%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN483-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:39:17 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.71s
% Output : Proof 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SYN483-1 : TPTP v9.0.0. Released v2.1.0.
% 0.09/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n011.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % 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 12:36:57 EDT 2025
% 0.16/0.32 % CPUTime :
% 0.48/0.71 % SZS status Unsatisfiable
% 0.48/0.71 % SZS output start Proof
% 0.48/0.71 tff(c3_1_type, type, (
% 0.48/0.71 c3_1: $i > $o)).
% 0.48/0.71 tff(a1862_type, type, (
% 0.48/0.71 a1862: $i)).
% 0.48/0.71 tff(c2_1_type, type, (
% 0.48/0.71 c2_1: $i > $o)).
% 0.48/0.71 tff(c0_1_type, type, (
% 0.48/0.71 c0_1: $i > $o)).
% 0.48/0.71 tff(c1_1_type, type, (
% 0.48/0.71 c1_1: $i > $o)).
% 0.48/0.71 tff(ndr1_0_type, type, (
% 0.48/0.71 ndr1_0: $o)).
% 0.48/0.71 tff(hskp8_type, type, (
% 0.48/0.71 hskp8: $o)).
% 0.48/0.71 tff(hskp9_type, type, (
% 0.48/0.71 hskp9: $o)).
% 0.48/0.71 tff(a1890_type, type, (
% 0.48/0.71 a1890: $i)).
% 0.48/0.71 tff(hskp20_type, type, (
% 0.48/0.71 hskp20: $o)).
% 0.48/0.71 tff(a1864_type, type, (
% 0.48/0.71 a1864: $i)).
% 0.48/0.71 tff(hskp24_type, type, (
% 0.48/0.71 hskp24: $o)).
% 0.48/0.71 tff(a1919_type, type, (
% 0.48/0.71 a1919: $i)).
% 0.48/0.71 tff(a1853_type, type, (
% 0.48/0.71 a1853: $i)).
% 0.48/0.71 tff(hskp1_type, type, (
% 0.48/0.71 hskp1: $o)).
% 0.48/0.71 tff(a1877_type, type, (
% 0.48/0.71 a1877: $i)).
% 0.48/0.71 tff(a1852_type, type, (
% 0.48/0.71 a1852: $i)).
% 0.48/0.71 tff(hskp0_type, type, (
% 0.48/0.71 hskp0: $o)).
% 0.48/0.71 tff(a1858_type, type, (
% 0.48/0.71 a1858: $i)).
% 0.48/0.71 tff(hskp26_type, type, (
% 0.48/0.71 hskp26: $o)).
% 0.48/0.71 tff(hskp23_type, type, (
% 0.48/0.71 hskp23: $o)).
% 0.48/0.71 tff(a1878_type, type, (
% 0.48/0.71 a1878: $i)).
% 0.48/0.71 tff(hskp28_type, type, (
% 0.48/0.71 hskp28: $o)).
% 0.48/0.71 tff(hskp27_type, type, (
% 0.48/0.71 hskp27: $o)).
% 0.48/0.71 tff(hskp29_type, type, (
% 0.48/0.71 hskp29: $o)).
% 0.48/0.71 tff(a1885_type, type, (
% 0.48/0.71 a1885: $i)).
% 0.48/0.71 tff(a1911_type, type, (
% 0.48/0.71 a1911: $i)).
% 0.48/0.71 tff(a1899_type, type, (
% 0.48/0.71 a1899: $i)).
% 0.48/0.71 tff(hskp22_type, type, (
% 0.48/0.71 hskp22: $o)).
% 0.48/0.71 tff(hskp3_type, type, (
% 0.48/0.71 hskp3: $o)).
% 0.48/0.71 tff(a1855_type, type, (
% 0.48/0.71 a1855: $i)).
% 0.48/0.71 tff(a1872_type, type, (
% 0.48/0.71 a1872: $i)).
% 0.48/0.71 tff(hskp16_type, type, (
% 0.48/0.71 hskp16: $o)).
% 0.48/0.71 tff(hskp10_type, type, (
% 0.48/0.71 hskp10: $o)).
% 0.48/0.71 tff(hskp13_type, type, (
% 0.48/0.71 hskp13: $o)).
% 0.48/0.71 tff(a1898_type, type, (
% 0.48/0.71 a1898: $i)).
% 0.48/0.71 tff(hskp21_type, type, (
% 0.48/0.71 hskp21: $o)).
% 0.48/0.71 tff(a1875_type, type, (
% 0.48/0.71 a1875: $i)).
% 0.48/0.71 tff(a1867_type, type, (
% 0.48/0.71 a1867: $i)).
% 0.48/0.71 tff(a1863_type, type, (
% 0.48/0.71 a1863: $i)).
% 0.48/0.71 tff(a1866_type, type, (
% 0.48/0.71 a1866: $i)).
% 0.48/0.71 tff(hskp12_type, type, (
% 0.48/0.71 hskp12: $o)).
% 0.48/0.71 tff(hskp18_type, type, (
% 0.48/0.71 hskp18: $o)).
% 0.48/0.71 tff(a1874_type, type, (
% 0.48/0.71 a1874: $i)).
% 0.48/0.71 tff(hskp17_type, type, (
% 0.48/0.71 hskp17: $o)).
% 0.48/0.71 tff(a1870_type, type, (
% 0.48/0.71 a1870: $i)).
% 0.48/0.71 tff(hskp15_type, type, (
% 0.48/0.71 hskp15: $o)).
% 0.48/0.71 tff(1,plain,
% 0.48/0.71 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 0.48/0.71 inference(bind,[status(th)],[])).
% 0.48/0.71 tff(2,plain,
% 0.48/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_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) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.48/0.71 inference(quant_intro,[status(thm)],[1])).
% 0.48/0.71 tff(3,plain,
% 0.48/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_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) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(4,plain,
% 0.48/0.71 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 0.48/0.71 inference(bind,[status(th)],[])).
% 0.48/0.71 tff(5,plain,
% 0.48/0.71 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.48/0.71 inference(quant_intro,[status(thm)],[4])).
% 0.48/0.71 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.48/0.71 tff(7,plain,
% 0.48/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.48/0.71 tff(8,plain,
% 0.48/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.48/0.71 tff(9,plain,(
% 0.48/0.71 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.48/0.71 inference(skolemize,[status(sab)],[8])).
% 0.48/0.71 tff(10,plain,
% 0.48/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.48/0.71 tff(11,plain,
% 0.48/0.71 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.48/0.71 inference(bind,[status(th)],[])).
% 0.48/0.71 tff(12,plain,
% 0.48/0.71 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.48/0.71 inference(quant_intro,[status(thm)],[11])).
% 0.48/0.71 tff(13,plain,
% 0.48/0.71 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(14,plain,
% 0.48/0.71 (^[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)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.48/0.71 inference(bind,[status(th)],[])).
% 0.48/0.71 tff(15,plain,
% 0.48/0.71 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.48/0.71 inference(quant_intro,[status(thm)],[14])).
% 0.48/0.71 tff(16,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.48/0.71 tff(17,plain,
% 0.48/0.71 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.48/0.71 tff(18,plain,
% 0.48/0.71 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.48/0.71 tff(19,plain,(
% 0.48/0.71 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.48/0.71 inference(skolemize,[status(sab)],[18])).
% 0.48/0.71 tff(20,plain,
% 0.48/0.71 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.48/0.71 tff(21,assumption,(~hskp8), introduced(assumption)).
% 0.48/0.71 tff(22,plain,
% 0.48/0.71 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.48/0.71 inference(bind,[status(th)],[])).
% 0.48/0.71 tff(23,plain,
% 0.48/0.71 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.71 inference(quant_intro,[status(thm)],[22])).
% 0.48/0.71 tff(24,plain,
% 0.48/0.71 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(25,plain,
% 0.48/0.71 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.48/0.71 inference(bind,[status(th)],[])).
% 0.48/0.71 tff(26,plain,
% 0.48/0.71 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.71 inference(quant_intro,[status(thm)],[25])).
% 0.48/0.71 tff(27,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 0.48/0.71 tff(28,plain,
% 0.48/0.71 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.48/0.71 tff(29,plain,
% 0.48/0.71 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.48/0.71 tff(30,plain,(
% 0.48/0.71 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.71 inference(skolemize,[status(sab)],[29])).
% 0.48/0.71 tff(31,plain,
% 0.48/0.71 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.48/0.71 tff(32,assumption,(~hskp1), introduced(assumption)).
% 0.48/0.71 tff(33,plain,
% 0.48/0.71 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 0.48/0.71 inference(bind,[status(th)],[])).
% 0.48/0.71 tff(34,plain,
% 0.48/0.71 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.48/0.71 inference(quant_intro,[status(thm)],[33])).
% 0.48/0.71 tff(35,plain,
% 0.48/0.71 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(36,plain,
% 0.48/0.71 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 0.48/0.71 inference(bind,[status(th)],[])).
% 0.48/0.71 tff(37,plain,
% 0.48/0.71 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.48/0.71 inference(quant_intro,[status(thm)],[36])).
% 0.48/0.71 tff(38,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.48/0.71 tff(39,plain,
% 0.48/0.71 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.48/0.71 tff(40,plain,
% 0.48/0.71 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.48/0.71 tff(41,plain,(
% 0.48/0.71 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.48/0.71 inference(skolemize,[status(sab)],[40])).
% 0.48/0.71 tff(42,plain,
% 0.48/0.71 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.48/0.72 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.48/0.72 tff(43,assumption,(~hskp0), introduced(assumption)).
% 0.48/0.72 tff(44,plain,
% 0.48/0.72 (^[U: $i] : refl((hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.48/0.72 inference(bind,[status(th)],[])).
% 0.48/0.72 tff(45,plain,
% 0.48/0.72 (![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.48/0.72 inference(quant_intro,[status(thm)],[44])).
% 0.48/0.72 tff(46,plain,
% 0.48/0.72 (![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.48/0.72 inference(rewrite,[status(thm)],[])).
% 0.48/0.72 tff(47,plain,
% 0.48/0.72 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp24) <=> ((hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp24) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.48/0.72 inference(bind,[status(th)],[])).
% 0.48/0.72 tff(48,plain,
% 0.48/0.72 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp24) <=> ![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.48/0.72 inference(quant_intro,[status(thm)],[47])).
% 0.48/0.72 tff(49,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 0.48/0.72 tff(50,plain,
% 0.48/0.72 (![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.48/0.72 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.48/0.72 tff(51,plain,
% 0.48/0.72 (![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.48/0.72 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.48/0.72 tff(52,plain,(
% 0.48/0.72 ![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.48/0.72 inference(skolemize,[status(sab)],[51])).
% 0.57/0.72 tff(53,plain,
% 0.57/0.72 (![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.57/0.72 tff(54,plain,
% 0.57/0.72 (^[U: $i] : refl((hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 0.57/0.72 inference(bind,[status(th)],[])).
% 0.57/0.72 tff(55,plain,
% 0.57/0.72 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.72 inference(quant_intro,[status(thm)],[54])).
% 0.57/0.72 tff(56,plain,
% 0.57/0.72 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(57,plain,
% 0.57/0.72 (^[U: $i] : 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)) | hskp28) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) | hskp0) <=> ((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp0))), rewrite(((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) | hskp0) <=> (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.57/0.72 inference(bind,[status(th)],[])).
% 0.57/0.72 tff(58,plain,
% 0.57/0.72 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) | hskp0) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.72 inference(quant_intro,[status(thm)],[57])).
% 0.57/0.72 tff(59,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 0.57/0.72 tff(60,plain,
% 0.57/0.72 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.57/0.72 tff(61,plain,
% 0.57/0.72 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.57/0.72 tff(62,plain,(
% 0.57/0.72 ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.72 inference(skolemize,[status(sab)],[61])).
% 0.57/0.72 tff(63,plain,
% 0.57/0.72 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.57/0.72 tff(64,assumption,(~hskp24), introduced(assumption)).
% 0.57/0.72 tff(65,assumption,(hskp29), introduced(assumption)).
% 0.57/0.72 tff(66,plain,
% 0.57/0.72 (((~hskp29) | c2_1(a1885)) <=> ((~hskp29) | c2_1(a1885))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(67,axiom,((~hskp29) | c2_1(a1885)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.57/0.72 tff(68,plain,
% 0.57/0.72 ((~hskp29) | c2_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.57/0.72 tff(69,plain,
% 0.57/0.72 ((~hskp29) | c2_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[68, 66])).
% 0.57/0.72 tff(70,plain,
% 0.57/0.72 ((~hskp29) | c2_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.57/0.72 tff(71,plain,
% 0.57/0.72 ((~hskp29) | c2_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.57/0.72 tff(72,plain,
% 0.57/0.72 ((~hskp29) | c2_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[71, 66])).
% 0.57/0.72 tff(73,plain,
% 0.57/0.72 (c2_1(a1885)),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[72, 65])).
% 0.57/0.72 tff(74,plain,
% 0.57/0.72 (((~hskp29) | c1_1(a1885)) <=> ((~hskp29) | c1_1(a1885))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(75,axiom,((~hskp29) | c1_1(a1885)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.57/0.72 tff(76,plain,
% 0.57/0.72 ((~hskp29) | c1_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.57/0.72 tff(77,plain,
% 0.57/0.72 ((~hskp29) | c1_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[76, 74])).
% 0.57/0.72 tff(78,plain,
% 0.57/0.72 ((~hskp29) | c1_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[77, 74])).
% 0.57/0.72 tff(79,plain,
% 0.57/0.72 ((~hskp29) | c1_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.57/0.72 tff(80,plain,
% 0.57/0.72 ((~hskp29) | c1_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[79, 74])).
% 0.57/0.72 tff(81,plain,
% 0.57/0.72 (c1_1(a1885)),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[80, 65])).
% 0.57/0.72 tff(82,plain,
% 0.57/0.72 (((~hskp29) | c0_1(a1885)) <=> ((~hskp29) | c0_1(a1885))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(83,axiom,((~hskp29) | c0_1(a1885)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.57/0.72 tff(84,plain,
% 0.57/0.72 ((~hskp29) | c0_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.57/0.72 tff(85,plain,
% 0.57/0.72 ((~hskp29) | c0_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[84, 82])).
% 0.57/0.72 tff(86,plain,
% 0.57/0.72 ((~hskp29) | c0_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[85, 82])).
% 0.57/0.72 tff(87,plain,
% 0.57/0.72 ((~hskp29) | c0_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.57/0.72 tff(88,plain,
% 0.57/0.72 ((~hskp29) | c0_1(a1885)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[87, 82])).
% 0.57/0.72 tff(89,plain,
% 0.57/0.72 (c0_1(a1885)),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[88, 65])).
% 0.57/0.72 tff(90,assumption,(~ndr1_0), introduced(assumption)).
% 0.57/0.72 tff(91,plain,
% 0.57/0.72 ((ndr1_0 | (~hskp1)) <=> (ndr1_0 | (~hskp1))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(92,plain,
% 0.57/0.72 (((~hskp1) | ndr1_0) <=> (ndr1_0 | (~hskp1))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(93,axiom,((~hskp1) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause29')).
% 0.57/0.72 tff(94,plain,
% 0.57/0.72 (ndr1_0 | (~hskp1)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.57/0.72 tff(95,plain,
% 0.57/0.72 (ndr1_0 | (~hskp1)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[94, 91])).
% 0.57/0.72 tff(96,plain,
% 0.57/0.72 (~hskp1),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[95, 90])).
% 0.57/0.72 tff(97,plain,
% 0.57/0.72 (((~hskp29) | ndr1_0) <=> ((~hskp29) | ndr1_0)),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(98,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.57/0.72 tff(99,plain,
% 0.57/0.72 ((~hskp29) | ndr1_0),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.57/0.72 tff(100,plain,
% 0.57/0.72 ((~hskp29) | ndr1_0),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[99, 97])).
% 0.57/0.72 tff(101,plain,
% 0.57/0.72 ((~hskp29) | ndr1_0),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[100, 97])).
% 0.57/0.72 tff(102,plain,
% 0.57/0.72 ((~hskp29) | ndr1_0),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.57/0.72 tff(103,plain,
% 0.57/0.72 ((~hskp29) | ndr1_0),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[102, 97])).
% 0.57/0.72 tff(104,plain,
% 0.57/0.72 (~hskp29),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[103, 90])).
% 0.57/0.72 tff(105,plain,
% 0.57/0.72 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(106,plain,
% 0.57/0.72 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(107,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.57/0.72 tff(108,plain,
% 0.57/0.72 (ndr1_0 | (~hskp27)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.57/0.72 tff(109,plain,
% 0.57/0.72 (ndr1_0 | (~hskp27)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[108, 105])).
% 0.57/0.72 tff(110,plain,
% 0.57/0.72 (~hskp27),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[109, 90])).
% 0.57/0.72 tff(111,plain,
% 0.57/0.72 ((hskp29 | hskp27 | hskp1) <=> (hskp29 | hskp27 | hskp1)),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(112,plain,
% 0.57/0.72 (((hskp29 | hskp27) | hskp1) <=> (hskp29 | hskp27 | hskp1)),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(113,plain,
% 0.57/0.72 ((hskp29 | hskp27) <=> (hskp29 | hskp27)),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(114,plain,
% 0.57/0.72 (((hskp29 | hskp27) | hskp1) <=> ((hskp29 | hskp27) | hskp1)),
% 0.57/0.72 inference(monotonicity,[status(thm)],[113])).
% 0.57/0.72 tff(115,plain,
% 0.57/0.72 (((hskp29 | hskp27) | hskp1) <=> (hskp29 | hskp27 | hskp1)),
% 0.57/0.72 inference(transitivity,[status(thm)],[114, 112])).
% 0.57/0.72 tff(116,axiom,((hskp29 | hskp27) | hskp1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause31')).
% 0.57/0.72 tff(117,plain,
% 0.57/0.72 (hskp29 | hskp27 | hskp1),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.57/0.72 tff(118,plain,
% 0.57/0.72 (hskp29 | hskp27 | hskp1),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[117, 111])).
% 0.57/0.72 tff(119,plain,
% 0.57/0.72 (hskp29 | hskp27 | hskp1),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.57/0.72 tff(120,plain,
% 0.57/0.72 (hskp29 | hskp27 | hskp1),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[119, 111])).
% 0.57/0.72 tff(121,plain,
% 0.57/0.72 (hskp29 | hskp27 | hskp1),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[120, 111])).
% 0.57/0.72 tff(122,plain,
% 0.57/0.72 ($false),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[121, 110, 104, 32])).
% 0.57/0.72 tff(123,plain,(ndr1_0 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.57/0.72 tff(124,plain,
% 0.57/0.72 ($false),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[123, 96, 90])).
% 0.57/0.72 tff(125,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.57/0.72 tff(126,plain,
% 0.57/0.72 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(127,plain,
% 0.57/0.72 ((hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885))) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(128,plain,
% 0.57/0.72 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885))))),
% 0.57/0.72 inference(monotonicity,[status(thm)],[127])).
% 0.57/0.72 tff(129,plain,
% 0.57/0.72 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)))),
% 0.57/0.72 inference(transitivity,[status(thm)],[128, 126])).
% 0.57/0.72 tff(130,plain,
% 0.57/0.72 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)))),
% 0.57/0.72 inference(quant_inst,[status(thm)],[])).
% 0.57/0.72 tff(131,plain,
% 0.57/0.72 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885))),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.57/0.72 tff(132,plain,
% 0.57/0.72 ($false),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[131, 125, 64, 43, 89, 81, 73, 53])).
% 0.57/0.72 tff(133,plain,((~hskp29) | hskp24 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.57/0.72 tff(134,plain,
% 0.57/0.72 (~hskp29),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[133, 64, 43])).
% 0.57/0.72 tff(135,plain,
% 0.57/0.72 (hskp27),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[121, 134, 32])).
% 0.57/0.72 tff(136,plain,
% 0.57/0.72 (((~hskp27) | c3_1(a1877)) <=> ((~hskp27) | c3_1(a1877))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(137,axiom,((~hskp27) | c3_1(a1877)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.57/0.72 tff(138,plain,
% 0.57/0.72 ((~hskp27) | c3_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.57/0.72 tff(139,plain,
% 0.57/0.72 ((~hskp27) | c3_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[138, 136])).
% 0.57/0.72 tff(140,plain,
% 0.57/0.72 ((~hskp27) | c3_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[139, 136])).
% 0.57/0.72 tff(141,plain,
% 0.57/0.72 ((~hskp27) | c3_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.57/0.72 tff(142,plain,
% 0.57/0.72 ((~hskp27) | c3_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[141, 136])).
% 0.57/0.72 tff(143,plain,
% 0.57/0.72 (c3_1(a1877)),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[142, 135])).
% 0.57/0.72 tff(144,plain,
% 0.57/0.72 (((~hskp27) | c2_1(a1877)) <=> ((~hskp27) | c2_1(a1877))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(145,axiom,((~hskp27) | c2_1(a1877)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.57/0.72 tff(146,plain,
% 0.57/0.72 ((~hskp27) | c2_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.57/0.72 tff(147,plain,
% 0.57/0.72 ((~hskp27) | c2_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[146, 144])).
% 0.57/0.72 tff(148,plain,
% 0.57/0.72 ((~hskp27) | c2_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[147, 144])).
% 0.57/0.72 tff(149,plain,
% 0.57/0.72 ((~hskp27) | c2_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.57/0.72 tff(150,plain,
% 0.57/0.72 ((~hskp27) | c2_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[149, 144])).
% 0.57/0.72 tff(151,plain,
% 0.57/0.72 (c2_1(a1877)),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[150, 135])).
% 0.57/0.72 tff(152,plain,
% 0.57/0.72 (((~hskp27) | c0_1(a1877)) <=> ((~hskp27) | c0_1(a1877))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(153,axiom,((~hskp27) | c0_1(a1877)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.57/0.72 tff(154,plain,
% 0.57/0.72 ((~hskp27) | c0_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.57/0.72 tff(155,plain,
% 0.57/0.72 ((~hskp27) | c0_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[154, 152])).
% 0.57/0.72 tff(156,plain,
% 0.57/0.72 ((~hskp27) | c0_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[155, 152])).
% 0.57/0.72 tff(157,plain,
% 0.57/0.72 ((~hskp27) | c0_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.57/0.72 tff(158,plain,
% 0.57/0.72 ((~hskp27) | c0_1(a1877)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[157, 152])).
% 0.57/0.72 tff(159,plain,
% 0.57/0.72 (c0_1(a1877)),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[158, 135])).
% 0.57/0.72 tff(160,plain,
% 0.57/0.72 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(161,plain,
% 0.57/0.72 ((hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877))) <=> (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(162,plain,
% 0.57/0.72 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.57/0.72 inference(monotonicity,[status(thm)],[161])).
% 0.57/0.72 tff(163,plain,
% 0.57/0.72 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.57/0.72 inference(transitivity,[status(thm)],[162, 160])).
% 0.57/0.72 tff(164,plain,
% 0.57/0.72 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)))),
% 0.57/0.72 inference(quant_inst,[status(thm)],[])).
% 0.57/0.72 tff(165,plain,
% 0.57/0.72 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.57/0.72 tff(166,plain,
% 0.57/0.72 (hskp28),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[165, 125, 43, 159, 151, 143, 63])).
% 0.57/0.72 tff(167,plain,
% 0.57/0.72 (((~hskp28) | c2_1(a1878)) <=> ((~hskp28) | c2_1(a1878))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(168,axiom,((~hskp28) | c2_1(a1878)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.57/0.72 tff(169,plain,
% 0.57/0.72 ((~hskp28) | c2_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.57/0.72 tff(170,plain,
% 0.57/0.72 ((~hskp28) | c2_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[169, 167])).
% 0.57/0.72 tff(171,plain,
% 0.57/0.72 ((~hskp28) | c2_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[170, 167])).
% 0.57/0.72 tff(172,plain,
% 0.57/0.72 ((~hskp28) | c2_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.57/0.72 tff(173,plain,
% 0.57/0.72 ((~hskp28) | c2_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[172, 167])).
% 0.57/0.72 tff(174,plain,
% 0.57/0.72 (c2_1(a1878)),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[173, 166])).
% 0.57/0.72 tff(175,plain,
% 0.57/0.72 (((~hskp28) | c1_1(a1878)) <=> ((~hskp28) | c1_1(a1878))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(176,axiom,((~hskp28) | c1_1(a1878)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.57/0.72 tff(177,plain,
% 0.57/0.72 ((~hskp28) | c1_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.57/0.72 tff(178,plain,
% 0.57/0.72 ((~hskp28) | c1_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[177, 175])).
% 0.57/0.72 tff(179,plain,
% 0.57/0.72 ((~hskp28) | c1_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[178, 175])).
% 0.57/0.72 tff(180,plain,
% 0.57/0.72 ((~hskp28) | c1_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.57/0.72 tff(181,plain,
% 0.57/0.72 ((~hskp28) | c1_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[180, 175])).
% 0.57/0.72 tff(182,plain,
% 0.57/0.72 (c1_1(a1878)),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[181, 166])).
% 0.57/0.72 tff(183,plain,
% 0.57/0.72 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(184,plain,
% 0.57/0.72 ((hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878))) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(185,plain,
% 0.57/0.72 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878))))),
% 0.57/0.72 inference(monotonicity,[status(thm)],[184])).
% 0.57/0.72 tff(186,plain,
% 0.57/0.72 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.57/0.72 inference(transitivity,[status(thm)],[185, 183])).
% 0.57/0.72 tff(187,plain,
% 0.57/0.72 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878)))),
% 0.57/0.72 inference(quant_inst,[status(thm)],[])).
% 0.57/0.72 tff(188,plain,
% 0.57/0.72 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878))),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.57/0.72 tff(189,plain,
% 0.57/0.72 (~c0_1(a1878)),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[188, 125, 64, 43, 182, 174, 53])).
% 0.57/0.72 tff(190,plain,
% 0.57/0.72 (((~hskp28) | c3_1(a1878)) <=> ((~hskp28) | c3_1(a1878))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(191,axiom,((~hskp28) | c3_1(a1878)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.57/0.72 tff(192,plain,
% 0.57/0.72 ((~hskp28) | c3_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.57/0.72 tff(193,plain,
% 0.57/0.72 ((~hskp28) | c3_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[192, 190])).
% 0.57/0.72 tff(194,plain,
% 0.57/0.72 ((~hskp28) | c3_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[193, 190])).
% 0.57/0.72 tff(195,plain,
% 0.57/0.72 ((~hskp28) | c3_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.57/0.72 tff(196,plain,
% 0.57/0.72 ((~hskp28) | c3_1(a1878)),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[195, 190])).
% 0.57/0.72 tff(197,plain,
% 0.57/0.72 (c3_1(a1878)),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[196, 166])).
% 0.57/0.72 tff(198,assumption,(~c0_1(a1878)), introduced(assumption)).
% 0.57/0.72 tff(199,plain,
% 0.57/0.72 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_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)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 0.57/0.72 inference(bind,[status(th)],[])).
% 0.57/0.72 tff(200,plain,
% 0.57/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.57/0.72 inference(quant_intro,[status(thm)],[199])).
% 0.57/0.72 tff(201,plain,
% 0.57/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(202,plain,
% 0.57/0.72 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | 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(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_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)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | 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)) | (~c1_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)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 0.57/0.72 inference(bind,[status(th)],[])).
% 0.57/0.72 tff(203,plain,
% 0.57/0.72 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.57/0.72 inference(quant_intro,[status(thm)],[202])).
