain,
% 1.51/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a43) | c0_1(a20) | (~c3_1(a20)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c1_1(a20) | c2_1(a43) | (~c0_1(a43))),
% 1.51/1.71 inference(modus_ponens,[status(thm)],[3197, 3196])).
% 1.51/1.71 tff(3199,plain,
% 1.51/1.71 ($false),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3198, 92, 3184, 3153, 3192, 33, 3130, 3151, 953, 3137, 3191, 3160])).
% 1.51/1.71 tff(3200,plain,(c2_1(a20) | c0_1(a20) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.51/1.71 tff(3201,plain,
% 1.51/1.71 (c2_1(a20)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3200, 1941, 33])).
% 1.51/1.71 tff(3202,plain,
% 1.51/1.71 (~c1_1(a20)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2050, 3201, 3131, 3130])).
% 1.51/1.71 tff(3203,plain,
% 1.51/1.71 (hskp0),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2953, 3201, 1941, 3202])).
% 1.51/1.71 tff(3204,plain,
% 1.51/1.71 (~c2_1(a1)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[256, 3203])).
% 1.51/1.71 tff(3205,plain,
% 1.51/1.71 (c1_1(a1)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[272, 3203])).
% 1.51/1.71 tff(3206,plain,
% 1.51/1.71 (~c0_1(a1)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2535, 92, 3205, 33, 3201, 3130, 3204, 1465, 3202])).
% 1.51/1.71 tff(3207,plain,
% 1.51/1.71 ($false),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2542, 92, 3205, 33, 3201, 3130, 3204, 2475, 3202, 3206])).
% 1.51/1.71 tff(3208,plain,(hskp4 | c0_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.71 tff(3209,plain,
% 1.51/1.71 (hskp4),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3208, 33])).
% 1.51/1.71 tff(3210,plain,
% 1.51/1.71 (~c0_1(a7)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2387, 3209])).
% 1.51/1.71 tff(3211,plain,
% 1.51/1.71 (~c1_1(a7)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[1791, 3209])).
% 1.51/1.71 tff(3212,plain,
% 1.51/1.71 (~c3_1(a7)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[1451, 3209])).
% 1.51/1.71 tff(3213,plain,
% 1.51/1.71 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp3 | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3214,plain,
% 1.51/1.71 ((hskp26 | hskp3 | (~ndr1_0) | c3_1(a7) | c1_1(a7) | c0_1(a7)) <=> (hskp26 | hskp3 | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3215,plain,
% 1.51/1.71 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | (~ndr1_0) | c3_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0)))),
% 1.51/1.71 inference(monotonicity,[status(thm)],[3214])).
% 1.51/1.71 tff(3216,plain,
% 1.51/1.71 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | (~ndr1_0) | c3_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp3 | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0))),
% 1.51/1.71 inference(transitivity,[status(thm)],[3215, 3213])).
% 1.51/1.71 tff(3217,plain,
% 1.51/1.71 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp3 | (~ndr1_0) | c3_1(a7) | c1_1(a7) | c0_1(a7))),
% 1.51/1.71 inference(quant_inst,[status(thm)],[])).
% 1.51/1.71 tff(3218,plain,
% 1.51/1.71 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp3 | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0)),
% 1.51/1.71 inference(modus_ponens,[status(thm)],[3217, 3216])).
% 1.51/1.71 tff(3219,plain,
% 1.51/1.71 (hskp26 | hskp3),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3218, 92, 45, 57, 58, 2641])).
% 1.51/1.71 tff(3220,plain,
% 1.51/1.71 (hskp26),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3219, 594])).
% 1.51/1.71 tff(3221,plain,
% 1.51/1.71 (c1_1(a4)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2664, 3220])).
% 1.51/1.71 tff(3222,plain,
% 1.51/1.71 (c0_1(a4)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2672, 3220])).
% 1.51/1.71 tff(3223,plain,
% 1.51/1.71 (c3_1(a4)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2656, 3220])).
% 1.51/1.71 tff(3224,plain,
% 1.51/1.71 (c3_1(a2)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2878, 108, 594, 116, 99])).
% 1.51/1.71 tff(3225,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a7) | c3_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a7)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a7) | c3_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a7)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3226,plain,
% 1.51/1.71 (((~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7))) <=> (c1_1(a7) | c3_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a7)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3227,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a7) | c3_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a7)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4))))),
% 1.51/1.71 inference(monotonicity,[status(thm)],[3226])).
% 1.51/1.71 tff(3228,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a7) | c3_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a7)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.51/1.71 inference(transitivity,[status(thm)],[3227, 3225])).
% 1.51/1.71 tff(3229,plain,
% 1.51/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)))),
% 1.51/1.71 inference(quant_inst,[status(thm)],[])).
% 1.51/1.71 tff(3230,plain,
% 1.51/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a7) | c3_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a7)) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4))),
% 1.51/1.71 inference(modus_ponens,[status(thm)],[3229, 3228])).
% 1.51/1.71 tff(3231,plain,
% 1.51/1.71 ((~c3_1(a2)) | (~c2_1(a7))),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3230, 92, 3222, 3221, 3223, 2758, 57, 58, 2626, 322])).
% 1.51/1.71 tff(3232,plain,
% 1.51/1.71 (~c2_1(a7)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3231, 3224])).
% 1.51/1.71 tff(3233,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a19) | c0_1(a7) | c1_1(a7) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | c2_1(a7) | (~c3_1(a19)) | (~c1_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a19) | c0_1(a7) | c1_1(a7) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | c2_1(a7) | (~c3_1(a19)) | (~c1_1(a19)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3234,plain,
% 1.51/1.71 (((~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)) | c2_1(a7) | c1_1(a7) | c0_1(a7)) <=> (c0_1(a19) | c0_1(a7) | c1_1(a7) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | c2_1(a7) | (~c3_1(a19)) | (~c1_1(a19)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3235,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a19) | c0_1(a7) | c1_1(a7) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | c2_1(a7) | (~c3_1(a19)) | (~c1_1(a19))))),
% 1.51/1.71 inference(monotonicity,[status(thm)],[3234])).
% 1.51/1.71 tff(3236,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a19) | c0_1(a7) | c1_1(a7) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | c2_1(a7) | (~c3_1(a19)) | (~c1_1(a19)))),
% 1.51/1.71 inference(transitivity,[status(thm)],[3235, 3233])).
% 1.51/1.71 tff(3237,plain,
% 1.51/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)) | c2_1(a7) | c1_1(a7) | c0_1(a7))),
% 1.51/1.71 inference(quant_inst,[status(thm)],[])).
% 1.51/1.71 tff(3238,plain,
% 1.51/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a19) | c0_1(a7) | c1_1(a7) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | c2_1(a7) | (~c3_1(a19)) | (~c1_1(a19))),
% 1.51/1.71 inference(modus_ponens,[status(thm)],[3237, 3236])).
% 1.51/1.71 tff(3239,plain,
% 1.51/1.71 (~c3_1(a19)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3238, 92, 108, 2758, 99, 45, 57, 2620, 690, 3224, 3232])).
% 1.51/1.71 tff(3240,plain,
% 1.51/1.71 (hskp25),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2853, 92, 3222, 3221, 3223, 1555])).
% 1.51/1.71 tff(3241,plain,
% 1.51/1.71 (~c3_1(a73)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[1138, 3240])).
% 1.51/1.71 tff(3242,plain,
% 1.51/1.71 (c0_1(a73)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[1146, 3240])).
% 1.51/1.71 tff(3243,plain,
% 1.51/1.71 (c1_1(a73)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2947, 92, 594, 3242, 108, 116, 3241, 99, 31])).
% 1.51/1.71 tff(3244,plain,
% 1.51/1.71 ($false),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2937, 3243, 3239, 3223, 99, 108, 3222, 3221, 116])).
% 1.51/1.71 tff(3245,plain,((~hskp11) | hskp3 | c0_1(a7) | c1_1(a7) | c3_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.71 tff(3246,plain,
% 1.51/1.71 (~hskp11),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3245, 594, 3210, 3211, 3212])).
% 1.51/1.71 tff(3247,plain,
% 1.51/1.71 (c2_1(a48)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2726, 92, 154, 177, 33, 390, 44, 194, 498])).
% 1.51/1.71 tff(3248,plain,
% 1.51/1.71 (hskp26 | hskp3),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3218, 92, 3210, 3211, 3212, 2641])).
% 1.51/1.71 tff(3249,plain,
% 1.51/1.71 (hskp26),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3248, 594])).
% 1.51/1.71 tff(3250,plain,
% 1.51/1.71 (c3_1(a4)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2656, 3249])).
% 1.51/1.71 tff(3251,plain,
% 1.51/1.71 (c1_1(a4)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2664, 3249])).
% 1.51/1.71 tff(3252,plain,
% 1.51/1.71 (c0_1(a4)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2672, 3249])).
% 1.51/1.71 tff(3253,plain,
% 1.51/1.71 (hskp25),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[2853, 92, 3252, 3251, 3250, 1555])).
% 1.51/1.71 tff(3254,plain,
% 1.51/1.71 (~c3_1(a73)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[1138, 3253])).
% 1.51/1.71 tff(3255,plain,
% 1.51/1.71 (c0_1(a73)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[1146, 3253])).
% 1.51/1.71 tff(3256,plain,
% 1.51/1.71 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | c3_1(a73) | c0_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a73) | (~c0_1(a73)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c3_1(a73) | c0_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a73) | (~c0_1(a73)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3257,plain,
% 1.51/1.71 ((hskp3 | (~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c0_1(a73)) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48))) <=> (hskp3 | c3_1(a73) | c0_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a73) | (~c0_1(a73)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3258,plain,
% 1.51/1.71 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c0_1(a73)) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | c3_1(a73) | c0_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a73) | (~c0_1(a73))))),
% 1.51/1.71 inference(monotonicity,[status(thm)],[3257])).
% 1.51/1.71 tff(3259,plain,
% 1.51/1.71 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c0_1(a73)) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c3_1(a73) | c0_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a73) | (~c0_1(a73)))),
% 1.51/1.71 inference(transitivity,[status(thm)],[3258, 3256])).
% 1.51/1.71 tff(3260,plain,
% 1.51/1.71 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c0_1(a73)) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.51/1.71 inference(quant_inst,[status(thm)],[])).
% 1.51/1.71 tff(3261,plain,
% 1.51/1.71 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c3_1(a73) | c0_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a73) | (~c0_1(a73))),
% 1.51/1.71 inference(modus_ponens,[status(thm)],[3260, 3259])).
% 1.51/1.71 tff(3262,plain,
% 1.51/1.71 ((~c2_1(a48)) | c1_1(a73)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3261, 92, 594, 3255, 154, 3254, 146, 31])).
% 1.51/1.71 tff(3263,plain,
% 1.51/1.71 (c1_1(a73)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3262, 3247])).
% 1.51/1.71 tff(3264,plain,
% 1.51/1.71 (c2_1(a73)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[1187, 3253])).
% 1.51/1.71 tff(3265,plain,
% 1.51/1.71 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | c3_1(a73) | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a73)) | (~c0_1(a73)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a73) | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3266,plain,
% 1.51/1.71 ((hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48))) <=> (hskp14 | c3_1(a73) | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3267,plain,
% 1.51/1.71 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | c3_1(a73) | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a73)) | (~c0_1(a73))))),
% 1.51/1.71 inference(monotonicity,[status(thm)],[3266])).
% 1.51/1.71 tff(3268,plain,
% 1.51/1.71 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a73) | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.71 inference(transitivity,[status(thm)],[3267, 3265])).
% 1.51/1.71 tff(3269,plain,
% 1.51/1.71 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a73) | (~c2_1(a73)) | (~c0_1(a73)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48)))),
% 1.51/1.71 inference(quant_inst,[status(thm)],[])).
% 1.51/1.71 tff(3270,plain,
% 1.51/1.71 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp14 | c3_1(a73) | c0_1(a48) | c3_1(a48) | (~ndr1_0) | (~c1_1(a48)) | (~c2_1(a73)) | (~c0_1(a73))),
% 1.51/1.71 inference(modus_ponens,[status(thm)],[3269, 3268])).
% 1.51/1.71 tff(3271,plain,
% 1.51/1.71 (hskp14),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[3270, 92, 3255, 3264, 154, 3254, 146, 177, 1863])).
% 1.51/1.71 tff(3272,plain,
% 1.51/1.71 (~c2_1(a25)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[1886, 3271])).
% 1.51/1.71 tff(3273,plain,
% 1.51/1.71 (c0_1(a25)),
% 1.51/1.71 inference(unit_resolution,[status(thm)],[1928, 3271])).
% 1.51/1.71 tff(3274,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a48) | c3_1(a48) | c2_1(a25) | (~ndr1_0) | (~c0_1(a25)) | c3_1(a25) | (~c2_1(a48)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a48) | c3_1(a48) | c2_1(a25) | (~ndr1_0) | (~c0_1(a25)) | c3_1(a25) | (~c2_1(a48)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3275,plain,
% 1.51/1.71 (((~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)) | c0_1(a48) | c3_1(a48) | (~c2_1(a48))) <=> (c0_1(a48) | c3_1(a48) | c2_1(a25) | (~ndr1_0) | (~c0_1(a25)) | c3_1(a25) | (~c2_1(a48)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.71 inference(rewrite,[status(thm)],[])).
% 1.51/1.71 tff(3276,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)) | c0_1(a48) | c3_1(a48) | (~c2_1(a48)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a48) | c3_1(a48) | c2_1(a25) | (~ndr1_0) | (~c0_1(a25)) | c3_1(a25) | (~c2_1(a48)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73))))),
% 1.51/1.71 inference(monotonicity,[status(thm)],[3275])).
% 1.51/1.71 tff(3277,plain,
% 1.51/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)) | c0_1(a48) | c3_1(a48) | (~c2_1(a48)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a48) | c3_1(a48) | c2_1(a25) | (~ndr1_0) | (~c0_1(a25)) | c3_1(a25) | (~c2_1(a48)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.71 inference(transitivity,[status(thm)],[3276, 3274])).
% 1.51/1.71 tff(3278,plain,
% 1.51/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a25) | c3_1(a25) | (~c0_1(a25)) | c0_1(a48) | c3_1(a48) | (~c2_1(a48)))),
% 1.51/1.71 inference(quant_inst,[status(thm)],[])).
% 1.51/1.71 tff(3279,plain,
% 1.51/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a48) | c3_1(a48) | c2_1(a25) | (~ndr1_0) | (~c0_1(a25)) | c3_1(a25) | (~c2_1(a48)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73))),
% 1.51/1.72 inference(modus_ponens,[status(thm)],[3278, 3277])).
% 1.51/1.72 tff(3280,plain,
% 1.51/1.72 (c3_1(a25)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3279, 92, 3255, 3264, 3273, 146, 177, 3272, 1643, 3263, 3247])).
% 1.51/1.72 tff(3281,plain,
% 1.51/1.72 (c1_1(a25)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[1920, 3271])).