% 0.57/0.72 tff(204,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.57/0.72 tff(205,plain,
% 0.57/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.57/0.72 tff(206,plain,
% 0.57/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.57/0.72 tff(207,plain,(
% 0.57/0.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.57/0.72 inference(skolemize,[status(sab)],[206])).
% 0.57/0.72 tff(208,plain,
% 0.57/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.57/0.72 tff(209,assumption,(hskp23), introduced(assumption)).
% 0.57/0.72 tff(210,plain,
% 0.57/0.72 (((~hskp23) | (~c3_1(a1911))) <=> ((~hskp23) | (~c3_1(a1911)))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(211,plain,
% 0.57/0.72 (((~c3_1(a1911)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1911)))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(212,axiom,((~c3_1(a1911)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.57/0.72 tff(213,plain,
% 0.57/0.72 ((~hskp23) | (~c3_1(a1911))),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.57/0.72 tff(214,plain,
% 0.57/0.72 ((~hskp23) | (~c3_1(a1911))),
% 0.57/0.72 inference(modus_ponens,[status(thm)],[213, 210])).
% 0.57/0.72 tff(215,plain,
% 0.57/0.72 (~c3_1(a1911)),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[214, 209])).
% 0.57/0.72 tff(216,plain,
% 0.57/0.72 (((~hskp23) | (~c1_1(a1911))) <=> ((~hskp23) | (~c1_1(a1911)))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(217,plain,
% 0.57/0.72 (((~c1_1(a1911)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a1911)))),
% 0.57/0.72 inference(rewrite,[status(thm)],[])).
% 0.57/0.72 tff(218,axiom,((~c1_1(a1911)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.57/0.73 tff(219,plain,
% 0.57/0.73 ((~hskp23) | (~c1_1(a1911))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.57/0.73 tff(220,plain,
% 0.57/0.73 ((~hskp23) | (~c1_1(a1911))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[219, 216])).
% 0.57/0.73 tff(221,plain,
% 0.57/0.73 (~c1_1(a1911)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[220, 209])).
% 0.57/0.73 tff(222,plain,
% 0.57/0.73 (((~hskp23) | c0_1(a1911)) <=> ((~hskp23) | c0_1(a1911))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(223,axiom,((~hskp23) | c0_1(a1911)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.57/0.73 tff(224,plain,
% 0.57/0.73 ((~hskp23) | c0_1(a1911)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.57/0.73 tff(225,plain,
% 0.57/0.73 ((~hskp23) | c0_1(a1911)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[224, 222])).
% 0.57/0.73 tff(226,plain,
% 0.57/0.73 ((~hskp23) | c0_1(a1911)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[225, 222])).
% 0.57/0.73 tff(227,plain,
% 0.57/0.73 ((~hskp23) | c0_1(a1911)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.57/0.73 tff(228,plain,
% 0.57/0.73 ((~hskp23) | c0_1(a1911)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[227, 222])).
% 0.57/0.73 tff(229,plain,
% 0.57/0.73 (c0_1(a1911)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[228, 209])).
% 0.57/0.73 tff(230,assumption,(c3_1(a1878)), introduced(assumption)).
% 0.57/0.73 tff(231,assumption,(c1_1(a1878)), introduced(assumption)).
% 0.57/0.73 tff(232,plain,
% 0.57/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c0_1(a1911)) | (~c2_1(a1911)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(233,plain,
% 0.57/0.73 (((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1911) | c1_1(a1911) | (~c2_1(a1911)) | c0_1(a1878) | (~c3_1(a1878)) | (~c1_1(a1878))) <=> (c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(234,plain,
% 0.57/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1911) | c1_1(a1911) | (~c2_1(a1911)) | c0_1(a1878) | (~c3_1(a1878)) | (~c1_1(a1878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c0_1(a1911)) | (~c2_1(a1911))))),
% 0.57/0.73 inference(monotonicity,[status(thm)],[233])).
% 0.57/0.73 tff(235,plain,
% 0.57/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1911) | c1_1(a1911) | (~c2_1(a1911)) | c0_1(a1878) | (~c3_1(a1878)) | (~c1_1(a1878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.57/0.73 inference(transitivity,[status(thm)],[234, 232])).
% 0.57/0.73 tff(236,plain,
% 0.57/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1911) | c1_1(a1911) | (~c2_1(a1911)) | c0_1(a1878) | (~c3_1(a1878)) | (~c1_1(a1878)))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(237,plain,
% 0.57/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c0_1(a1911)) | (~c2_1(a1911))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.57/0.73 tff(238,plain,
% 0.57/0.73 (~c2_1(a1911)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[237, 125, 231, 230, 229, 221, 215, 208, 198])).
% 0.57/0.73 tff(239,plain,
% 0.57/0.73 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.57/0.73 inference(bind,[status(th)],[])).
% 0.57/0.73 tff(240,plain,
% 0.57/0.73 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.57/0.73 inference(quant_intro,[status(thm)],[239])).
% 0.57/0.73 tff(241,plain,
% 0.57/0.73 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(242,plain,
% 0.57/0.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp24) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp24))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.57/0.73 inference(bind,[status(th)],[])).
% 0.57/0.73 tff(243,plain,
% 0.57/0.73 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.57/0.73 inference(quant_intro,[status(thm)],[242])).
% 0.57/0.73 tff(244,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.57/0.73 tff(245,plain,
% 0.57/0.73 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.57/0.73 tff(246,plain,
% 0.57/0.73 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[245, 241])).
% 0.57/0.73 tff(247,plain,(
% 0.57/0.73 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.57/0.73 inference(skolemize,[status(sab)],[246])).
% 0.57/0.73 tff(248,plain,
% 0.57/0.73 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[247, 240])).
% 0.57/0.73 tff(249,assumption,(c3_1(a1877)), introduced(assumption)).
% 0.57/0.73 tff(250,assumption,(c2_1(a1877)), introduced(assumption)).
% 0.57/0.73 tff(251,assumption,(c0_1(a1877)), introduced(assumption)).
% 0.57/0.73 tff(252,plain,
% 0.57/0.73 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c3_1(a1911) | (~ndr1_0) | (~c0_1(a1911)) | c2_1(a1911) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1911) | (~ndr1_0) | (~c0_1(a1911)) | c2_1(a1911) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(253,plain,
% 0.57/0.73 ((hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1911) | c2_1(a1911) | (~c0_1(a1911))) <=> (hskp24 | c3_1(a1911) | (~ndr1_0) | (~c0_1(a1911)) | c2_1(a1911) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(254,plain,
% 0.57/0.73 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1911) | c2_1(a1911) | (~c0_1(a1911)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c3_1(a1911) | (~ndr1_0) | (~c0_1(a1911)) | c2_1(a1911) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.57/0.73 inference(monotonicity,[status(thm)],[253])).
% 0.57/0.73 tff(255,plain,
% 0.57/0.73 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1911) | c2_1(a1911) | (~c0_1(a1911)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1911) | (~ndr1_0) | (~c0_1(a1911)) | c2_1(a1911) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.57/0.73 inference(transitivity,[status(thm)],[254, 252])).
% 0.57/0.73 tff(256,plain,
% 0.57/0.73 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1911) | c2_1(a1911) | (~c0_1(a1911)))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(257,plain,
% 0.57/0.73 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1911) | (~ndr1_0) | (~c0_1(a1911)) | c2_1(a1911) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.57/0.73 tff(258,plain,
% 0.57/0.73 ($false),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[257, 125, 64, 251, 250, 249, 229, 215, 248, 238])).
% 0.57/0.73 tff(259,plain,((~hskp23) | hskp24 | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1878)) | (~c3_1(a1878)) | c0_1(a1878)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.73 tff(260,plain,
% 0.57/0.73 (~hskp23),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[259, 64, 159, 151, 143, 182, 197, 189])).
% 0.57/0.73 tff(261,plain,
% 0.57/0.73 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(262,plain,
% 0.57/0.73 ((hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877))) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(263,plain,
% 0.57/0.73 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))))),
% 0.57/0.73 inference(monotonicity,[status(thm)],[262])).
% 0.57/0.73 tff(264,plain,
% 0.57/0.73 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.57/0.73 inference(transitivity,[status(thm)],[263, 261])).
% 0.57/0.73 tff(265,plain,
% 0.57/0.73 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877)))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(266,plain,
% 0.57/0.73 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.57/0.73 tff(267,plain,
% 0.57/0.73 (~c1_1(a1877)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[266, 125, 64, 43, 159, 151, 53])).
% 0.57/0.73 tff(268,plain,
% 0.57/0.73 (^[U: $i] : refl((hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.57/0.73 inference(bind,[status(th)],[])).
% 0.57/0.73 tff(269,plain,
% 0.57/0.73 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.73 inference(quant_intro,[status(thm)],[268])).
% 0.57/0.73 tff(270,plain,
% 0.57/0.73 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(271,plain,
% 0.57/0.73 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23) <=> ((hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23) <=> (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.57/0.73 inference(bind,[status(th)],[])).
% 0.57/0.73 tff(272,plain,
% 0.57/0.73 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23) <=> ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.73 inference(quant_intro,[status(thm)],[271])).
% 0.57/0.73 tff(273,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 0.57/0.73 tff(274,plain,
% 0.57/0.73 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.57/0.73 tff(275,plain,
% 0.57/0.73 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.57/0.73 tff(276,plain,(
% 0.57/0.73 ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.73 inference(skolemize,[status(sab)],[275])).
% 0.57/0.73 tff(277,plain,
% 0.57/0.73 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[276, 269])).
% 0.57/0.73 tff(278,plain,
% 0.57/0.73 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(279,plain,
% 0.57/0.73 ((hskp26 | hskp23 | (~ndr1_0) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877))) <=> (hskp26 | hskp23 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(280,plain,
% 0.57/0.73 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877)))),
% 0.57/0.73 inference(monotonicity,[status(thm)],[279])).
% 0.57/0.73 tff(281,plain,
% 0.57/0.73 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.57/0.73 inference(transitivity,[status(thm)],[280, 278])).
% 0.57/0.73 tff(282,plain,
% 0.57/0.73 ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(283,plain,
% 0.57/0.73 ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.57/0.73 tff(284,plain,
% 0.57/0.73 (hskp26 | hskp23),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[283, 125, 159, 143, 277, 267])).
% 0.57/0.73 tff(285,plain,
% 0.57/0.73 (hskp26),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[284, 260])).
% 0.57/0.73 tff(286,plain,
% 0.57/0.73 (((~hskp26) | c1_1(a1858)) <=> ((~hskp26) | c1_1(a1858))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(287,axiom,((~hskp26) | c1_1(a1858)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.57/0.73 tff(288,plain,
% 0.57/0.73 ((~hskp26) | c1_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.57/0.73 tff(289,plain,
% 0.57/0.73 ((~hskp26) | c1_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[288, 286])).
% 0.57/0.73 tff(290,plain,
% 0.57/0.73 ((~hskp26) | c1_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[289, 286])).
% 0.57/0.73 tff(291,plain,
% 0.57/0.73 ((~hskp26) | c1_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[290, 286])).
% 0.57/0.73 tff(292,plain,
% 0.57/0.73 ((~hskp26) | c1_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[291, 286])).
% 0.57/0.73 tff(293,plain,
% 0.57/0.73 (c1_1(a1858)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[292, 285])).
% 0.57/0.73 tff(294,plain,
% 0.57/0.73 (((~hskp26) | c0_1(a1858)) <=> ((~hskp26) | c0_1(a1858))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(295,axiom,((~hskp26) | c0_1(a1858)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.57/0.73 tff(296,plain,
% 0.57/0.73 ((~hskp26) | c0_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.57/0.73 tff(297,plain,
% 0.57/0.73 ((~hskp26) | c0_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[296, 294])).
% 0.57/0.73 tff(298,plain,
% 0.57/0.73 ((~hskp26) | c0_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[297, 294])).
% 0.57/0.73 tff(299,plain,
% 0.57/0.73 ((~hskp26) | c0_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[298, 294])).
% 0.57/0.73 tff(300,plain,
% 0.57/0.73 ((~hskp26) | c0_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[299, 294])).
% 0.57/0.73 tff(301,plain,
% 0.57/0.73 (c0_1(a1858)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[300, 285])).
% 0.57/0.73 tff(302,plain,
% 0.57/0.73 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1858)) | (~c2_1(a1858)) | (~c1_1(a1858)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1858)) | (~c2_1(a1858)) | (~c1_1(a1858)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(303,plain,
% 0.57/0.73 ((hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858))) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1858)) | (~c2_1(a1858)) | (~c1_1(a1858)))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(304,plain,
% 0.57/0.73 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1858)) | (~c2_1(a1858)) | (~c1_1(a1858))))),
% 0.57/0.73 inference(monotonicity,[status(thm)],[303])).
% 0.57/0.73 tff(305,plain,
% 0.57/0.73 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1858)) | (~c2_1(a1858)) | (~c1_1(a1858)))),
% 0.57/0.73 inference(transitivity,[status(thm)],[304, 302])).
% 0.57/0.73 tff(306,plain,
% 0.57/0.73 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)))),
% 0.57/0.73 inference(quant_inst,[status(thm)],[])).
% 0.57/0.73 tff(307,plain,
% 0.57/0.73 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1858)) | (~c2_1(a1858)) | (~c1_1(a1858))),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.57/0.73 tff(308,plain,
% 0.57/0.73 (~c2_1(a1858)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[307, 125, 64, 43, 301, 293, 53])).
% 0.57/0.73 tff(309,plain,
% 0.57/0.73 (((~hskp26) | c3_1(a1858)) <=> ((~hskp26) | c3_1(a1858))),
% 0.57/0.73 inference(rewrite,[status(thm)],[])).
% 0.57/0.73 tff(310,axiom,((~hskp26) | c3_1(a1858)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.57/0.73 tff(311,plain,
% 0.57/0.73 ((~hskp26) | c3_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.57/0.73 tff(312,plain,
% 0.57/0.73 ((~hskp26) | c3_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[311, 309])).
% 0.57/0.73 tff(313,plain,
% 0.57/0.73 ((~hskp26) | c3_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[312, 309])).
% 0.57/0.73 tff(314,plain,
% 0.57/0.73 ((~hskp26) | c3_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[313, 309])).
% 0.57/0.73 tff(315,plain,
% 0.57/0.73 ((~hskp26) | c3_1(a1858)),
% 0.57/0.73 inference(modus_ponens,[status(thm)],[314, 309])).
% 0.57/0.73 tff(316,plain,
% 0.57/0.73 (c3_1(a1858)),
% 0.57/0.73 inference(unit_resolution,[status(thm)],[315, 285])).
% 0.57/0.73 tff(317,plain,
% 0.57/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c3_1(a1858)) | c2_1(a1858) | (~c1_1(a1858)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~ndr1_0) | (~c2_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c3_1(a1858)) | c2_1(a1858) | (~c1_1(a1858)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(318,plain,
% 0.57/0.74 (((~ndr1_0) | c2_1(a1858) | (~c3_1(a1858)) | (~c1_1(a1858)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1878) | (~c3_1(a1878)) | (~c2_1(a1878))) <=> ((~ndr1_0) | (~c2_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c3_1(a1858)) | c2_1(a1858) | (~c1_1(a1858)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(319,plain,
% 0.57/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1858) | (~c3_1(a1858)) | (~c1_1(a1858)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1878) | (~c3_1(a1878)) | (~c2_1(a1878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c3_1(a1858)) | c2_1(a1858) | (~c1_1(a1858)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877)))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[318])).
% 0.57/0.74 tff(320,plain,
% 0.57/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1858) | (~c3_1(a1858)) | (~c1_1(a1858)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1878) | (~c3_1(a1878)) | (~c2_1(a1878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~ndr1_0) | (~c2_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c3_1(a1858)) | c2_1(a1858) | (~c1_1(a1858)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.57/0.74 inference(transitivity,[status(thm)],[319, 317])).
% 0.57/0.74 tff(321,plain,
% 0.57/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1858) | (~c3_1(a1858)) | (~c1_1(a1858)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1878) | (~c3_1(a1878)) | (~c2_1(a1878)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(322,plain,
% 0.57/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~ndr1_0) | (~c2_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c3_1(a1858)) | c2_1(a1858) | (~c1_1(a1858)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.57/0.74 tff(323,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[322, 125, 174, 197, 159, 143, 293, 316, 10, 267, 189, 308])).
% 0.57/0.74 tff(324,plain,(hskp24 | hskp0 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(325,plain,
% 0.57/0.74 (hskp24),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[324, 43, 32])).
% 0.57/0.74 tff(326,plain,
% 0.57/0.74 (((~hskp24) | (~c2_1(a1919))) <=> ((~hskp24) | (~c2_1(a1919)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(327,plain,
% 0.57/0.74 (((~c2_1(a1919)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a1919)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(328,axiom,((~c2_1(a1919)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.57/0.74 tff(329,plain,
% 0.57/0.74 ((~hskp24) | (~c2_1(a1919))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.57/0.74 tff(330,plain,
% 0.57/0.74 ((~hskp24) | (~c2_1(a1919))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[329, 326])).
% 0.57/0.74 tff(331,plain,
% 0.57/0.74 (~c2_1(a1919)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[330, 325])).
% 0.57/0.74 tff(332,plain,
% 0.57/0.74 (((~hskp24) | (~c1_1(a1919))) <=> ((~hskp24) | (~c1_1(a1919)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(333,plain,
% 0.57/0.74 (((~c1_1(a1919)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a1919)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(334,axiom,((~c1_1(a1919)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.57/0.74 tff(335,plain,
% 0.57/0.74 ((~hskp24) | (~c1_1(a1919))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.57/0.74 tff(336,plain,
% 0.57/0.74 ((~hskp24) | (~c1_1(a1919))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[335, 332])).
% 0.57/0.74 tff(337,plain,
% 0.57/0.74 (~c1_1(a1919)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[336, 325])).
% 0.57/0.74 tff(338,plain,
% 0.57/0.74 (((~hskp24) | c3_1(a1919)) <=> ((~hskp24) | c3_1(a1919))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(339,axiom,((~hskp24) | c3_1(a1919)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.57/0.74 tff(340,plain,
% 0.57/0.74 ((~hskp24) | c3_1(a1919)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.57/0.74 tff(341,plain,
% 0.57/0.74 ((~hskp24) | c3_1(a1919)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[340, 338])).
% 0.57/0.74 tff(342,plain,
% 0.57/0.74 ((~hskp24) | c3_1(a1919)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[341, 338])).
% 0.57/0.74 tff(343,plain,
% 0.57/0.74 ((~hskp24) | c3_1(a1919)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[342, 338])).
% 0.57/0.74 tff(344,plain,
% 0.57/0.74 ((~hskp24) | c3_1(a1919)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[343, 338])).
% 0.57/0.74 tff(345,plain,
% 0.57/0.74 (c3_1(a1919)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[344, 325])).
% 0.57/0.74 tff(346,plain,
% 0.57/0.74 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | c0_1(a1919))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | c0_1(a1919))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(347,plain,
% 0.57/0.74 ((hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919)) <=> (hskp1 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | c0_1(a1919))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(348,plain,
% 0.57/0.74 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | c0_1(a1919)))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[347])).
% 0.57/0.74 tff(349,plain,
% 0.57/0.74 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | c0_1(a1919))),
% 0.57/0.74 inference(transitivity,[status(thm)],[348, 346])).
% 0.57/0.74 tff(350,plain,
% 0.57/0.74 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(351,plain,
% 0.57/0.74 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | c0_1(a1919)),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.57/0.74 tff(352,plain,
% 0.57/0.74 (c0_1(a1919)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[351, 125, 32, 345, 337, 331, 42])).
% 0.57/0.74 tff(353,plain,
% 0.57/0.74 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(354,plain,
% 0.57/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[353])).
% 0.57/0.74 tff(355,plain,
% 0.57/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(356,plain,
% 0.57/0.74 (^[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)) | (~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))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(357,plain,
% 0.57/0.74 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[356])).
% 0.57/0.74 tff(358,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 0.57/0.74 tff(359,plain,
% 0.57/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.57/0.74 tff(360,plain,
% 0.57/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[359, 355])).
% 0.57/0.74 tff(361,plain,(
% 0.57/0.74 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.57/0.74 inference(skolemize,[status(sab)],[360])).
% 0.57/0.74 tff(362,plain,
% 0.57/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[361, 354])).
% 0.57/0.74 tff(363,assumption,(hskp3), introduced(assumption)).
% 0.57/0.74 tff(364,plain,
% 0.57/0.74 (((~hskp3) | (~c2_1(a1855))) <=> ((~hskp3) | (~c2_1(a1855)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(365,plain,
% 0.57/0.74 (((~c2_1(a1855)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a1855)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(366,axiom,((~c2_1(a1855)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.57/0.74 tff(367,plain,
% 0.57/0.74 ((~hskp3) | (~c2_1(a1855))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.57/0.74 tff(368,plain,
% 0.57/0.74 ((~hskp3) | (~c2_1(a1855))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[367, 364])).
% 0.57/0.74 tff(369,plain,
% 0.57/0.74 (~c2_1(a1855)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[368, 363])).
% 0.57/0.74 tff(370,assumption,(hskp24), introduced(assumption)).
% 0.57/0.74 tff(371,plain,
% 0.57/0.74 (((~hskp3) | (~c0_1(a1855))) <=> ((~hskp3) | (~c0_1(a1855)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(372,plain,
% 0.57/0.74 (((~c0_1(a1855)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a1855)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(373,axiom,((~c0_1(a1855)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.57/0.74 tff(374,plain,
% 0.57/0.74 ((~hskp3) | (~c0_1(a1855))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.57/0.74 tff(375,plain,
% 0.57/0.74 ((~hskp3) | (~c0_1(a1855))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[374, 371])).
% 0.57/0.74 tff(376,plain,
% 0.57/0.74 (~c0_1(a1855)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[375, 363])).
% 0.57/0.74 tff(377,plain,
% 0.57/0.74 (((~hskp3) | (~c1_1(a1855))) <=> ((~hskp3) | (~c1_1(a1855)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(378,plain,
% 0.57/0.74 (((~c1_1(a1855)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a1855)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(379,axiom,((~c1_1(a1855)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.57/0.74 tff(380,plain,
% 0.57/0.74 ((~hskp3) | (~c1_1(a1855))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.57/0.74 tff(381,plain,
% 0.57/0.74 ((~hskp3) | (~c1_1(a1855))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[380, 377])).
% 0.57/0.74 tff(382,plain,
% 0.57/0.74 (~c1_1(a1855)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[381, 363])).
% 0.57/0.74 tff(383,assumption,(~c2_1(a1855)), introduced(assumption)).
% 0.57/0.74 tff(384,assumption,(~c1_1(a1855)), introduced(assumption)).
% 0.57/0.74 tff(385,assumption,(~c0_1(a1855)), introduced(assumption)).
% 0.57/0.74 tff(386,plain,
% 0.57/0.74 (~c2_1(a1919)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[330, 370])).
% 0.57/0.74 tff(387,plain,
% 0.57/0.74 (~c1_1(a1919)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[336, 370])).
% 0.57/0.74 tff(388,plain,
% 0.57/0.74 (c3_1(a1919)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[344, 370])).
% 0.57/0.74 tff(389,plain,
% 0.57/0.74 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1855) | c1_1(a1855) | c2_1(a1855) | (~ndr1_0) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1855) | c1_1(a1855) | c2_1(a1855) | (~ndr1_0) | (~c3_1(a1919)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(390,plain,
% 0.57/0.74 ((hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1855) | c0_1(a1855) | c2_1(a1855)) <=> (hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1855) | c1_1(a1855) | c2_1(a1855) | (~ndr1_0) | (~c3_1(a1919)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(391,plain,
% 0.57/0.74 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1855) | c0_1(a1855) | c2_1(a1855))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1855) | c1_1(a1855) | c2_1(a1855) | (~ndr1_0) | (~c3_1(a1919))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[390])).
% 0.57/0.74 tff(392,plain,
% 0.57/0.74 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1855) | c0_1(a1855) | c2_1(a1855))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1855) | c1_1(a1855) | c2_1(a1855) | (~ndr1_0) | (~c3_1(a1919)))),
% 0.57/0.74 inference(transitivity,[status(thm)],[391, 389])).
% 0.57/0.74 tff(393,plain,
% 0.57/0.74 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1855) | c0_1(a1855) | c2_1(a1855))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(394,plain,
% 0.57/0.74 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1855) | c1_1(a1855) | c2_1(a1855) | (~ndr1_0) | (~c3_1(a1919))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.57/0.74 tff(395,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[394, 125, 32, 388, 387, 386, 385, 384, 383, 42])).
% 0.57/0.74 tff(396,plain,((~hskp24) | hskp1 | c0_1(a1855) | c1_1(a1855) | c2_1(a1855)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(397,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[396, 382, 376, 370, 369, 32])).
% 0.57/0.74 tff(398,plain,((~hskp3) | (~hskp24) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.57/0.74 tff(399,plain,
% 0.57/0.74 (~hskp3),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[398, 325, 32])).
% 0.57/0.74 tff(400,assumption,(c0_1(a1919)), introduced(assumption)).
% 0.57/0.74 tff(401,assumption,(~hskp22), introduced(assumption)).
% 0.57/0.74 tff(402,plain,
% 0.57/0.74 (^[U: $i] : refl((hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(403,plain,
% 0.57/0.74 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[402])).
% 0.57/0.74 tff(404,plain,
% 0.57/0.74 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(405,plain,
% 0.57/0.74 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp22) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp22))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp22) <=> (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.57/0.74 inference(bind,[status(th)],[])).
% 0.57/0.74 tff(406,plain,
% 0.57/0.74 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp22) <=> ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.74 inference(quant_intro,[status(thm)],[405])).
% 0.57/0.74 tff(407,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.57/0.74 tff(408,plain,
% 0.57/0.74 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.57/0.74 tff(409,plain,
% 0.57/0.74 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[408, 404])).
% 0.57/0.74 tff(410,plain,(
% 0.57/0.74 ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.74 inference(skolemize,[status(sab)],[409])).
% 0.57/0.74 tff(411,plain,
% 0.57/0.74 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[410, 403])).
% 0.57/0.74 tff(412,assumption,(~c2_1(a1919)), introduced(assumption)).
% 0.57/0.74 tff(413,assumption,(c3_1(a1919)), introduced(assumption)).
% 0.57/0.74 tff(414,plain,
% 0.57/0.74 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(415,plain,
% 0.57/0.74 ((hskp27 | hskp22 | (~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919))) <=> (hskp27 | hskp22 | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(416,plain,
% 0.57/0.74 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[415])).
% 0.57/0.74 tff(417,plain,
% 0.57/0.74 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.57/0.74 inference(transitivity,[status(thm)],[416, 414])).
% 0.57/0.74 tff(418,plain,
% 0.57/0.74 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(419,plain,
% 0.57/0.75 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.57/0.75 tff(420,plain,
% 0.57/0.75 (hskp27 | hskp22 | (~c0_1(a1919))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[419, 125, 413, 412, 411])).
% 0.57/0.75 tff(421,plain,
% 0.57/0.75 (hskp27),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[420, 401, 400])).
% 0.57/0.75 tff(422,plain,
% 0.57/0.75 (c3_1(a1877)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[142, 421])).
% 0.57/0.75 tff(423,plain,
% 0.57/0.75 (c2_1(a1877)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[150, 421])).
% 0.57/0.75 tff(424,plain,
% 0.57/0.75 (c0_1(a1877)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[158, 421])).
% 0.57/0.75 tff(425,assumption,(~c1_1(a1919)), introduced(assumption)).
% 0.57/0.75 tff(426,assumption,(~hskp28), introduced(assumption)).
% 0.57/0.75 tff(427,plain,
% 0.57/0.75 ((hskp28 | hskp10 | hskp0) <=> (hskp28 | hskp10 | hskp0)),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(428,plain,
% 0.57/0.75 (((hskp10 | hskp28) | hskp0) <=> (hskp28 | hskp10 | hskp0)),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(429,axiom,((hskp10 | hskp28) | hskp0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.57/0.75 tff(430,plain,
% 0.57/0.75 (hskp28 | hskp10 | hskp0),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.57/0.75 tff(431,plain,
% 0.57/0.75 (hskp28 | hskp10 | hskp0),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[430, 427])).
% 0.57/0.75 tff(432,plain,
% 0.57/0.75 (hskp28 | hskp10 | hskp0),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[431, 427])).
% 0.57/0.75 tff(433,plain,
% 0.57/0.75 (hskp28 | hskp10 | hskp0),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[432, 427])).
% 0.57/0.75 tff(434,plain,
% 0.57/0.75 (hskp28 | hskp10 | hskp0),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[433, 427])).
% 0.57/0.75 tff(435,plain,
% 0.57/0.75 (hskp10),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[434, 426, 43])).
% 0.57/0.75 tff(436,plain,
% 0.57/0.75 (((~hskp10) | c3_1(a1864)) <=> ((~hskp10) | c3_1(a1864))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(437,axiom,((~hskp10) | c3_1(a1864)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.57/0.75 tff(438,plain,
% 0.57/0.75 ((~hskp10) | c3_1(a1864)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.57/0.75 tff(439,plain,
% 0.57/0.75 ((~hskp10) | c3_1(a1864)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[438, 436])).
% 0.57/0.75 tff(440,plain,
% 0.57/0.75 ((~hskp10) | c3_1(a1864)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[439, 436])).
% 0.57/0.75 tff(441,plain,
% 0.57/0.75 ((~hskp10) | c3_1(a1864)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[440, 436])).
% 0.57/0.75 tff(442,plain,
% 0.57/0.75 ((~hskp10) | c3_1(a1864)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[441, 436])).
% 0.57/0.75 tff(443,plain,
% 0.57/0.75 (c3_1(a1864)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[442, 435])).
% 0.57/0.75 tff(444,plain,
% 0.57/0.75 (((~hskp10) | c0_1(a1864)) <=> ((~hskp10) | c0_1(a1864))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(445,axiom,((~hskp10) | c0_1(a1864)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.57/0.75 tff(446,plain,
% 0.57/0.75 ((~hskp10) | c0_1(a1864)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.57/0.75 tff(447,plain,
% 0.57/0.75 ((~hskp10) | c0_1(a1864)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[446, 444])).
% 0.57/0.75 tff(448,plain,
% 0.57/0.75 ((~hskp10) | c0_1(a1864)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[447, 444])).
% 0.57/0.75 tff(449,plain,
% 0.57/0.75 ((~hskp10) | c0_1(a1864)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[448, 444])).
% 0.57/0.75 tff(450,plain,
% 0.57/0.75 ((~hskp10) | c0_1(a1864)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[449, 444])).
% 0.57/0.75 tff(451,plain,
% 0.57/0.75 (c0_1(a1864)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[450, 435])).
% 0.57/0.75 tff(452,plain,
% 0.57/0.75 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(453,plain,
% 0.57/0.75 ((hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864))) <=> (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(454,plain,
% 0.57/0.75 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[453])).
% 0.57/0.75 tff(455,plain,
% 0.57/0.75 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[454, 452])).
% 0.57/0.75 tff(456,plain,
% 0.57/0.75 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(457,plain,
% 0.57/0.75 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.57/0.75 tff(458,plain,
% 0.57/0.75 (~c2_1(a1864)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[457, 125, 426, 43, 451, 443, 63])).
% 0.57/0.75 tff(459,plain,
% 0.57/0.75 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(460,plain,
% 0.57/0.75 ((hskp27 | hskp22 | (~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864))) <=> (hskp27 | hskp22 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(461,plain,
% 0.57/0.75 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864)))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[460])).
% 0.57/0.75 tff(462,plain,
% 0.57/0.75 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864))),
% 0.57/0.75 inference(transitivity,[status(thm)],[461, 459])).
% 0.57/0.75 tff(463,plain,
% 0.57/0.75 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(464,plain,
% 0.57/0.75 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864)),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.57/0.75 tff(465,plain,
% 0.57/0.75 (hskp27),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[464, 125, 401, 451, 443, 411, 458])).
% 0.57/0.75 tff(466,plain,
% 0.57/0.75 (c3_1(a1877)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[142, 465])).
% 0.57/0.75 tff(467,plain,
% 0.57/0.75 (c2_1(a1877)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[150, 465])).
% 0.57/0.75 tff(468,plain,
% 0.57/0.75 (c0_1(a1877)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[158, 465])).
% 0.57/0.75 tff(469,plain,
% 0.57/0.75 ($false),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[165, 125, 426, 43, 468, 467, 466, 63])).
% 0.57/0.75 tff(470,plain,(hskp28 | hskp0 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.57/0.75 tff(471,plain,
% 0.57/0.75 (hskp28),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[470, 401, 43])).
% 0.57/0.75 tff(472,plain,
% 0.57/0.75 (c1_1(a1878)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[181, 471])).
% 0.57/0.75 tff(473,plain,
% 0.57/0.75 (c3_1(a1878)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[196, 471])).
% 0.57/0.75 tff(474,assumption,(~hskp3), introduced(assumption)).
% 0.57/0.75 tff(475,plain,
% 0.57/0.75 (c2_1(a1878)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[173, 471])).
% 0.57/0.75 tff(476,plain,
% 0.57/0.75 (^[U: $i] : refl((hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(477,plain,
% 0.57/0.75 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[476])).
% 0.57/0.75 tff(478,plain,
% 0.57/0.75 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(479,plain,
% 0.57/0.75 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp26) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp26) | hskp3) <=> ((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp3))), rewrite(((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp26) | hskp3) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(480,plain,
% 0.57/0.75 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp26) | hskp3) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[479])).
% 0.57/0.75 tff(481,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp26) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 0.57/0.75 tff(482,plain,
% 0.57/0.75 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[481, 480])).
% 0.57/0.75 tff(483,plain,
% 0.57/0.75 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[482, 478])).
% 0.57/0.75 tff(484,plain,(
% 0.57/0.75 ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.57/0.75 inference(skolemize,[status(sab)],[483])).
% 0.57/0.75 tff(485,plain,
% 0.57/0.75 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[484, 477])).
% 0.57/0.75 tff(486,assumption,(c2_1(a1878)), introduced(assumption)).
% 0.57/0.75 tff(487,assumption,(~hskp26), introduced(assumption)).
% 0.57/0.75 tff(488,plain,
% 0.57/0.75 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(489,plain,
% 0.57/0.75 ((hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878))) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(490,plain,
% 0.57/0.75 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[489])).
% 0.57/0.75 tff(491,plain,
% 0.57/0.75 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[490, 488])).
% 0.57/0.75 tff(492,plain,
% 0.57/0.75 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(493,plain,
% 0.57/0.75 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.57/0.75 tff(494,plain,
% 0.57/0.75 (hskp3 | (~c0_1(a1878))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[493, 125, 487, 231, 486, 485])).
% 0.57/0.75 tff(495,plain,
% 0.57/0.75 (~c0_1(a1878)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[494, 474])).
% 0.57/0.75 tff(496,plain,
% 0.57/0.75 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(497,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[496])).
% 0.57/0.75 tff(498,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(499,plain,
% 0.57/0.75 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(500,plain,
% 0.57/0.75 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[499])).
% 0.57/0.75 tff(501,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.57/0.75 tff(502,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.57/0.75 tff(503,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[502, 498])).
% 0.57/0.75 tff(504,plain,(
% 0.57/0.75 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.57/0.75 inference(skolemize,[status(sab)],[503])).
% 0.57/0.75 tff(505,plain,
% 0.57/0.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[504, 497])).
% 0.57/0.75 tff(506,plain,
% 0.57/0.75 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1919)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(507,plain,
% 0.57/0.75 ((hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1878) | (~c2_1(a1878)) | (~c1_1(a1878))) <=> (hskp8 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1919)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(508,plain,
% 0.57/0.75 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1878) | (~c2_1(a1878)) | (~c1_1(a1878)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1919))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[507])).
% 0.57/0.75 tff(509,plain,
% 0.57/0.75 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1878) | (~c2_1(a1878)) | (~c1_1(a1878)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1919)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[508, 506])).
% 0.57/0.75 tff(510,plain,
% 0.57/0.75 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1878) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(511,plain,
% 0.57/0.75 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1919))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.57/0.75 tff(512,plain,
% 0.57/0.75 (hskp8),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[511, 125, 231, 486, 413, 425, 412, 505, 495])).
% 0.57/0.75 tff(513,plain,
% 0.57/0.75 (((~hskp8) | (~c2_1(a1862))) <=> ((~hskp8) | (~c2_1(a1862)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(514,plain,
% 0.57/0.75 (((~c2_1(a1862)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a1862)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(515,axiom,((~c2_1(a1862)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.57/0.75 tff(516,plain,
% 0.57/0.75 ((~hskp8) | (~c2_1(a1862))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.57/0.75 tff(517,plain,
% 0.57/0.75 ((~hskp8) | (~c2_1(a1862))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[516, 513])).
% 0.57/0.75 tff(518,plain,
% 0.57/0.75 (~c2_1(a1862)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[517, 512])).
% 0.57/0.75 tff(519,plain,
% 0.57/0.75 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | c1_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | c1_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(520,plain,
% 0.57/0.75 ((hskp26 | hskp23 | (~ndr1_0) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919))) <=> (hskp26 | hskp23 | c1_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(521,plain,
% 0.57/0.75 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | c1_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919))))),
% 0.57/0.75 inference(monotonicity,[status(thm)],[520])).
% 0.57/0.75 tff(522,plain,
% 0.57/0.75 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | c1_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.57/0.75 inference(transitivity,[status(thm)],[521, 519])).
% 0.57/0.75 tff(523,plain,
% 0.57/0.75 ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(524,plain,
% 0.57/0.75 ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | c1_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.57/0.75 tff(525,plain,
% 0.57/0.75 (hskp26 | hskp23 | (~c0_1(a1919))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[524, 125, 413, 425, 277])).
% 0.57/0.75 tff(526,plain,
% 0.57/0.75 (hskp23),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[525, 487, 400])).
% 0.57/0.75 tff(527,plain,
% 0.57/0.75 (~c3_1(a1911)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[214, 526])).
% 0.57/0.75 tff(528,plain,
% 0.57/0.75 (~c1_1(a1911)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[220, 526])).
% 0.57/0.75 tff(529,plain,
% 0.57/0.75 (c0_1(a1911)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[228, 526])).
% 0.57/0.75 tff(530,plain,
% 0.57/0.75 (~c2_1(a1911)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[237, 125, 231, 230, 529, 528, 527, 208, 495])).
% 0.57/0.75 tff(531,plain,
% 0.57/0.75 (^[U: $i] : refl((hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(532,plain,
% 0.57/0.76 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[531])).
% 0.57/0.76 tff(533,plain,
% 0.57/0.76 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(534,plain,
% 0.57/0.76 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp16) <=> ((hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp16))), rewrite(((hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp16) <=> (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp16) <=> (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(535,plain,
% 0.57/0.76 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp16) <=> ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[534])).
% 0.57/0.76 tff(536,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 0.57/0.76 tff(537,plain,
% 0.57/0.76 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.57/0.76 tff(538,plain,
% 0.57/0.76 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[537, 533])).
% 0.57/0.76 tff(539,plain,(
% 0.57/0.76 ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.76 inference(skolemize,[status(sab)],[538])).
% 0.57/0.76 tff(540,plain,
% 0.57/0.76 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[539, 532])).
% 0.57/0.76 tff(541,plain,
% 0.57/0.76 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | c2_1(a1911))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp22 | hskp16 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | c2_1(a1911))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(542,plain,
% 0.57/0.76 ((hskp22 | hskp16 | (~ndr1_0) | c2_1(a1911) | c1_1(a1911) | c3_1(a1911)) <=> (hskp22 | hskp16 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | c2_1(a1911))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(543,plain,
% 0.57/0.76 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | (~ndr1_0) | c2_1(a1911) | c1_1(a1911) | c3_1(a1911))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | c2_1(a1911)))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[542])).
% 0.57/0.76 tff(544,plain,
% 0.57/0.76 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | (~ndr1_0) | c2_1(a1911) | c1_1(a1911) | c3_1(a1911))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp22 | hskp16 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | c2_1(a1911))),
% 0.57/0.76 inference(transitivity,[status(thm)],[543, 541])).
% 0.57/0.76 tff(545,plain,
% 0.57/0.76 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | (~ndr1_0) | c2_1(a1911) | c1_1(a1911) | c3_1(a1911))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(546,plain,
% 0.57/0.76 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp22 | hskp16 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | c2_1(a1911)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.57/0.76 tff(547,plain,
% 0.57/0.76 (hskp22 | hskp16 | c2_1(a1911)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[546, 125, 528, 527, 540])).
% 0.57/0.76 tff(548,plain,
% 0.57/0.76 (hskp16),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[547, 530, 401])).
% 0.57/0.76 tff(549,plain,
% 0.57/0.76 (((~hskp16) | (~c0_1(a1872))) <=> ((~hskp16) | (~c0_1(a1872)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(550,plain,
% 0.57/0.76 (((~c0_1(a1872)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a1872)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(551,axiom,((~c0_1(a1872)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.57/0.76 tff(552,plain,
% 0.57/0.76 ((~hskp16) | (~c0_1(a1872))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[551, 550])).
% 0.57/0.76 tff(553,plain,
% 0.57/0.76 ((~hskp16) | (~c0_1(a1872))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[552, 549])).
% 0.57/0.76 tff(554,plain,
% 0.57/0.76 (~c0_1(a1872)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[553, 548])).
% 0.57/0.76 tff(555,plain,
% 0.57/0.76 (((~hskp8) | c1_1(a1862)) <=> ((~hskp8) | c1_1(a1862))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(556,axiom,((~hskp8) | c1_1(a1862)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.57/0.76 tff(557,plain,
% 0.57/0.76 ((~hskp8) | c1_1(a1862)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.57/0.76 tff(558,plain,
% 0.57/0.76 ((~hskp8) | c1_1(a1862)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[557, 555])).
% 0.57/0.76 tff(559,plain,
% 0.57/0.76 ((~hskp8) | c1_1(a1862)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[558, 555])).
% 0.57/0.76 tff(560,plain,
% 0.57/0.76 ((~hskp8) | c1_1(a1862)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[559, 555])).
% 0.57/0.76 tff(561,plain,
% 0.57/0.76 ((~hskp8) | c1_1(a1862)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[560, 555])).
% 0.57/0.76 tff(562,plain,
% 0.57/0.76 (c1_1(a1862)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[561, 512])).
% 0.57/0.76 tff(563,plain,
% 0.57/0.76 (((~hskp16) | c3_1(a1872)) <=> ((~hskp16) | c3_1(a1872))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(564,axiom,((~hskp16) | c3_1(a1872)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.57/0.76 tff(565,plain,
% 0.57/0.76 ((~hskp16) | c3_1(a1872)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[564, 563])).
% 0.57/0.76 tff(566,plain,
% 0.57/0.76 ((~hskp16) | c3_1(a1872)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[565, 563])).
% 0.57/0.76 tff(567,plain,
% 0.57/0.76 ((~hskp16) | c3_1(a1872)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[566, 563])).
% 0.57/0.76 tff(568,plain,
% 0.57/0.76 ((~hskp16) | c3_1(a1872)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[567, 563])).
% 0.57/0.76 tff(569,plain,
% 0.57/0.76 ((~hskp16) | c3_1(a1872)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[568, 563])).
% 0.57/0.76 tff(570,plain,
% 0.57/0.76 (c3_1(a1872)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[569, 548])).
% 0.57/0.76 tff(571,plain,
% 0.57/0.76 (((~hskp16) | c2_1(a1872)) <=> ((~hskp16) | c2_1(a1872))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(572,axiom,((~hskp16) | c2_1(a1872)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.57/0.76 tff(573,plain,
% 0.57/0.76 ((~hskp16) | c2_1(a1872)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[572, 571])).
% 0.57/0.76 tff(574,plain,
% 0.57/0.76 ((~hskp16) | c2_1(a1872)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[573, 571])).
% 0.57/0.76 tff(575,plain,
% 0.57/0.76 ((~hskp16) | c2_1(a1872)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[574, 571])).
% 0.57/0.76 tff(576,plain,
% 0.57/0.76 ((~hskp16) | c2_1(a1872)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[575, 571])).
% 0.57/0.76 tff(577,plain,
% 0.57/0.76 ((~hskp16) | c2_1(a1872)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[576, 571])).
% 0.57/0.76 tff(578,plain,
% 0.57/0.76 (c2_1(a1872)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[577, 548])).
% 0.57/0.76 tff(579,plain,
% 0.57/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1919) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1919) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(580,plain,
% 0.57/0.76 (((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872))) <=> (c1_1(a1919) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(581,plain,
% 0.57/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1919) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1919)) | (~c0_1(a1919))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[580])).
% 0.57/0.76 tff(582,plain,
% 0.57/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1919) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[581, 579])).
% 0.57/0.76 tff(583,plain,
% 0.57/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(584,plain,
% 0.57/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1919) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1919)) | (~c0_1(a1919))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[583, 582])).
% 0.57/0.76 tff(585,plain,
% 0.57/0.76 (~c3_1(a1862)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[584, 125, 413, 578, 570, 562, 425, 554, 518, 10, 400])).
% 0.57/0.76 tff(586,plain,
% 0.57/0.76 (^[U: $i] : refl((hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(587,plain,
% 0.57/0.76 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[586])).
% 0.57/0.76 tff(588,plain,
% 0.57/0.76 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(589,plain,
% 0.57/0.76 (^[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)) | 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)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp27) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp27))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp27) <=> (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp27) <=> (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(590,plain,
% 0.57/0.76 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp27) <=> ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[589])).
% 0.57/0.76 tff(591,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.57/0.76 tff(592,plain,
% 0.57/0.76 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.57/0.76 tff(593,plain,
% 0.57/0.76 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[592, 588])).
% 0.57/0.76 tff(594,plain,(
% 0.57/0.76 ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.57/0.76 inference(skolemize,[status(sab)],[593])).
% 0.57/0.76 tff(595,plain,
% 0.57/0.76 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[594, 587])).
% 0.57/0.76 tff(596,plain,
% 0.57/0.76 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp26 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp26 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(597,plain,
% 0.57/0.76 ((hskp27 | hskp26 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919))) <=> (hskp27 | hskp26 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(598,plain,
% 0.57/0.76 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp26 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[597])).
% 0.57/0.76 tff(599,plain,
% 0.57/0.76 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp26 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[598, 596])).
% 0.57/0.76 tff(600,plain,
% 0.57/0.76 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(601,plain,
% 0.57/0.76 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp26 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.57/0.76 tff(602,plain,
% 0.57/0.76 (hskp27 | hskp26),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[601, 125, 425, 412, 595, 400])).
% 0.57/0.76 tff(603,plain,
% 0.57/0.76 (hskp27),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[602, 487])).
% 0.57/0.76 tff(604,plain,
% 0.57/0.76 (c2_1(a1877)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[150, 603])).
% 0.57/0.76 tff(605,plain,
% 0.57/0.76 (c0_1(a1877)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[158, 603])).
% 0.57/0.76 tff(606,plain,
% 0.57/0.76 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(607,plain,
% 0.57/0.76 ((hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877))) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(608,plain,
% 0.57/0.76 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[607])).
% 0.57/0.76 tff(609,plain,
% 0.57/0.76 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[608, 606])).
% 0.57/0.76 tff(610,plain,
% 0.57/0.76 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(611,plain,
% 0.57/0.76 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.57/0.76 tff(612,plain,
% 0.57/0.76 (hskp3 | (~c1_1(a1877))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[611, 125, 487, 605, 604, 485])).
% 0.57/0.76 tff(613,plain,
% 0.57/0.76 (~c1_1(a1877)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[612, 474])).
% 0.57/0.76 tff(614,plain,
% 0.57/0.76 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(615,plain,
% 0.57/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[614])).
% 0.57/0.76 tff(616,plain,
% 0.57/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(617,plain,
% 0.57/0.76 (^[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(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(618,plain,
% 0.57/0.77 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[617])).
% 0.57/0.77 tff(619,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.57/0.77 tff(620,plain,
% 0.57/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.57/0.77 tff(621,plain,
% 0.57/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[620, 616])).
% 0.57/0.77 tff(622,plain,(
% 0.57/0.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.57/0.77 inference(skolemize,[status(sab)],[621])).
% 0.57/0.77 tff(623,plain,
% 0.57/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[622, 615])).
% 0.57/0.77 tff(624,plain,
% 0.57/0.77 (c3_1(a1877)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[142, 603])).
% 0.57/0.77 tff(625,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c2_1(a1877)) | c1_1(a1877))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c2_1(a1877)) | c1_1(a1877))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(626,plain,
% 0.57/0.77 (((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1877) | (~c2_1(a1877)) | (~c3_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872))) <=> (c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c2_1(a1877)) | c1_1(a1877))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(627,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1877) | (~c2_1(a1877)) | (~c3_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c2_1(a1877)) | c1_1(a1877)))),
% 0.57/0.77 inference(monotonicity,[status(thm)],[626])).
% 0.57/0.77 tff(628,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1877) | (~c2_1(a1877)) | (~c3_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c2_1(a1877)) | c1_1(a1877))),
% 0.57/0.77 inference(transitivity,[status(thm)],[627, 625])).
% 0.57/0.77 tff(629,plain,
% 0.57/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1877) | (~c2_1(a1877)) | (~c3_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(630,plain,
% 0.57/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c2_1(a1877)) | c1_1(a1877)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.57/0.77 tff(631,plain,
% 0.57/0.77 ($false),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[630, 125, 604, 624, 578, 570, 562, 554, 518, 623, 613, 585])).
% 0.57/0.77 tff(632,plain,(hskp3 | (~c3_1(a1919)) | c1_1(a1919) | (~c0_1(a1919)) | hskp22 | (~c1_1(a1878)) | (~c2_1(a1878)) | c2_1(a1919) | (~c3_1(a1878)) | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.57/0.77 tff(633,plain,
% 0.57/0.77 (hskp26),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[632, 475, 425, 400, 413, 474, 401, 412, 473, 472])).
% 0.57/0.77 tff(634,plain,
% 0.57/0.77 (c3_1(a1858)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[315, 633])).
% 0.57/0.77 tff(635,plain,
% 0.57/0.77 (c1_1(a1858)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[292, 633])).
% 0.57/0.77 tff(636,plain,
% 0.57/0.77 (c0_1(a1858)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[300, 633])).
% 0.57/0.77 tff(637,plain,
% 0.57/0.77 (^[U: $i] : refl((hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(638,plain,
% 0.57/0.77 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[637])).
% 0.57/0.77 tff(639,plain,
% 0.57/0.77 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(640,plain,
% 0.57/0.77 (^[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)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp16) | hskp13) <=> ((hskp16 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp13))), rewrite(((hskp16 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp13) <=> (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp16) | hskp13) <=> (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(641,plain,
% 0.57/0.77 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp16) | hskp13) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[640])).
% 0.57/0.77 tff(642,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp16) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.57/0.77 tff(643,plain,
% 0.57/0.77 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[642, 641])).
% 0.57/0.77 tff(644,plain,
% 0.57/0.77 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[643, 639])).
% 0.57/0.77 tff(645,plain,(
% 0.57/0.77 ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.57/0.77 inference(skolemize,[status(sab)],[644])).
% 0.57/0.77 tff(646,plain,
% 0.57/0.77 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[645, 638])).
% 0.57/0.77 tff(647,assumption,(~hskp16), introduced(assumption)).
% 0.57/0.77 tff(648,plain,
% 0.57/0.77 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(649,plain,
% 0.57/0.77 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[648])).
% 0.57/0.77 tff(650,plain,
% 0.57/0.77 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(651,plain,
% 0.57/0.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.57/0.77 inference(bind,[status(th)],[])).
% 0.57/0.77 tff(652,plain,
% 0.57/0.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.57/0.77 inference(quant_intro,[status(thm)],[651])).
% 0.57/0.77 tff(653,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 0.57/0.77 tff(654,plain,
% 0.57/0.77 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[653, 652])).
% 0.57/0.77 tff(655,plain,
% 0.57/0.77 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[654, 650])).
% 0.57/0.77 tff(656,plain,(
% 0.57/0.77 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.57/0.77 inference(skolemize,[status(sab)],[655])).
% 0.57/0.77 tff(657,plain,
% 0.57/0.77 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[656, 649])).
% 0.57/0.77 tff(658,assumption,(hskp8), introduced(assumption)).
% 0.57/0.77 tff(659,plain,
% 0.57/0.77 (~c2_1(a1862)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[517, 658])).
% 0.57/0.77 tff(660,plain,
% 0.57/0.77 (c1_1(a1862)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[561, 658])).
% 0.57/0.77 tff(661,plain,
% 0.57/0.77 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(662,plain,
% 0.57/0.77 ((hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862))) <=> (hskp16 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(663,plain,
% 0.57/0.77 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.57/0.77 inference(monotonicity,[status(thm)],[662])).
% 0.57/0.77 tff(664,plain,
% 0.57/0.77 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.57/0.77 inference(transitivity,[status(thm)],[663, 661])).
% 0.57/0.77 tff(665,plain,
% 0.57/0.77 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(666,plain,
% 0.57/0.77 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[665, 664])).
% 0.57/0.77 tff(667,plain,
% 0.57/0.77 (~c3_1(a1862)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[666, 125, 647, 251, 250, 249, 660, 659, 657])).
% 0.57/0.77 tff(668,plain,
% 0.57/0.77 (((~hskp8) | c0_1(a1862)) <=> ((~hskp8) | c0_1(a1862))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(669,axiom,((~hskp8) | c0_1(a1862)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.57/0.77 tff(670,plain,
% 0.57/0.77 ((~hskp8) | c0_1(a1862)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[669, 668])).
% 0.57/0.77 tff(671,plain,
% 0.57/0.77 ((~hskp8) | c0_1(a1862)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[670, 668])).
% 0.57/0.77 tff(672,plain,
% 0.57/0.77 ((~hskp8) | c0_1(a1862)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[671, 668])).
% 0.57/0.77 tff(673,plain,
% 0.57/0.77 ((~hskp8) | c0_1(a1862)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[672, 668])).
% 0.57/0.77 tff(674,plain,
% 0.57/0.77 ((~hskp8) | c0_1(a1862)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[673, 668])).
% 0.57/0.77 tff(675,plain,
% 0.57/0.77 (c0_1(a1862)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[674, 658])).
% 0.57/0.77 tff(676,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(677,plain,
% 0.57/0.77 (((~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c3_1(a1862) | c2_1(a1862) | (~c1_1(a1862))) <=> (c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(678,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c3_1(a1862) | c2_1(a1862) | (~c1_1(a1862)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862))))),
% 0.57/0.77 inference(monotonicity,[status(thm)],[677])).
% 0.57/0.77 tff(679,plain,
% 0.57/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c3_1(a1862) | c2_1(a1862) | (~c1_1(a1862)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.57/0.77 inference(transitivity,[status(thm)],[678, 676])).