% 1.51/1.72 tff(3282,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a25) | c0_1(a20) | c2_1(a20) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | c1_1(a20) | (~c1_1(a25)) | (~c3_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a25) | c0_1(a20) | c2_1(a20) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | c1_1(a20) | (~c1_1(a25)) | (~c3_1(a25)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3283,plain,
% 1.51/1.72 (((~ndr1_0) | c2_1(a25) | (~c1_1(a25)) | (~c3_1(a25)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a20) | c1_1(a20) | c0_1(a20)) <=> (c2_1(a25) | c0_1(a20) | c2_1(a20) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | c1_1(a20) | (~c1_1(a25)) | (~c3_1(a25)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3284,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a25) | (~c1_1(a25)) | (~c3_1(a25)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a25) | c0_1(a20) | c2_1(a20) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | c1_1(a20) | (~c1_1(a25)) | (~c3_1(a25))))),
% 1.51/1.72 inference(monotonicity,[status(thm)],[3283])).
% 1.51/1.72 tff(3285,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a25) | (~c1_1(a25)) | (~c3_1(a25)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a20) | c1_1(a20) | c0_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a25) | c0_1(a20) | c2_1(a20) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | c1_1(a20) | (~c1_1(a25)) | (~c3_1(a25)))),
% 1.51/1.72 inference(transitivity,[status(thm)],[3284, 3282])).
% 1.51/1.72 tff(3286,plain,
% 1.51/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a25) | (~c1_1(a25)) | (~c3_1(a25)) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c2_1(a20) | c1_1(a20) | c0_1(a20))),
% 1.51/1.72 inference(quant_inst,[status(thm)],[])).
% 1.51/1.72 tff(3287,plain,
% 1.51/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a25) | c0_1(a20) | c2_1(a20) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | c1_1(a20) | (~c1_1(a25)) | (~c3_1(a25))),
% 1.51/1.72 inference(modus_ponens,[status(thm)],[3286, 3285])).
% 1.51/1.72 tff(3288,plain,
% 1.51/1.72 (~c3_1(a2)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3287, 92, 3281, 2758, 3272, 33, 390, 2620, 424, 498, 3280])).
% 1.51/1.72 tff(3289,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a48) | c3_1(a48) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a48)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a48) | c3_1(a48) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a48)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3290,plain,
% 1.51/1.72 (((~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a48) | c3_1(a48) | (~c2_1(a48))) <=> (c0_1(a48) | c3_1(a48) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a48)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3291,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a48) | c3_1(a48) | (~c2_1(a48)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a48) | c3_1(a48) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a48)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73))))),
% 1.51/1.72 inference(monotonicity,[status(thm)],[3290])).
% 1.51/1.72 tff(3292,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a48) | c3_1(a48) | (~c2_1(a48)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a48) | c3_1(a48) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a48)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)))),
% 1.51/1.72 inference(transitivity,[status(thm)],[3291, 3289])).
% 1.51/1.72 tff(3293,plain,
% 1.51/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a48) | c3_1(a48) | (~c2_1(a48)))),
% 1.51/1.72 inference(quant_inst,[status(thm)],[])).
% 1.51/1.72 tff(3294,plain,
% 1.51/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a48) | c3_1(a48) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a48)) | (~c1_1(a73)) | (~c2_1(a73)) | (~c0_1(a73))),
% 1.51/1.72 inference(modus_ponens,[status(thm)],[3293, 3292])).
% 1.51/1.72 tff(3295,plain,
% 1.51/1.72 ($false),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3294, 92, 3255, 3264, 2758, 146, 177, 2626, 1643, 3288, 3263, 3247])).
% 1.51/1.72 tff(3296,plain,((~hskp22) | c0_1(a20) | c2_1(a20) | c1_1(a20) | hskp3 | c3_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.72 tff(3297,plain,
% 1.51/1.72 (~hskp22),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3296, 498, 390, 33, 594, 44])).
% 1.51/1.72 tff(3298,plain,
% 1.51/1.72 (hskp0),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[250, 3297, 3246])).
% 1.51/1.72 tff(3299,plain,
% 1.51/1.72 (~c2_1(a1)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[256, 3298])).
% 1.51/1.72 tff(3300,plain,
% 1.51/1.72 (c3_1(a1)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[264, 3298])).
% 1.51/1.72 tff(3301,plain,
% 1.51/1.72 (c1_1(a1)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[272, 3298])).
% 1.51/1.72 tff(3302,plain,
% 1.51/1.72 (~c3_1(a2)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[2764, 92, 2758, 3301, 3300, 33, 390, 2620, 3299, 424, 498])).
% 1.51/1.72 tff(3303,plain,
% 1.51/1.72 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.51/1.72 inference(bind,[status(th)],[])).
% 1.51/1.72 tff(3304,plain,
% 1.51/1.72 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.72 inference(quant_intro,[status(thm)],[3303])).
% 1.51/1.72 tff(3305,plain,
% 1.51/1.72 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3306,plain,
% 1.51/1.72 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp13))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.51/1.72 inference(bind,[status(th)],[])).
% 1.51/1.72 tff(3307,plain,
% 1.51/1.72 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.72 inference(quant_intro,[status(thm)],[3306])).
% 1.51/1.72 tff(3308,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 1.51/1.72 tff(3309,plain,
% 1.51/1.72 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.72 inference(modus_ponens,[status(thm)],[3308, 3307])).
% 1.51/1.72 tff(3310,plain,
% 1.51/1.72 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.72 inference(modus_ponens,[status(thm)],[3309, 3305])).
% 1.51/1.72 tff(3311,plain,(
% 1.51/1.72 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.72 inference(skolemize,[status(sab)],[3310])).
% 1.51/1.72 tff(3312,plain,
% 1.51/1.72 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.51/1.72 inference(modus_ponens,[status(thm)],[3311, 3304])).
% 1.51/1.72 tff(3313,plain,
% 1.51/1.72 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp13 | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp13 | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3314,plain,
% 1.51/1.72 ((hskp13 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2))) <=> (hskp13 | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3315,plain,
% 1.51/1.72 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp13 | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4))))),
% 1.51/1.72 inference(monotonicity,[status(thm)],[3314])).
% 1.51/1.72 tff(3316,plain,
% 1.51/1.72 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp13 | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.51/1.72 inference(transitivity,[status(thm)],[3315, 3313])).
% 1.51/1.72 tff(3317,plain,
% 1.51/1.72 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)))),
% 1.51/1.72 inference(quant_inst,[status(thm)],[])).
% 1.51/1.72 tff(3318,plain,
% 1.51/1.72 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp13 | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4))),
% 1.51/1.72 inference(modus_ponens,[status(thm)],[3317, 3316])).
% 1.51/1.72 tff(3319,plain,
% 1.51/1.72 (hskp13 | c3_1(a2)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3318, 92, 3252, 3251, 3250, 2758, 2626, 3312])).
% 1.51/1.72 tff(3320,plain,
% 1.51/1.72 (hskp13),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3319, 3302])).
% 1.51/1.72 tff(3321,plain,
% 1.51/1.72 (~c1_1(a22)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[1846, 3320])).
% 1.51/1.72 tff(3322,plain,
% 1.51/1.72 (~c0_1(a22)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[1852, 3320])).
% 1.51/1.72 tff(3323,plain,
% 1.51/1.72 (c3_1(a22)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[1894, 3320])).
% 1.51/1.72 tff(3324,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a22) | c1_1(a22) | c1_1(a7) | c3_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a7)) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a22) | c1_1(a22) | c1_1(a7) | c3_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a7)) | (~c3_1(a22)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3325,plain,
% 1.51/1.72 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22))) <=> (c0_1(a22) | c1_1(a22) | c1_1(a7) | c3_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a7)) | (~c3_1(a22)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3326,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a22) | c1_1(a22) | c1_1(a7) | c3_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a7)) | (~c3_1(a22))))),
% 1.51/1.72 inference(monotonicity,[status(thm)],[3325])).
% 1.51/1.72 tff(3327,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a22) | c1_1(a22) | c1_1(a7) | c3_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a7)) | (~c3_1(a22)))),
% 1.51/1.72 inference(transitivity,[status(thm)],[3326, 3324])).
% 1.51/1.72 tff(3328,plain,
% 1.51/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))),
% 1.51/1.72 inference(quant_inst,[status(thm)],[])).
% 1.51/1.72 tff(3329,plain,
% 1.51/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a22) | c1_1(a22) | c1_1(a7) | c3_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a7)) | (~c3_1(a22))),
% 1.51/1.72 inference(modus_ponens,[status(thm)],[3328, 3327])).
% 1.51/1.72 tff(3330,plain,
% 1.51/1.72 (~c2_1(a7)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3329, 92, 3323, 2758, 3322, 3321, 3211, 3212, 2626, 953, 3302])).
% 1.51/1.72 tff(3331,plain,
% 1.51/1.72 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp24 | hskp22 | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp24 | hskp22 | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3332,plain,
% 1.51/1.72 ((hskp24 | hskp22 | (~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2))) <=> (hskp24 | hskp22 | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3333,plain,
% 1.51/1.72 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp24 | hskp22 | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2)))),
% 1.51/1.72 inference(monotonicity,[status(thm)],[3332])).
% 1.51/1.72 tff(3334,plain,
% 1.51/1.72 (((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp24 | hskp22 | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2))),
% 1.51/1.72 inference(transitivity,[status(thm)],[3333, 3331])).
% 1.51/1.72 tff(3335,plain,
% 1.51/1.72 ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp24 | hskp22 | (~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)))),
% 1.51/1.72 inference(quant_inst,[status(thm)],[])).
% 1.51/1.72 tff(3336,plain,
% 1.51/1.72 ((~![U: $i] : (hskp24 | hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp24 | hskp22 | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2)),
% 1.51/1.72 inference(modus_ponens,[status(thm)],[3335, 3334])).
% 1.51/1.72 tff(3337,plain,
% 1.51/1.72 (hskp24 | hskp22 | c3_1(a2)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3336, 92, 2758, 2626, 746])).
% 1.51/1.72 tff(3338,plain,
% 1.51/1.72 (hskp24),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3337, 3302, 3297])).
% 1.51/1.72 tff(3339,plain,
% 1.51/1.72 (~c0_1(a64)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[575, 3338])).
% 1.51/1.72 tff(3340,plain,
% 1.51/1.72 (c3_1(a64)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[584, 3338])).
% 1.51/1.72 tff(3341,plain,
% 1.51/1.72 (c1_1(a64)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[592, 3338])).
% 1.51/1.72 tff(3342,plain,
% 1.51/1.72 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a64) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c3_1(a64)) | (~c1_1(a64)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a64) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c3_1(a64)) | (~c1_1(a64)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3343,plain,
% 1.51/1.72 ((hskp15 | (~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c0_1(a64) | (~c1_1(a64)) | (~c3_1(a64))) <=> (hskp15 | c0_1(a64) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c3_1(a64)) | (~c1_1(a64)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3344,plain,
% 1.51/1.72 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c0_1(a64) | (~c1_1(a64)) | (~c3_1(a64)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a64) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c3_1(a64)) | (~c1_1(a64))))),
% 1.51/1.72 inference(monotonicity,[status(thm)],[3343])).
% 1.51/1.72 tff(3345,plain,
% 1.51/1.72 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c0_1(a64) | (~c1_1(a64)) | (~c3_1(a64)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a64) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c3_1(a64)) | (~c1_1(a64)))),
% 1.51/1.72 inference(transitivity,[status(thm)],[3344, 3342])).
% 1.51/1.72 tff(3346,plain,
% 1.51/1.72 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c0_1(a64) | (~c1_1(a64)) | (~c3_1(a64)))),
% 1.51/1.72 inference(quant_inst,[status(thm)],[])).
% 1.51/1.72 tff(3347,plain,
% 1.51/1.72 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a64) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c3_1(a64)) | (~c1_1(a64))),
% 1.51/1.72 inference(modus_ponens,[status(thm)],[3346, 3345])).
% 1.51/1.72 tff(3348,plain,
% 1.51/1.72 (hskp15),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3347, 92, 3341, 3340, 2758, 3339, 2626, 648, 3302])).
% 1.51/1.72 tff(3349,plain,
% 1.51/1.72 (~c1_1(a28)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[664, 3348])).
% 1.51/1.72 tff(3350,plain,
% 1.51/1.72 (c3_1(a28)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[697, 3348])).
% 1.51/1.72 tff(3351,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a28) | c0_1(a7) | c1_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c2_1(a7) | (~c3_1(a28)) | (~c0_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a28) | c0_1(a7) | c1_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c2_1(a7) | (~c3_1(a28)) | (~c0_1(a28)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3352,plain,
% 1.51/1.72 (((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a28) | (~c3_1(a28)) | (~c0_1(a28)) | c2_1(a7) | c1_1(a7) | c0_1(a7)) <=> (c1_1(a28) | c0_1(a7) | c1_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c2_1(a7) | (~c3_1(a28)) | (~c0_1(a28)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3353,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a28) | (~c3_1(a28)) | (~c0_1(a28)) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a28) | c0_1(a7) | c1_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c2_1(a7) | (~c3_1(a28)) | (~c0_1(a28))))),
% 1.51/1.72 inference(monotonicity,[status(thm)],[3352])).
% 1.51/1.72 tff(3354,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a28) | (~c3_1(a28)) | (~c0_1(a28)) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a28) | c0_1(a7) | c1_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c2_1(a7) | (~c3_1(a28)) | (~c0_1(a28)))),
% 1.51/1.72 inference(transitivity,[status(thm)],[3353, 3351])).
% 1.51/1.72 tff(3355,plain,
% 1.51/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a28) | (~c3_1(a28)) | (~c0_1(a28)) | c2_1(a7) | c1_1(a7) | c0_1(a7))),
% 1.51/1.72 inference(quant_inst,[status(thm)],[])).
% 1.51/1.72 tff(3356,plain,
% 1.51/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a28) | c0_1(a7) | c1_1(a7) | c2_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | c2_1(a7) | (~c3_1(a28)) | (~c0_1(a28))),
% 1.51/1.72 inference(modus_ponens,[status(thm)],[3355, 3354])).
% 1.51/1.72 tff(3357,plain,
% 1.51/1.72 (~c0_1(a28)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3356, 92, 3350, 3301, 3300, 3349, 3210, 3211, 3299, 424, 3330])).
% 1.51/1.72 tff(3358,plain,
% 1.51/1.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | c0_1(a64) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a64)) | (~c2_1(a64)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c0_1(a64) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a64)) | (~c2_1(a64)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3359,plain,
% 1.51/1.72 ((hskp3 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c0_1(a64) | (~c1_1(a64)) | (~c2_1(a64))) <=> (hskp3 | c0_1(a64) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a64)) | (~c2_1(a64)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3360,plain,
% 1.51/1.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c0_1(a64) | (~c1_1(a64)) | (~c2_1(a64)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | c0_1(a64) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a64)) | (~c2_1(a64))))),
% 1.51/1.72 inference(monotonicity,[status(thm)],[3359])).
% 1.51/1.72 tff(3361,plain,
% 1.51/1.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c0_1(a64) | (~c1_1(a64)) | (~c2_1(a64)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c0_1(a64) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a64)) | (~c2_1(a64)))),
% 1.51/1.72 inference(transitivity,[status(thm)],[3360, 3358])).
% 1.51/1.72 tff(3362,plain,
% 1.51/1.72 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c0_1(a64) | (~c1_1(a64)) | (~c2_1(a64)))),
% 1.51/1.72 inference(quant_inst,[status(thm)],[])).
% 1.51/1.72 tff(3363,plain,
% 1.51/1.72 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp3 | c0_1(a64) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a64)) | (~c2_1(a64))),
% 1.51/1.72 inference(modus_ponens,[status(thm)],[3362, 3361])).