% 0.57/0.77 tff(680,plain,
% 0.57/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c3_1(a1862) | c2_1(a1862) | (~c1_1(a1862)))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(681,plain,
% 0.57/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.57/0.77 tff(682,plain,
% 0.57/0.77 ($false),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[681, 125, 675, 660, 659, 362, 667])).
% 0.57/0.77 tff(683,plain,((~hskp8) | hskp16 | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c3_1(a1877))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.77 tff(684,plain,
% 0.57/0.77 (~hskp8),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[683, 647, 251, 250, 249])).
% 0.57/0.77 tff(685,assumption,(hskp13), introduced(assumption)).
% 0.57/0.77 tff(686,plain,
% 0.57/0.77 (((~hskp13) | (~c3_1(a1867))) <=> ((~hskp13) | (~c3_1(a1867)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(687,plain,
% 0.57/0.77 (((~c3_1(a1867)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a1867)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(688,axiom,((~c3_1(a1867)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.57/0.77 tff(689,plain,
% 0.57/0.77 ((~hskp13) | (~c3_1(a1867))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[688, 687])).
% 0.57/0.77 tff(690,plain,
% 0.57/0.77 ((~hskp13) | (~c3_1(a1867))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[689, 686])).
% 0.57/0.77 tff(691,plain,
% 0.57/0.77 (~c3_1(a1867)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[690, 685])).
% 0.57/0.77 tff(692,plain,
% 0.57/0.77 (((~hskp13) | (~c2_1(a1867))) <=> ((~hskp13) | (~c2_1(a1867)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(693,plain,
% 0.57/0.77 (((~c2_1(a1867)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a1867)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(694,axiom,((~c2_1(a1867)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.57/0.77 tff(695,plain,
% 0.57/0.77 ((~hskp13) | (~c2_1(a1867))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[694, 693])).
% 0.57/0.77 tff(696,plain,
% 0.57/0.77 ((~hskp13) | (~c2_1(a1867))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[695, 692])).
% 0.57/0.77 tff(697,plain,
% 0.57/0.77 (~c2_1(a1867)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[696, 685])).
% 0.57/0.77 tff(698,plain,
% 0.57/0.77 (((~hskp13) | (~c1_1(a1867))) <=> ((~hskp13) | (~c1_1(a1867)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(699,plain,
% 0.57/0.77 (((~c1_1(a1867)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1867)))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(700,axiom,((~c1_1(a1867)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.57/0.77 tff(701,plain,
% 0.57/0.77 ((~hskp13) | (~c1_1(a1867))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.57/0.77 tff(702,plain,
% 0.57/0.77 ((~hskp13) | (~c1_1(a1867))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[701, 698])).
% 0.57/0.77 tff(703,plain,
% 0.57/0.77 (~c1_1(a1867)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[702, 685])).
% 0.57/0.77 tff(704,plain,
% 0.57/0.77 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | c1_1(a1867) | c2_1(a1867) | c3_1(a1867) | (~ndr1_0))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp22 | hskp16 | c1_1(a1867) | c2_1(a1867) | c3_1(a1867) | (~ndr1_0))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(705,plain,
% 0.57/0.77 ((hskp22 | hskp16 | (~ndr1_0) | c2_1(a1867) | c1_1(a1867) | c3_1(a1867)) <=> (hskp22 | hskp16 | c1_1(a1867) | c2_1(a1867) | c3_1(a1867) | (~ndr1_0))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(706,plain,
% 0.57/0.77 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | (~ndr1_0) | c2_1(a1867) | c1_1(a1867) | c3_1(a1867))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | c1_1(a1867) | c2_1(a1867) | c3_1(a1867) | (~ndr1_0)))),
% 0.57/0.77 inference(monotonicity,[status(thm)],[705])).
% 0.57/0.77 tff(707,plain,
% 0.57/0.77 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | (~ndr1_0) | c2_1(a1867) | c1_1(a1867) | c3_1(a1867))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp22 | hskp16 | c1_1(a1867) | c2_1(a1867) | c3_1(a1867) | (~ndr1_0))),
% 0.57/0.77 inference(transitivity,[status(thm)],[706, 704])).
% 0.57/0.77 tff(708,plain,
% 0.57/0.77 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | (~ndr1_0) | c2_1(a1867) | c1_1(a1867) | c3_1(a1867))),
% 0.57/0.77 inference(quant_inst,[status(thm)],[])).
% 0.57/0.77 tff(709,plain,
% 0.57/0.77 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp22 | hskp16 | c1_1(a1867) | c2_1(a1867) | c3_1(a1867) | (~ndr1_0)),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.57/0.77 tff(710,plain,
% 0.57/0.77 ($false),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[709, 125, 401, 647, 703, 697, 691, 540])).
% 0.57/0.77 tff(711,plain,((~hskp13) | hskp22 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.57/0.78 tff(712,plain,
% 0.57/0.78 (~hskp13),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[711, 647, 401])).
% 0.57/0.78 tff(713,plain,
% 0.57/0.78 (^[U: $i] : refl((hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.57/0.78 inference(bind,[status(th)],[])).
% 0.57/0.78 tff(714,plain,
% 0.57/0.78 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.57/0.78 inference(quant_intro,[status(thm)],[713])).
% 0.57/0.78 tff(715,plain,
% 0.57/0.78 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(716,plain,
% 0.57/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp13) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp13))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp13) <=> (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp13) <=> (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.57/0.78 inference(bind,[status(th)],[])).
% 0.57/0.78 tff(717,plain,
% 0.57/0.78 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp13) <=> ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.57/0.78 inference(quant_intro,[status(thm)],[716])).
% 0.57/0.78 tff(718,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.57/0.78 tff(719,plain,
% 0.57/0.78 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[718, 717])).
% 0.57/0.78 tff(720,plain,
% 0.57/0.78 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[719, 715])).
% 0.57/0.78 tff(721,plain,(
% 0.57/0.78 ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.57/0.78 inference(skolemize,[status(sab)],[720])).
% 0.57/0.78 tff(722,plain,
% 0.57/0.78 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[721, 714])).
% 0.57/0.78 tff(723,plain,
% 0.57/0.78 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp13 | hskp9 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp13 | hskp9 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(724,plain,
% 0.57/0.78 ((hskp13 | hskp9 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919))) <=> (hskp13 | hskp9 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(725,plain,
% 0.57/0.78 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp13 | hskp9 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919))))),
% 0.57/0.78 inference(monotonicity,[status(thm)],[724])).
% 0.57/0.78 tff(726,plain,
% 0.57/0.78 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp13 | hskp9 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)))),
% 0.57/0.78 inference(transitivity,[status(thm)],[725, 723])).
% 0.57/0.78 tff(727,plain,
% 0.57/0.78 ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)))),
% 0.57/0.78 inference(quant_inst,[status(thm)],[])).
% 0.57/0.78 tff(728,plain,
% 0.57/0.78 ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp13 | hskp9 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[727, 726])).
% 0.57/0.78 tff(729,plain,
% 0.57/0.78 (hskp13 | hskp9),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[728, 125, 413, 425, 412, 722])).
% 0.57/0.78 tff(730,plain,
% 0.57/0.78 (hskp9),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[729, 712])).
% 0.57/0.78 tff(731,plain,
% 0.57/0.78 (^[U: $i] : refl((hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.57/0.78 inference(bind,[status(th)],[])).
% 0.57/0.78 tff(732,plain,
% 0.57/0.78 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(quant_intro,[status(thm)],[731])).
% 0.57/0.78 tff(733,plain,
% 0.57/0.78 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(734,plain,
% 0.57/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp23))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp23) <=> (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.57/0.78 inference(bind,[status(th)],[])).
% 0.57/0.78 tff(735,plain,
% 0.57/0.78 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(quant_intro,[status(thm)],[734])).
% 0.57/0.78 tff(736,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.57/0.78 tff(737,plain,
% 0.57/0.78 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.57/0.78 tff(738,plain,
% 0.57/0.78 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[737, 733])).
% 0.57/0.78 tff(739,plain,(
% 0.57/0.78 ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(skolemize,[status(sab)],[738])).
% 0.57/0.78 tff(740,plain,
% 0.57/0.78 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[739, 732])).
% 0.57/0.78 tff(741,assumption,(hskp9), introduced(assumption)).
% 0.57/0.78 tff(742,plain,
% 0.57/0.78 (((~hskp9) | (~c3_1(a1863))) <=> ((~hskp9) | (~c3_1(a1863)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(743,plain,
% 0.57/0.78 (((~c3_1(a1863)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a1863)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(744,axiom,((~c3_1(a1863)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.57/0.78 tff(745,plain,
% 0.57/0.78 ((~hskp9) | (~c3_1(a1863))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[744, 743])).
% 0.57/0.78 tff(746,plain,
% 0.57/0.78 ((~hskp9) | (~c3_1(a1863))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[745, 742])).
% 0.57/0.78 tff(747,plain,
% 0.57/0.78 (~c3_1(a1863)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[746, 741])).
% 0.57/0.78 tff(748,plain,
% 0.57/0.78 (((~hskp9) | (~c1_1(a1863))) <=> ((~hskp9) | (~c1_1(a1863)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(749,plain,
% 0.57/0.78 (((~c1_1(a1863)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a1863)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(750,axiom,((~c1_1(a1863)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.57/0.78 tff(751,plain,
% 0.57/0.78 ((~hskp9) | (~c1_1(a1863))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[750, 749])).
% 0.57/0.78 tff(752,plain,
% 0.57/0.78 ((~hskp9) | (~c1_1(a1863))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[751, 748])).
% 0.57/0.78 tff(753,plain,
% 0.57/0.78 (~c1_1(a1863)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[752, 741])).
% 0.57/0.78 tff(754,plain,
% 0.57/0.78 (((~hskp9) | c2_1(a1863)) <=> ((~hskp9) | c2_1(a1863))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(755,axiom,((~hskp9) | c2_1(a1863)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.57/0.78 tff(756,plain,
% 0.57/0.78 ((~hskp9) | c2_1(a1863)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[755, 754])).
% 0.57/0.78 tff(757,plain,
% 0.57/0.78 ((~hskp9) | c2_1(a1863)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[756, 754])).
% 0.57/0.78 tff(758,plain,
% 0.57/0.78 ((~hskp9) | c2_1(a1863)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[757, 754])).
% 0.57/0.78 tff(759,plain,
% 0.57/0.78 ((~hskp9) | c2_1(a1863)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[758, 754])).
% 0.57/0.78 tff(760,plain,
% 0.57/0.78 ((~hskp9) | c2_1(a1863)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[759, 754])).
% 0.57/0.78 tff(761,plain,
% 0.57/0.78 (c2_1(a1863)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[760, 741])).
% 0.57/0.78 tff(762,assumption,(~hskp23), introduced(assumption)).
% 0.57/0.78 tff(763,plain,
% 0.57/0.78 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(764,plain,
% 0.57/0.78 ((hskp23 | hskp8 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863))) <=> (hskp23 | hskp8 | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(765,plain,
% 0.57/0.78 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863))))),
% 0.57/0.78 inference(monotonicity,[status(thm)],[764])).
% 0.57/0.78 tff(766,plain,
% 0.57/0.78 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)))),
% 0.57/0.78 inference(transitivity,[status(thm)],[765, 763])).
% 0.57/0.78 tff(767,plain,
% 0.57/0.78 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)))),
% 0.57/0.78 inference(quant_inst,[status(thm)],[])).
% 0.57/0.78 tff(768,plain,
% 0.57/0.78 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.57/0.78 tff(769,plain,
% 0.57/0.78 ($false),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[768, 125, 762, 21, 761, 753, 747, 740])).
% 0.57/0.78 tff(770,plain,((~hskp9) | hskp23 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.57/0.78 tff(771,plain,
% 0.57/0.78 (hskp23),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[770, 730, 684])).
% 0.57/0.78 tff(772,plain,
% 0.57/0.78 (~c3_1(a1911)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[214, 771])).
% 0.57/0.78 tff(773,plain,
% 0.57/0.78 (~c1_1(a1911)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[220, 771])).
% 0.57/0.78 tff(774,plain,
% 0.57/0.78 (c2_1(a1911)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[546, 125, 401, 647, 773, 772, 540])).
% 0.57/0.78 tff(775,plain,
% 0.57/0.78 (c0_1(a1911)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[228, 771])).
% 0.57/0.78 tff(776,assumption,(hskp20), introduced(assumption)).
% 0.57/0.78 tff(777,plain,
% 0.57/0.78 (((~hskp20) | (~c1_1(a1890))) <=> ((~hskp20) | (~c1_1(a1890)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(778,plain,
% 0.57/0.78 (((~c1_1(a1890)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a1890)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(779,axiom,((~c1_1(a1890)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.57/0.78 tff(780,plain,
% 0.57/0.78 ((~hskp20) | (~c1_1(a1890))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[779, 778])).
% 0.57/0.78 tff(781,plain,
% 0.57/0.78 ((~hskp20) | (~c1_1(a1890))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[780, 777])).
% 0.57/0.78 tff(782,plain,
% 0.57/0.78 (~c1_1(a1890)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[781, 776])).
% 0.57/0.78 tff(783,plain,
% 0.57/0.78 (((~hskp20) | (~c0_1(a1890))) <=> ((~hskp20) | (~c0_1(a1890)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(784,plain,
% 0.57/0.78 (((~c0_1(a1890)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a1890)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(785,axiom,((~c0_1(a1890)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.57/0.78 tff(786,plain,
% 0.57/0.78 ((~hskp20) | (~c0_1(a1890))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[785, 784])).
% 0.57/0.78 tff(787,plain,
% 0.57/0.78 ((~hskp20) | (~c0_1(a1890))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[786, 783])).
% 0.57/0.78 tff(788,plain,
% 0.57/0.78 (~c0_1(a1890)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[787, 776])).
% 0.57/0.78 tff(789,assumption,(~hskp13), introduced(assumption)).
% 0.57/0.78 tff(790,plain,
% 0.57/0.78 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c3_1(a1890)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c3_1(a1890)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(791,plain,
% 0.57/0.78 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c3_1(a1890))) <=> (hskp16 | hskp13 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c3_1(a1890)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(792,plain,
% 0.57/0.78 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c3_1(a1890)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c3_1(a1890))))),
% 0.57/0.78 inference(monotonicity,[status(thm)],[791])).
% 0.57/0.78 tff(793,plain,
% 0.57/0.78 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c3_1(a1890)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c3_1(a1890)))),
% 0.57/0.78 inference(transitivity,[status(thm)],[792, 790])).
% 0.57/0.78 tff(794,plain,
% 0.57/0.78 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c3_1(a1890)))),
% 0.57/0.78 inference(quant_inst,[status(thm)],[])).
% 0.57/0.78 tff(795,plain,
% 0.57/0.78 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c3_1(a1890))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.57/0.78 tff(796,plain,
% 0.57/0.78 (~c3_1(a1890)),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[795, 125, 647, 789, 788, 782, 646])).
% 0.57/0.78 tff(797,assumption,(c2_1(a1911)), introduced(assumption)).
% 0.57/0.78 tff(798,plain,
% 0.57/0.78 (^[U: $i] : refl((hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.57/0.78 inference(bind,[status(th)],[])).
% 0.57/0.78 tff(799,plain,
% 0.57/0.78 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(quant_intro,[status(thm)],[798])).
% 0.57/0.78 tff(800,plain,
% 0.57/0.78 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(801,plain,
% 0.57/0.78 (^[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)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) | hskp13) <=> ((hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp13))), rewrite(((hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.57/0.78 inference(bind,[status(th)],[])).
% 0.57/0.78 tff(802,plain,
% 0.57/0.78 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) | hskp13) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(quant_intro,[status(thm)],[801])).
% 0.57/0.78 tff(803,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 0.57/0.78 tff(804,plain,
% 0.57/0.78 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[803, 802])).
% 0.57/0.78 tff(805,plain,
% 0.57/0.78 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[804, 800])).
% 0.57/0.78 tff(806,plain,(
% 0.57/0.78 ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(skolemize,[status(sab)],[805])).
% 0.57/0.78 tff(807,plain,
% 0.57/0.78 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[806, 799])).
% 0.57/0.78 tff(808,plain,
% 0.57/0.78 (((~hskp20) | c2_1(a1890)) <=> ((~hskp20) | c2_1(a1890))),
% 0.57/0.78 inference(rewrite,[status(thm)],[])).
% 0.57/0.78 tff(809,axiom,((~hskp20) | c2_1(a1890)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.57/0.78 tff(810,plain,
% 0.57/0.78 ((~hskp20) | c2_1(a1890)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[809, 808])).
% 0.57/0.78 tff(811,plain,
% 0.57/0.78 ((~hskp20) | c2_1(a1890)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[810, 808])).
% 0.57/0.78 tff(812,plain,
% 0.57/0.78 ((~hskp20) | c2_1(a1890)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[811, 808])).
% 0.57/0.78 tff(813,plain,
% 0.57/0.78 ((~hskp20) | c2_1(a1890)),
% 0.57/0.78 inference(modus_ponens,[status(thm)],[812, 808])).
% 0.63/0.78 tff(814,plain,
% 0.63/0.78 ((~hskp20) | c2_1(a1890)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[813, 808])).
% 0.63/0.78 tff(815,plain,
% 0.63/0.78 (c2_1(a1890)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[814, 776])).
% 0.63/0.78 tff(816,plain,
% 0.63/0.78 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp13 | hskp12 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp13 | hskp12 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(817,plain,
% 0.63/0.78 ((hskp13 | hskp12 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890))) <=> (hskp13 | hskp12 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(818,plain,
% 0.63/0.78 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp13 | hskp12 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890))))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[817])).
% 0.63/0.78 tff(819,plain,
% 0.63/0.78 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp13 | hskp12 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))),
% 0.63/0.78 inference(transitivity,[status(thm)],[818, 816])).
% 0.63/0.78 tff(820,plain,
% 0.63/0.78 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)))),
% 0.63/0.78 inference(quant_inst,[status(thm)],[])).
% 0.63/0.78 tff(821,plain,
% 0.63/0.78 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp13 | hskp12 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[820, 819])).
% 0.63/0.78 tff(822,plain,
% 0.63/0.78 (hskp12),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[821, 125, 789, 815, 788, 782, 807])).
% 0.63/0.78 tff(823,plain,
% 0.63/0.78 (((~hskp12) | (~c0_1(a1866))) <=> ((~hskp12) | (~c0_1(a1866)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(824,plain,
% 0.63/0.78 (((~c0_1(a1866)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a1866)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(825,axiom,((~c0_1(a1866)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.63/0.78 tff(826,plain,
% 0.63/0.78 ((~hskp12) | (~c0_1(a1866))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[825, 824])).
% 0.63/0.78 tff(827,plain,
% 0.63/0.78 ((~hskp12) | (~c0_1(a1866))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[826, 823])).
% 0.63/0.78 tff(828,plain,
% 0.63/0.78 (~c0_1(a1866)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[827, 822])).
% 0.63/0.78 tff(829,assumption,(~c3_1(a1911)), introduced(assumption)).
% 0.63/0.78 tff(830,plain,
% 0.63/0.78 (((~hskp12) | c3_1(a1866)) <=> ((~hskp12) | c3_1(a1866))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(831,axiom,((~hskp12) | c3_1(a1866)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.63/0.78 tff(832,plain,
% 0.63/0.78 ((~hskp12) | c3_1(a1866)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[831, 830])).
% 0.63/0.78 tff(833,plain,
% 0.63/0.78 ((~hskp12) | c3_1(a1866)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[832, 830])).
% 0.63/0.78 tff(834,plain,
% 0.63/0.78 ((~hskp12) | c3_1(a1866)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[833, 830])).
% 0.63/0.78 tff(835,plain,
% 0.63/0.78 ((~hskp12) | c3_1(a1866)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[834, 830])).
% 0.63/0.78 tff(836,plain,
% 0.63/0.78 ((~hskp12) | c3_1(a1866)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[835, 830])).
% 0.63/0.78 tff(837,plain,
% 0.63/0.78 (c3_1(a1866)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[836, 822])).
% 0.63/0.78 tff(838,assumption,(c0_1(a1911)), introduced(assumption)).
% 0.63/0.78 tff(839,plain,
% 0.63/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a1911) | c1_1(a1890) | c0_1(a1866) | (~ndr1_0) | (~c2_1(a1890)) | c3_1(a1890) | (~c3_1(a1866)) | (~c1_1(a1866)) | (~c0_1(a1911)) | (~c2_1(a1911)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1911) | c1_1(a1890) | c0_1(a1866) | (~ndr1_0) | (~c2_1(a1890)) | c3_1(a1890) | (~c3_1(a1866)) | (~c1_1(a1866)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(840,plain,
% 0.63/0.78 (((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1890) | c1_1(a1890) | (~c2_1(a1890)) | c0_1(a1866) | (~c3_1(a1866)) | (~c1_1(a1866))) <=> (c3_1(a1911) | c1_1(a1890) | c0_1(a1866) | (~ndr1_0) | (~c2_1(a1890)) | c3_1(a1890) | (~c3_1(a1866)) | (~c1_1(a1866)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(841,plain,
% 0.63/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1890) | c1_1(a1890) | (~c2_1(a1890)) | c0_1(a1866) | (~c3_1(a1866)) | (~c1_1(a1866)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a1911) | c1_1(a1890) | c0_1(a1866) | (~ndr1_0) | (~c2_1(a1890)) | c3_1(a1890) | (~c3_1(a1866)) | (~c1_1(a1866)) | (~c0_1(a1911)) | (~c2_1(a1911))))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[840])).
% 0.63/0.78 tff(842,plain,
% 0.63/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1890) | c1_1(a1890) | (~c2_1(a1890)) | c0_1(a1866) | (~c3_1(a1866)) | (~c1_1(a1866)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1911) | c1_1(a1890) | c0_1(a1866) | (~ndr1_0) | (~c2_1(a1890)) | c3_1(a1890) | (~c3_1(a1866)) | (~c1_1(a1866)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.63/0.78 inference(transitivity,[status(thm)],[841, 839])).
% 0.63/0.78 tff(843,plain,
% 0.63/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1890) | c1_1(a1890) | (~c2_1(a1890)) | c0_1(a1866) | (~c3_1(a1866)) | (~c1_1(a1866)))),
% 0.63/0.78 inference(quant_inst,[status(thm)],[])).
% 0.63/0.78 tff(844,plain,
% 0.63/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1911) | c1_1(a1890) | c0_1(a1866) | (~ndr1_0) | (~c2_1(a1890)) | c3_1(a1890) | (~c3_1(a1866)) | (~c1_1(a1866)) | (~c0_1(a1911)) | (~c2_1(a1911))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[843, 842])).
% 0.63/0.78 tff(845,plain,
% 0.63/0.78 (~c1_1(a1866)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[844, 125, 838, 815, 837, 829, 782, 828, 208, 797, 796])).
% 0.63/0.78 tff(846,plain,
% 0.63/0.78 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | c0_1(a1866) | (~ndr1_0) | (~c3_1(a1866)) | c1_1(a1866))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1866) | (~ndr1_0) | (~c3_1(a1866)) | c1_1(a1866))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(847,plain,
% 0.63/0.78 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a1866) | c0_1(a1866) | (~c3_1(a1866))) <=> (hskp16 | hskp13 | c0_1(a1866) | (~ndr1_0) | (~c3_1(a1866)) | c1_1(a1866))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(848,plain,
% 0.63/0.78 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1866) | c0_1(a1866) | (~c3_1(a1866)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | c0_1(a1866) | (~ndr1_0) | (~c3_1(a1866)) | c1_1(a1866)))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[847])).
% 0.63/0.78 tff(849,plain,
% 0.63/0.78 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1866) | c0_1(a1866) | (~c3_1(a1866)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1866) | (~ndr1_0) | (~c3_1(a1866)) | c1_1(a1866))),
% 0.63/0.78 inference(transitivity,[status(thm)],[848, 846])).
% 0.63/0.78 tff(850,plain,
% 0.63/0.78 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1866) | c0_1(a1866) | (~c3_1(a1866)))),
% 0.63/0.78 inference(quant_inst,[status(thm)],[])).
% 0.63/0.78 tff(851,plain,
% 0.63/0.78 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1866) | (~ndr1_0) | (~c3_1(a1866)) | c1_1(a1866)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[850, 849])).
% 0.63/0.78 tff(852,plain,
% 0.63/0.78 ($false),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[851, 125, 647, 789, 837, 828, 646, 845])).
% 0.63/0.78 tff(853,plain,((~hskp20) | hskp16 | hskp13 | (~c0_1(a1911)) | c3_1(a1911) | (~c2_1(a1911))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.78 tff(854,plain,
% 0.63/0.78 (~hskp20),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[853, 647, 712, 775, 772, 774])).
% 0.63/0.78 tff(855,plain,
% 0.63/0.78 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.63/0.78 inference(bind,[status(th)],[])).
% 0.63/0.78 tff(856,plain,
% 0.63/0.78 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.63/0.78 inference(quant_intro,[status(thm)],[855])).
% 0.63/0.78 tff(857,plain,
% 0.63/0.78 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(858,plain,
% 0.63/0.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp20) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.63/0.79 inference(bind,[status(th)],[])).
% 0.63/0.79 tff(859,plain,
% 0.63/0.79 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.63/0.79 inference(quant_intro,[status(thm)],[858])).
% 0.63/0.79 tff(860,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 0.63/0.79 tff(861,plain,
% 0.63/0.79 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[860, 859])).
% 0.63/0.79 tff(862,plain,
% 0.63/0.79 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[861, 857])).
% 0.63/0.79 tff(863,plain,(
% 0.63/0.79 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.63/0.79 inference(skolemize,[status(sab)],[862])).
% 0.63/0.79 tff(864,plain,
% 0.63/0.79 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[863, 856])).
% 0.63/0.79 tff(865,plain,
% 0.63/0.79 (^[U: $i] : refl((hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.63/0.79 inference(bind,[status(th)],[])).
% 0.63/0.79 tff(866,plain,
% 0.63/0.79 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.79 inference(quant_intro,[status(thm)],[865])).
% 0.63/0.79 tff(867,plain,
% 0.63/0.79 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(868,plain,
% 0.63/0.79 (^[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)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp18) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp18))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp18) <=> (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.63/0.79 inference(bind,[status(th)],[])).
% 0.63/0.79 tff(869,plain,
% 0.63/0.79 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp18) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.79 inference(quant_intro,[status(thm)],[868])).
% 0.63/0.79 tff(870,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.63/0.79 tff(871,plain,
% 0.63/0.79 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[870, 869])).
% 0.63/0.79 tff(872,plain,
% 0.63/0.79 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[871, 867])).
% 0.63/0.79 tff(873,plain,(
% 0.63/0.79 ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.79 inference(skolemize,[status(sab)],[872])).
% 0.63/0.79 tff(874,plain,
% 0.63/0.79 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[873, 866])).
% 0.63/0.79 tff(875,plain,
% 0.63/0.79 ((hskp17 | hskp16 | hskp8) <=> (hskp17 | hskp16 | hskp8)),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(876,plain,
% 0.63/0.79 (((hskp17 | hskp8) | hskp16) <=> (hskp17 | hskp16 | hskp8)),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(877,plain,
% 0.63/0.79 ((hskp8 | hskp17) <=> (hskp17 | hskp8)),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(878,plain,
% 0.63/0.79 (((hskp8 | hskp17) | hskp16) <=> ((hskp17 | hskp8) | hskp16)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[877])).
% 0.63/0.79 tff(879,plain,
% 0.63/0.79 (((hskp8 | hskp17) | hskp16) <=> (hskp17 | hskp16 | hskp8)),
% 0.63/0.79 inference(transitivity,[status(thm)],[878, 876])).
% 0.63/0.79 tff(880,axiom,((hskp8 | hskp17) | hskp16), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.63/0.79 tff(881,plain,
% 0.63/0.79 (hskp17 | hskp16 | hskp8),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[880, 879])).
% 0.63/0.79 tff(882,plain,
% 0.63/0.79 (hskp17 | hskp16 | hskp8),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[881, 875])).
% 0.63/0.79 tff(883,plain,
% 0.63/0.79 (hskp17 | hskp16 | hskp8),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[882, 875])).
% 0.63/0.79 tff(884,plain,
% 0.63/0.79 (hskp17 | hskp16 | hskp8),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[883, 875])).
% 0.63/0.79 tff(885,plain,
% 0.63/0.79 (hskp17 | hskp16 | hskp8),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[884, 875])).
% 0.63/0.79 tff(886,plain,
% 0.63/0.79 (hskp17),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[885, 684, 647])).
% 0.63/0.79 tff(887,plain,
% 0.63/0.79 (((~hskp17) | (~c1_1(a1874))) <=> ((~hskp17) | (~c1_1(a1874)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(888,plain,
% 0.63/0.79 (((~c1_1(a1874)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1874)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(889,axiom,((~c1_1(a1874)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.63/0.79 tff(890,plain,
% 0.63/0.79 ((~hskp17) | (~c1_1(a1874))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[889, 888])).
% 0.63/0.79 tff(891,plain,
% 0.63/0.79 ((~hskp17) | (~c1_1(a1874))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[890, 887])).
% 0.63/0.79 tff(892,plain,
% 0.63/0.79 (~c1_1(a1874)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[891, 886])).
% 0.63/0.79 tff(893,plain,
% 0.63/0.79 (((~hskp17) | c2_1(a1874)) <=> ((~hskp17) | c2_1(a1874))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(894,axiom,((~hskp17) | c2_1(a1874)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.63/0.79 tff(895,plain,
% 0.63/0.79 ((~hskp17) | c2_1(a1874)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[894, 893])).
% 0.63/0.79 tff(896,plain,
% 0.63/0.79 ((~hskp17) | c2_1(a1874)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[895, 893])).
% 0.63/0.79 tff(897,plain,
% 0.63/0.79 ((~hskp17) | c2_1(a1874)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[896, 893])).
% 0.63/0.79 tff(898,plain,
% 0.63/0.79 ((~hskp17) | c2_1(a1874)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[897, 893])).
% 0.63/0.79 tff(899,plain,
% 0.63/0.79 ((~hskp17) | c2_1(a1874)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[898, 893])).
% 0.63/0.79 tff(900,plain,
% 0.63/0.79 (c2_1(a1874)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[899, 886])).
% 0.63/0.79 tff(901,plain,
% 0.63/0.79 (((~hskp17) | c0_1(a1874)) <=> ((~hskp17) | c0_1(a1874))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(902,axiom,((~hskp17) | c0_1(a1874)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.63/0.79 tff(903,plain,
% 0.63/0.79 ((~hskp17) | c0_1(a1874)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[902, 901])).
% 0.63/0.79 tff(904,plain,
% 0.63/0.79 ((~hskp17) | c0_1(a1874)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[903, 901])).
% 0.63/0.79 tff(905,plain,
% 0.63/0.79 ((~hskp17) | c0_1(a1874)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[904, 901])).
% 0.63/0.79 tff(906,plain,
% 0.63/0.79 ((~hskp17) | c0_1(a1874)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[905, 901])).
% 0.63/0.79 tff(907,plain,
% 0.63/0.79 ((~hskp17) | c0_1(a1874)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[906, 901])).
% 0.63/0.79 tff(908,plain,
% 0.63/0.79 (c0_1(a1874)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[907, 886])).
% 0.63/0.79 tff(909,plain,
% 0.63/0.79 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | c1_1(a1874) | (~ndr1_0) | (~c0_1(a1874)) | (~c2_1(a1874)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp8 | c1_1(a1874) | (~ndr1_0) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(910,plain,
% 0.63/0.79 ((hskp18 | hskp8 | (~ndr1_0) | c1_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874))) <=> (hskp18 | hskp8 | c1_1(a1874) | (~ndr1_0) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(911,plain,
% 0.63/0.79 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c1_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | c1_1(a1874) | (~ndr1_0) | (~c0_1(a1874)) | (~c2_1(a1874))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[910])).
% 0.63/0.79 tff(912,plain,
% 0.63/0.79 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c1_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp8 | c1_1(a1874) | (~ndr1_0) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.63/0.79 inference(transitivity,[status(thm)],[911, 909])).
% 0.63/0.79 tff(913,plain,
% 0.63/0.79 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c1_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(914,plain,
% 0.63/0.79 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp8 | c1_1(a1874) | (~ndr1_0) | (~c0_1(a1874)) | (~c2_1(a1874))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[913, 912])).
% 0.63/0.79 tff(915,plain,
% 0.63/0.79 (hskp18),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[914, 125, 684, 908, 900, 892, 874])).
% 0.63/0.79 tff(916,plain,
% 0.63/0.79 (((~hskp18) | (~c3_1(a1875))) <=> ((~hskp18) | (~c3_1(a1875)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(917,plain,
% 0.63/0.79 (((~c3_1(a1875)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a1875)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(918,axiom,((~c3_1(a1875)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.63/0.79 tff(919,plain,
% 0.63/0.79 ((~hskp18) | (~c3_1(a1875))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[918, 917])).
% 0.63/0.79 tff(920,plain,
% 0.63/0.79 ((~hskp18) | (~c3_1(a1875))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[919, 916])).
% 0.63/0.79 tff(921,plain,
% 0.63/0.79 (~c3_1(a1875)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[920, 915])).
% 0.63/0.79 tff(922,plain,
% 0.63/0.79 (((~hskp18) | c1_1(a1875)) <=> ((~hskp18) | c1_1(a1875))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(923,axiom,((~hskp18) | c1_1(a1875)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.63/0.79 tff(924,plain,
% 0.63/0.79 ((~hskp18) | c1_1(a1875)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[923, 922])).
% 0.63/0.79 tff(925,plain,
% 0.63/0.79 ((~hskp18) | c1_1(a1875)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[924, 922])).
% 0.63/0.79 tff(926,plain,
% 0.63/0.79 ((~hskp18) | c1_1(a1875)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[925, 922])).
% 0.63/0.79 tff(927,plain,
% 0.63/0.79 ((~hskp18) | c1_1(a1875)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[926, 922])).
% 0.63/0.79 tff(928,plain,
% 0.63/0.79 ((~hskp18) | c1_1(a1875)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[927, 922])).
% 0.63/0.79 tff(929,plain,
% 0.63/0.79 (c1_1(a1875)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[928, 915])).
% 0.63/0.79 tff(930,assumption,(c3_1(a1858)), introduced(assumption)).
% 0.63/0.79 tff(931,assumption,(c1_1(a1858)), introduced(assumption)).
% 0.63/0.79 tff(932,assumption,(c0_1(a1858)), introduced(assumption)).
% 0.63/0.79 tff(933,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp20 | c3_1(a1875) | (~ndr1_0) | (~c1_1(a1875)) | c2_1(a1875) | (~c3_1(a1858)) | (~c0_1(a1858)) | (~c1_1(a1858)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp20 | c3_1(a1875) | (~ndr1_0) | (~c1_1(a1875)) | c2_1(a1875) | (~c3_1(a1858)) | (~c0_1(a1858)) | (~c1_1(a1858)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(934,plain,
% 0.63/0.79 ((hskp20 | (~ndr1_0) | (~c3_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)) | c3_1(a1875) | c2_1(a1875) | (~c1_1(a1875))) <=> (hskp20 | c3_1(a1875) | (~ndr1_0) | (~c1_1(a1875)) | c2_1(a1875) | (~c3_1(a1858)) | (~c0_1(a1858)) | (~c1_1(a1858)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(935,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)) | c3_1(a1875) | c2_1(a1875) | (~c1_1(a1875)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp20 | c3_1(a1875) | (~ndr1_0) | (~c1_1(a1875)) | c2_1(a1875) | (~c3_1(a1858)) | (~c0_1(a1858)) | (~c1_1(a1858))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[934])).
% 0.63/0.79 tff(936,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)) | c3_1(a1875) | c2_1(a1875) | (~c1_1(a1875)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp20 | c3_1(a1875) | (~ndr1_0) | (~c1_1(a1875)) | c2_1(a1875) | (~c3_1(a1858)) | (~c0_1(a1858)) | (~c1_1(a1858)))),
% 0.63/0.79 inference(transitivity,[status(thm)],[935, 933])).
% 0.63/0.79 tff(937,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)) | c3_1(a1875) | c2_1(a1875) | (~c1_1(a1875)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(938,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp20 | c3_1(a1875) | (~ndr1_0) | (~c1_1(a1875)) | c2_1(a1875) | (~c3_1(a1858)) | (~c0_1(a1858)) | (~c1_1(a1858))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[937, 936])).
% 0.63/0.79 tff(939,plain,
% 0.63/0.79 (hskp20 | c2_1(a1875)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[938, 125, 932, 931, 930, 929, 921, 864])).
% 0.63/0.79 tff(940,plain,
% 0.63/0.79 (c2_1(a1875)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[939, 854])).
% 0.63/0.79 tff(941,plain,
% 0.63/0.79 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.63/0.79 inference(bind,[status(th)],[])).
% 0.63/0.79 tff(942,plain,
% 0.63/0.79 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.79 inference(quant_intro,[status(thm)],[941])).
% 0.63/0.79 tff(943,plain,
% 0.63/0.79 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(944,plain,
% 0.63/0.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp21) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.63/0.79 inference(bind,[status(th)],[])).
% 0.63/0.79 tff(945,plain,
% 0.63/0.79 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.79 inference(quant_intro,[status(thm)],[944])).
% 0.63/0.79 tff(946,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 0.63/0.79 tff(947,plain,
% 0.63/0.79 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[946, 945])).
% 0.63/0.79 tff(948,plain,
% 0.63/0.79 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[947, 943])).
% 0.63/0.79 tff(949,plain,(
% 0.63/0.79 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.79 inference(skolemize,[status(sab)],[948])).
% 0.63/0.79 tff(950,plain,
% 0.63/0.79 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[949, 942])).
% 0.63/0.79 tff(951,plain,
% 0.63/0.79 (((~hskp18) | c0_1(a1875)) <=> ((~hskp18) | c0_1(a1875))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(952,axiom,((~hskp18) | c0_1(a1875)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.63/0.79 tff(953,plain,
% 0.63/0.79 ((~hskp18) | c0_1(a1875)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[952, 951])).
% 0.63/0.79 tff(954,plain,
% 0.63/0.79 ((~hskp18) | c0_1(a1875)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[953, 951])).
% 0.63/0.79 tff(955,plain,
% 0.63/0.79 ((~hskp18) | c0_1(a1875)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[954, 951])).
% 0.63/0.79 tff(956,plain,
% 0.63/0.79 ((~hskp18) | c0_1(a1875)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[955, 951])).
% 0.63/0.79 tff(957,plain,
% 0.63/0.79 ((~hskp18) | c0_1(a1875)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[956, 951])).
% 0.63/0.79 tff(958,plain,
% 0.63/0.79 (c0_1(a1875)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[957, 915])).
% 0.63/0.79 tff(959,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)) | (~c0_1(a1911)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)) | (~c0_1(a1911)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(960,plain,
% 0.63/0.79 ((hskp21 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)) | c3_1(a1911) | c1_1(a1911) | (~c0_1(a1911))) <=> (hskp21 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)) | (~c0_1(a1911)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(961,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)) | c3_1(a1911) | c1_1(a1911) | (~c0_1(a1911)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)) | (~c0_1(a1911))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[960])).
% 0.63/0.79 tff(962,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)) | c3_1(a1911) | c1_1(a1911) | (~c0_1(a1911)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)) | (~c0_1(a1911)))),
% 0.63/0.79 inference(transitivity,[status(thm)],[961, 959])).
% 0.63/0.79 tff(963,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)) | c3_1(a1911) | c1_1(a1911) | (~c0_1(a1911)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(964,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)) | (~c0_1(a1911))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[963, 962])).
% 0.63/0.79 tff(965,plain,
% 0.63/0.79 (hskp21),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[964, 125, 775, 958, 929, 773, 772, 950, 940])).
% 0.63/0.79 tff(966,plain,
% 0.63/0.79 (((~hskp21) | (~c1_1(a1898))) <=> ((~hskp21) | (~c1_1(a1898)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(967,plain,
% 0.63/0.79 (((~c1_1(a1898)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a1898)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(968,axiom,((~c1_1(a1898)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.63/0.79 tff(969,plain,
% 0.63/0.79 ((~hskp21) | (~c1_1(a1898))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[968, 967])).
% 0.63/0.79 tff(970,plain,
% 0.63/0.79 ((~hskp21) | (~c1_1(a1898))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[969, 966])).
% 0.63/0.79 tff(971,plain,
% 0.63/0.79 (~c1_1(a1898)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[970, 965])).
% 0.63/0.79 tff(972,plain,
% 0.63/0.79 (((~hskp21) | (~c0_1(a1898))) <=> ((~hskp21) | (~c0_1(a1898)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(973,plain,
% 0.63/0.79 (((~c0_1(a1898)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a1898)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(974,axiom,((~c0_1(a1898)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.63/0.79 tff(975,plain,
% 0.63/0.79 ((~hskp21) | (~c0_1(a1898))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[974, 973])).
% 0.63/0.79 tff(976,plain,
% 0.63/0.79 ((~hskp21) | (~c0_1(a1898))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[975, 972])).
% 0.63/0.79 tff(977,plain,
% 0.63/0.79 (~c0_1(a1898)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[976, 965])).
% 0.63/0.79 tff(978,plain,
% 0.63/0.79 (((~hskp21) | c3_1(a1898)) <=> ((~hskp21) | c3_1(a1898))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(979,axiom,((~hskp21) | c3_1(a1898)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.63/0.79 tff(980,plain,
% 0.63/0.79 ((~hskp21) | c3_1(a1898)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.63/0.79 tff(981,plain,
% 0.63/0.79 ((~hskp21) | c3_1(a1898)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[980, 978])).
% 0.63/0.79 tff(982,plain,
% 0.63/0.79 ((~hskp21) | c3_1(a1898)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[981, 978])).
% 0.63/0.79 tff(983,plain,
% 0.63/0.79 ((~hskp21) | c3_1(a1898)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[982, 978])).
% 0.63/0.79 tff(984,plain,
% 0.63/0.79 ((~hskp21) | c3_1(a1898)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[983, 978])).
% 0.63/0.79 tff(985,plain,
% 0.63/0.79 (c3_1(a1898)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[984, 965])).
% 0.63/0.79 tff(986,plain,
% 0.63/0.79 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(987,plain,
% 0.63/0.79 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898))) <=> (hskp16 | hskp13 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(988,plain,
% 0.63/0.79 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[987])).
% 0.63/0.79 tff(989,plain,
% 0.63/0.79 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))),
% 0.63/0.79 inference(transitivity,[status(thm)],[988, 986])).
% 0.63/0.79 tff(990,plain,
% 0.63/0.79 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(991,plain,
% 0.63/0.79 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[990, 989])).
% 0.63/0.79 tff(992,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[991, 125, 647, 712, 985, 977, 971, 646])).
% 0.63/0.79 tff(993,plain,(hskp16 | (~c0_1(a1858)) | (~c1_1(a1858)) | (~c3_1(a1858)) | hskp22 | (~c3_1(a1919)) | c1_1(a1919) | c2_1(a1919) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c3_1(a1877))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(994,plain,
% 0.63/0.79 (hskp16),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[993, 636, 635, 634, 401, 413, 425, 412, 424, 423, 422])).
% 0.63/0.79 tff(995,plain,
% 0.63/0.79 (c2_1(a1872)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[577, 994])).
% 0.63/0.79 tff(996,plain,
% 0.63/0.79 (~c0_1(a1872)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[553, 994])).
% 0.63/0.79 tff(997,plain,
% 0.63/0.79 (c3_1(a1872)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[569, 994])).
% 0.63/0.79 tff(998,assumption,(~c0_1(a1872)), introduced(assumption)).
% 0.63/0.79 tff(999,assumption,(c2_1(a1872)), introduced(assumption)).
% 0.63/0.79 tff(1000,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | (~c1_1(a1872)) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | (~c1_1(a1872)) | (~c3_1(a1919)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1001,plain,
% 0.63/0.79 ((hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872))) <=> (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | (~c1_1(a1872)) | (~c3_1(a1919)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1002,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | (~c1_1(a1872)) | (~c3_1(a1919))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1001])).
% 0.63/0.79 tff(1003,plain,
% 0.63/0.79 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | (~c1_1(a1872)) | (~c3_1(a1919)))),
% 0.63/0.79 inference(transitivity,[status(thm)],[1002, 1000])).
% 0.63/0.79 tff(1004,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872)))),
% 0.63/0.79 inference(quant_inst,[status(thm)],[])).
% 0.63/0.79 tff(1005,plain,
% 0.63/0.79 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | (~c1_1(a1872)) | (~c3_1(a1919))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 0.63/0.79 tff(1006,plain,
% 0.63/0.79 (hskp8 | (~c1_1(a1872))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1005, 125, 413, 999, 425, 412, 998, 505])).
% 0.63/0.79 tff(1007,plain,
% 0.63/0.79 (~c1_1(a1872)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1006, 21])).
% 0.63/0.79 tff(1008,plain,
% 0.63/0.79 (^[U: $i] : refl((hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.63/0.79 inference(bind,[status(th)],[])).
% 0.63/0.79 tff(1009,plain,
% 0.63/0.79 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.79 inference(quant_intro,[status(thm)],[1008])).
% 0.63/0.79 tff(1010,plain,
% 0.63/0.79 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1011,plain,
% 0.63/0.79 (^[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)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp15) | hskp3) <=> ((hskp15 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp3))), rewrite(((hskp15 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp3) <=> (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp15) | hskp3) <=> (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(1012,plain,
% 0.63/0.80 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp15) | hskp3) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[1011])).
% 0.63/0.80 tff(1013,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp15) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.63/0.80 tff(1014,plain,
% 0.63/0.80 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 0.63/0.80 tff(1015,plain,
% 0.63/0.80 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1014, 1010])).
% 0.63/0.80 tff(1016,plain,(
% 0.63/0.80 ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.80 inference(skolemize,[status(sab)],[1015])).
% 0.63/0.80 tff(1017,plain,
% 0.63/0.80 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1016, 1009])).
% 0.63/0.80 tff(1018,assumption,(c3_1(a1872)), introduced(assumption)).
% 0.63/0.80 tff(1019,plain,
% 0.63/0.80 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | c0_1(a1872) | (~ndr1_0) | (~c3_1(a1872)) | c1_1(a1872))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp3 | c0_1(a1872) | (~ndr1_0) | (~c3_1(a1872)) | c1_1(a1872))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1020,plain,
% 0.63/0.80 ((hskp15 | hskp3 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c3_1(a1872))) <=> (hskp15 | hskp3 | c0_1(a1872) | (~ndr1_0) | (~c3_1(a1872)) | c1_1(a1872))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1021,plain,
% 0.63/0.80 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c3_1(a1872)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | c0_1(a1872) | (~ndr1_0) | (~c3_1(a1872)) | c1_1(a1872)))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1020])).
% 0.63/0.80 tff(1022,plain,
% 0.63/0.80 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c3_1(a1872)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp3 | c0_1(a1872) | (~ndr1_0) | (~c3_1(a1872)) | c1_1(a1872))),
% 0.63/0.80 inference(transitivity,[status(thm)],[1021, 1019])).
% 0.63/0.80 tff(1023,plain,
% 0.63/0.80 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c3_1(a1872)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(1024,plain,
% 0.63/0.80 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp3 | c0_1(a1872) | (~ndr1_0) | (~c3_1(a1872)) | c1_1(a1872)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 0.63/0.80 tff(1025,plain,
% 0.63/0.80 (hskp15 | c1_1(a1872)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1024, 125, 474, 1018, 998, 1017])).
% 0.63/0.80 tff(1026,plain,
% 0.63/0.80 (hskp15),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1025, 1007])).
% 0.63/0.80 tff(1027,plain,
% 0.63/0.80 (((~hskp15) | (~c0_1(a1870))) <=> ((~hskp15) | (~c0_1(a1870)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1028,plain,
% 0.63/0.80 (((~c0_1(a1870)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a1870)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1029,axiom,((~c0_1(a1870)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.63/0.80 tff(1030,plain,
% 0.63/0.80 ((~hskp15) | (~c0_1(a1870))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 0.63/0.80 tff(1031,plain,
% 0.63/0.80 ((~hskp15) | (~c0_1(a1870))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1030, 1027])).
% 0.63/0.80 tff(1032,plain,
% 0.63/0.80 (~c0_1(a1870)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1031, 1026])).
% 0.63/0.80 tff(1033,plain,
% 0.63/0.80 (((~hskp15) | c1_1(a1870)) <=> ((~hskp15) | c1_1(a1870))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1034,axiom,((~hskp15) | c1_1(a1870)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.63/0.80 tff(1035,plain,
% 0.63/0.80 ((~hskp15) | c1_1(a1870)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 0.63/0.80 tff(1036,plain,
% 0.63/0.80 ((~hskp15) | c1_1(a1870)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1035, 1033])).
% 0.63/0.80 tff(1037,plain,
% 0.63/0.80 ((~hskp15) | c1_1(a1870)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1036, 1033])).
% 0.63/0.80 tff(1038,plain,
% 0.63/0.80 ((~hskp15) | c1_1(a1870)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1037, 1033])).
% 0.63/0.80 tff(1039,plain,
% 0.63/0.80 ((~hskp15) | c1_1(a1870)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1038, 1033])).
% 0.63/0.80 tff(1040,plain,
% 0.63/0.80 (c1_1(a1870)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1039, 1026])).
% 0.63/0.80 tff(1041,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | c2_1(a1870) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | c2_1(a1870) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1042,plain,
% 0.63/0.80 ((hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1870) | c2_1(a1870) | (~c1_1(a1870))) <=> (hskp8 | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | c2_1(a1870) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1043,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1870) | c2_1(a1870) | (~c1_1(a1870)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | c2_1(a1870) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1042])).
% 0.63/0.80 tff(1044,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1870) | c2_1(a1870) | (~c1_1(a1870)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | c2_1(a1870) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[1043, 1041])).
% 0.63/0.80 tff(1045,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1870) | c2_1(a1870) | (~c1_1(a1870)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(1046,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | c2_1(a1870) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 0.63/0.80 tff(1047,plain,
% 0.63/0.80 (c2_1(a1870)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1046, 125, 21, 251, 250, 249, 1040, 1032, 31])).
% 0.63/0.80 tff(1048,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | (~c2_1(a1870)) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | (~c2_1(a1870)) | (~c3_1(a1919)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1049,plain,
% 0.63/0.80 ((hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1870) | (~c2_1(a1870)) | (~c1_1(a1870))) <=> (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | (~c2_1(a1870)) | (~c3_1(a1919)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1050,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1870) | (~c2_1(a1870)) | (~c1_1(a1870)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | (~c2_1(a1870)) | (~c3_1(a1919))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1049])).
% 0.63/0.80 tff(1051,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1870) | (~c2_1(a1870)) | (~c1_1(a1870)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | (~c2_1(a1870)) | (~c3_1(a1919)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[1050, 1048])).
% 0.63/0.80 tff(1052,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1870) | (~c2_1(a1870)) | (~c1_1(a1870)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(1053,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | (~c2_1(a1870)) | (~c3_1(a1919))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 0.63/0.80 tff(1054,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1053, 125, 21, 413, 1040, 425, 412, 1032, 505, 1047])).
% 0.63/0.80 tff(1055,plain,(hskp8 | (~c3_1(a1919)) | c1_1(a1919) | c2_1(a1919) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c3_1(a1877)) | hskp3 | (~c3_1(a1872)) | c0_1(a1872) | (~c2_1(a1872))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(1056,plain,
% 0.63/0.80 (hskp8),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1055, 424, 425, 412, 413, 423, 422, 474, 997, 996, 995])).
% 0.63/0.80 tff(1057,plain,
% 0.63/0.80 (~c2_1(a1862)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[517, 1056])).
% 0.63/0.80 tff(1058,plain,
% 0.63/0.80 (c1_1(a1862)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[561, 1056])).
% 0.63/0.80 tff(1059,plain,
% 0.63/0.80 (~c3_1(a1862)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[584, 125, 413, 995, 997, 1058, 425, 996, 1057, 10, 400])).
% 0.63/0.80 tff(1060,plain,
% 0.63/0.80 (c0_1(a1862)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[674, 1056])).
% 0.63/0.80 tff(1061,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[681, 125, 1060, 1058, 1057, 362, 1059])).
% 0.63/0.80 tff(1062,plain,(hskp22 | (~c3_1(a1919)) | c1_1(a1919) | (~c0_1(a1919)) | c2_1(a1919) | hskp3 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(1063,plain,
% 0.63/0.80 (hskp22),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1062, 345, 337, 352, 331, 399, 43])).
% 0.63/0.80 tff(1064,plain,
% 0.63/0.80 (((~hskp22) | (~c3_1(a1899))) <=> ((~hskp22) | (~c3_1(a1899)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1065,plain,
% 0.63/0.80 (((~c3_1(a1899)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a1899)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1066,axiom,((~c3_1(a1899)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.63/0.80 tff(1067,plain,
% 0.63/0.80 ((~hskp22) | (~c3_1(a1899))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 0.63/0.80 tff(1068,plain,
% 0.63/0.80 ((~hskp22) | (~c3_1(a1899))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1067, 1064])).
% 0.63/0.80 tff(1069,plain,
% 0.63/0.80 (~c3_1(a1899)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1068, 1063])).
% 0.63/0.80 tff(1070,plain,
% 0.63/0.80 (((~hskp22) | (~c2_1(a1899))) <=> ((~hskp22) | (~c2_1(a1899)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1071,plain,
% 0.63/0.80 (((~c2_1(a1899)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a1899)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1072,axiom,((~c2_1(a1899)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.63/0.80 tff(1073,plain,
% 0.63/0.80 ((~hskp22) | (~c2_1(a1899))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 0.63/0.80 tff(1074,plain,
% 0.63/0.80 ((~hskp22) | (~c2_1(a1899))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1073, 1070])).
% 0.63/0.80 tff(1075,plain,
% 0.63/0.80 (~c2_1(a1899)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1074, 1063])).
% 0.63/0.80 tff(1076,plain,
% 0.63/0.80 (((~hskp22) | c0_1(a1899)) <=> ((~hskp22) | c0_1(a1899))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1077,axiom,((~hskp22) | c0_1(a1899)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.63/0.80 tff(1078,plain,
% 0.63/0.80 ((~hskp22) | c0_1(a1899)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 0.63/0.80 tff(1079,plain,
% 0.63/0.80 ((~hskp22) | c0_1(a1899)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1078, 1076])).
% 0.63/0.80 tff(1080,plain,
% 0.63/0.80 ((~hskp22) | c0_1(a1899)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1079, 1076])).
% 0.63/0.80 tff(1081,plain,
% 0.63/0.80 ((~hskp22) | c0_1(a1899)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1080, 1076])).
% 0.63/0.80 tff(1082,plain,
% 0.63/0.80 ((~hskp22) | c0_1(a1899)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1081, 1076])).