% 1.51/1.72 tff(3364,plain,
% 1.51/1.72 (~c2_1(a64)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3363, 92, 594, 3341, 2758, 3339, 2620, 31, 3302])).
% 1.51/1.72 tff(3365,plain,
% 1.51/1.72 (c2_1(a28)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[672, 3348])).
% 1.51/1.72 tff(3366,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a64) | c1_1(a28) | (~ndr1_0) | (~c2_1(a28)) | (~c3_1(a28)) | c0_1(a28) | (~c1_1(a64)) | c2_1(a64))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a64) | c1_1(a28) | (~ndr1_0) | (~c2_1(a28)) | (~c3_1(a28)) | c0_1(a28) | (~c1_1(a64)) | c2_1(a64))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3367,plain,
% 1.51/1.72 (((~ndr1_0) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c2_1(a64) | c0_1(a64) | (~c1_1(a64)) | c1_1(a28) | c0_1(a28) | (~c3_1(a28))) <=> (c0_1(a64) | c1_1(a28) | (~ndr1_0) | (~c2_1(a28)) | (~c3_1(a28)) | c0_1(a28) | (~c1_1(a64)) | c2_1(a64))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3368,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c2_1(a64) | c0_1(a64) | (~c1_1(a64)) | c1_1(a28) | c0_1(a28) | (~c3_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a64) | c1_1(a28) | (~ndr1_0) | (~c2_1(a28)) | (~c3_1(a28)) | c0_1(a28) | (~c1_1(a64)) | c2_1(a64)))),
% 1.51/1.72 inference(monotonicity,[status(thm)],[3367])).
% 1.51/1.72 tff(3369,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c2_1(a64) | c0_1(a64) | (~c1_1(a64)) | c1_1(a28) | c0_1(a28) | (~c3_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a64) | c1_1(a28) | (~ndr1_0) | (~c2_1(a28)) | (~c3_1(a28)) | c0_1(a28) | (~c1_1(a64)) | c2_1(a64))),
% 1.51/1.72 inference(transitivity,[status(thm)],[3368, 3366])).
% 1.51/1.72 tff(3370,plain,
% 1.51/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a28) | (~c2_1(a28)) | (~c3_1(a28)) | c2_1(a64) | c0_1(a64) | (~c1_1(a64)) | c1_1(a28) | c0_1(a28) | (~c3_1(a28)))),
% 1.51/1.72 inference(quant_inst,[status(thm)],[])).
% 1.51/1.72 tff(3371,plain,
% 1.51/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a64) | c1_1(a28) | (~ndr1_0) | (~c2_1(a28)) | (~c3_1(a28)) | c0_1(a28) | (~c1_1(a64)) | c2_1(a64)),
% 1.51/1.72 inference(modus_ponens,[status(thm)],[3370, 3369])).
% 1.51/1.72 tff(3372,plain,
% 1.51/1.72 ($false),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3371, 92, 3341, 3365, 3350, 3339, 3349, 2475, 3364, 3357])).
% 1.51/1.72 tff(3373,plain,(c1_1(a20) | hskp3 | c0_1(a20) | c2_1(a20) | c3_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.72 tff(3374,plain,
% 1.51/1.72 (c1_1(a20)),
% 1.51/1.72 inference(unit_resolution,[status(thm)],[3373, 594, 33, 390, 44])).
% 1.51/1.72 tff(3375,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a20)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3376,plain,
% 1.51/1.72 (((~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20))) <=> (c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a20)))),
% 1.51/1.72 inference(rewrite,[status(thm)],[])).
% 1.51/1.72 tff(3377,plain,
% 1.51/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a20))))),
% 1.51/1.73 inference(monotonicity,[status(thm)],[3376])).
% 1.51/1.73 tff(3378,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a20)))),
% 1.51/1.73 inference(transitivity,[status(thm)],[3377, 3375])).
% 1.51/1.73 tff(3379,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a20) | c3_1(a20) | (~c1_1(a20)))),
% 1.51/1.73 inference(quant_inst,[status(thm)],[])).
% 1.51/1.73 tff(3380,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a20))),
% 1.51/1.73 inference(modus_ponens,[status(thm)],[3379, 3378])).
% 1.51/1.73 tff(3381,plain,
% 1.51/1.73 (c2_1(a20) | c3_1(a2) | (~c1_1(a20))),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3380, 92, 2758, 33, 44, 2620, 11])).
% 1.51/1.73 tff(3382,plain,
% 1.51/1.73 (c3_1(a2)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3381, 3374, 390])).
% 1.51/1.73 tff(3383,plain,
% 1.51/1.73 ((~c3_1(a2)) | (~c2_1(a7))),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3230, 92, 3252, 3251, 3250, 2758, 3211, 3212, 2626, 322])).
% 1.51/1.73 tff(3384,plain,
% 1.51/1.73 (~c2_1(a7)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3383, 3382])).
% 1.51/1.73 tff(3385,plain,
% 1.51/1.73 ($false),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[1411, 92, 390, 44, 3210, 3211, 3212, 194, 3374, 3384])).
% 1.51/1.73 tff(3386,plain,(hskp3 | c2_1(a20) | c3_1(a20) | c0_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.73 tff(3387,plain,
% 1.51/1.73 (hskp3),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3386, 390, 44, 33])).
% 1.51/1.73 tff(3388,plain,
% 1.51/1.73 (c3_1(a2)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[2777, 498, 44, 33, 3387])).
% 1.51/1.73 tff(3389,plain,
% 1.51/1.73 (~c1_1(a5)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[712, 3387])).
% 1.51/1.73 tff(3390,plain,
% 1.51/1.73 (~c0_1(a5)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[718, 3387])).
% 1.51/1.73 tff(3391,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a48)) | (~c2_1(a48)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3392,plain,
% 1.51/1.73 (((~ndr1_0) | c3_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c2_1(a20) | c0_1(a20) | c3_1(a20)) <=> (c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3393,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a48)) | (~c2_1(a48))))),
% 1.51/1.73 inference(monotonicity,[status(thm)],[3392])).
% 1.51/1.73 tff(3394,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.51/1.73 inference(transitivity,[status(thm)],[3393, 3391])).
% 1.51/1.73 tff(3395,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c2_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.51/1.73 inference(quant_inst,[status(thm)],[])).
% 1.51/1.73 tff(3396,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c1_1(a48)) | (~c2_1(a48))),
% 1.51/1.73 inference(modus_ponens,[status(thm)],[3395, 3394])).
% 1.51/1.73 tff(3397,plain,
% 1.51/1.73 ((~c2_1(a7)) | (~c2_1(a48))),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3396, 92, 154, 177, 33, 390, 44, 3211, 3212, 1002])).
% 1.51/1.73 tff(3398,plain,
% 1.51/1.73 (~c2_1(a7)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3397, 3247])).
% 1.51/1.73 tff(3399,plain,
% 1.51/1.73 (c2_1(a5)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[726, 3387])).
% 1.51/1.73 tff(3400,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a48)) | (~c2_1(a48)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3401,plain,
% 1.51/1.73 (((~ndr1_0) | c3_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20)) <=> (c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3402,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a48)) | (~c2_1(a48))))),
% 1.51/1.73 inference(monotonicity,[status(thm)],[3401])).
% 1.51/1.73 tff(3403,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.51/1.73 inference(transitivity,[status(thm)],[3402, 3400])).
% 1.51/1.73 tff(3404,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.51/1.73 inference(quant_inst,[status(thm)],[])).
% 1.51/1.73 tff(3405,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a48) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a48)) | (~c2_1(a48))),
% 1.51/1.73 inference(modus_ponens,[status(thm)],[3404, 3403])).
% 1.51/1.73 tff(3406,plain,
% 1.51/1.73 (c3_1(a5) | (~c2_1(a48))),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3405, 92, 154, 3399, 177, 33, 390, 44, 3389, 1002])).
% 1.51/1.73 tff(3407,plain,
% 1.51/1.73 (c3_1(a5)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3406, 3247])).
% 1.51/1.73 tff(3408,plain,
% 1.51/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a48) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a48)) | (~c2_1(a48)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a48) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3409,plain,
% 1.51/1.73 ((hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5))) <=> (hskp5 | c0_1(a48) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3410,plain,
% 1.51/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a48) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a48)) | (~c2_1(a48))))),
% 1.51/1.73 inference(monotonicity,[status(thm)],[3409])).
% 1.51/1.73 tff(3411,plain,
% 1.51/1.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a48) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a48)) | (~c2_1(a48)))),
% 1.51/1.73 inference(transitivity,[status(thm)],[3410, 3408])).
% 1.51/1.73 tff(3412,plain,
% 1.51/1.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a48) | (~c1_1(a48)) | (~c2_1(a48)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))),
% 1.51/1.73 inference(quant_inst,[status(thm)],[])).
% 1.51/1.73 tff(3413,plain,
% 1.51/1.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a48) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a48)) | (~c2_1(a48))),
% 1.51/1.73 inference(modus_ponens,[status(thm)],[3412, 3411])).
% 1.51/1.73 tff(3414,plain,
% 1.51/1.73 (hskp5 | (~c3_1(a5)) | (~c2_1(a48))),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3413, 92, 154, 146, 3390, 3389, 21])).
% 1.51/1.73 tff(3415,plain,
% 1.51/1.73 (hskp5),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3414, 3407, 3247])).
% 1.51/1.73 tff(3416,plain,
% 1.51/1.73 (~c3_1(a8)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[1656, 3415])).
% 1.51/1.73 tff(3417,plain,
% 1.51/1.73 (~c2_1(a8)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[1662, 3415])).
% 1.51/1.73 tff(3418,plain,
% 1.51/1.73 (c1_1(a8)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[1718, 3415])).
% 1.51/1.73 tff(3419,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a8)) | c1_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a8)) | c1_1(a20))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3420,plain,
% 1.51/1.73 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a20) | c1_1(a20) | c3_1(a20) | c2_1(a7) | c1_1(a7) | c0_1(a7)) <=> (c2_1(a20) | c3_1(a20) | c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a8)) | c1_1(a20))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3421,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a20) | c1_1(a20) | c3_1(a20) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a8)) | c1_1(a20)))),
% 1.51/1.73 inference(monotonicity,[status(thm)],[3420])).
% 1.51/1.73 tff(3422,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a20) | c1_1(a20) | c3_1(a20) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a20) | c3_1(a20) | c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a8)) | c1_1(a20))),
% 1.51/1.73 inference(transitivity,[status(thm)],[3421, 3419])).
% 1.51/1.73 tff(3423,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a20) | c1_1(a20) | c3_1(a20) | c2_1(a7) | c1_1(a7) | c0_1(a7))),
% 1.51/1.73 inference(quant_inst,[status(thm)],[])).
% 1.51/1.73 tff(3424,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a20) | c3_1(a20) | c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a8)) | c1_1(a20)),
% 1.51/1.73 inference(modus_ponens,[status(thm)],[3423, 3422])).
% 1.51/1.73 tff(3425,plain,
% 1.51/1.73 ($false),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3424, 92, 3418, 390, 44, 3417, 3416, 3210, 3211, 194, 498, 3398])).
% 1.51/1.73 tff(3426,plain,((~hskp22) | c2_1(a20) | c3_1(a20) | c1_1(a20) | c0_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.73 tff(3427,plain,
% 1.51/1.73 (~hskp22),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3426, 498, 44, 390, 33])).
% 1.51/1.73 tff(3428,plain,
% 1.51/1.73 ($false),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[2764, 92, 2758, 1455, 1489, 33, 390, 2620, 1454, 424, 498, 2956])).
% 1.51/1.73 tff(3429,plain,((~hskp0) | c0_1(a20) | c2_1(a20) | c1_1(a20) | (~c3_1(a2))), inference(lemma,lemma(discharge,[]))).
% 1.51/1.73 tff(3430,plain,
% 1.51/1.73 (~hskp0),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3429, 498, 390, 33, 3388])).
% 1.51/1.73 tff(3431,plain,
% 1.51/1.73 (hskp11),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[250, 3430, 3427])).
% 1.51/1.73 tff(3432,plain,
% 1.51/1.73 (~c0_1(a19)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[98, 3431])).
% 1.51/1.73 tff(3433,plain,
% 1.51/1.73 (c1_1(a19)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[107, 3431])).
% 1.51/1.73 tff(3434,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a19) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a19)) | (~c1_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a19) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a19)) | (~c1_1(a19)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3435,plain,
% 1.51/1.73 (((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5))) <=> (c0_1(a19) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a19)) | (~c1_1(a19)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3436,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a19) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a19)) | (~c1_1(a19))))),
% 1.51/1.73 inference(monotonicity,[status(thm)],[3435])).
% 1.51/1.73 tff(3437,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a19) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a19)) | (~c1_1(a19)))),
% 1.51/1.73 inference(transitivity,[status(thm)],[3436, 3434])).
% 1.51/1.73 tff(3438,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a19) | (~c1_1(a19)) | (~c3_1(a19)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))),
% 1.51/1.73 inference(quant_inst,[status(thm)],[])).
% 1.51/1.73 tff(3439,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a19) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a19)) | (~c1_1(a19))),
% 1.51/1.73 inference(modus_ponens,[status(thm)],[3438, 3437])).
% 1.51/1.73 tff(3440,plain,
% 1.51/1.73 (~c3_1(a19)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3439, 92, 3433, 3399, 2758, 3432, 3390, 3389, 2626, 567, 3388])).
% 1.51/1.73 tff(3441,plain,
% 1.51/1.73 (c2_1(a19)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[115, 3431])).
% 1.51/1.73 tff(3442,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3443,plain,
% 1.51/1.73 (((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c2_1(a20) | c0_1(a20) | c3_1(a20)) <=> (c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3444,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19))))),
% 1.51/1.73 inference(monotonicity,[status(thm)],[3443])).
% 1.51/1.73 tff(3445,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.73 inference(transitivity,[status(thm)],[3444, 3442])).
% 1.51/1.73 tff(3446,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a7) | c3_1(a7) | (~c2_1(a7)) | c2_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.51/1.73 inference(quant_inst,[status(thm)],[])).
% 1.51/1.73 tff(3447,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19))),
% 1.51/1.73 inference(modus_ponens,[status(thm)],[3446, 3445])).
% 1.51/1.73 tff(3448,plain,
% 1.51/1.73 (~c2_1(a7)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3447, 92, 3433, 3441, 33, 390, 44, 3211, 3212, 1002, 3440])).
% 1.51/1.73 tff(3449,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3450,plain,
% 1.51/1.73 (((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20)) <=> (c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3451,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19))))),
% 1.51/1.73 inference(monotonicity,[status(thm)],[3450])).
% 1.51/1.73 tff(3452,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.51/1.73 inference(transitivity,[status(thm)],[3451, 3449])).
% 1.51/1.73 tff(3453,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.51/1.73 inference(quant_inst,[status(thm)],[])).
% 1.51/1.73 tff(3454,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19))),
% 1.51/1.73 inference(modus_ponens,[status(thm)],[3453, 3452])).
% 1.51/1.73 tff(3455,plain,
% 1.51/1.73 (c3_1(a5)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3454, 92, 3433, 3441, 3399, 33, 390, 44, 3389, 1002, 3440])).
% 1.51/1.73 tff(3456,plain,
% 1.51/1.73 (hskp5 | (~c3_1(a5))),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[2605, 92, 3433, 3441, 3432, 3390, 3389, 21])).
% 1.51/1.73 tff(3457,plain,
% 1.51/1.73 (hskp5),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3456, 3455])).
% 1.51/1.73 tff(3458,plain,
% 1.51/1.73 (~c3_1(a8)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[1656, 3457])).
% 1.51/1.73 tff(3459,plain,
% 1.51/1.73 (~c2_1(a8)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[1662, 3457])).
% 1.51/1.73 tff(3460,plain,
% 1.51/1.73 (c1_1(a8)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[1718, 3457])).
% 1.51/1.73 tff(3461,plain,
% 1.51/1.73 ($false),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3424, 92, 3460, 390, 44, 3459, 3458, 3210, 3211, 194, 498, 3448])).
% 1.51/1.73 tff(3462,plain,(c1_1(a20) | c2_1(a20) | c3_1(a20) | c0_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.73 tff(3463,plain,
% 1.51/1.73 (c1_1(a20)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3462, 390, 44, 33])).
% 1.51/1.73 tff(3464,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a20) | c2_1(a20) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a20) | c2_1(a20) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a20)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3465,plain,
% 1.51/1.73 (((~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5))) <=> (c0_1(a20) | c2_1(a20) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a20)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3466,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a20) | c2_1(a20) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a20))))),
% 1.51/1.73 inference(monotonicity,[status(thm)],[3465])).
% 1.51/1.73 tff(3467,plain,
% 1.51/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a20) | c2_1(a20) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a20)))),
% 1.51/1.73 inference(transitivity,[status(thm)],[3466, 3464])).
% 1.51/1.73 tff(3468,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a20) | c0_1(a20) | (~c1_1(a20)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))),
% 1.51/1.73 inference(quant_inst,[status(thm)],[])).
% 1.51/1.73 tff(3469,plain,
% 1.51/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a20) | c2_1(a20) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a20))),
% 1.51/1.73 inference(modus_ponens,[status(thm)],[3468, 3467])).
% 1.51/1.73 tff(3470,plain,
% 1.51/1.73 ((~c3_1(a5)) | (~c1_1(a20))),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3469, 92, 3399, 33, 390, 3390, 3389, 2475])).
% 1.51/1.73 tff(3471,plain,
% 1.51/1.73 (~c3_1(a5)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3470, 3463])).
% 1.51/1.73 tff(3472,plain,
% 1.51/1.73 (c3_1(a2)),
% 1.51/1.73 inference(unit_resolution,[status(thm)],[3381, 3463, 390])).
% 1.51/1.73 tff(3473,plain,
% 1.51/1.73 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)))),
% 1.51/1.73 inference(rewrite,[status(thm)],[])).
% 1.51/1.73 tff(3474,plain,
% 1.51/1.73 ((hskp19 | (~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20))) <=> (hskp19 | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)))),
% 1.51/1.74 inference(rewrite,[status(thm)],[])).
% 1.51/1.74 tff(3475,plain,
% 1.51/1.74 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20))))),
% 1.51/1.74 inference(monotonicity,[status(thm)],[3474])).
% 1.51/1.74 tff(3476,plain,
% 1.51/1.74 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)))),
% 1.51/1.74 inference(transitivity,[status(thm)],[3475, 3473])).
% 1.51/1.74 tff(3477,plain,
% 1.51/1.74 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)))),
% 1.51/1.74 inference(quant_inst,[status(thm)],[])).
% 1.51/1.74 tff(3478,plain,
% 1.51/1.74 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20))),
% 1.51/1.74 inference(modus_ponens,[status(thm)],[3477, 3476])).
% 1.51/1.74 tff(3479,plain,
% 1.51/1.74 (hskp19 | c2_1(a20) | (~c1_1(a20))),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[3478, 92, 44, 930])).
% 1.51/1.74 tff(3480,plain,
% 1.51/1.74 (hskp19),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[3479, 3463, 390])).
% 1.51/1.74 tff(3481,plain,
% 1.51/1.74 (~c3_1(a40)),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[854, 3480])).
% 1.51/1.74 tff(3482,plain,
% 1.51/1.74 (c2_1(a40)),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[841, 3480])).
% 1.51/1.74 tff(3483,plain,
% 1.51/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a40) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a40)) | (~c2_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a40) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a40)) | (~c2_1(a40)))),
% 1.51/1.74 inference(rewrite,[status(thm)],[])).
% 1.51/1.74 tff(3484,plain,
% 1.51/1.74 (((~ndr1_0) | c3_1(a40) | (~c1_1(a40)) | (~c2_1(a40)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20)) <=> (c3_1(a40) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a40)) | (~c2_1(a40)))),
% 1.51/1.74 inference(rewrite,[status(thm)],[])).
% 1.51/1.74 tff(3485,plain,
% 1.51/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a40) | (~c1_1(a40)) | (~c2_1(a40)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a40) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a40)) | (~c2_1(a40))))),
% 1.51/1.74 inference(monotonicity,[status(thm)],[3484])).
% 1.51/1.74 tff(3486,plain,
% 1.51/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a40) | (~c1_1(a40)) | (~c2_1(a40)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a40) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a40)) | (~c2_1(a40)))),
% 1.51/1.74 inference(transitivity,[status(thm)],[3485, 3483])).
% 1.51/1.74 tff(3487,plain,
% 1.51/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a40) | (~c1_1(a40)) | (~c2_1(a40)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a20) | c0_1(a20) | c3_1(a20))),
% 1.51/1.74 inference(quant_inst,[status(thm)],[])).
% 1.51/1.74 tff(3488,plain,
% 1.51/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a40) | c0_1(a20) | c2_1(a20) | c3_1(a20) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a40)) | (~c2_1(a40))),
% 1.51/1.74 inference(modus_ponens,[status(thm)],[3487, 3486])).
% 1.51/1.74 tff(3489,plain,
% 1.51/1.74 (~c1_1(a40)),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[3488, 92, 3482, 3399, 3481, 33, 390, 44, 3389, 1002, 3471])).
% 1.51/1.74 tff(3490,plain,
% 1.51/1.74 (^[U: $i] : refl((hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.51/1.74 inference(bind,[status(th)],[])).
% 1.51/1.74 tff(3491,plain,
% 1.51/1.74 (![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.51/1.74 inference(quant_intro,[status(thm)],[3490])).
% 1.51/1.74 tff(3492,plain,
% 1.51/1.74 (![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.51/1.74 inference(rewrite,[status(thm)],[])).
% 1.51/1.74 tff(3493,plain,
% 1.51/1.74 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | 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) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp13) <=> ((hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp13))), rewrite(((hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp13) <=> (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp13) <=> (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.51/1.74 inference(bind,[status(th)],[])).
% 1.51/1.74 tff(3494,plain,
% 1.51/1.74 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp13) <=> ![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.51/1.74 inference(quant_intro,[status(thm)],[3493])).
% 1.51/1.74 tff(3495,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 1.51/1.74 tff(3496,plain,
% 1.51/1.74 (![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.51/1.74 inference(modus_ponens,[status(thm)],[3495, 3494])).
% 1.51/1.74 tff(3497,plain,
% 1.51/1.74 (![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.51/1.74 inference(modus_ponens,[status(thm)],[3496, 3492])).
% 1.51/1.74 tff(3498,plain,(
% 1.51/1.74 ![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.51/1.74 inference(skolemize,[status(sab)],[3497])).
% 1.51/1.74 tff(3499,plain,
% 1.51/1.74 (![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.51/1.74 inference(modus_ponens,[status(thm)],[3498, 3491])).
% 1.51/1.74 tff(3500,plain,
% 1.51/1.74 (((~![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp13 | hskp0 | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)))) <=> ((~![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp13 | hskp0 | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)))),
% 1.51/1.74 inference(rewrite,[status(thm)],[])).
% 1.51/1.74 tff(3501,plain,
% 1.51/1.74 ((hskp13 | hskp0 | (~ndr1_0) | c0_1(a20) | c2_1(a20) | (~c1_1(a20))) <=> (hskp13 | hskp0 | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)))),
% 1.51/1.74 inference(rewrite,[status(thm)],[])).
% 1.51/1.74 tff(3502,plain,
% 1.51/1.74 (((~![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp13 | hskp0 | (~ndr1_0) | c0_1(a20) | c2_1(a20) | (~c1_1(a20)))) <=> ((~![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp13 | hskp0 | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20))))),
% 1.51/1.74 inference(monotonicity,[status(thm)],[3501])).
% 1.51/1.74 tff(3503,plain,
% 1.51/1.74 (((~![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp13 | hskp0 | (~ndr1_0) | c0_1(a20) | c2_1(a20) | (~c1_1(a20)))) <=> ((~![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp13 | hskp0 | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20)))),
% 1.51/1.74 inference(transitivity,[status(thm)],[3502, 3500])).
% 1.51/1.74 tff(3504,plain,
% 1.51/1.74 ((~![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp13 | hskp0 | (~ndr1_0) | c0_1(a20) | c2_1(a20) | (~c1_1(a20)))),
% 1.51/1.74 inference(quant_inst,[status(thm)],[])).
% 1.51/1.74 tff(3505,plain,
% 1.51/1.74 ((~![U: $i] : (hskp13 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp13 | hskp0 | c0_1(a20) | c2_1(a20) | (~ndr1_0) | (~c1_1(a20))),
% 1.51/1.74 inference(modus_ponens,[status(thm)],[3504, 3503])).
% 1.51/1.74 tff(3506,plain,
% 1.51/1.74 (hskp13 | hskp0 | c2_1(a20) | (~c1_1(a20))),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[3505, 92, 33, 3499])).
% 1.51/1.74 tff(3507,plain,
% 1.51/1.74 (hskp13),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[3506, 1942, 390, 3463])).
% 1.51/1.74 tff(3508,plain,
% 1.51/1.74 (~c1_1(a22)),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[1846, 3507])).
% 1.51/1.74 tff(3509,plain,
% 1.51/1.74 (~c0_1(a22)),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[1852, 3507])).
% 1.51/1.74 tff(3510,plain,
% 1.51/1.74 (c3_1(a22)),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[1894, 3507])).
% 1.51/1.74 tff(3511,plain,
% 1.51/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a40) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a40) | (~c2_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a40) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a40) | (~c2_1(a40)))),
% 1.51/1.74 inference(rewrite,[status(thm)],[])).
% 1.51/1.74 tff(3512,plain,
% 1.51/1.74 (((~ndr1_0) | c3_1(a40) | c1_1(a40) | (~c2_1(a40)) | c0_1(a22) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22))) <=> (c3_1(a40) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a40) | (~c2_1(a40)))),
% 1.51/1.74 inference(rewrite,[status(thm)],[])).
% 1.51/1.74 tff(3513,plain,
% 1.51/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a40) | c1_1(a40) | (~c2_1(a40)) | c0_1(a22) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a40) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a40) | (~c2_1(a40))))),
% 1.51/1.74 inference(monotonicity,[status(thm)],[3512])).
% 1.51/1.74 tff(3514,plain,
% 1.51/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a40) | c1_1(a40) | (~c2_1(a40)) | c0_1(a22) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a40) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a40) | (~c2_1(a40)))),
% 1.51/1.74 inference(transitivity,[status(thm)],[3513, 3511])).
% 1.51/1.74 tff(3515,plain,
% 1.51/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a40) | c1_1(a40) | (~c2_1(a40)) | c0_1(a22) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))),
% 1.51/1.74 inference(quant_inst,[status(thm)],[])).
% 1.51/1.74 tff(3516,plain,
% 1.51/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a40) | c0_1(a22) | c1_1(a22) | (~ndr1_0) | (~c2_1(a22)) | (~c3_1(a22)) | c1_1(a40) | (~c2_1(a40))),
% 1.51/1.74 inference(modus_ponens,[status(thm)],[3515, 3514])).
% 1.51/1.74 tff(3517,plain,
% 1.51/1.74 (~c2_1(a22)),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[3516, 92, 3482, 3510, 3481, 3509, 3508, 1073, 3489])).
% 1.51/1.74 tff(3518,plain,
% 1.51/1.74 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a22) | c1_1(a22) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | c2_1(a22))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a22) | c1_1(a22) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | c2_1(a22))),
% 1.51/1.74 inference(rewrite,[status(thm)],[])).
% 1.51/1.74 tff(3519,plain,
% 1.51/1.74 ((hskp0 | (~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a22) | c1_1(a22) | c0_1(a22)) <=> (hskp0 | c0_1(a22) | c1_1(a22) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | c2_1(a22))),
% 1.51/1.74 inference(rewrite,[status(thm)],[])).
% 1.51/1.74 tff(3520,plain,
% 1.51/1.74 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a22) | c1_1(a22) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | c2_1(a22)))),
% 1.51/1.74 inference(monotonicity,[status(thm)],[3519])).
% 1.51/1.74 tff(3521,plain,
% 1.51/1.74 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a22) | c1_1(a22) | c0_1(a22))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a22) | c1_1(a22) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | c2_1(a22))),
% 1.51/1.74 inference(transitivity,[status(thm)],[3520, 3518])).
% 1.51/1.74 tff(3522,plain,
% 1.51/1.74 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a20) | c2_1(a20) | (~c1_1(a20)) | c2_1(a22) | c1_1(a22) | c0_1(a22))),
% 1.51/1.74 inference(quant_inst,[status(thm)],[])).
% 1.51/1.74 tff(3523,plain,
% 1.51/1.74 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a22) | c1_1(a22) | c2_1(a20) | c3_1(a20) | (~ndr1_0) | (~c1_1(a20)) | c2_1(a22)),
% 1.51/1.74 inference(modus_ponens,[status(thm)],[3522, 3521])).
% 1.51/1.74 tff(3524,plain,
% 1.51/1.74 ($false),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[3523, 92, 1942, 3509, 3508, 390, 44, 1623, 3463, 3517])).
% 1.51/1.74 tff(3525,plain,(hskp0 | c2_1(a20) | c3_1(a20) | c0_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.74 tff(3526,plain,
% 1.51/1.74 (hskp0),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[3525, 390, 44, 33])).
% 1.51/1.74 tff(3527,plain,
% 1.51/1.74 (c3_1(a1)),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[264, 3526])).
% 1.51/1.74 tff(3528,plain,
% 1.51/1.74 (c1_1(a1)),
% 1.51/1.74 inference(unit_resolution,[status(thm)],[272, 3526])).
% 1.51/1.74 tff(3529,plain,
% 1.51/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | c3_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | c3_1(a5))),
% 1.51/1.74 inference(rewrite,[status(thm)],[])).
% 1.57/1.74 tff(3530,plain,
% 1.57/1.74 (((~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5))) <=> (c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | c3_1(a5))),
% 1.57/1.74 inference(rewrite,[status(thm)],[])).
% 1.57/1.74 tff(3531,plain,
% 1.57/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | c3_1(a5)))),
% 1.57/1.74 inference(monotonicity,[status(thm)],[3530])).
% 1.57/1.74 tff(3532,plain,
% 1.57/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | c3_1(a5))),
% 1.57/1.74 inference(transitivity,[status(thm)],[3531, 3529])).
% 1.57/1.74 tff(3533,plain,
% 1.57/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a1)) | (~c3_1(a1)) | (~c0_1(a1)) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)))),
% 1.57/1.74 inference(quant_inst,[status(thm)],[])).
% 1.57/1.74 tff(3534,plain,
% 1.57/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | c3_1(a5)),
% 1.57/1.74 inference(modus_ponens,[status(thm)],[3533, 3532])).