% 0.63/0.80 tff(1083,plain,
% 0.63/0.80 (c0_1(a1899)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1082, 1063])).
% 0.63/0.80 tff(1084,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1899)) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1899)) | (~c0_1(a1899)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1085,plain,
% 0.63/0.80 (((~ndr1_0) | c3_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c2_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c3_1(a1899) | c2_1(a1899) | (~c1_1(a1899))) <=> (c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1899)) | (~c0_1(a1899)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1086,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c2_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c3_1(a1899) | c2_1(a1899) | (~c1_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1899)) | (~c0_1(a1899))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1085])).
% 0.63/0.80 tff(1087,plain,
% 0.63/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c2_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c3_1(a1899) | c2_1(a1899) | (~c1_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1899)) | (~c0_1(a1899)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[1086, 1084])).
% 0.63/0.80 tff(1088,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c2_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c3_1(a1899) | c2_1(a1899) | (~c1_1(a1899)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(1089,plain,
% 0.63/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1899)) | (~c0_1(a1899))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 0.63/0.80 tff(1090,plain,
% 0.63/0.80 (~c1_1(a1899)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1089, 125, 1083, 1075, 1069, 362])).
% 0.63/0.80 tff(1091,plain,
% 0.63/0.80 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(1092,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[1091])).
% 0.63/0.80 tff(1093,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1094,plain,
% 0.63/0.80 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(1095,plain,
% 0.63/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[1094])).
% 0.63/0.80 tff(1096,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.63/0.80 tff(1097,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 0.63/0.80 tff(1098,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1097, 1093])).
% 0.63/0.80 tff(1099,plain,(
% 0.63/0.80 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(skolemize,[status(sab)],[1098])).
% 0.63/0.80 tff(1100,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1099, 1092])).
% 0.63/0.80 tff(1101,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a1919) | c2_1(a1919) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c0_1(a1899)) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a1919) | c2_1(a1919) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c0_1(a1899)) | (~c3_1(a1919)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1102,plain,
% 0.63/0.80 ((hskp9 | (~ndr1_0) | c2_1(a1899) | c3_1(a1899) | (~c0_1(a1899)) | c1_1(a1919) | c2_1(a1919) | (~c3_1(a1919))) <=> (hskp9 | c1_1(a1919) | c2_1(a1919) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c0_1(a1899)) | (~c3_1(a1919)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1103,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a1899) | c3_1(a1899) | (~c0_1(a1899)) | c1_1(a1919) | c2_1(a1919) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a1919) | c2_1(a1919) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c0_1(a1899)) | (~c3_1(a1919))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1102])).
% 0.63/0.80 tff(1104,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a1899) | c3_1(a1899) | (~c0_1(a1899)) | c1_1(a1919) | c2_1(a1919) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a1919) | c2_1(a1919) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c0_1(a1899)) | (~c3_1(a1919)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[1103, 1101])).
% 0.63/0.80 tff(1105,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a1899) | c3_1(a1899) | (~c0_1(a1899)) | c1_1(a1919) | c2_1(a1919) | (~c3_1(a1919)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(1106,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a1919) | c2_1(a1919) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c0_1(a1899)) | (~c3_1(a1919))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 0.63/0.80 tff(1107,plain,
% 0.63/0.80 (hskp9),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1106, 125, 345, 1083, 337, 331, 1075, 1069, 1100])).
% 0.63/0.80 tff(1108,plain,
% 0.63/0.80 (~c3_1(a1863)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[746, 1107])).
% 0.63/0.80 tff(1109,plain,
% 0.63/0.80 (~c1_1(a1863)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[752, 1107])).
% 0.63/0.80 tff(1110,plain,
% 0.63/0.80 (c2_1(a1863)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[760, 1107])).
% 0.63/0.80 tff(1111,plain,
% 0.63/0.80 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(1112,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[1111])).
% 0.63/0.80 tff(1113,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1114,plain,
% 0.63/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~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))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp27) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp27))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(1115,plain,
% 0.63/0.80 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[1114])).
% 0.63/0.80 tff(1116,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.63/0.80 tff(1117,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 0.63/0.80 tff(1118,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1117, 1113])).
% 0.63/0.80 tff(1119,plain,(
% 0.63/0.80 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.80 inference(skolemize,[status(sab)],[1118])).
% 0.63/0.80 tff(1120,plain,
% 0.63/0.80 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1119, 1112])).
% 0.63/0.80 tff(1121,assumption,(~c3_1(a1863)), introduced(assumption)).
% 0.63/0.80 tff(1122,assumption,(~c1_1(a1863)), introduced(assumption)).
% 0.63/0.80 tff(1123,assumption,(~c1_1(a1899)), introduced(assumption)).
% 0.63/0.80 tff(1124,assumption,(~c3_1(a1899)), introduced(assumption)).
% 0.63/0.80 tff(1125,assumption,(c0_1(a1899)), introduced(assumption)).
% 0.63/0.80 tff(1126,assumption,(~hskp27), introduced(assumption)).
% 0.63/0.80 tff(1127,plain,
% 0.63/0.80 (hskp29),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[121, 1126, 32])).
% 0.63/0.80 tff(1128,plain,
% 0.63/0.80 (c2_1(a1885)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[72, 1127])).
% 0.63/0.80 tff(1129,plain,
% 0.63/0.80 (c1_1(a1885)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[80, 1127])).
% 0.63/0.80 tff(1130,plain,
% 0.63/0.80 (c0_1(a1885)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[88, 1127])).
% 0.63/0.80 tff(1131,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)) | c1_1(a1899) | (~c0_1(a1899)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)) | c1_1(a1899) | (~c0_1(a1899)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1132,plain,
% 0.63/0.80 ((hskp21 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)) | c3_1(a1899) | c1_1(a1899) | (~c0_1(a1899))) <=> (hskp21 | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)) | c1_1(a1899) | (~c0_1(a1899)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1133,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)) | c3_1(a1899) | c1_1(a1899) | (~c0_1(a1899)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)) | c1_1(a1899) | (~c0_1(a1899))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1132])).
% 0.63/0.80 tff(1134,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)) | c3_1(a1899) | c1_1(a1899) | (~c0_1(a1899)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)) | c1_1(a1899) | (~c0_1(a1899)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[1133, 1131])).
% 0.63/0.80 tff(1135,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)) | c3_1(a1899) | c1_1(a1899) | (~c0_1(a1899)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(1136,plain,
% 0.63/0.80 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)) | c1_1(a1899) | (~c0_1(a1899))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1135, 1134])).
% 0.63/0.80 tff(1137,plain,
% 0.63/0.80 (hskp21),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1136, 125, 1130, 1129, 1128, 1125, 1124, 950, 1123])).
% 0.63/0.80 tff(1138,plain,
% 0.63/0.80 (~c0_1(a1898)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[976, 1137])).
% 0.63/0.80 tff(1139,assumption,(c2_1(a1863)), introduced(assumption)).
% 0.63/0.80 tff(1140,plain,
% 0.63/0.80 (c3_1(a1898)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[984, 1137])).
% 0.63/0.80 tff(1141,plain,
% 0.63/0.80 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c0_1(a1898) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1898)) | (~c2_1(a1898)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c0_1(a1898) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1898)) | (~c2_1(a1898)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1142,plain,
% 0.63/0.81 ((hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1898) | (~c2_1(a1898)) | (~c3_1(a1898))) <=> (hskp27 | c0_1(a1898) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1898)) | (~c2_1(a1898)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1143,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1898) | (~c2_1(a1898)) | (~c3_1(a1898)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c0_1(a1898) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1898)) | (~c2_1(a1898))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1142])).
% 0.63/0.81 tff(1144,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1898) | (~c2_1(a1898)) | (~c3_1(a1898)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c0_1(a1898) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1898)) | (~c2_1(a1898)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1143, 1141])).
% 0.63/0.81 tff(1145,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1898) | (~c2_1(a1898)) | (~c3_1(a1898)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1146,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c0_1(a1898) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1898)) | (~c2_1(a1898))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 0.63/0.81 tff(1147,plain,
% 0.63/0.81 (~c2_1(a1898)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1146, 125, 1126, 1140, 1139, 1138, 1122, 1121, 1120])).
% 0.63/0.81 tff(1148,plain,
% 0.63/0.81 (~c1_1(a1898)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[970, 1137])).
% 0.63/0.81 tff(1149,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | c2_1(a1898) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | c2_1(a1898) | (~c3_1(a1919)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1150,plain,
% 0.63/0.81 ((hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898)) <=> (hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | c2_1(a1898) | (~c3_1(a1919)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1151,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | c2_1(a1898) | (~c3_1(a1919))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1150])).
% 0.63/0.81 tff(1152,plain,
% 0.63/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | c2_1(a1898) | (~c3_1(a1919)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1151, 1149])).
% 0.63/0.81 tff(1153,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1154,plain,
% 0.63/0.81 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | c2_1(a1898) | (~c3_1(a1919))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 0.63/0.81 tff(1155,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1154, 125, 32, 413, 425, 412, 1138, 1148, 42, 1147])).
% 0.63/0.81 tff(1156,plain,(hskp27 | hskp1 | (~c3_1(a1919)) | c1_1(a1919) | c2_1(a1919) | (~c2_1(a1863)) | c1_1(a1863) | c3_1(a1863) | (~c0_1(a1899)) | c3_1(a1899) | c1_1(a1899)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(1157,plain,
% 0.63/0.81 (hskp27),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1156, 345, 32, 337, 331, 1110, 1109, 1108, 1083, 1069, 1090])).
% 0.63/0.81 tff(1158,plain,
% 0.63/0.81 (c3_1(a1877)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[142, 1157])).
% 0.63/0.81 tff(1159,plain,
% 0.63/0.81 (c2_1(a1877)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[150, 1157])).
% 0.63/0.81 tff(1160,plain,
% 0.63/0.81 (c0_1(a1877)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[158, 1157])).
% 0.63/0.81 tff(1161,plain,
% 0.63/0.81 (^[U: $i] : refl((hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(1162,plain,
% 0.63/0.81 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[1161])).
% 0.63/0.81 tff(1163,plain,
% 0.63/0.81 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1164,plain,
% 0.63/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp21) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp21))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp21) <=> (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp21) <=> (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(1165,plain,
% 0.63/0.81 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp21) <=> ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[1164])).
% 0.63/0.81 tff(1166,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.63/0.81 tff(1167,plain,
% 0.63/0.81 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 0.63/0.81 tff(1168,plain,
% 0.63/0.81 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1167, 1163])).
% 0.63/0.81 tff(1169,plain,(
% 0.63/0.81 ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.63/0.81 inference(skolemize,[status(sab)],[1168])).
% 0.63/0.81 tff(1170,plain,
% 0.63/0.81 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1169, 1162])).
% 0.63/0.81 tff(1171,assumption,(~c2_1(a1899)), introduced(assumption)).
% 0.63/0.81 tff(1172,plain,
% 0.63/0.81 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | c1_1(a1899))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp21 | hskp8 | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | c1_1(a1899))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1173,plain,
% 0.63/0.81 ((hskp21 | hskp8 | (~ndr1_0) | c2_1(a1899) | c1_1(a1899) | c3_1(a1899)) <=> (hskp21 | hskp8 | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | c1_1(a1899))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1174,plain,
% 0.63/0.81 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | (~ndr1_0) | c2_1(a1899) | c1_1(a1899) | c3_1(a1899))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | c1_1(a1899)))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1173])).
% 0.63/0.81 tff(1175,plain,
% 0.63/0.81 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | (~ndr1_0) | c2_1(a1899) | c1_1(a1899) | c3_1(a1899))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp21 | hskp8 | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | c1_1(a1899))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1174, 1172])).
% 0.63/0.81 tff(1176,plain,
% 0.63/0.81 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | (~ndr1_0) | c2_1(a1899) | c1_1(a1899) | c3_1(a1899))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1177,plain,
% 0.63/0.81 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp21 | hskp8 | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | c1_1(a1899)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 0.63/0.81 tff(1178,plain,
% 0.63/0.81 (hskp21 | hskp8),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1177, 125, 1171, 1124, 1170, 1123])).
% 0.63/0.81 tff(1179,plain,
% 0.63/0.81 (hskp21),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1178, 21])).
% 0.63/0.81 tff(1180,plain,
% 0.63/0.81 (~c1_1(a1898)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[970, 1179])).
% 0.63/0.81 tff(1181,plain,
% 0.63/0.81 (~c0_1(a1898)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[976, 1179])).
% 0.63/0.81 tff(1182,plain,
% 0.63/0.81 (c3_1(a1898)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[984, 1179])).
% 0.63/0.81 tff(1183,plain,
% 0.63/0.81 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp3 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1184,plain,
% 0.63/0.81 ((hskp15 | hskp3 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898))) <=> (hskp15 | hskp3 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1185,plain,
% 0.63/0.81 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1184])).
% 0.63/0.81 tff(1186,plain,
% 0.63/0.81 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp3 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1185, 1183])).
% 0.63/0.81 tff(1187,plain,
% 0.63/0.81 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1188,plain,
% 0.63/0.81 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp3 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 0.63/0.81 tff(1189,plain,
% 0.63/0.81 (hskp15),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1188, 125, 474, 1182, 1181, 1180, 1017])).
% 0.63/0.81 tff(1190,plain,
% 0.63/0.81 (~c0_1(a1870)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1031, 1189])).
% 0.63/0.81 tff(1191,plain,
% 0.63/0.81 (c1_1(a1870)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1039, 1189])).
% 0.63/0.81 tff(1192,plain,
% 0.63/0.81 (c2_1(a1870)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1046, 125, 21, 251, 250, 249, 1191, 1190, 31])).
% 0.63/0.81 tff(1193,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1053, 125, 21, 413, 1191, 425, 412, 1190, 505, 1192])).
% 0.63/0.81 tff(1194,plain,(hskp8 | (~c3_1(a1919)) | c1_1(a1919) | c2_1(a1919) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c3_1(a1877)) | hskp3 | c2_1(a1899) | c3_1(a1899) | c1_1(a1899)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(1195,plain,
% 0.63/0.81 (hskp8),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1194, 345, 337, 331, 1160, 1159, 1158, 399, 1075, 1069, 1090])).
% 0.63/0.81 tff(1196,plain,
% 0.63/0.81 (~c2_1(a1862)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[517, 1195])).
% 0.63/0.81 tff(1197,plain,
% 0.63/0.81 (hskp16),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[683, 1195, 1160, 1159, 1158])).
% 0.63/0.81 tff(1198,plain,
% 0.63/0.81 (~c0_1(a1872)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[553, 1197])).
% 0.63/0.81 tff(1199,plain,
% 0.63/0.81 (c1_1(a1862)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[561, 1195])).
% 0.63/0.81 tff(1200,plain,
% 0.63/0.81 (c3_1(a1872)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[569, 1197])).
% 0.63/0.81 tff(1201,plain,
% 0.63/0.81 (c2_1(a1872)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[577, 1197])).
% 0.63/0.81 tff(1202,plain,
% 0.63/0.81 (~c3_1(a1862)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[584, 125, 345, 1201, 1200, 1199, 337, 1198, 1196, 10, 352])).
% 0.63/0.81 tff(1203,plain,
% 0.63/0.81 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(1204,plain,
% 0.63/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[1203])).
% 0.63/0.81 tff(1205,plain,
% 0.63/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1206,plain,
% 0.63/0.81 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_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))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_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))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(1207,plain,
% 0.63/0.81 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[1206])).
% 0.63/0.81 tff(1208,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.63/0.81 tff(1209,plain,
% 0.63/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 0.63/0.81 tff(1210,plain,
% 0.63/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1209, 1205])).
% 0.63/0.81 tff(1211,plain,(
% 0.63/0.81 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.63/0.81 inference(skolemize,[status(sab)],[1210])).
% 0.63/0.81 tff(1212,plain,
% 0.63/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1211, 1204])).
% 0.63/0.81 tff(1213,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a1919) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1899) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a1919) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1899) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1214,plain,
% 0.63/0.81 (((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c3_1(a1899) | c2_1(a1899) | c1_1(a1899)) <=> (c1_1(a1919) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1899) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1215,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c3_1(a1899) | c2_1(a1899) | c1_1(a1899))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a1919) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1899) | (~c3_1(a1919)) | (~c0_1(a1919))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[1214])).
% 0.63/0.81 tff(1216,plain,
% 0.63/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c3_1(a1899) | c2_1(a1899) | c1_1(a1899))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a1919) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1899) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[1215, 1213])).
% 0.63/0.81 tff(1217,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c3_1(a1899) | c2_1(a1899) | c1_1(a1899))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(1218,plain,
% 0.63/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a1919) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1899) | (~c3_1(a1919)) | (~c0_1(a1919))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 0.63/0.81 tff(1219,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1218, 125, 345, 1199, 337, 1075, 1069, 1196, 1212, 352, 1090, 1202])).
% 0.63/0.81 tff(1220,plain,(hskp0 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(1221,plain,
% 0.63/0.81 (hskp0),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1220, 32])).
% 0.63/0.81 tff(1222,plain,
% 0.63/0.81 (((~hskp0) | (~c2_1(a1852))) <=> ((~hskp0) | (~c2_1(a1852)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1223,plain,
% 0.63/0.81 (((~c2_1(a1852)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1852)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1224,axiom,((~c2_1(a1852)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.63/0.81 tff(1225,plain,
% 0.63/0.81 ((~hskp0) | (~c2_1(a1852))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 0.63/0.81 tff(1226,plain,
% 0.63/0.81 ((~hskp0) | (~c2_1(a1852))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1225, 1222])).
% 0.63/0.81 tff(1227,plain,
% 0.63/0.81 (~c2_1(a1852)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1226, 1221])).
% 0.63/0.81 tff(1228,plain,
% 0.63/0.81 (((~hskp0) | c3_1(a1852)) <=> ((~hskp0) | c3_1(a1852))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1229,axiom,((~hskp0) | c3_1(a1852)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.63/0.81 tff(1230,plain,
% 0.63/0.81 ((~hskp0) | c3_1(a1852)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 0.63/0.81 tff(1231,plain,
% 0.63/0.81 ((~hskp0) | c3_1(a1852)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1230, 1228])).
% 0.63/0.81 tff(1232,plain,
% 0.63/0.81 ((~hskp0) | c3_1(a1852)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1231, 1228])).
% 0.63/0.81 tff(1233,plain,
% 0.63/0.81 ((~hskp0) | c3_1(a1852)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1232, 1228])).
% 0.63/0.81 tff(1234,plain,
% 0.63/0.81 ((~hskp0) | c3_1(a1852)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1233, 1228])).
% 0.63/0.81 tff(1235,plain,
% 0.63/0.81 (c3_1(a1852)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1234, 1221])).
% 0.63/0.81 tff(1236,plain,
% 0.63/0.81 (((~hskp0) | c1_1(a1852)) <=> ((~hskp0) | c1_1(a1852))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1237,axiom,((~hskp0) | c1_1(a1852)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.63/0.81 tff(1238,plain,
% 0.63/0.81 ((~hskp0) | c1_1(a1852)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 0.63/0.81 tff(1239,plain,
% 0.63/0.81 ((~hskp0) | c1_1(a1852)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1238, 1236])).
% 0.63/0.81 tff(1240,plain,
% 0.63/0.81 ((~hskp0) | c1_1(a1852)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1239, 1236])).
% 0.63/0.81 tff(1241,plain,
% 0.63/0.81 ((~hskp0) | c1_1(a1852)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1240, 1236])).
% 0.63/0.81 tff(1242,plain,
% 0.63/0.81 ((~hskp0) | c1_1(a1852)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1241, 1236])).
% 0.63/0.81 tff(1243,plain,
% 0.63/0.81 (c1_1(a1852)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1242, 1221])).
% 0.63/0.81 tff(1244,assumption,(c0_1(a1852)), introduced(assumption)).
% 0.63/0.81 tff(1245,plain,
% 0.63/0.81 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(1246,plain,
% 0.63/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[1245])).
% 0.63/0.81 tff(1247,plain,
% 0.63/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(1248,plain,
% 0.63/0.81 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(1249,plain,
% 0.63/0.81 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[1248])).
% 0.63/0.82 tff(1250,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.63/0.82 tff(1251,plain,
% 0.63/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 0.63/0.82 tff(1252,plain,
% 0.63/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1251, 1247])).
% 0.63/0.82 tff(1253,plain,(
% 0.63/0.82 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.63/0.82 inference(skolemize,[status(sab)],[1252])).
% 0.63/0.82 tff(1254,plain,
% 0.63/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1253, 1246])).
% 0.63/0.82 tff(1255,assumption,(~c2_1(a1852)), introduced(assumption)).
% 0.63/0.82 tff(1256,assumption,(c3_1(a1852)), introduced(assumption)).
% 0.63/0.82 tff(1257,plain,
% 0.63/0.82 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c0_1(a1852)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c0_1(a1852)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1258,plain,
% 0.63/0.82 ((hskp27 | hskp22 | (~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c0_1(a1852))) <=> (hskp27 | hskp22 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c0_1(a1852)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1259,plain,
% 0.63/0.82 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c0_1(a1852)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c0_1(a1852))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1258])).
% 0.63/0.82 tff(1260,plain,
% 0.63/0.82 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c0_1(a1852)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c0_1(a1852)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1259, 1257])).
% 0.63/0.82 tff(1261,plain,
% 0.63/0.82 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c0_1(a1852)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1262,plain,
% 0.63/0.82 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c0_1(a1852))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 0.63/0.82 tff(1263,plain,
% 0.63/0.82 (hskp27 | hskp22 | (~c0_1(a1852))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1262, 125, 1256, 1255, 411])).
% 0.63/0.82 tff(1264,plain,
% 0.63/0.82 (hskp22),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1263, 1244, 1126])).
% 0.63/0.82 tff(1265,plain,
% 0.63/0.82 (~c3_1(a1899)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1068, 1264])).
% 0.63/0.82 tff(1266,plain,
% 0.63/0.82 (~c2_1(a1899)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1074, 1264])).
% 0.63/0.82 tff(1267,assumption,(c1_1(a1852)), introduced(assumption)).
% 0.63/0.82 tff(1268,plain,
% 0.63/0.82 (c0_1(a1899)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1082, 1264])).
% 0.63/0.82 tff(1269,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a1899) | c3_1(a1899) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1899) | c3_1(a1899) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c0_1(a1899)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1270,plain,
% 0.63/0.82 (((~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899))) <=> (c2_1(a1899) | c3_1(a1899) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c0_1(a1899)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1271,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a1899) | c3_1(a1899) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c0_1(a1899))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1270])).
% 0.63/0.82 tff(1272,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1899) | c3_1(a1899) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c0_1(a1899)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1271, 1269])).
% 0.63/0.82 tff(1273,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1274,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1899) | c3_1(a1899) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c0_1(a1899))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 0.63/0.82 tff(1275,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1274, 125, 1268, 1267, 1256, 1266, 1265, 1255, 1254, 1244])).
% 0.63/0.82 tff(1276,plain,((~c0_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1852)) | c2_1(a1852) | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(1277,plain,
% 0.63/0.82 (~c0_1(a1852)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1276, 1126, 1235, 1227, 1243])).
% 0.63/0.82 tff(1278,plain,
% 0.63/0.82 (^[U: $i] : refl((hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(1279,plain,
% 0.63/0.82 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[1278])).
% 0.63/0.82 tff(1280,plain,
% 0.63/0.82 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1281,plain,
% 0.63/0.82 (^[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) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp9) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9) <=> (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp9) <=> (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(1282,plain,
% 0.63/0.82 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp9) <=> ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[1281])).
% 0.63/0.82 tff(1283,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.63/0.82 tff(1284,plain,
% 0.63/0.82 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 0.63/0.82 tff(1285,plain,
% 0.63/0.82 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1284, 1280])).
% 0.63/0.82 tff(1286,plain,(
% 0.63/0.82 ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.63/0.82 inference(skolemize,[status(sab)],[1285])).
% 0.63/0.82 tff(1287,plain,
% 0.63/0.82 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1286, 1279])).
% 0.63/0.82 tff(1288,plain,
% 0.63/0.82 (((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp1 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852))) <=> ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp1 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1289,plain,
% 0.63/0.82 ((hskp9 | hskp1 | (~ndr1_0) | c2_1(a1852) | c0_1(a1852) | (~c1_1(a1852))) <=> (hskp9 | hskp1 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1290,plain,
% 0.63/0.82 (((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp1 | (~ndr1_0) | c2_1(a1852) | c0_1(a1852) | (~c1_1(a1852)))) <=> ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp1 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852)))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1289])).
% 0.63/0.82 tff(1291,plain,
% 0.63/0.82 (((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp1 | (~ndr1_0) | c2_1(a1852) | c0_1(a1852) | (~c1_1(a1852)))) <=> ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp1 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1290, 1288])).
% 0.63/0.82 tff(1292,plain,
% 0.63/0.82 ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp1 | (~ndr1_0) | c2_1(a1852) | c0_1(a1852) | (~c1_1(a1852)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1293,plain,
% 0.63/0.82 ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp1 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 0.63/0.82 tff(1294,plain,
% 0.63/0.82 (hskp9 | c0_1(a1852)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1293, 125, 32, 1243, 1227, 1287])).
% 0.63/0.82 tff(1295,plain,
% 0.63/0.82 (hskp9),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1294, 1277])).
% 0.63/0.82 tff(1296,plain,
% 0.63/0.82 (~c3_1(a1863)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[746, 1295])).
% 0.63/0.82 tff(1297,plain,
% 0.63/0.82 (~c1_1(a1863)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[752, 1295])).
% 0.63/0.82 tff(1298,assumption,(~c3_1(a1885)), introduced(assumption)).
% 0.63/0.82 tff(1299,assumption,(~c0_1(a1852)), introduced(assumption)).
% 0.63/0.82 tff(1300,plain,
% 0.63/0.82 (hskp9),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1294, 1299])).
% 0.63/0.82 tff(1301,plain,
% 0.63/0.82 (~c3_1(a1863)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[746, 1300])).
% 0.63/0.82 tff(1302,plain,
% 0.63/0.82 (~c1_1(a1863)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[752, 1300])).
% 0.63/0.82 tff(1303,plain,
% 0.63/0.82 (c2_1(a1863)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[760, 1300])).
% 0.63/0.82 tff(1304,assumption,(c2_1(a1885)), introduced(assumption)).
% 0.63/0.82 tff(1305,assumption,(c0_1(a1885)), introduced(assumption)).
% 0.63/0.82 tff(1306,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | (~c2_1(a1863)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | (~c2_1(a1863)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1307,plain,
% 0.63/0.82 (((~ndr1_0) | c3_1(a1885) | (~c2_1(a1885)) | (~c0_1(a1885)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852))) <=> (c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | (~c2_1(a1863)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1308,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1885) | (~c2_1(a1885)) | (~c0_1(a1885)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | (~c2_1(a1863))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1307])).
% 0.63/0.82 tff(1309,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1885) | (~c2_1(a1885)) | (~c0_1(a1885)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | (~c2_1(a1863)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1308, 1306])).
% 0.63/0.82 tff(1310,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1885) | (~c2_1(a1885)) | (~c0_1(a1885)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1311,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | (~c2_1(a1863))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 0.63/0.82 tff(1312,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1311, 125, 1305, 1304, 1303, 1243, 1235, 1302, 1301, 208, 1299, 1298])).
% 0.63/0.82 tff(1313,plain,(c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(1314,plain,
% 0.63/0.82 (c3_1(a1885)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1313, 1277, 1128, 1130, 32])).