% 1.57/1.74 tff(3535,plain,
% 1.57/1.74 (~c0_1(a1)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[3534, 92, 3399, 2758, 3528, 3527, 3389, 2626, 322, 3472, 3471])).
% 1.57/1.74 tff(3536,plain,
% 1.57/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)))),
% 1.57/1.74 inference(rewrite,[status(thm)],[])).
% 1.57/1.74 tff(3537,plain,
% 1.57/1.74 (((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5))) <=> (c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)))),
% 1.57/1.74 inference(rewrite,[status(thm)],[])).
% 1.57/1.74 tff(3538,plain,
% 1.57/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5))))),
% 1.57/1.74 inference(monotonicity,[status(thm)],[3537])).
% 1.57/1.74 tff(3539,plain,
% 1.57/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)))),
% 1.57/1.74 inference(transitivity,[status(thm)],[3538, 3536])).
% 1.57/1.74 tff(3540,plain,
% 1.57/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a1) | (~c1_1(a1)) | (~c3_1(a1)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))),
% 1.57/1.74 inference(quant_inst,[status(thm)],[])).
% 1.57/1.74 tff(3541,plain,
% 1.57/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a1)) | c0_1(a1) | (~c3_1(a1)) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5))),
% 1.57/1.74 inference(modus_ponens,[status(thm)],[3540, 3539])).
% 1.57/1.74 tff(3542,plain,
% 1.57/1.74 ($false),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[3541, 92, 3399, 2758, 3528, 3527, 3390, 3389, 2626, 567, 3472, 3535])).
% 1.57/1.74 tff(3543,plain,(c2_1(a20) | c3_1(a20) | c0_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.57/1.74 tff(3544,plain,
% 1.57/1.74 (c2_1(a20)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[3543, 44, 33])).
% 1.57/1.74 tff(3545,plain,
% 1.57/1.74 (~hskp12),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[344, 3544])).
% 1.57/1.74 tff(3546,plain,
% 1.57/1.74 (~hskp11),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[3245, 594, 45, 57, 58])).
% 1.57/1.74 tff(3547,plain,
% 1.57/1.74 (hskp12 | hskp11 | c2_1(a7)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[290, 92, 57, 58, 284])).
% 1.57/1.74 tff(3548,plain,
% 1.57/1.74 (c2_1(a7)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[3547, 3546, 46])).
% 1.57/1.74 tff(3549,plain,
% 1.57/1.74 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp12 | hskp11 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | c3_1(a2))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp12 | hskp11 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | c3_1(a2))),
% 1.57/1.74 inference(rewrite,[status(thm)],[])).
% 1.57/1.74 tff(3550,plain,
% 1.57/1.74 ((hskp12 | hskp11 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c2_1(a2)) <=> (hskp12 | hskp11 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | c3_1(a2))),
% 1.57/1.74 inference(rewrite,[status(thm)],[])).
% 1.57/1.74 tff(3551,plain,
% 1.57/1.74 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c2_1(a2))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp12 | hskp11 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | c3_1(a2)))),
% 1.57/1.74 inference(monotonicity,[status(thm)],[3550])).
% 1.57/1.74 tff(3552,plain,
% 1.57/1.74 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c2_1(a2))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp12 | hskp11 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | c3_1(a2))),
% 1.57/1.74 inference(transitivity,[status(thm)],[3551, 3549])).
% 1.57/1.74 tff(3553,plain,
% 1.57/1.74 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c2_1(a2))),
% 1.57/1.74 inference(quant_inst,[status(thm)],[])).
% 1.57/1.74 tff(3554,plain,
% 1.57/1.74 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp12 | hskp11 | c1_1(a2) | c2_1(a2) | (~ndr1_0) | c3_1(a2)),
% 1.57/1.74 inference(modus_ponens,[status(thm)],[3553, 3552])).
% 1.57/1.74 tff(3555,plain,
% 1.57/1.74 (hskp12 | hskp11 | c3_1(a2)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[3554, 92, 2620, 2626, 284])).
% 1.57/1.74 tff(3556,plain,
% 1.57/1.74 (c3_1(a2)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[3555, 3546, 46])).
% 1.57/1.74 tff(3557,plain,
% 1.57/1.74 ($false),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[3230, 92, 3222, 3221, 3223, 2758, 57, 58, 2626, 322, 3556, 3548])).
% 1.57/1.74 tff(3558,plain,(hskp3 | c1_1(a7) | c3_1(a7) | hskp12 | c0_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.57/1.74 tff(3559,plain,
% 1.57/1.74 (hskp3),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[3558, 3545, 3212, 3211, 3210])).
% 1.57/1.74 tff(3560,plain,
% 1.57/1.74 (~c1_1(a5)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[712, 3559])).
% 1.57/1.74 tff(3561,plain,
% 1.57/1.74 (~c0_1(a5)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[718, 3559])).
% 1.57/1.74 tff(3562,plain,
% 1.57/1.74 (c2_1(a5)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[726, 3559])).
% 1.57/1.74 tff(3563,plain,
% 1.57/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c2_1(a20)) | c3_1(a20) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a20))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (~c2_1(a20)) | c3_1(a20) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a20))),
% 1.57/1.74 inference(rewrite,[status(thm)],[])).
% 1.57/1.74 tff(3564,plain,
% 1.57/1.74 (((~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5))) <=> ((~c2_1(a20)) | c3_1(a20) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a20))),
% 1.57/1.74 inference(rewrite,[status(thm)],[])).
% 1.57/1.74 tff(3565,plain,
% 1.57/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c2_1(a20)) | c3_1(a20) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a20)))),
% 1.57/1.74 inference(monotonicity,[status(thm)],[3564])).
% 1.57/1.74 tff(3566,plain,
% 1.57/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (~c2_1(a20)) | c3_1(a20) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a20))),
% 1.57/1.74 inference(transitivity,[status(thm)],[3565, 3563])).
% 1.57/1.74 tff(3567,plain,
% 1.57/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))),
% 1.57/1.74 inference(quant_inst,[status(thm)],[])).
% 1.57/1.74 tff(3568,plain,
% 1.57/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (~c2_1(a20)) | c3_1(a20) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a20)),
% 1.57/1.74 inference(modus_ponens,[status(thm)],[3567, 3566])).
% 1.57/1.74 tff(3569,plain,
% 1.57/1.74 ((~c3_1(a5)) | c1_1(a20)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[3568, 92, 3562, 3544, 44, 3561, 3560, 1073])).
% 1.57/1.74 tff(3570,plain,
% 1.57/1.74 (~c3_1(a5)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[3569, 498])).
% 1.57/1.74 tff(3571,plain,
% 1.57/1.74 (c3_1(a2)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[2777, 498, 44, 33, 3559])).
% 1.57/1.74 tff(3572,plain,
% 1.57/1.74 (c2_1(a7)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[3547, 274, 3030])).
% 1.57/1.74 tff(3573,plain,
% 1.57/1.74 (hskp21),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[1474, 274, 3030])).
% 1.57/1.74 tff(3574,plain,
% 1.57/1.74 (~c0_1(a47)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[777, 3573])).
% 1.57/1.74 tff(3575,plain,
% 1.57/1.74 (c3_1(a47)),
% 1.57/1.74 inference(unit_resolution,[status(thm)],[785, 3573])).
% 1.57/1.74 tff(3576,plain,
% 1.57/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a47) | c0_1(a7) | c1_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a7)) | (~c3_1(a47)) | (~c1_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a47) | c0_1(a7) | c1_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a7)) | (~c3_1(a47)) | (~c1_1(a47)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3577,plain,
% 1.57/1.75 (((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a47) | (~c1_1(a47)) | (~c3_1(a47)) | c1_1(a7) | c0_1(a7) | (~c2_1(a7))) <=> (c0_1(a47) | c0_1(a7) | c1_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a7)) | (~c3_1(a47)) | (~c1_1(a47)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3578,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a47) | (~c1_1(a47)) | (~c3_1(a47)) | c1_1(a7) | c0_1(a7) | (~c2_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a47) | c0_1(a7) | c1_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a7)) | (~c3_1(a47)) | (~c1_1(a47))))),
% 1.57/1.75 inference(monotonicity,[status(thm)],[3577])).
% 1.57/1.75 tff(3579,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a47) | (~c1_1(a47)) | (~c3_1(a47)) | c1_1(a7) | c0_1(a7) | (~c2_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a47) | c0_1(a7) | c1_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a7)) | (~c3_1(a47)) | (~c1_1(a47)))),
% 1.57/1.75 inference(transitivity,[status(thm)],[3578, 3576])).
% 1.57/1.75 tff(3580,plain,
% 1.57/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a47) | (~c1_1(a47)) | (~c3_1(a47)) | c1_1(a7) | c0_1(a7) | (~c2_1(a7)))),
% 1.57/1.75 inference(quant_inst,[status(thm)],[])).
% 1.57/1.75 tff(3581,plain,
% 1.57/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a47) | c0_1(a7) | c1_1(a7) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a7)) | (~c3_1(a47)) | (~c1_1(a47))),
% 1.57/1.75 inference(modus_ponens,[status(thm)],[3580, 3579])).
% 1.57/1.75 tff(3582,plain,
% 1.57/1.75 (~c1_1(a47)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3581, 92, 3575, 2758, 3574, 45, 57, 2626, 567, 2956, 3572])).
% 1.57/1.75 tff(3583,plain,
% 1.57/1.75 (c2_1(a47)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[793, 3573])).
% 1.57/1.75 tff(3584,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | (~c2_1(a20)) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | (~c2_1(a20)) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3585,plain,
% 1.57/1.75 (((~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47))) <=> (c0_1(a47) | (~c2_1(a20)) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3586,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | (~c2_1(a20)) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47))))),
% 1.57/1.75 inference(monotonicity,[status(thm)],[3585])).
% 1.57/1.75 tff(3587,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | (~c2_1(a20)) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))),
% 1.57/1.75 inference(transitivity,[status(thm)],[3586, 3584])).
% 1.57/1.75 tff(3588,plain,
% 1.57/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))),
% 1.57/1.75 inference(quant_inst,[status(thm)],[])).
% 1.57/1.75 tff(3589,plain,
% 1.57/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | (~c2_1(a20)) | c3_1(a20) | (~ndr1_0) | c1_1(a20) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47))),
% 1.57/1.75 inference(modus_ponens,[status(thm)],[3588, 3587])).
% 1.57/1.75 tff(3590,plain,
% 1.57/1.75 ($false),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3589, 92, 3583, 3575, 3574, 2959, 44, 1073, 498, 3582])).
% 1.57/1.75 tff(3591,plain,(hskp11 | (~c2_1(a20)) | c3_1(a20) | c1_1(a20) | c0_1(a7) | c1_1(a7) | (~c3_1(a2)) | c3_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.57/1.75 tff(3592,plain,
% 1.57/1.75 (hskp11),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3591, 498, 44, 3544, 3210, 3211, 3571, 3212])).
% 1.57/1.75 tff(3593,plain,
% 1.57/1.75 (~c0_1(a19)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[98, 3592])).
% 1.57/1.75 tff(3594,plain,
% 1.57/1.75 (c1_1(a19)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[107, 3592])).
% 1.57/1.75 tff(3595,plain,
% 1.57/1.75 (~c3_1(a19)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3439, 92, 3594, 3562, 2758, 3593, 3561, 3560, 2626, 567, 3571])).
% 1.57/1.75 tff(3596,plain,
% 1.57/1.75 (c2_1(a19)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[115, 3592])).
% 1.57/1.75 tff(3597,assumption,(~c3_1(a5)), introduced(assumption)).
% 1.57/1.75 tff(3598,assumption,(~c2_1(a7)), introduced(assumption)).
% 1.57/1.75 tff(3599,assumption,(~c1_1(a5)), introduced(assumption)).
% 1.57/1.75 tff(3600,assumption,(c2_1(a5)), introduced(assumption)).
% 1.57/1.75 tff(3601,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a7) | c3_1(a7) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c2_1(a7) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a7) | c3_1(a7) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c2_1(a7) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3602,plain,
% 1.57/1.75 (((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a7) | c0_1(a7) | c3_1(a7)) <=> (c0_1(a7) | c3_1(a7) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c2_1(a7) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3603,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a7) | c3_1(a7) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c2_1(a7) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19))))),
% 1.57/1.75 inference(monotonicity,[status(thm)],[3602])).
% 1.57/1.75 tff(3604,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a7) | c3_1(a7) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c2_1(a7) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19)))),
% 1.57/1.75 inference(transitivity,[status(thm)],[3603, 3601])).
% 1.57/1.75 tff(3605,plain,
% 1.57/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c2_1(a19)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)) | c2_1(a7) | c0_1(a7) | c3_1(a7))),
% 1.57/1.75 inference(quant_inst,[status(thm)],[])).
% 1.57/1.75 tff(3606,plain,
% 1.57/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a7) | c3_1(a7) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c2_1(a7) | (~c2_1(a19)) | c3_1(a19) | (~c1_1(a19))),
% 1.57/1.75 inference(modus_ponens,[status(thm)],[3605, 3604])).
% 1.57/1.75 tff(3607,plain,
% 1.57/1.75 ($false),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3606, 92, 2122, 2121, 3600, 45, 58, 3599, 1002, 2060, 3598, 3597])).
% 1.57/1.75 tff(3608,plain,(c2_1(a7) | (~c1_1(a19)) | (~c2_1(a19)) | (~c2_1(a5)) | c0_1(a7) | c3_1(a7) | c1_1(a5) | c3_1(a19) | c3_1(a5)), inference(lemma,lemma(discharge,[]))).
% 1.57/1.75 tff(3609,plain,
% 1.57/1.75 (c2_1(a7)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3608, 3594, 3596, 3562, 3210, 3212, 3560, 3595, 3570])).
% 1.57/1.75 tff(3610,assumption,(hskp16), introduced(assumption)).
% 1.57/1.75 tff(3611,plain,
% 1.57/1.75 (~c1_1(a32)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3011, 3610])).
% 1.57/1.75 tff(3612,plain,
% 1.57/1.75 (c2_1(a32)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3020, 3610])).
% 1.57/1.75 tff(3613,plain,
% 1.57/1.75 (c0_1(a32)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3028, 3610])).
% 1.57/1.75 tff(3614,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a32) | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a32)) | (~c0_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a32) | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a32)) | (~c0_1(a32)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3615,plain,
% 1.57/1.75 (((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2))) <=> (c1_1(a32) | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a32)) | (~c0_1(a32)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3616,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a32) | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a32)) | (~c0_1(a32))))),
% 1.57/1.75 inference(monotonicity,[status(thm)],[3615])).
% 1.57/1.75 tff(3617,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a32) | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a32)) | (~c0_1(a32)))),
% 1.57/1.75 inference(transitivity,[status(thm)],[3616, 3614])).
% 1.57/1.75 tff(3618,plain,
% 1.57/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a32) | (~c2_1(a32)) | (~c0_1(a32)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)))),
% 1.57/1.75 inference(quant_inst,[status(thm)],[])).
% 1.57/1.75 tff(3619,plain,
% 1.57/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a32) | c1_1(a2) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a32)) | (~c0_1(a32))),
% 1.57/1.75 inference(modus_ponens,[status(thm)],[3618, 3617])).
% 1.57/1.75 tff(3620,plain,
% 1.57/1.75 ($false),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3619, 92, 3613, 3612, 2758, 3611, 2620, 2626, 630, 2956])).
% 1.57/1.75 tff(3621,plain,((~hskp16) | (~c3_1(a2))), inference(lemma,lemma(discharge,[]))).
% 1.57/1.75 tff(3622,plain,
% 1.57/1.75 (~hskp16),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3621, 3571])).
% 1.57/1.75 tff(3623,plain,
% 1.57/1.75 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp26 | hskp16 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp26 | hskp16 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3624,plain,
% 1.57/1.75 ((hskp26 | hskp16 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19))) <=> (hskp26 | hskp16 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3625,plain,
% 1.57/1.75 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp26 | hskp16 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19))))),
% 1.57/1.75 inference(monotonicity,[status(thm)],[3624])).
% 1.57/1.75 tff(3626,plain,
% 1.57/1.75 (((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))) <=> ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp26 | hskp16 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19)))),
% 1.57/1.75 inference(transitivity,[status(thm)],[3625, 3623])).
% 1.57/1.75 tff(3627,plain,
% 1.57/1.75 ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp26 | hskp16 | (~ndr1_0) | c0_1(a19) | (~c1_1(a19)) | (~c2_1(a19)))),
% 1.57/1.75 inference(quant_inst,[status(thm)],[])).
% 1.57/1.75 tff(3628,plain,
% 1.57/1.75 ((~![U: $i] : (hskp26 | hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp26 | hskp16 | c0_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c1_1(a19))),
% 1.57/1.75 inference(modus_ponens,[status(thm)],[3627, 3626])).
% 1.57/1.75 tff(3629,plain,
% 1.57/1.75 (hskp26 | hskp16),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3628, 92, 3594, 3596, 3593, 2998])).
% 1.57/1.75 tff(3630,plain,
% 1.57/1.75 (hskp26),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3629, 3622])).
% 1.57/1.75 tff(3631,plain,
% 1.57/1.75 (c3_1(a4)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[2656, 3630])).
% 1.57/1.75 tff(3632,plain,
% 1.57/1.75 (c1_1(a4)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[2664, 3630])).
% 1.57/1.75 tff(3633,plain,
% 1.57/1.75 (c0_1(a4)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[2672, 3630])).
% 1.57/1.75 tff(3634,plain,
% 1.57/1.75 ($false),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3230, 92, 3633, 3632, 3631, 2758, 3211, 3212, 2626, 322, 3571, 3609])).
% 1.57/1.75 tff(3635,plain,(c1_1(a20) | c3_1(a20) | c0_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.57/1.75 tff(3636,plain,
% 1.57/1.75 (c1_1(a20)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3635, 44, 33])).
% 1.57/1.75 tff(3637,plain,
% 1.57/1.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp20 | (~c2_1(a20)) | c3_1(a20) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp20 | (~c2_1(a20)) | c3_1(a20) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a20)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3638,plain,
% 1.57/1.75 ((hskp20 | (~ndr1_0) | c3_1(a20) | (~c1_1(a20)) | (~c2_1(a20)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2))) <=> (hskp20 | (~c2_1(a20)) | c3_1(a20) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a20)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3639,plain,
% 1.57/1.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a20) | (~c1_1(a20)) | (~c2_1(a20)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp20 | (~c2_1(a20)) | c3_1(a20) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a20))))),
% 1.57/1.75 inference(monotonicity,[status(thm)],[3638])).
% 1.57/1.75 tff(3640,plain,
% 1.57/1.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a20) | (~c1_1(a20)) | (~c2_1(a20)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp20 | (~c2_1(a20)) | c3_1(a20) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a20)))),
% 1.57/1.75 inference(transitivity,[status(thm)],[3639, 3637])).
% 1.57/1.75 tff(3641,plain,
% 1.57/1.75 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a20) | (~c1_1(a20)) | (~c2_1(a20)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)))),
% 1.57/1.75 inference(quant_inst,[status(thm)],[])).
% 1.57/1.75 tff(3642,plain,
% 1.57/1.75 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp20 | (~c2_1(a20)) | c3_1(a20) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a20))),
% 1.57/1.75 inference(modus_ponens,[status(thm)],[3641, 3640])).
% 1.57/1.75 tff(3643,plain,
% 1.57/1.75 (hskp20 | (~c2_1(a20)) | c3_1(a2) | (~c1_1(a20))),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3642, 92, 2758, 44, 2626, 3174])).
% 1.57/1.75 tff(3644,plain,
% 1.57/1.75 (hskp20),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[3643, 1, 3544, 3636])).
% 1.57/1.75 tff(3645,plain,
% 1.57/1.75 (c1_1(a43)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[1033, 3644])).
% 1.57/1.75 tff(3646,plain,
% 1.57/1.75 (c0_1(a43)),
% 1.57/1.75 inference(unit_resolution,[status(thm)],[1048, 3644])).
% 1.57/1.75 tff(3647,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a20) | (~c2_1(a20)) | c3_1(a20) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a20) | (~c2_1(a20)) | c3_1(a20) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3648,plain,
% 1.57/1.75 (((~ndr1_0) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a20) | c3_1(a20) | (~c2_1(a20))) <=> (c0_1(a20) | (~c2_1(a20)) | c3_1(a20) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(3649,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a20) | c3_1(a20) | (~c2_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a20) | (~c2_1(a20)) | c3_1(a20) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 1.57/1.75 inference(monotonicity,[status(thm)],[3648])).
% 1.57/1.75 tff(3650,plain,
% 1.57/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a20) | c3_1(a20) | (~c2_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a20) | (~c2_1(a20)) | c3_1(a20) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 1.58/1.75 inference(transitivity,[status(thm)],[3649, 3647])).
% 1.58/1.75 tff(3651,plain,
% 1.58/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a20) | c3_1(a20) | (~c2_1(a20)))),
% 1.58/1.75 inference(quant_inst,[status(thm)],[])).
% 1.58/1.75 tff(3652,plain,
% 1.58/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a20) | (~c2_1(a20)) | c3_1(a20) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a43)) | (~c2_1(a43)) | (~c0_1(a43))),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[3651, 3650])).
% 1.58/1.75 tff(3653,plain,
% 1.58/1.75 (~c2_1(a43)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[3652, 92, 3646, 3645, 2758, 33, 3544, 44, 2626, 1643, 1])).
% 1.58/1.75 tff(3654,plain,
% 1.58/1.75 (hskp11),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[3555, 1, 3545])).
% 1.58/1.75 tff(3655,plain,
% 1.58/1.75 (~c0_1(a19)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[98, 3654])).
% 1.58/1.75 tff(3656,plain,
% 1.58/1.75 (~c3_1(a43)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[1025, 3644])).
% 1.58/1.75 tff(3657,plain,
% 1.58/1.75 (c1_1(a19)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[107, 3654])).
% 1.58/1.75 tff(3658,plain,
% 1.58/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a43) | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a43)) | c2_1(a43))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a43) | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a43)) | c2_1(a43))),
% 1.58/1.75 inference(rewrite,[status(thm)],[])).
% 1.58/1.75 tff(3659,plain,
% 1.58/1.75 (((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19))) <=> (c3_1(a43) | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a43)) | c2_1(a43))),
% 1.58/1.75 inference(rewrite,[status(thm)],[])).
% 1.58/1.75 tff(3660,plain,
% 1.58/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a43) | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a43)) | c2_1(a43)))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[3659])).
% 1.58/1.75 tff(3661,plain,
% 1.58/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a43) | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a43)) | c2_1(a43))),
% 1.58/1.75 inference(transitivity,[status(thm)],[3660, 3658])).
% 1.58/1.75 tff(3662,plain,
% 1.58/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a19) | c3_1(a19) | (~c1_1(a19)))),
% 1.58/1.75 inference(quant_inst,[status(thm)],[])).
% 1.58/1.75 tff(3663,plain,
% 1.58/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a43) | c0_1(a19) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | c3_1(a19) | (~c1_1(a19)) | (~c1_1(a43)) | c2_1(a43)),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[3662, 3661])).
% 1.58/1.75 tff(3664,plain,
% 1.58/1.75 (c3_1(a19)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[3663, 92, 3645, 3657, 2758, 3656, 3655, 2620, 11, 1, 3653])).
% 1.58/1.75 tff(3665,plain,
% 1.58/1.75 (c2_1(a19)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[115, 3654])).
% 1.58/1.75 tff(3666,plain,
% 1.58/1.75 ($false),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[2057, 92, 3545, 3657, 3665, 3655, 43, 3664])).
% 1.58/1.75 tff(3667,plain,(c3_1(a2) | c0_1(a20) | c3_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.75 tff(3668,plain,
% 1.58/1.75 (c3_1(a2)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[3667, 44, 33])).
% 1.58/1.75 tff(3669,plain,
% 1.58/1.75 (~hskp16),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[3621, 3668])).
% 1.58/1.75 tff(3670,plain,
% 1.58/1.75 (hskp26),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[3005, 3669, 3544, 3636])).
% 1.58/1.75 tff(3671,plain,
% 1.58/1.75 (c3_1(a4)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[2656, 3670])).
% 1.58/1.75 tff(3672,plain,
% 1.58/1.75 (c1_1(a4)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[2664, 3670])).
% 1.58/1.75 tff(3673,plain,
% 1.58/1.75 (c0_1(a4)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[2672, 3670])).
% 1.58/1.75 tff(3674,plain,
% 1.58/1.75 (~c2_1(a7)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[3230, 92, 3673, 3672, 3671, 2758, 3211, 3212, 2626, 322, 3668])).
% 1.58/1.75 tff(3675,plain,
% 1.58/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | c3_1(a5) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | c3_1(a5) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.58/1.75 inference(rewrite,[status(thm)],[])).
% 1.58/1.75 tff(3676,plain,
% 1.58/1.75 (((~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5))) <=> (c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | c3_1(a5) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.58/1.75 inference(rewrite,[status(thm)],[])).
% 1.58/1.75 tff(3677,plain,
% 1.58/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | c3_1(a5) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4))))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[3676])).
% 1.58/1.75 tff(3678,plain,
% 1.58/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | c3_1(a5) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4)))),
% 1.58/1.75 inference(transitivity,[status(thm)],[3677, 3675])).
% 1.58/1.75 tff(3679,plain,
% 1.58/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a4)) | (~c3_1(a4)) | (~c0_1(a4)) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a5) | c3_1(a5) | (~c2_1(a5)))),
% 1.58/1.76 inference(quant_inst,[status(thm)],[])).
% 1.58/1.76 tff(3680,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | c3_1(a5) | (~c0_1(a4)) | (~c1_1(a4)) | (~c3_1(a4))),
% 1.58/1.76 inference(modus_ponens,[status(thm)],[3679, 3678])).
% 1.58/1.76 tff(3681,plain,
% 1.58/1.76 (c3_1(a5)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3680, 92, 3673, 3672, 3671, 3562, 2758, 3560, 2626, 322, 3668])).
% 1.58/1.76 tff(3682,plain,
% 1.58/1.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a20) | (~c2_1(a20)) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a20) | (~c2_1(a20)) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a20)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3683,plain,
% 1.58/1.76 ((hskp5 | (~ndr1_0) | c0_1(a20) | (~c1_1(a20)) | (~c2_1(a20)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5))) <=> (hskp5 | c0_1(a20) | (~c2_1(a20)) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a20)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3684,plain,
% 1.58/1.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a20) | (~c1_1(a20)) | (~c2_1(a20)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a20) | (~c2_1(a20)) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a20))))),
% 1.58/1.76 inference(monotonicity,[status(thm)],[3683])).
% 1.58/1.76 tff(3685,plain,
% 1.58/1.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a20) | (~c1_1(a20)) | (~c2_1(a20)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a20) | (~c2_1(a20)) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a20)))),
% 1.58/1.76 inference(transitivity,[status(thm)],[3684, 3682])).
% 1.58/1.76 tff(3686,plain,
% 1.58/1.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a20) | (~c1_1(a20)) | (~c2_1(a20)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))),
% 1.58/1.76 inference(quant_inst,[status(thm)],[])).
% 1.58/1.76 tff(3687,plain,
% 1.58/1.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a20) | (~c2_1(a20)) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a20))),
% 1.58/1.76 inference(modus_ponens,[status(thm)],[3686, 3685])).
% 1.58/1.76 tff(3688,plain,
% 1.58/1.76 (hskp5 | (~c3_1(a5)) | (~c1_1(a20))),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3687, 92, 33, 3544, 3561, 3560, 21])).
% 1.58/1.76 tff(3689,plain,
% 1.58/1.76 (hskp5),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3688, 3681, 3636])).
% 1.58/1.76 tff(3690,plain,
% 1.58/1.76 (~c3_1(a8)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[1656, 3689])).
% 1.58/1.76 tff(3691,plain,
% 1.58/1.76 (~c2_1(a8)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[1662, 3689])).
% 1.58/1.76 tff(3692,plain,
% 1.58/1.76 (c1_1(a8)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[1718, 3689])).
% 1.58/1.76 tff(3693,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a8)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3694,plain,
% 1.58/1.76 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a7) | c1_1(a7) | c0_1(a7)) <=> (c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a8)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3695,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a8))))),
% 1.58/1.76 inference(monotonicity,[status(thm)],[3694])).
% 1.58/1.76 tff(3696,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a7) | c1_1(a7) | c0_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a8)))),
% 1.58/1.76 inference(transitivity,[status(thm)],[3695, 3693])).
% 1.58/1.76 tff(3697,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a7) | c1_1(a7) | c3_1(a7) | c2_1(a7) | c1_1(a7) | c0_1(a7))),
% 1.58/1.76 inference(quant_inst,[status(thm)],[])).
% 1.58/1.76 tff(3698,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | c2_1(a7) | (~c1_1(a8))),
% 1.58/1.76 inference(modus_ponens,[status(thm)],[3697, 3696])).
% 1.58/1.76 tff(3699,plain,
% 1.58/1.76 ($false),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3698, 92, 3692, 3691, 3690, 3210, 3211, 3212, 194, 3674])).
% 1.58/1.76 tff(3700,plain,(c3_1(a20) | c0_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.76 tff(3701,plain,
% 1.58/1.76 (c3_1(a20)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3700, 33])).
% 1.58/1.76 tff(3702,plain,
% 1.58/1.76 (~hskp12),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[388, 3701])).
% 1.58/1.76 tff(3703,plain,
% 1.58/1.76 (hskp3),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3558, 3702, 3212, 3211, 3210])).
% 1.58/1.76 tff(3704,plain,
% 1.58/1.76 (~c1_1(a5)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[712, 3703])).
% 1.58/1.76 tff(3705,plain,
% 1.58/1.76 (~c0_1(a5)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[718, 3703])).
% 1.58/1.76 tff(3706,plain,
% 1.58/1.76 (c2_1(a5)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[726, 3703])).
% 1.58/1.76 tff(3707,assumption,(~c0_1(a5)), introduced(assumption)).
% 1.58/1.76 tff(3708,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3709,plain,
% 1.58/1.76 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a7) | c0_1(a7) | c3_1(a7)) <=> (c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3710,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5))))),
% 1.58/1.76 inference(monotonicity,[status(thm)],[3709])).
% 1.58/1.76 tff(3711,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)))),
% 1.58/1.76 inference(transitivity,[status(thm)],[3710, 3708])).