% 0.63/0.82 tff(1315,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1885)) | (~c2_1(a1885)) | (~c3_1(a1885)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1885)) | (~c2_1(a1885)) | (~c3_1(a1885)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1316,plain,
% 0.63/0.82 ((hskp16 | (~ndr1_0) | (~c2_1(a1885)) | (~c3_1(a1885)) | (~c0_1(a1885)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852))) <=> (hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1885)) | (~c2_1(a1885)) | (~c3_1(a1885)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1317,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1885)) | (~c3_1(a1885)) | (~c0_1(a1885)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1885)) | (~c2_1(a1885)) | (~c3_1(a1885))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1316])).
% 0.63/0.82 tff(1318,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1885)) | (~c3_1(a1885)) | (~c0_1(a1885)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1885)) | (~c2_1(a1885)) | (~c3_1(a1885)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1317, 1315])).
% 0.63/0.82 tff(1319,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1885)) | (~c3_1(a1885)) | (~c0_1(a1885)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1320,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1885)) | (~c2_1(a1885)) | (~c3_1(a1885))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 0.63/0.82 tff(1321,plain,
% 0.63/0.82 (hskp16 | (~c3_1(a1885))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1320, 125, 1130, 1128, 1243, 1235, 1227, 657])).
% 0.63/0.82 tff(1322,plain,
% 0.63/0.82 (hskp16),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1321, 1314])).
% 0.63/0.82 tff(1323,plain,
% 0.63/0.82 (~c0_1(a1872)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[553, 1322])).
% 0.63/0.82 tff(1324,plain,
% 0.63/0.82 (c2_1(a1863)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[760, 1295])).
% 0.63/0.82 tff(1325,plain,
% 0.63/0.82 (c3_1(a1872)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[569, 1322])).
% 0.63/0.82 tff(1326,plain,
% 0.63/0.82 (c2_1(a1872)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[577, 1322])).
% 0.63/0.82 tff(1327,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c0_1(a1872) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c0_1(a1872) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1328,plain,
% 0.63/0.82 ((hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1872) | (~c2_1(a1872)) | (~c3_1(a1872))) <=> (hskp27 | c0_1(a1872) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1329,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1872) | (~c2_1(a1872)) | (~c3_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c0_1(a1872) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1872)) | (~c2_1(a1872))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1328])).
% 0.63/0.82 tff(1330,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1872) | (~c2_1(a1872)) | (~c3_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c0_1(a1872) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1329, 1327])).
% 0.63/0.82 tff(1331,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1872) | (~c2_1(a1872)) | (~c3_1(a1872)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1332,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c0_1(a1872) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1872)) | (~c2_1(a1872))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 0.63/0.82 tff(1333,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1332, 125, 1126, 1326, 1325, 1324, 1323, 1297, 1296, 1120])).
% 0.63/0.82 tff(1334,plain,(hskp27 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(1335,plain,
% 0.63/0.82 (hskp27),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1334, 32])).
% 0.63/0.82 tff(1336,plain,
% 0.63/0.82 (c3_1(a1877)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[142, 1335])).
% 0.63/0.82 tff(1337,plain,
% 0.63/0.82 (c2_1(a1877)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[150, 1335])).
% 0.63/0.82 tff(1338,plain,
% 0.63/0.82 (c0_1(a1877)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[158, 1335])).
% 0.63/0.82 tff(1339,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1340,plain,
% 0.63/0.82 ((hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852))) <=> (hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1341,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1340])).
% 0.63/0.82 tff(1342,plain,
% 0.63/0.82 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1341, 1339])).
% 0.63/0.82 tff(1343,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1344,plain,
% 0.63/0.82 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 0.63/0.82 tff(1345,plain,
% 0.63/0.82 (hskp16),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1344, 125, 1338, 1337, 1336, 1243, 1235, 1227, 657])).
% 0.63/0.82 tff(1346,plain,
% 0.63/0.82 (~c0_1(a1872)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[553, 1345])).
% 0.63/0.82 tff(1347,plain,
% 0.63/0.82 (c3_1(a1872)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[569, 1345])).
% 0.63/0.82 tff(1348,plain,
% 0.63/0.82 (c2_1(a1872)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[577, 1345])).
% 0.63/0.82 tff(1349,assumption,(~c1_1(a1877)), introduced(assumption)).
% 0.63/0.82 tff(1350,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1351,plain,
% 0.63/0.82 (((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872))) <=> (c0_1(a1872) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(1352,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877)))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1351])).
% 0.63/0.82 tff(1353,plain,
% 0.63/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.63/0.82 inference(transitivity,[status(thm)],[1352, 1350])).
% 0.63/0.82 tff(1354,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(1355,plain,
% 0.63/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1354, 1353])).
% 0.63/0.82 tff(1356,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1355, 125, 251, 249, 999, 1018, 1267, 1256, 998, 1255, 10, 1349])).
% 0.63/0.82 tff(1357,plain,(c1_1(a1877) | (~c0_1(a1877)) | (~c3_1(a1877)) | (~c2_1(a1872)) | (~c3_1(a1872)) | (~c1_1(a1852)) | (~c3_1(a1852)) | c0_1(a1872) | c2_1(a1852)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(1358,plain,
% 0.63/0.83 (c1_1(a1877)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1357, 1338, 1336, 1348, 1347, 1243, 1235, 1346, 1227])).
% 0.63/0.83 tff(1359,plain,
% 0.63/0.83 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1360,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1359])).
% 0.63/0.83 tff(1361,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1362,plain,
% 0.63/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1363,plain,
% 0.63/0.83 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1362])).
% 0.63/0.83 tff(1364,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.63/0.83 tff(1365,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 0.63/0.83 tff(1366,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1365, 1361])).
% 0.63/0.83 tff(1367,plain,(
% 0.63/0.83 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.63/0.83 inference(skolemize,[status(sab)],[1366])).
% 0.63/0.83 tff(1368,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1367, 1360])).
% 0.63/0.83 tff(1369,assumption,(hskp10), introduced(assumption)).
% 0.63/0.83 tff(1370,plain,
% 0.63/0.83 (((~hskp10) | (~c1_1(a1864))) <=> ((~hskp10) | (~c1_1(a1864)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1371,plain,
% 0.63/0.83 (((~c1_1(a1864)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1864)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1372,axiom,((~c1_1(a1864)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.63/0.83 tff(1373,plain,
% 0.63/0.83 ((~hskp10) | (~c1_1(a1864))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1372, 1371])).
% 0.63/0.83 tff(1374,plain,
% 0.63/0.83 ((~hskp10) | (~c1_1(a1864))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1373, 1370])).
% 0.63/0.83 tff(1375,plain,
% 0.63/0.83 (~c1_1(a1864)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1374, 1369])).
% 0.63/0.83 tff(1376,plain,
% 0.63/0.83 (c3_1(a1864)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[442, 1369])).
% 0.63/0.83 tff(1377,plain,
% 0.63/0.83 (c0_1(a1864)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[450, 1369])).
% 0.63/0.83 tff(1378,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c1_1(a1864) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c1_1(a1864) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1379,plain,
% 0.63/0.83 (((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872))) <=> (c0_1(a1872) | c1_1(a1864) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1380,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c1_1(a1864) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1379])).
% 0.63/0.83 tff(1381,plain,
% 0.63/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c1_1(a1864) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1380, 1378])).
% 0.63/0.83 tff(1382,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1383,plain,
% 0.63/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c1_1(a1864) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1382, 1381])).
% 0.63/0.83 tff(1384,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1383, 125, 999, 1018, 1377, 1376, 1267, 1256, 998, 1375, 1255, 10])).
% 0.63/0.83 tff(1385,plain,((~hskp10) | (~c2_1(a1872)) | (~c3_1(a1872)) | (~c1_1(a1852)) | (~c3_1(a1852)) | c0_1(a1872) | c2_1(a1852)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(1386,plain,
% 0.63/0.83 (~hskp10),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1385, 1348, 1347, 1243, 1235, 1346, 1227])).
% 0.63/0.83 tff(1387,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1388,plain,
% 0.63/0.83 ((hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1852) | (~c1_1(a1852)) | (~c0_1(a1852))) <=> (hskp10 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1389,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1852) | (~c1_1(a1852)) | (~c0_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1388])).
% 0.63/0.83 tff(1390,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1852) | (~c1_1(a1852)) | (~c0_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1389, 1387])).
% 0.63/0.83 tff(1391,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1852) | (~c1_1(a1852)) | (~c0_1(a1852)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1392,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 0.63/0.83 tff(1393,plain,
% 0.63/0.83 (hskp10 | (~c0_1(a1852)) | (~c1_1(a1877))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1392, 125, 1337, 1336, 1243, 1227, 1368])).
% 0.63/0.83 tff(1394,plain,
% 0.63/0.83 (~c0_1(a1852)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1393, 1358, 1386])).
% 0.63/0.83 tff(1395,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1396,plain,
% 0.63/0.83 ((hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1852) | c2_1(a1852) | (~c1_1(a1852))) <=> (hskp8 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1397,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1852) | c2_1(a1852) | (~c1_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1396])).
% 0.63/0.83 tff(1398,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1852) | c2_1(a1852) | (~c1_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1397, 1395])).
% 0.63/0.83 tff(1399,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1852) | c2_1(a1852) | (~c1_1(a1852)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1400,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1399, 1398])).
% 0.63/0.83 tff(1401,plain,
% 0.63/0.83 (hskp8),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1400, 125, 1338, 1337, 1336, 1243, 1227, 31, 1394])).
% 0.63/0.83 tff(1402,plain,
% 0.63/0.83 (~c2_1(a1862)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[517, 1401])).
% 0.63/0.83 tff(1403,plain,
% 0.63/0.83 (c1_1(a1862)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[561, 1401])).
% 0.63/0.83 tff(1404,plain,
% 0.63/0.83 (c0_1(a1862)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[674, 1401])).
% 0.63/0.83 tff(1405,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1862) | (~ndr1_0) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1862) | (~ndr1_0) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1406,plain,
% 0.63/0.83 ((hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862))) <=> (hskp10 | c2_1(a1862) | (~ndr1_0) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1407,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1862) | (~ndr1_0) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1406])).
% 0.63/0.83 tff(1408,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1862) | (~ndr1_0) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1407, 1405])).
% 0.63/0.83 tff(1409,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1410,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1862) | (~ndr1_0) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1409, 1408])).
% 0.63/0.83 tff(1411,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1410, 125, 1386, 1337, 1336, 1404, 1403, 1402, 1368, 1358])).
% 0.63/0.83 tff(1412,plain,(hskp1), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(1413,plain,
% 0.63/0.83 (((~hskp1) | (~c0_1(a1853))) <=> ((~hskp1) | (~c0_1(a1853)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1414,plain,
% 0.63/0.83 (((~c0_1(a1853)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a1853)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1415,axiom,((~c0_1(a1853)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.63/0.83 tff(1416,plain,
% 0.63/0.83 ((~hskp1) | (~c0_1(a1853))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 0.63/0.83 tff(1417,plain,
% 0.63/0.83 ((~hskp1) | (~c0_1(a1853))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1416, 1413])).
% 0.63/0.83 tff(1418,plain,
% 0.63/0.83 (~c0_1(a1853)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1417, 1412])).
% 0.63/0.83 tff(1419,plain,
% 0.63/0.83 (((~hskp1) | c1_1(a1853)) <=> ((~hskp1) | c1_1(a1853))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1420,axiom,((~hskp1) | c1_1(a1853)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.63/0.83 tff(1421,plain,
% 0.63/0.83 ((~hskp1) | c1_1(a1853)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 0.63/0.83 tff(1422,plain,
% 0.63/0.83 ((~hskp1) | c1_1(a1853)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1421, 1419])).
% 0.63/0.83 tff(1423,plain,
% 0.63/0.83 ((~hskp1) | c1_1(a1853)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1422, 1419])).
% 0.63/0.83 tff(1424,plain,
% 0.63/0.83 ((~hskp1) | c1_1(a1853)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1423, 1419])).
% 0.63/0.83 tff(1425,plain,
% 0.63/0.83 ((~hskp1) | c1_1(a1853)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1424, 1419])).
% 0.63/0.83 tff(1426,plain,
% 0.63/0.83 (c1_1(a1853)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1425, 1412])).
% 0.63/0.83 tff(1427,assumption,(c3_1(a1862)), introduced(assumption)).
% 0.63/0.83 tff(1428,plain,
% 0.63/0.83 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1429,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1428])).
% 0.63/0.83 tff(1430,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1431,plain,
% 0.63/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~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)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1432,plain,
% 0.63/0.83 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1431])).
% 0.63/0.83 tff(1433,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 0.63/0.83 tff(1434,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1433, 1432])).
% 0.63/0.83 tff(1435,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1434, 1430])).
% 0.63/0.83 tff(1436,plain,(
% 0.63/0.83 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.63/0.83 inference(skolemize,[status(sab)],[1435])).
% 0.63/0.83 tff(1437,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1436, 1429])).
% 0.63/0.83 tff(1438,plain,
% 0.63/0.83 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1439,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1438])).
% 0.63/0.83 tff(1440,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1441,plain,
% 0.63/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~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(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~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(U)) <=> ((~ndr1_0) | c3_1(U) | (~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(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(1442,plain,
% 0.63/0.83 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[1441])).
% 0.63/0.83 tff(1443,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.63/0.83 tff(1444,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 0.63/0.83 tff(1445,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1444, 1440])).
% 0.63/0.83 tff(1446,plain,(
% 0.63/0.83 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.83 inference(skolemize,[status(sab)],[1445])).
% 0.63/0.83 tff(1447,plain,
% 0.63/0.83 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1446, 1439])).
% 0.63/0.83 tff(1448,plain,
% 0.63/0.83 (hskp17),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[885, 21, 647])).
% 0.63/0.83 tff(1449,plain,
% 0.63/0.83 (~c1_1(a1874)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[891, 1448])).
% 0.63/0.83 tff(1450,plain,
% 0.63/0.83 (c2_1(a1874)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[899, 1448])).
% 0.63/0.83 tff(1451,plain,
% 0.63/0.83 (c0_1(a1874)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[907, 1448])).
% 0.63/0.83 tff(1452,plain,
% 0.63/0.83 (hskp18),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[914, 125, 21, 1451, 1450, 1449, 874])).
% 0.63/0.83 tff(1453,plain,
% 0.63/0.83 (~c3_1(a1875)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[920, 1452])).
% 0.63/0.83 tff(1454,plain,
% 0.63/0.83 (((~hskp1) | c3_1(a1853)) <=> ((~hskp1) | c3_1(a1853))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1455,axiom,((~hskp1) | c3_1(a1853)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.63/0.83 tff(1456,plain,
% 0.63/0.83 ((~hskp1) | c3_1(a1853)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 0.63/0.83 tff(1457,plain,
% 0.63/0.83 ((~hskp1) | c3_1(a1853)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1456, 1454])).
% 0.63/0.83 tff(1458,plain,
% 0.63/0.83 ((~hskp1) | c3_1(a1853)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1457, 1454])).
% 0.63/0.83 tff(1459,plain,
% 0.63/0.83 ((~hskp1) | c3_1(a1853)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1458, 1454])).
% 0.63/0.83 tff(1460,plain,
% 0.63/0.83 ((~hskp1) | c3_1(a1853)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1459, 1454])).
% 0.63/0.83 tff(1461,plain,
% 0.63/0.83 (c3_1(a1853)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1460, 1412])).
% 0.63/0.83 tff(1462,plain,
% 0.63/0.83 (c1_1(a1875)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[928, 1452])).
% 0.63/0.83 tff(1463,plain,
% 0.63/0.83 (c0_1(a1875)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[957, 1452])).
% 0.63/0.83 tff(1464,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c3_1(a1875) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1875)) | (~c0_1(a1875)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c3_1(a1875) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1875)) | (~c0_1(a1875)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1465,plain,
% 0.63/0.83 ((hskp27 | (~ndr1_0) | c3_1(a1875) | (~c1_1(a1875)) | (~c0_1(a1875)) | c0_1(a1853) | (~c2_1(a1853)) | (~c3_1(a1853))) <=> (hskp27 | c3_1(a1875) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1875)) | (~c0_1(a1875)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1466,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1875) | (~c1_1(a1875)) | (~c0_1(a1875)) | c0_1(a1853) | (~c2_1(a1853)) | (~c3_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c3_1(a1875) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1875)) | (~c0_1(a1875))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1465])).
% 0.63/0.83 tff(1467,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1875) | (~c1_1(a1875)) | (~c0_1(a1875)) | c0_1(a1853) | (~c2_1(a1853)) | (~c3_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c3_1(a1875) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1875)) | (~c0_1(a1875)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[1466, 1464])).
% 0.63/0.83 tff(1468,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1875) | (~c1_1(a1875)) | (~c0_1(a1875)) | c0_1(a1853) | (~c2_1(a1853)) | (~c3_1(a1853)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(1469,plain,
% 0.63/0.83 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c3_1(a1875) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1875)) | (~c0_1(a1875))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1468, 1467])).
% 0.63/0.83 tff(1470,plain,
% 0.63/0.83 (~c2_1(a1853)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1469, 125, 1126, 1463, 1462, 1461, 1453, 1418, 1447])).
% 0.63/0.83 tff(1471,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1874)) | (~c0_1(a1874)) | (~c2_1(a1874)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1874)) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1472,plain,
% 0.63/0.83 ((hskp8 | (~ndr1_0) | (~c2_1(a1874)) | (~c3_1(a1874)) | (~c0_1(a1874)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853))) <=> (hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1874)) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(1473,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1874)) | (~c3_1(a1874)) | (~c0_1(a1874)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1874)) | (~c0_1(a1874)) | (~c2_1(a1874))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1472])).
% 0.63/0.83 tff(1474,plain,
% 0.63/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1874)) | (~c3_1(a1874)) | (~c0_1(a1874)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1874)) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1473, 1471])).
% 0.63/0.84 tff(1475,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1874)) | (~c3_1(a1874)) | (~c0_1(a1874)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1476,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1874)) | (~c0_1(a1874)) | (~c2_1(a1874))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1475, 1474])).
% 0.63/0.84 tff(1477,plain,
% 0.63/0.84 (c2_1(a1853) | (~c3_1(a1874))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1476, 125, 21, 1451, 1450, 1426, 1418, 31])).
% 0.63/0.84 tff(1478,plain,
% 0.63/0.84 (~c3_1(a1874)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1477, 1470])).
% 0.63/0.84 tff(1479,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1874) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | c3_1(a1874) | (~c0_1(a1874)) | (~c2_1(a1874)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1874) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | c3_1(a1874) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1480,plain,
% 0.63/0.84 (((~ndr1_0) | c3_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)) | c3_1(a1874) | c1_1(a1874) | (~c2_1(a1874)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853))) <=> (c1_1(a1874) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | c3_1(a1874) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1481,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)) | c3_1(a1874) | c1_1(a1874) | (~c2_1(a1874)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1874) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | c3_1(a1874) | (~c0_1(a1874)) | (~c2_1(a1874))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1480])).
% 0.63/0.84 tff(1482,plain,
% 0.63/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)) | c3_1(a1874) | c1_1(a1874) | (~c2_1(a1874)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1874) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | c3_1(a1874) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1481, 1479])).
% 0.63/0.84 tff(1483,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)) | c3_1(a1874) | c1_1(a1874) | (~c2_1(a1874)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1484,plain,
% 0.63/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1874) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | c3_1(a1874) | (~c0_1(a1874)) | (~c2_1(a1874))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 0.63/0.84 tff(1485,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1484, 125, 1451, 1450, 1426, 1461, 1449, 1418, 208, 1478])).
% 0.63/0.84 tff(1486,plain,(hskp8 | hskp27 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(1487,plain,
% 0.63/0.84 (hskp8),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1486, 647, 1126])).
% 0.63/0.84 tff(1488,plain,
% 0.63/0.84 (~c2_1(a1862)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[517, 1487])).
% 0.63/0.84 tff(1489,plain,
% 0.63/0.84 (c1_1(a1862)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[561, 1487])).
% 0.63/0.84 tff(1490,plain,
% 0.63/0.84 (c0_1(a1862)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[674, 1487])).
% 0.63/0.84 tff(1491,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1862) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1862) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1492,plain,
% 0.63/0.84 ((hskp16 | (~ndr1_0) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853))) <=> (hskp16 | c2_1(a1862) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1493,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1862) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1862)) | (~c0_1(a1862))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1492])).
% 0.63/0.84 tff(1494,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1862) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1493, 1491])).
% 0.63/0.84 tff(1495,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1496,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1862) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1862)) | (~c0_1(a1862))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 0.63/0.84 tff(1497,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1496, 125, 647, 1490, 1489, 1426, 1461, 1488, 1418, 1437])).
% 0.63/0.84 tff(1498,plain,(hskp16 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(1499,plain,
% 0.63/0.84 (hskp16),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1498, 1126])).
% 0.63/0.84 tff(1500,plain,
% 0.63/0.84 (~c0_1(a1872)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[553, 1499])).
% 0.63/0.84 tff(1501,plain,
% 0.63/0.84 (c3_1(a1872)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[569, 1499])).
% 0.63/0.84 tff(1502,plain,
% 0.63/0.84 (c2_1(a1872)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[577, 1499])).
% 0.63/0.84 tff(1503,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1332, 125, 1126, 1502, 1501, 761, 1500, 753, 747, 1120])).
% 0.63/0.84 tff(1504,plain,((~hskp9) | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(1505,plain,
% 0.63/0.84 (~hskp9),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1504, 1126])).
% 0.63/0.84 tff(1506,plain,
% 0.63/0.84 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1507,plain,
% 0.63/0.84 ((hskp9 | hskp8 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872))) <=> (hskp9 | hskp8 | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1508,plain,
% 0.63/0.84 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872)))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1507])).
% 0.63/0.84 tff(1509,plain,
% 0.63/0.84 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1508, 1506])).
% 0.63/0.84 tff(1510,plain,
% 0.63/0.84 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1511,plain,
% 0.63/0.84 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 0.63/0.84 tff(1512,plain,
% 0.63/0.84 (hskp9 | hskp8 | c1_1(a1872)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1511, 125, 1502, 1500, 20])).
% 0.63/0.84 tff(1513,plain,
% 0.63/0.84 (c1_1(a1872)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1512, 21, 1505])).
% 0.63/0.84 tff(1514,assumption,(c2_1(a1864)), introduced(assumption)).
% 0.63/0.84 tff(1515,plain,
% 0.63/0.84 ((hskp24 | hskp10 | hskp8) <=> (hskp24 | hskp10 | hskp8)),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1516,plain,
% 0.63/0.84 (((hskp10 | hskp8) | hskp24) <=> (hskp24 | hskp10 | hskp8)),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1517,plain,
% 0.63/0.84 ((hskp8 | hskp10) <=> (hskp10 | hskp8)),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1518,plain,
% 0.63/0.84 (((hskp8 | hskp10) | hskp24) <=> ((hskp10 | hskp8) | hskp24)),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1517])).
% 0.63/0.84 tff(1519,plain,
% 0.63/0.84 (((hskp8 | hskp10) | hskp24) <=> (hskp24 | hskp10 | hskp8)),
% 0.63/0.84 inference(transitivity,[status(thm)],[1518, 1516])).
% 0.63/0.84 tff(1520,axiom,((hskp8 | hskp10) | hskp24), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.63/0.84 tff(1521,plain,
% 0.63/0.84 (hskp24 | hskp10 | hskp8),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1520, 1519])).
% 0.63/0.84 tff(1522,plain,
% 0.63/0.84 (hskp24 | hskp10 | hskp8),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1521, 1515])).
% 0.63/0.84 tff(1523,plain,
% 0.63/0.84 (hskp24 | hskp10 | hskp8),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1522, 1515])).
% 0.63/0.84 tff(1524,plain,
% 0.63/0.84 (hskp24 | hskp10 | hskp8),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1523, 1515])).
% 0.63/0.84 tff(1525,plain,
% 0.63/0.84 (hskp24 | hskp10 | hskp8),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1524, 1515])).
% 0.63/0.84 tff(1526,plain,
% 0.63/0.84 (hskp10),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1525, 64, 21])).
% 0.63/0.84 tff(1527,plain,
% 0.63/0.84 (~c1_1(a1864)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1374, 1526])).
% 0.63/0.84 tff(1528,plain,
% 0.63/0.84 (c0_1(a1864)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[450, 1526])).
% 0.63/0.84 tff(1529,plain,
% 0.63/0.84 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | c1_1(a1864) | (~ndr1_0) | (~c0_1(a1864)) | (~c2_1(a1864)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp8 | c1_1(a1864) | (~ndr1_0) | (~c0_1(a1864)) | (~c2_1(a1864)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1530,plain,
% 0.63/0.84 ((hskp18 | hskp8 | (~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864))) <=> (hskp18 | hskp8 | c1_1(a1864) | (~ndr1_0) | (~c0_1(a1864)) | (~c2_1(a1864)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1531,plain,
% 0.63/0.84 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | c1_1(a1864) | (~ndr1_0) | (~c0_1(a1864)) | (~c2_1(a1864))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1530])).
% 0.63/0.84 tff(1532,plain,
% 0.63/0.84 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp8 | c1_1(a1864) | (~ndr1_0) | (~c0_1(a1864)) | (~c2_1(a1864)))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1531, 1529])).
% 0.63/0.84 tff(1533,plain,
% 0.63/0.84 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1534,plain,
% 0.63/0.84 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp8 | c1_1(a1864) | (~ndr1_0) | (~c0_1(a1864)) | (~c2_1(a1864))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 0.63/0.84 tff(1535,plain,
% 0.63/0.84 (hskp18 | (~c2_1(a1864))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1534, 125, 21, 1528, 1527, 874])).
% 0.63/0.84 tff(1536,plain,
% 0.63/0.84 (hskp18),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1535, 1514])).
% 0.63/0.84 tff(1537,plain,
% 0.63/0.84 (~c3_1(a1875)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[920, 1536])).
% 0.63/0.84 tff(1538,plain,
% 0.63/0.84 (c3_1(a1864)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[442, 1526])).
% 0.63/0.84 tff(1539,plain,
% 0.63/0.84 (c0_1(a1875)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[957, 1536])).
% 0.63/0.84 tff(1540,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c3_1(a1875) | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)) | (~c0_1(a1875)) | c2_1(a1875))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1875) | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)) | (~c0_1(a1875)) | c2_1(a1875))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1541,plain,
% 0.63/0.84 ((hskp24 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c3_1(a1875) | c2_1(a1875) | (~c0_1(a1875))) <=> (hskp24 | c3_1(a1875) | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)) | (~c0_1(a1875)) | c2_1(a1875))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1542,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c3_1(a1875) | c2_1(a1875) | (~c0_1(a1875)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c3_1(a1875) | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)) | (~c0_1(a1875)) | c2_1(a1875)))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1541])).
% 0.63/0.84 tff(1543,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c3_1(a1875) | c2_1(a1875) | (~c0_1(a1875)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1875) | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)) | (~c0_1(a1875)) | c2_1(a1875))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1542, 1540])).
% 0.63/0.84 tff(1544,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c3_1(a1875) | c2_1(a1875) | (~c0_1(a1875)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1545,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1875) | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)) | (~c0_1(a1875)) | c2_1(a1875)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1544, 1543])).
% 0.63/0.84 tff(1546,plain,
% 0.63/0.84 (c2_1(a1875)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1545, 125, 64, 1539, 1528, 1538, 1537, 248, 1514])).