% 1.58/1.76 tff(3712,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a7) | c0_1(a7) | c3_1(a7))),
% 1.58/1.76 inference(quant_inst,[status(thm)],[])).
% 1.58/1.76 tff(3713,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5))),
% 1.58/1.76 inference(modus_ponens,[status(thm)],[3712, 3711])).
% 1.58/1.76 tff(3714,plain,
% 1.58/1.76 ($false),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3713, 92, 3600, 2758, 45, 57, 58, 3707, 3599, 2626, 1164, 1])).
% 1.58/1.76 tff(3715,plain,(c3_1(a2) | (~c2_1(a5)) | c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.76 tff(3716,plain,
% 1.58/1.76 (c3_1(a2)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3715, 3706, 3210, 3211, 3212, 3705, 3704])).
% 1.58/1.76 tff(3717,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a20) | (~c3_1(a20)) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | (~c1_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a20) | (~c3_1(a20)) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | (~c1_1(a20)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3718,plain,
% 1.58/1.76 (((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a20) | (~c1_1(a20)) | (~c3_1(a20)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5))) <=> (c0_1(a20) | (~c3_1(a20)) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | (~c1_1(a20)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3719,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a20) | (~c1_1(a20)) | (~c3_1(a20)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a20) | (~c3_1(a20)) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | (~c1_1(a20))))),
% 1.58/1.76 inference(monotonicity,[status(thm)],[3718])).
% 1.58/1.76 tff(3720,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a20) | (~c1_1(a20)) | (~c3_1(a20)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a20) | (~c3_1(a20)) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | (~c1_1(a20)))),
% 1.58/1.76 inference(transitivity,[status(thm)],[3719, 3717])).
% 1.58/1.76 tff(3721,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a20) | (~c1_1(a20)) | (~c3_1(a20)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)))),
% 1.58/1.76 inference(quant_inst,[status(thm)],[])).
% 1.58/1.76 tff(3722,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a20) | (~c3_1(a20)) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | (~c3_1(a2)) | (~c2_1(a5)) | (~c1_1(a20))),
% 1.58/1.76 inference(modus_ponens,[status(thm)],[3721, 3720])).
% 1.58/1.76 tff(3723,plain,
% 1.58/1.76 ((~c3_1(a2)) | (~c1_1(a20))),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3722, 92, 3706, 2758, 33, 3701, 3705, 3704, 2626, 567])).
% 1.58/1.76 tff(3724,plain,
% 1.58/1.76 (~c1_1(a20)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3723, 3716])).
% 1.58/1.76 tff(3725,plain,
% 1.58/1.76 (hskp12 | hskp11 | c2_1(a7)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[290, 92, 3211, 3212, 284])).
% 1.58/1.76 tff(3726,plain,
% 1.58/1.76 (c2_1(a7)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3725, 274, 3702])).
% 1.58/1.76 tff(3727,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c2_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c2_1(a7)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3728,plain,
% 1.58/1.76 (((~ndr1_0) | c3_1(a7) | c1_1(a7) | (~c2_1(a7)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5))) <=> (c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c2_1(a7)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3729,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a7) | c1_1(a7) | (~c2_1(a7)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c2_1(a7))))),
% 1.58/1.76 inference(monotonicity,[status(thm)],[3728])).
% 1.58/1.76 tff(3730,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a7) | c1_1(a7) | (~c2_1(a7)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c2_1(a7)))),
% 1.58/1.76 inference(transitivity,[status(thm)],[3729, 3727])).
% 1.58/1.76 tff(3731,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a7) | c1_1(a7) | (~c2_1(a7)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))),
% 1.58/1.76 inference(quant_inst,[status(thm)],[])).
% 1.58/1.76 tff(3732,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c2_1(a7))),
% 1.58/1.76 inference(modus_ponens,[status(thm)],[3731, 3730])).
% 1.58/1.76 tff(3733,plain,
% 1.58/1.76 ((~c3_1(a5)) | (~c2_1(a7))),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3732, 92, 3706, 3211, 3212, 3705, 3704, 1073])).
% 1.58/1.76 tff(3734,plain,
% 1.58/1.76 (~c3_1(a5)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3733, 3726])).
% 1.58/1.76 tff(3735,plain,
% 1.58/1.76 (hskp21),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[1474, 274, 3702])).
% 1.58/1.76 tff(3736,plain,
% 1.58/1.76 (~c0_1(a47)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[777, 3735])).
% 1.58/1.76 tff(3737,plain,
% 1.58/1.76 (c3_1(a47)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[785, 3735])).
% 1.58/1.76 tff(3738,plain,
% 1.58/1.76 (c2_1(a47)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[793, 3735])).
% 1.58/1.76 tff(3739,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c0_1(a20) | (~c3_1(a20)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c1_1(a20) | (~c3_1(a47)) | (~c2_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c0_1(a20) | (~c3_1(a20)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c1_1(a20) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3740,plain,
% 1.58/1.76 (((~ndr1_0) | c3_1(a5) | c1_1(a5) | (~c2_1(a5)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20))) <=> (c0_1(a47) | c0_1(a20) | (~c3_1(a20)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c1_1(a20) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3741,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a5) | c1_1(a5) | (~c2_1(a5)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c0_1(a20) | (~c3_1(a20)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c1_1(a20) | (~c3_1(a47)) | (~c2_1(a47))))),
% 1.58/1.76 inference(monotonicity,[status(thm)],[3740])).
% 1.58/1.76 tff(3742,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a5) | c1_1(a5) | (~c2_1(a5)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c0_1(a20) | (~c3_1(a20)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c1_1(a20) | (~c3_1(a47)) | (~c2_1(a47)))),
% 1.58/1.76 inference(transitivity,[status(thm)],[3741, 3739])).
% 1.58/1.76 tff(3743,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a5) | c1_1(a5) | (~c2_1(a5)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a20) | c0_1(a20) | (~c3_1(a20)))),
% 1.58/1.76 inference(quant_inst,[status(thm)],[])).
% 1.58/1.76 tff(3744,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c0_1(a20) | (~c3_1(a20)) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | c1_1(a20) | (~c3_1(a47)) | (~c2_1(a47))),
% 1.58/1.76 inference(modus_ponens,[status(thm)],[3743, 3742])).
% 1.58/1.76 tff(3745,plain,
% 1.58/1.76 ($false),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3744, 92, 3738, 3737, 3706, 3736, 33, 3701, 3704, 1073, 3724, 3734])).
% 1.58/1.76 tff(3746,plain,(hskp11 | c0_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.76 tff(3747,plain,
% 1.58/1.76 (hskp11),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3746, 33])).
% 1.58/1.76 tff(3748,plain,
% 1.58/1.76 (~c0_1(a19)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[98, 3747])).
% 1.58/1.76 tff(3749,plain,
% 1.58/1.76 (c2_1(a19)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[115, 3747])).
% 1.58/1.76 tff(3750,plain,
% 1.58/1.76 (c1_1(a19)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[107, 3747])).
% 1.58/1.76 tff(3751,plain,
% 1.58/1.76 (hskp5),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[2026, 92, 3750, 3749, 33, 3701, 3748, 21, 3724])).
% 1.58/1.76 tff(3752,plain,
% 1.58/1.76 (~c3_1(a8)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[1656, 3751])).
% 1.58/1.76 tff(3753,plain,
% 1.58/1.76 (~c2_1(a8)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[1662, 3751])).
% 1.58/1.76 tff(3754,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a8)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3755,plain,
% 1.58/1.76 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a7) | c0_1(a7) | c3_1(a7)) <=> (c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a8)))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3756,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a8))))),
% 1.58/1.76 inference(monotonicity,[status(thm)],[3755])).
% 1.58/1.76 tff(3757,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a7) | c0_1(a7) | c3_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a8)))),
% 1.58/1.76 inference(transitivity,[status(thm)],[3756, 3754])).
% 1.58/1.76 tff(3758,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a7) | c0_1(a7) | c3_1(a7))),
% 1.58/1.76 inference(quant_inst,[status(thm)],[])).
% 1.58/1.76 tff(3759,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a7) | c1_1(a7) | c3_1(a7) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a8))),
% 1.58/1.76 inference(modus_ponens,[status(thm)],[3758, 3757])).
% 1.58/1.76 tff(3760,plain,
% 1.58/1.76 (~c0_1(a8)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3759, 92, 3706, 3753, 3752, 3210, 3211, 3212, 3705, 3704, 1164])).
% 1.58/1.76 tff(3761,plain,
% 1.58/1.76 (~hskp16),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3621, 3716])).
% 1.58/1.76 tff(3762,plain,
% 1.58/1.76 (hskp26),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3628, 92, 3761, 3750, 3749, 3748, 2998])).
% 1.58/1.76 tff(3763,plain,
% 1.58/1.76 (c3_1(a4)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[2656, 3762])).
% 1.58/1.76 tff(3764,plain,
% 1.58/1.76 (c1_1(a4)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[2664, 3762])).
% 1.58/1.76 tff(3765,plain,
% 1.58/1.76 (c0_1(a4)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[2672, 3762])).
% 1.58/1.76 tff(3766,plain,
% 1.58/1.76 (c3_1(a5)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3680, 92, 3765, 3764, 3763, 3706, 2758, 3704, 2626, 322, 3716])).
% 1.58/1.76 tff(3767,plain,
% 1.58/1.76 (c1_1(a8)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[1718, 3751])).
% 1.58/1.76 tff(3768,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a8) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a8)) | c0_1(a8))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a8) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a8)) | c0_1(a8))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3769,plain,
% 1.58/1.76 (((~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5))) <=> (c2_1(a8) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a8)) | c0_1(a8))),
% 1.58/1.76 inference(rewrite,[status(thm)],[])).
% 1.58/1.76 tff(3770,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a8) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a8)) | c0_1(a8)))),
% 1.58/1.76 inference(monotonicity,[status(thm)],[3769])).
% 1.58/1.76 tff(3771,plain,
% 1.58/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a8) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a8)) | c0_1(a8))),
% 1.58/1.76 inference(transitivity,[status(thm)],[3770, 3768])).
% 1.58/1.76 tff(3772,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))),
% 1.58/1.76 inference(quant_inst,[status(thm)],[])).
% 1.58/1.76 tff(3773,plain,
% 1.58/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a8) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a8)) | c0_1(a8)),
% 1.58/1.76 inference(modus_ponens,[status(thm)],[3772, 3771])).
% 1.58/1.76 tff(3774,plain,
% 1.58/1.76 ($false),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3773, 92, 3767, 3706, 3753, 3705, 3704, 2475, 3766, 3760])).
% 1.58/1.76 tff(3775,plain,(c0_1(a20)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.76 tff(3776,plain,
% 1.58/1.76 (~hskp12),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[338, 3775])).
% 1.58/1.76 tff(3777,plain,
% 1.58/1.76 (hskp3 | c1_1(a7) | c3_1(a7) | c0_1(a7)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3558, 3776])).
% 1.58/1.76 tff(3778,plain,
% 1.58/1.76 ($false),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3777, 2630, 2629, 594, 2628])).
% 1.58/1.76 tff(3779,plain,((~hskp4) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.58/1.76 tff(3780,plain,
% 1.58/1.76 (~hskp4),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3779, 594])).
% 1.58/1.76 tff(3781,plain,
% 1.58/1.76 (hskp11 | hskp4),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[2680, 3776])).
% 1.58/1.76 tff(3782,plain,
% 1.58/1.76 (hskp11),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3781, 3780])).
% 1.58/1.76 tff(3783,plain,
% 1.58/1.76 (~c0_1(a19)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[98, 3782])).
% 1.58/1.76 tff(3784,plain,
% 1.58/1.76 (c2_1(a19)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[115, 3782])).
% 1.58/1.76 tff(3785,plain,
% 1.58/1.76 (c1_1(a19)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[107, 3782])).
% 1.58/1.76 tff(3786,assumption,(~hskp16), introduced(assumption)).
% 1.58/1.76 tff(3787,plain,
% 1.58/1.76 (hskp26),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[3628, 92, 3786, 3785, 3784, 3783, 2998])).
% 1.58/1.76 tff(3788,plain,
% 1.58/1.76 (c0_1(a4)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[2672, 3787])).
% 1.58/1.76 tff(3789,plain,
% 1.58/1.76 (c1_1(a4)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[2664, 3787])).
% 1.58/1.76 tff(3790,plain,
% 1.58/1.76 (~c3_1(a19)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[2057, 92, 3776, 3785, 3784, 3783, 43])).
% 1.58/1.76 tff(3791,plain,
% 1.58/1.76 (c3_1(a4)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[2656, 3787])).
% 1.58/1.76 tff(3792,plain,
% 1.58/1.76 (~c1_1(a73)),
% 1.58/1.76 inference(unit_resolution,[status(thm)],[2937, 3791, 3784, 3783, 3785, 3790, 3789, 3788])).
% 1.58/1.76 tff(3793,plain,
% 1.58/1.77 (hskp25),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[2853, 92, 3788, 3789, 3791, 1555])).
% 1.58/1.77 tff(3794,plain,
% 1.58/1.77 (~c3_1(a73)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[1138, 3793])).
% 1.58/1.77 tff(3795,plain,
% 1.58/1.77 (c0_1(a73)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[1146, 3793])).
% 1.58/1.77 tff(3796,plain,
% 1.58/1.77 ($false),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[2947, 92, 594, 3795, 3785, 3784, 3794, 3783, 31, 3792])).
% 1.58/1.77 tff(3797,plain,(hskp3 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.58/1.77 tff(3798,plain,
% 1.58/1.77 (hskp16),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3797, 594])).
% 1.58/1.77 tff(3799,plain,
% 1.58/1.77 (~c3_1(a2)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3621, 3798])).
% 1.58/1.77 tff(3800,plain,
% 1.58/1.77 ($false),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[2878, 3785, 3799, 594, 3784, 3783])).
% 1.58/1.77 tff(3801,plain,(hskp3), inference(lemma,lemma(discharge,[]))).
% 1.58/1.77 tff(3802,plain,
% 1.58/1.77 (~c1_1(a5)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[712, 3801])).
% 1.58/1.77 tff(3803,plain,
% 1.58/1.77 (~c0_1(a5)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[718, 3801])).
% 1.58/1.77 tff(3804,plain,
% 1.58/1.77 (c2_1(a5)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[726, 3801])).
% 1.58/1.77 tff(3805,plain,
% 1.58/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | c3_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | c3_1(a5))),
% 1.58/1.77 inference(rewrite,[status(thm)],[])).
% 1.58/1.77 tff(3806,plain,
% 1.58/1.77 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a5) | c0_1(a5) | c3_1(a5)) <=> (c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | c3_1(a5))),
% 1.58/1.77 inference(rewrite,[status(thm)],[])).
% 1.58/1.77 tff(3807,plain,
% 1.58/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a5) | c0_1(a5) | c3_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | c3_1(a5)))),
% 1.58/1.77 inference(monotonicity,[status(thm)],[3806])).
% 1.58/1.77 tff(3808,plain,
% 1.58/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a5) | c0_1(a5) | c3_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | c3_1(a5))),
% 1.58/1.77 inference(transitivity,[status(thm)],[3807, 3805])).
% 1.58/1.77 tff(3809,plain,
% 1.58/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5)) | c1_1(a5) | c0_1(a5) | c3_1(a5))),
% 1.58/1.77 inference(quant_inst,[status(thm)],[])).
% 1.58/1.77 tff(3810,plain,
% 1.58/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a5) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | c3_1(a5)),
% 1.58/1.77 inference(modus_ponens,[status(thm)],[3809, 3808])).
% 1.58/1.77 tff(3811,plain,
% 1.58/1.77 (c3_1(a5)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3810, 92, 3804, 2758, 3803, 3802, 2626, 1164, 1])).
% 1.58/1.77 tff(3812,plain,
% 1.58/1.77 (hskp11 | c3_1(a2)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3555, 3776])).
% 1.58/1.77 tff(3813,plain,
% 1.58/1.77 (hskp11),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3812, 1])).
% 1.58/1.77 tff(3814,plain,
% 1.58/1.77 (~c0_1(a19)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[98, 3813])).
% 1.58/1.77 tff(3815,plain,
% 1.58/1.77 (c2_1(a19)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[115, 3813])).
% 1.58/1.77 tff(3816,plain,
% 1.58/1.77 (c1_1(a19)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[107, 3813])).
% 1.58/1.77 tff(3817,plain,
% 1.58/1.77 (hskp5),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[2605, 92, 3816, 3815, 3814, 3803, 3802, 21, 3811])).
% 1.58/1.77 tff(3818,plain,
% 1.58/1.77 (~c3_1(a8)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[1656, 3817])).
% 1.58/1.77 tff(3819,plain,
% 1.58/1.77 (~c2_1(a8)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[1662, 3817])).
% 1.58/1.77 tff(3820,plain,
% 1.58/1.77 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.58/1.77 inference(bind,[status(th)],[])).
% 1.58/1.77 tff(3821,plain,
% 1.58/1.77 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.58/1.77 inference(quant_intro,[status(thm)],[3820])).
% 1.58/1.77 tff(3822,plain,
% 1.58/1.77 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.58/1.77 inference(rewrite,[status(thm)],[])).
% 1.58/1.77 tff(3823,plain,
% 1.58/1.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.58/1.77 inference(bind,[status(th)],[])).
% 1.58/1.77 tff(3824,plain,
% 1.58/1.77 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.58/1.77 inference(quant_intro,[status(thm)],[3823])).
% 1.58/1.77 tff(3825,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.58/1.77 tff(3826,plain,
% 1.58/1.77 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.58/1.77 inference(modus_ponens,[status(thm)],[3825, 3824])).
% 1.58/1.77 tff(3827,plain,
% 1.58/1.77 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.58/1.77 inference(modus_ponens,[status(thm)],[3826, 3822])).
% 1.58/1.77 tff(3828,plain,(
% 1.58/1.77 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.58/1.77 inference(skolemize,[status(sab)],[3827])).
% 1.58/1.77 tff(3829,plain,
% 1.58/1.77 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.58/1.77 inference(modus_ponens,[status(thm)],[3828, 3821])).
% 1.58/1.77 tff(3830,plain,
% 1.58/1.77 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a5) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a5) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.58/1.77 inference(rewrite,[status(thm)],[])).
% 1.58/1.77 tff(3831,plain,
% 1.58/1.77 ((hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2))) <=> (hskp22 | c1_1(a5) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.58/1.77 inference(rewrite,[status(thm)],[])).
% 1.58/1.77 tff(3832,plain,
% 1.58/1.77 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a5) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | (~c3_1(a5))))),
% 1.58/1.77 inference(monotonicity,[status(thm)],[3831])).
% 1.58/1.77 tff(3833,plain,
% 1.58/1.77 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a5) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.58/1.77 inference(transitivity,[status(thm)],[3832, 3830])).
% 1.58/1.77 tff(3834,plain,
% 1.58/1.77 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)))),
% 1.58/1.77 inference(quant_inst,[status(thm)],[])).
% 1.58/1.77 tff(3835,plain,
% 1.58/1.77 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a5) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c2_1(a5)) | (~c3_1(a5))),
% 1.58/1.77 inference(modus_ponens,[status(thm)],[3834, 3833])).
% 1.58/1.77 tff(3836,plain,
% 1.58/1.77 (hskp22 | c3_1(a2) | (~c3_1(a5))),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3835, 92, 3804, 2758, 3802, 2620, 3829])).
% 1.58/1.77 tff(3837,plain,
% 1.58/1.77 (hskp22),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3836, 3811, 1])).
% 1.58/1.77 tff(3838,plain,
% 1.58/1.77 (~c3_1(a48)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[176, 3837])).
% 1.58/1.77 tff(3839,plain,
% 1.58/1.77 (~c0_1(a48)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[145, 3837])).
% 1.58/1.77 tff(3840,plain,
% 1.58/1.77 (c1_1(a8)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[1718, 3817])).
% 1.58/1.77 tff(3841,plain,
% 1.58/1.77 (c1_1(a48)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[153, 3837])).
% 1.58/1.77 tff(3842,plain,
% 1.58/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a48) | c3_1(a48) | c2_1(a8) | c3_1(a8) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a8)) | (~c1_1(a48)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a48) | c3_1(a48) | c2_1(a8) | c3_1(a8) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a8)) | (~c1_1(a48)))),
% 1.58/1.77 inference(rewrite,[status(thm)],[])).
% 1.58/1.77 tff(3843,plain,
% 1.58/1.77 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48))) <=> (c0_1(a48) | c3_1(a48) | c2_1(a8) | c3_1(a8) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a8)) | (~c1_1(a48)))),
% 1.58/1.77 inference(rewrite,[status(thm)],[])).
% 1.58/1.77 tff(3844,plain,
% 1.58/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a48) | c3_1(a48) | c2_1(a8) | c3_1(a8) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a8)) | (~c1_1(a48))))),
% 1.58/1.77 inference(monotonicity,[status(thm)],[3843])).
% 1.58/1.77 tff(3845,plain,
% 1.58/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a48) | c3_1(a48) | c2_1(a8) | c3_1(a8) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a8)) | (~c1_1(a48)))),
% 1.58/1.77 inference(transitivity,[status(thm)],[3844, 3842])).
% 1.58/1.77 tff(3846,plain,
% 1.58/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c1_1(a2) | c3_1(a2) | (~c0_1(a2)) | c0_1(a48) | c3_1(a48) | (~c1_1(a48)))),
% 1.58/1.77 inference(quant_inst,[status(thm)],[])).
% 1.58/1.77 tff(3847,plain,
% 1.58/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a48) | c3_1(a48) | c2_1(a8) | c3_1(a8) | c1_1(a2) | (~ndr1_0) | (~c0_1(a2)) | c3_1(a2) | (~c1_1(a8)) | (~c1_1(a48))),
% 1.58/1.77 inference(modus_ponens,[status(thm)],[3846, 3845])).
% 1.58/1.77 tff(3848,plain,
% 1.58/1.77 ($false),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3847, 92, 3841, 3840, 2758, 3839, 3838, 3819, 3818, 2620, 11, 1])).
% 1.58/1.77 tff(3849,plain,(c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.77 tff(3850,plain,
% 1.58/1.77 (hskp4),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3781, 274])).
% 1.58/1.77 tff(3851,plain,
% 1.58/1.77 (~c3_1(a7)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[1451, 3850])).
% 1.58/1.77 tff(3852,plain,
% 1.58/1.77 (~c1_1(a7)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[1791, 3850])).
% 1.58/1.77 tff(3853,plain,
% 1.58/1.77 (c2_1(a7)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[290, 92, 3776, 274, 3852, 3851, 284])).
% 1.58/1.77 tff(3854,plain,
% 1.58/1.77 (~c0_1(a7)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[2387, 3850])).
% 1.58/1.77 tff(3855,plain,
% 1.58/1.77 (hskp21 | hskp11),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[1474, 3776])).
% 1.58/1.77 tff(3856,plain,
% 1.58/1.77 (hskp21),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3855, 274])).
% 1.58/1.77 tff(3857,plain,
% 1.58/1.77 (~c0_1(a47)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[777, 3856])).
% 1.58/1.77 tff(3858,plain,
% 1.58/1.77 (c3_1(a47)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[785, 3856])).
% 1.58/1.77 tff(3859,plain,
% 1.58/1.77 (~c1_1(a47)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3581, 92, 3858, 2758, 3857, 3854, 3852, 2626, 567, 3849, 3853])).
% 1.58/1.77 tff(3860,plain,
% 1.58/1.77 (c2_1(a47)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[793, 3856])).
% 1.58/1.77 tff(3861,plain,
% 1.58/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))),
% 1.58/1.77 inference(rewrite,[status(thm)],[])).
% 1.58/1.77 tff(3862,plain,
% 1.58/1.77 (((~ndr1_0) | c3_1(a7) | c1_1(a7) | (~c2_1(a7)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47))) <=> (c0_1(a47) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))),
% 1.58/1.77 inference(rewrite,[status(thm)],[])).
% 1.58/1.77 tff(3863,plain,
% 1.58/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a7) | c1_1(a7) | (~c2_1(a7)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a47) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47))))),
% 1.58/1.77 inference(monotonicity,[status(thm)],[3862])).
% 1.58/1.77 tff(3864,plain,
% 1.58/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a7) | c1_1(a7) | (~c2_1(a7)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47)))),
% 1.58/1.77 inference(transitivity,[status(thm)],[3863, 3861])).
% 1.58/1.77 tff(3865,plain,
% 1.58/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a7) | c1_1(a7) | (~c2_1(a7)) | c0_1(a47) | (~c2_1(a47)) | (~c3_1(a47)) | c1_1(a47) | c0_1(a47) | (~c3_1(a47)))),
% 1.58/1.77 inference(quant_inst,[status(thm)],[])).
% 1.58/1.77 tff(3866,plain,
% 1.58/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a47) | c1_1(a7) | c3_1(a7) | (~ndr1_0) | (~c2_1(a7)) | (~c3_1(a47)) | c1_1(a47) | (~c2_1(a47))),
% 1.58/1.77 inference(modus_ponens,[status(thm)],[3865, 3864])).
% 1.58/1.77 tff(3867,plain,
% 1.58/1.77 ($false),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3866, 92, 3860, 3858, 3857, 3852, 3851, 1073, 3853, 3859])).
% 1.58/1.77 tff(3868,plain,(hskp11), inference(lemma,lemma(discharge,[]))).
% 1.58/1.77 tff(3869,plain,
% 1.58/1.77 (~c0_1(a19)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[98, 3868])).
% 1.58/1.77 tff(3870,plain,
% 1.58/1.77 (c2_1(a19)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[115, 3868])).
% 1.58/1.77 tff(3871,plain,
% 1.58/1.77 (c1_1(a19)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[107, 3868])).
% 1.58/1.77 tff(3872,plain,
% 1.58/1.77 (~hskp16),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3621, 3849])).
% 1.58/1.77 tff(3873,plain,
% 1.58/1.77 (hskp26),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3628, 92, 3872, 3871, 3870, 3869, 2998])).
% 1.58/1.77 tff(3874,plain,
% 1.58/1.77 (c3_1(a4)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[2656, 3873])).
% 1.58/1.77 tff(3875,plain,
% 1.58/1.77 (c1_1(a4)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[2664, 3873])).
% 1.58/1.77 tff(3876,plain,
% 1.58/1.77 (c0_1(a4)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[2672, 3873])).
% 1.58/1.77 tff(3877,plain,
% 1.58/1.77 (c3_1(a5)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3680, 92, 3876, 3875, 3874, 3804, 2758, 3802, 2626, 322, 3849])).
% 1.58/1.77 tff(3878,plain,
% 1.58/1.77 (~c3_1(a19)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[3439, 92, 3871, 3804, 2758, 3869, 3803, 3802, 2626, 567, 3849])).
% 1.58/1.77 tff(3879,plain,
% 1.58/1.77 (~c1_1(a73)),
% 1.58/1.77 inference(unit_resolution,[status(thm)],[2937, 3874, 3870, 3869, 3871, 3878, 3875, 3876])).
% 1.58/1.78 tff(3880,plain,
% 1.58/1.78 (hskp13),
% 1.58/1.78 inference(unit_resolution,[status(thm)],[2895, 92, 3876, 3875, 3874, 3871, 3869, 1833, 3878])).
% 1.58/1.78 tff(3881,plain,
% 1.58/1.78 (~c1_1(a22)),
% 1.58/1.78 inference(unit_resolution,[status(thm)],[1846, 3880])).
% 1.58/1.78 tff(3882,plain,
% 1.58/1.78 (~c0_1(a22)),
% 1.58/1.78 inference(unit_resolution,[status(thm)],[1852, 3880])).
% 1.58/1.78 tff(3883,plain,
% 1.58/1.78 (hskp25),
% 1.58/1.78 inference(unit_resolution,[status(thm)],[2853, 92, 3876, 3875, 3874, 1555])).
% 1.58/1.78 tff(3884,plain,
% 1.58/1.78 (~c3_1(a73)),
% 1.58/1.78 inference(unit_resolution,[status(thm)],[1138, 3883])).
% 1.58/1.78 tff(3885,plain,
% 1.58/1.78 (c3_1(a22)),
% 1.58/1.78 inference(unit_resolution,[status(thm)],[1894, 3880])).
% 1.58/1.78 tff(3886,plain,
% 1.58/1.78 (c2_1(a73)),
% 1.58/1.78 inference(unit_resolution,[status(thm)],[1187, 3883])).
% 1.58/1.78 tff(3887,plain,
% 1.58/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a73) | c0_1(a22) | c1_1(a22) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a22)) | c1_1(a73) | (~c2_1(a73)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a73) | c0_1(a22) | c1_1(a22) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a22)) | c1_1(a73) | (~c2_1(a73)))),
% 1.58/1.78 inference(rewrite,[status(thm)],[])).
% 1.58/1.78 tff(3888,plain,
% 1.58/1.78 (((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22))) <=> (c3_1(a73) | c0_1(a22) | c1_1(a22) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a22)) | c1_1(a73) | (~c2_1(a73)))),
% 1.58/1.78 inference(rewrite,[status(thm)],[])).
% 1.58/1.78 tff(3889,plain,
% 1.58/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a73) | c0_1(a22) | c1_1(a22) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a22)) | c1_1(a73) | (~c2_1(a73))))),
% 1.58/1.78 inference(monotonicity,[status(thm)],[3888])).
% 1.58/1.78 tff(3890,plain,
% 1.58/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a73) | c0_1(a22) | c1_1(a22) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a22)) | c1_1(a73) | (~c2_1(a73)))),
% 1.58/1.78 inference(transitivity,[status(thm)],[3889, 3887])).
% 1.58/1.78 tff(3891,plain,
% 1.58/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a73) | c1_1(a73) | (~c2_1(a73)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a22) | c0_1(a22) | (~c3_1(a22)))),
% 1.58/1.78 inference(quant_inst,[status(thm)],[])).
% 1.58/1.78 tff(3892,plain,
% 1.58/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a73) | c0_1(a22) | c1_1(a22) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a22)) | c1_1(a73) | (~c2_1(a73))),
% 1.58/1.78 inference(modus_ponens,[status(thm)],[3891, 3890])).
% 1.58/1.78 tff(3893,plain,
% 1.58/1.78 ($false),
% 1.58/1.78 inference(unit_resolution,[status(thm)],[3892, 92, 3886, 3885, 3804, 3884, 3882, 3881, 3803, 1073, 3879, 3877])).
% 1.58/1.78 % SZS output end Proof
% 1.58/1.78 % E exiting
%------------------------------------------------------------------------------