% 0.63/0.84 tff(1547,plain,
% 0.63/0.84 (c1_1(a1875)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[928, 1536])).
% 0.63/0.84 tff(1548,plain,
% 0.63/0.84 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1549,plain,
% 0.63/0.84 ((hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875))) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1550,plain,
% 0.63/0.84 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1549])).
% 0.63/0.84 tff(1551,plain,
% 0.63/0.84 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1550, 1548])).
% 0.63/0.84 tff(1552,plain,
% 0.63/0.84 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1553,plain,
% 0.63/0.84 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1552, 1551])).
% 0.63/0.84 tff(1554,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1553, 125, 64, 43, 1539, 1547, 53, 1546])).
% 0.63/0.84 tff(1555,plain,((~c2_1(a1864)) | hskp24 | hskp0 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(1556,plain,
% 0.63/0.84 (~c2_1(a1864)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1555, 64, 43, 21])).
% 0.63/0.84 tff(1557,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a1872) | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864) | (~c2_1(a1872)) | (~c1_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a1872) | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864) | (~c2_1(a1872)) | (~c1_1(a1872)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1558,plain,
% 0.63/0.84 ((hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872))) <=> (hskp8 | c0_1(a1872) | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864) | (~c2_1(a1872)) | (~c1_1(a1872)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1559,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a1872) | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864) | (~c2_1(a1872)) | (~c1_1(a1872))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1558])).
% 0.63/0.84 tff(1560,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a1872) | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864) | (~c2_1(a1872)) | (~c1_1(a1872)))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1559, 1557])).
% 0.63/0.84 tff(1561,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1562,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a1872) | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864) | (~c2_1(a1872)) | (~c1_1(a1872))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 0.63/0.84 tff(1563,plain,
% 0.63/0.84 (~c1_1(a1872)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1562, 125, 21, 1502, 1538, 1500, 1527, 505, 1556])).
% 0.63/0.84 tff(1564,plain,
% 0.63/0.84 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(1565,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[1564])).
% 0.63/0.84 tff(1566,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1567,plain,
% 0.63/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(1568,plain,
% 0.63/0.84 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[1567])).
% 0.63/0.84 tff(1569,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 0.63/0.84 tff(1570,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1569, 1568])).
% 0.63/0.84 tff(1571,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1570, 1566])).
% 0.63/0.84 tff(1572,plain,(
% 0.63/0.84 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.84 inference(skolemize,[status(sab)],[1571])).
% 0.63/0.84 tff(1573,plain,
% 0.63/0.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1572, 1565])).
% 0.63/0.84 tff(1574,plain,
% 0.63/0.84 (hskp22),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[464, 125, 1126, 1528, 1538, 411, 1556])).
% 0.63/0.84 tff(1575,plain,
% 0.63/0.84 (~c3_1(a1899)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1068, 1574])).
% 0.63/0.84 tff(1576,plain,
% 0.63/0.84 (~c2_1(a1899)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1074, 1574])).
% 0.63/0.84 tff(1577,plain,
% 0.63/0.84 (c0_1(a1899)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1082, 1574])).
% 0.63/0.84 tff(1578,plain,
% 0.63/0.84 (~c1_1(a1899)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1089, 125, 1577, 1576, 1575, 362])).
% 0.63/0.84 tff(1579,plain,
% 0.63/0.84 (hskp21),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1177, 125, 21, 1576, 1575, 1170, 1578])).
% 0.63/0.84 tff(1580,plain,
% 0.63/0.84 (~c1_1(a1898)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[970, 1579])).
% 0.63/0.84 tff(1581,plain,
% 0.63/0.84 (~c0_1(a1898)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[976, 1579])).
% 0.63/0.84 tff(1582,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c2_1(a1898))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1583,plain,
% 0.63/0.84 ((hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898)) <=> (hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c2_1(a1898))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(1584,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c2_1(a1898)))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[1583])).
% 0.63/0.84 tff(1585,plain,
% 0.63/0.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c2_1(a1898))),
% 0.63/0.84 inference(transitivity,[status(thm)],[1584, 1582])).
% 0.63/0.84 tff(1586,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(1587,plain,
% 0.63/0.84 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c2_1(a1898)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[1586, 1585])).
% 0.63/0.84 tff(1588,plain,
% 0.63/0.84 (c2_1(a1898)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1587, 125, 43, 1502, 1581, 1580, 1500, 1573, 1563])).
% 0.63/0.84 tff(1589,plain,
% 0.63/0.84 (^[U: $i] : refl((hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(1590,plain,
% 0.63/0.85 (![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[1589])).
% 0.63/0.85 tff(1591,plain,
% 0.63/0.85 (![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1592,plain,
% 0.63/0.85 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp20) <=> ((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp20))), rewrite(((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp20) <=> (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp20) <=> (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(1593,plain,
% 0.63/0.85 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp20) <=> ![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[1592])).
% 0.63/0.85 tff(1594,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.63/0.85 tff(1595,plain,
% 0.63/0.85 (![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 0.63/0.85 tff(1596,plain,
% 0.63/0.85 (![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1595, 1591])).
% 0.63/0.85 tff(1597,plain,(
% 0.63/0.85 ![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.63/0.85 inference(skolemize,[status(sab)],[1596])).
% 0.63/0.85 tff(1598,plain,
% 0.63/0.85 (![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1597, 1590])).
% 0.63/0.85 tff(1599,plain,
% 0.63/0.85 (((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp29 | hskp20 | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864))) <=> ((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp29 | hskp20 | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1600,plain,
% 0.63/0.85 ((hskp29 | hskp20 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864))) <=> (hskp29 | hskp20 | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1601,plain,
% 0.63/0.85 (((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp29 | hskp20 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)))) <=> ((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp29 | hskp20 | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864)))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[1600])).
% 0.63/0.85 tff(1602,plain,
% 0.63/0.85 (((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp29 | hskp20 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)))) <=> ((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp29 | hskp20 | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864))),
% 0.63/0.85 inference(transitivity,[status(thm)],[1601, 1599])).
% 0.63/0.85 tff(1603,plain,
% 0.63/0.85 ((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp29 | hskp20 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(1604,plain,
% 0.63/0.85 ((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp29 | hskp20 | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864)),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 0.63/0.85 tff(1605,plain,
% 0.63/0.85 (hskp20),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1604, 134, 125, 1538, 1527, 1598, 1556])).
% 0.63/0.85 tff(1606,plain,
% 0.63/0.85 (~c1_1(a1890)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[781, 1605])).
% 0.63/0.85 tff(1607,plain,
% 0.63/0.85 (~c0_1(a1890)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[787, 1605])).
% 0.63/0.85 tff(1608,plain,
% 0.63/0.85 (c2_1(a1890)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[814, 1605])).
% 0.63/0.85 tff(1609,plain,
% 0.63/0.85 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1610,plain,
% 0.63/0.85 ((hskp9 | hskp8 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890))) <=> (hskp9 | hskp8 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1611,plain,
% 0.63/0.85 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[1610])).
% 0.63/0.85 tff(1612,plain,
% 0.63/0.85 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[1611, 1609])).
% 0.63/0.85 tff(1613,plain,
% 0.63/0.85 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(1614,plain,
% 0.63/0.85 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1613, 1612])).
% 0.63/0.85 tff(1615,plain,
% 0.63/0.85 (hskp9),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1614, 125, 21, 1608, 1607, 1606, 20])).
% 0.63/0.85 tff(1616,plain,
% 0.63/0.85 (~c3_1(a1863)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[746, 1615])).
% 0.63/0.85 tff(1617,plain,
% 0.63/0.85 (~c1_1(a1863)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[752, 1615])).
% 0.63/0.85 tff(1618,plain,
% 0.63/0.85 (c2_1(a1863)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[760, 1615])).
% 0.63/0.85 tff(1619,plain,
% 0.63/0.85 (c3_1(a1898)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[984, 1579])).
% 0.63/0.85 tff(1620,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1146, 125, 1126, 1619, 1618, 1581, 1617, 1616, 1120, 1588])).
% 0.63/0.85 tff(1621,plain,(hskp24 | hskp27 | hskp0 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(1622,plain,
% 0.63/0.85 (hskp24),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1621, 43, 1126, 21])).
% 0.63/0.85 tff(1623,plain,
% 0.63/0.85 (~c1_1(a1919)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[336, 1622])).
% 0.63/0.85 tff(1624,plain,
% 0.63/0.85 (~c2_1(a1919)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[330, 1622])).
% 0.63/0.85 tff(1625,assumption,(~c3_1(a1919)), introduced(assumption)).
% 0.63/0.85 tff(1626,plain,
% 0.63/0.85 (~hskp24),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[344, 1625])).
% 0.63/0.85 tff(1627,plain,
% 0.63/0.85 (~c2_1(a1864)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1555, 1626, 43, 21])).
% 0.63/0.85 tff(1628,plain,
% 0.63/0.85 (hskp10),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1525, 1626, 21])).
% 0.63/0.85 tff(1629,plain,
% 0.63/0.85 (~c1_1(a1864)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1374, 1628])).
% 0.63/0.85 tff(1630,plain,
% 0.63/0.85 (c3_1(a1864)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[442, 1628])).
% 0.63/0.85 tff(1631,plain,
% 0.63/0.85 (~hskp29),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[133, 1626, 43])).
% 0.63/0.85 tff(1632,plain,
% 0.63/0.85 (hskp20 | c2_1(a1864)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1604, 1631, 125, 1630, 1629, 1598])).
% 0.63/0.85 tff(1633,plain,
% 0.63/0.85 (hskp20),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1632, 1627])).
% 0.63/0.85 tff(1634,plain,
% 0.63/0.85 (~c1_1(a1890)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[781, 1633])).
% 0.63/0.85 tff(1635,plain,
% 0.63/0.85 (~c0_1(a1890)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[787, 1633])).
% 0.63/0.85 tff(1636,plain,
% 0.63/0.85 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | c3_1(a1919) | c1_1(a1919) | c2_1(a1919) | (~ndr1_0))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp21 | hskp8 | c3_1(a1919) | c1_1(a1919) | c2_1(a1919) | (~ndr1_0))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1637,plain,
% 0.63/0.85 ((hskp21 | hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | c3_1(a1919)) <=> (hskp21 | hskp8 | c3_1(a1919) | c1_1(a1919) | c2_1(a1919) | (~ndr1_0))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1638,plain,
% 0.63/0.85 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | c3_1(a1919))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | c3_1(a1919) | c1_1(a1919) | c2_1(a1919) | (~ndr1_0)))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[1637])).
% 0.63/0.85 tff(1639,plain,
% 0.63/0.85 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | c3_1(a1919))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp21 | hskp8 | c3_1(a1919) | c1_1(a1919) | c2_1(a1919) | (~ndr1_0))),
% 0.63/0.85 inference(transitivity,[status(thm)],[1638, 1636])).
% 0.63/0.85 tff(1640,plain,
% 0.63/0.85 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | c3_1(a1919))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(1641,plain,
% 0.63/0.85 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp21 | hskp8 | c3_1(a1919) | c1_1(a1919) | c2_1(a1919) | (~ndr1_0)),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1640, 1639])).
% 0.63/0.85 tff(1642,plain,
% 0.63/0.85 (hskp21 | c3_1(a1919) | c2_1(a1919)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1641, 125, 21, 425, 1170])).
% 0.63/0.85 tff(1643,plain,
% 0.63/0.85 (hskp21),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1642, 1625, 412])).
% 0.63/0.85 tff(1644,plain,
% 0.63/0.85 (~c1_1(a1898)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[970, 1643])).
% 0.63/0.85 tff(1645,plain,
% 0.63/0.85 (~c0_1(a1898)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[976, 1643])).
% 0.63/0.85 tff(1646,plain,
% 0.63/0.85 (c2_1(a1890)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[814, 1633])).
% 0.63/0.85 tff(1647,plain,
% 0.63/0.85 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)) | c2_1(a1898))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1648,plain,
% 0.63/0.85 ((hskp0 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898)) <=> (hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)) | c2_1(a1898))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1649,plain,
% 0.63/0.85 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)) | c2_1(a1898)))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[1648])).
% 0.63/0.85 tff(1650,plain,
% 0.63/0.85 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)) | c2_1(a1898))),
% 0.63/0.85 inference(transitivity,[status(thm)],[1649, 1647])).
% 0.63/0.85 tff(1651,plain,
% 0.63/0.85 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(1652,plain,
% 0.63/0.85 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)) | c2_1(a1898)),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1651, 1650])).
% 0.63/0.85 tff(1653,plain,
% 0.63/0.85 (c2_1(a1898)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1652, 125, 43, 1646, 1645, 1644, 1635, 1634, 1573])).
% 0.63/0.85 tff(1654,plain,
% 0.63/0.85 (hskp9),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1614, 125, 21, 1646, 1635, 1634, 20])).
% 0.63/0.85 tff(1655,plain,
% 0.63/0.85 (~c3_1(a1863)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[746, 1654])).
% 0.63/0.85 tff(1656,plain,
% 0.63/0.85 (~c1_1(a1863)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[752, 1654])).
% 0.63/0.85 tff(1657,plain,
% 0.63/0.85 (c2_1(a1863)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[760, 1654])).
% 0.63/0.85 tff(1658,plain,
% 0.63/0.85 (c3_1(a1898)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[984, 1643])).
% 0.63/0.85 tff(1659,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1146, 125, 1126, 1658, 1657, 1645, 1656, 1655, 1120, 1653])).
% 0.63/0.85 tff(1660,plain,(c3_1(a1919) | hskp27 | hskp0 | hskp8 | c2_1(a1919) | c1_1(a1919)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(1661,plain,
% 0.63/0.85 (c3_1(a1919)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1660, 412, 43, 21, 1126, 425])).
% 0.63/0.85 tff(1662,plain,
% 0.63/0.85 ((~c1_1(a1872)) | (~c3_1(a1919))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1005, 125, 21, 1502, 425, 412, 1500, 505])).
% 0.63/0.85 tff(1663,plain,
% 0.63/0.85 (~c1_1(a1872)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1662, 1661])).
% 0.63/0.85 tff(1664,plain,
% 0.63/0.85 (hskp9),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1512, 1663, 21])).
% 0.63/0.85 tff(1665,plain,
% 0.63/0.85 (~c3_1(a1863)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[746, 1664])).
% 0.63/0.85 tff(1666,plain,
% 0.63/0.85 (~c1_1(a1863)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[752, 1664])).
% 0.63/0.85 tff(1667,plain,
% 0.63/0.85 (c2_1(a1863)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[760, 1664])).
% 0.63/0.85 tff(1668,plain,
% 0.63/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c0_1(a1863)) | (~c2_1(a1863)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c0_1(a1863)) | (~c2_1(a1863)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1669,plain,
% 0.63/0.85 (((~ndr1_0) | c3_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1863)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853))) <=> (c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c0_1(a1863)) | (~c2_1(a1863)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1670,plain,
% 0.63/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1863)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c0_1(a1863)) | (~c2_1(a1863))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[1669])).
% 0.63/0.85 tff(1671,plain,
% 0.63/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1863)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c0_1(a1863)) | (~c2_1(a1863)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[1670, 1668])).
% 0.63/0.85 tff(1672,plain,
% 0.63/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1863)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(1673,plain,
% 0.63/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c0_1(a1863)) | (~c2_1(a1863))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1672, 1671])).
% 0.63/0.85 tff(1674,plain,
% 0.63/0.85 (~c0_1(a1863)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1673, 125, 1667, 1426, 1461, 1666, 1665, 1418, 208])).
% 0.63/0.85 tff(1675,plain,
% 0.63/0.85 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(1676,plain,
% 0.63/0.85 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[1675])).
% 0.63/0.85 tff(1677,plain,
% 0.63/0.85 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1678,plain,
% 0.63/0.85 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(1679,plain,
% 0.63/0.85 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[1678])).
% 0.63/0.85 tff(1680,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.63/0.85 tff(1681,plain,
% 0.63/0.85 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 0.63/0.85 tff(1682,plain,
% 0.63/0.85 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1681, 1677])).
% 0.63/0.85 tff(1683,plain,(
% 0.63/0.85 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.85 inference(skolemize,[status(sab)],[1682])).
% 0.63/0.85 tff(1684,plain,
% 0.63/0.85 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1683, 1676])).
% 0.63/0.85 tff(1685,plain,
% 0.63/0.85 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c1_1(a1919) | c2_1(a1919) | c3_1(a1863) | (~ndr1_0) | c0_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c1_1(a1919) | c2_1(a1919) | c3_1(a1863) | (~ndr1_0) | c0_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1919)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1686,plain,
% 0.63/0.85 ((hskp27 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)) | c3_1(a1863) | c0_1(a1863) | (~c2_1(a1863))) <=> (hskp27 | c1_1(a1919) | c2_1(a1919) | c3_1(a1863) | (~ndr1_0) | c0_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1919)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1687,plain,
% 0.63/0.85 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)) | c3_1(a1863) | c0_1(a1863) | (~c2_1(a1863)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c1_1(a1919) | c2_1(a1919) | c3_1(a1863) | (~ndr1_0) | c0_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1919))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[1686])).
% 0.63/0.85 tff(1688,plain,
% 0.63/0.85 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)) | c3_1(a1863) | c0_1(a1863) | (~c2_1(a1863)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c1_1(a1919) | c2_1(a1919) | c3_1(a1863) | (~ndr1_0) | c0_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1919)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[1687, 1685])).
% 0.63/0.85 tff(1689,plain,
% 0.63/0.85 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)) | c3_1(a1863) | c0_1(a1863) | (~c2_1(a1863)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(1690,plain,
% 0.63/0.85 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c1_1(a1919) | c2_1(a1919) | c3_1(a1863) | (~ndr1_0) | c0_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1919))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 0.63/0.85 tff(1691,plain,
% 0.63/0.85 (~c0_1(a1919)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1690, 125, 1126, 1667, 425, 412, 1665, 1684, 1674])).
% 0.63/0.85 tff(1692,plain,
% 0.63/0.85 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c0_1(a1919))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c0_1(a1919))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1693,plain,
% 0.63/0.85 ((hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919)) <=> (hskp0 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c0_1(a1919))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1694,plain,
% 0.63/0.85 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c0_1(a1919)))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[1693])).
% 0.63/0.85 tff(1695,plain,
% 0.63/0.85 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c0_1(a1919))),
% 0.63/0.85 inference(transitivity,[status(thm)],[1694, 1692])).
% 0.63/0.85 tff(1696,plain,
% 0.63/0.85 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(1697,plain,
% 0.63/0.85 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c0_1(a1919)),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 0.63/0.85 tff(1698,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1697, 125, 43, 1502, 425, 412, 1500, 1573, 1691, 1663])).
% 0.63/0.85 tff(1699,plain,(c2_1(a1919) | hskp0 | c1_1(a1919) | hskp27 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(1700,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1699, 1624, 1623, 43, 1126, 21])).
% 0.63/0.85 tff(1701,plain,(hskp0 | hskp27 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(1702,plain,
% 0.63/0.85 (hskp0),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1701, 21, 1126])).
% 0.63/0.85 tff(1703,plain,
% 0.63/0.85 (~c2_1(a1852)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1226, 1702])).
% 0.63/0.85 tff(1704,plain,
% 0.63/0.85 (c3_1(a1852)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1234, 1702])).
% 0.63/0.85 tff(1705,plain,
% 0.63/0.85 (c1_1(a1852)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1242, 1702])).
% 0.63/0.85 tff(1706,plain,
% 0.63/0.85 (~hskp10),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1385, 1705, 1501, 1502, 1704, 1500, 1703])).
% 0.63/0.85 tff(1707,plain,
% 0.63/0.85 (hskp24),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1525, 1706, 21])).
% 0.63/0.85 tff(1708,plain,
% 0.63/0.85 (~c2_1(a1919)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[330, 1707])).
% 0.63/0.85 tff(1709,plain,
% 0.63/0.85 (~c1_1(a1919)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[336, 1707])).
% 0.63/0.85 tff(1710,plain,
% 0.63/0.85 (c3_1(a1919)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[344, 1707])).
% 0.63/0.85 tff(1711,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1005, 125, 21, 1710, 1502, 1709, 1708, 1500, 505, 1513])).
% 0.63/0.85 tff(1712,plain,(hskp8 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(1713,plain,
% 0.63/0.85 (hskp8),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1712, 1126])).
% 0.63/0.85 tff(1714,plain,
% 0.63/0.85 (~c2_1(a1862)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[517, 1713])).
% 0.63/0.85 tff(1715,plain,
% 0.63/0.85 (c0_1(a1862)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[674, 1713])).
% 0.63/0.85 tff(1716,plain,
% 0.63/0.85 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c0_1(a1862)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c0_1(a1862)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1717,plain,
% 0.63/0.85 ((hskp27 | hskp22 | (~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c0_1(a1862))) <=> (hskp27 | hskp22 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c0_1(a1862)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1718,plain,
% 0.63/0.85 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c0_1(a1862)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c0_1(a1862))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[1717])).
% 0.63/0.85 tff(1719,plain,
% 0.63/0.85 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c0_1(a1862)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c0_1(a1862)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[1718, 1716])).
% 0.63/0.85 tff(1720,plain,
% 0.63/0.85 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c0_1(a1862)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(1721,plain,
% 0.63/0.85 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c0_1(a1862))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1720, 1719])).
% 0.63/0.85 tff(1722,plain,
% 0.63/0.85 (hskp22 | (~c3_1(a1862))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1721, 125, 1126, 1715, 1714, 411])).
% 0.63/0.85 tff(1723,plain,
% 0.63/0.85 (hskp22),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1722, 1427])).
% 0.63/0.85 tff(1724,plain,
% 0.63/0.85 (~c3_1(a1899)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1068, 1723])).
% 0.63/0.85 tff(1725,plain,
% 0.63/0.85 (~c2_1(a1899)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1074, 1723])).
% 0.63/0.85 tff(1726,plain,
% 0.63/0.85 (c1_1(a1862)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[561, 1713])).
% 0.63/0.85 tff(1727,plain,
% 0.63/0.85 (c0_1(a1899)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1082, 1723])).
% 0.63/0.85 tff(1728,plain,
% 0.63/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c0_1(a1899)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1729,plain,
% 0.63/0.85 (((~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899))) <=> (c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c0_1(a1899)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(1730,plain,
% 0.63/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c0_1(a1899))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[1729])).
% 0.63/0.85 tff(1731,plain,
% 0.63/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c0_1(a1899)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[1730, 1728])).
% 0.63/0.85 tff(1732,plain,
% 0.63/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(1733,plain,
% 0.63/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c0_1(a1899))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[1732, 1731])).
% 0.63/0.85 tff(1734,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1733, 125, 1727, 1715, 1726, 1725, 1724, 1714, 1254, 1427])).
% 0.63/0.86 tff(1735,plain,((~c3_1(a1862)) | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.63/0.86 tff(1736,plain,
% 0.63/0.86 (~c3_1(a1862)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1735, 1126])).
% 0.63/0.86 tff(1737,plain,
% 0.63/0.86 ($false),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[681, 125, 1715, 1726, 1714, 362, 1736])).
% 0.63/0.86 tff(1738,plain,(hskp27), inference(lemma,lemma(discharge,[]))).
% 0.63/0.86 tff(1739,plain,
% 0.63/0.86 (c3_1(a1877)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[142, 1738])).
% 0.63/0.86 tff(1740,plain,
% 0.63/0.86 (c2_1(a1877)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[150, 1738])).
% 0.63/0.86 tff(1741,plain,
% 0.63/0.86 (c0_1(a1877)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[158, 1738])).
% 0.63/0.86 tff(1742,plain,
% 0.63/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(1743,plain,
% 0.63/0.86 ((hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853))) <=> (hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(1744,plain,
% 0.63/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[1743])).
% 0.63/0.86 tff(1745,plain,
% 0.63/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.86 inference(transitivity,[status(thm)],[1744, 1742])).
% 0.63/0.86 tff(1746,plain,
% 0.63/0.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853)))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(1747,plain,
% 0.63/0.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 0.63/0.86 tff(1748,plain,
% 0.63/0.86 (hskp8 | c2_1(a1853)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1747, 125, 1741, 1740, 1739, 1426, 1418, 31])).
% 0.63/0.86 tff(1749,plain,
% 0.63/0.86 (c2_1(a1853)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1748, 21])).
% 0.63/0.86 tff(1750,plain,
% 0.63/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1919)))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(1751,plain,
% 0.63/0.86 ((hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853))) <=> (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1919)))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(1752,plain,
% 0.63/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1919))))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[1751])).
% 0.63/0.86 tff(1753,plain,
% 0.63/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1919)))),
% 0.63/0.86 inference(transitivity,[status(thm)],[1752, 1750])).
% 0.63/0.86 tff(1754,plain,
% 0.63/0.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(1755,plain,
% 0.63/0.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1919))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[1754, 1753])).
% 0.63/0.86 tff(1756,plain,
% 0.63/0.86 (c1_1(a1919) | (~c3_1(a1919))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1755, 125, 21, 1426, 412, 1418, 505, 1749])).
% 0.63/0.86 tff(1757,plain,
% 0.63/0.86 (~c3_1(a1919)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1756, 425])).
% 0.63/0.86 tff(1758,plain,
% 0.63/0.86 (~hskp24),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[344, 1757])).
% 0.63/0.86 tff(1759,plain,
% 0.63/0.86 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c3_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(1760,plain,
% 0.63/0.86 ((hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1919) | c2_1(a1919) | (~c0_1(a1919))) <=> (hskp24 | c3_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(1761,plain,
% 0.63/0.86 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1919) | c2_1(a1919) | (~c0_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c3_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[1760])).
% 0.63/0.86 tff(1762,plain,
% 0.63/0.86 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1919) | c2_1(a1919) | (~c0_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.63/0.86 inference(transitivity,[status(thm)],[1761, 1759])).
% 0.63/0.86 tff(1763,plain,
% 0.63/0.86 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1919) | c2_1(a1919) | (~c0_1(a1919)))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(1764,plain,
% 0.63/0.86 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 0.63/0.86 tff(1765,plain,
% 0.63/0.86 (~c0_1(a1919)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1764, 125, 1758, 1741, 1740, 1739, 1757, 412, 248])).
% 0.63/0.86 tff(1766,plain,
% 0.63/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.63/0.86 inference(bind,[status(th)],[])).
% 0.63/0.86 tff(1767,plain,
% 0.63/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.86 inference(quant_intro,[status(thm)],[1766])).
% 0.63/0.86 tff(1768,plain,
% 0.63/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(1769,plain,
% 0.63/0.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~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(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~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(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.63/0.86 inference(bind,[status(th)],[])).
% 0.63/0.86 tff(1770,plain,
% 0.63/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.86 inference(quant_intro,[status(thm)],[1769])).
% 0.63/0.86 tff(1771,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 0.63/0.86 tff(1772,plain,
% 0.63/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 0.63/0.86 tff(1773,plain,
% 0.63/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[1772, 1768])).
% 0.63/0.86 tff(1774,plain,(
% 0.63/0.86 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.86 inference(skolemize,[status(sab)],[1773])).
% 0.63/0.86 tff(1775,plain,
% 0.63/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[1774, 1767])).
% 0.63/0.86 tff(1776,plain,
% 0.63/0.86 (hskp10),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1525, 1758, 21])).
% 0.63/0.86 tff(1777,plain,
% 0.63/0.86 (~c1_1(a1864)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1374, 1776])).
% 0.63/0.86 tff(1778,plain,
% 0.63/0.86 (c0_1(a1864)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[450, 1776])).
% 0.63/0.86 tff(1779,plain,
% 0.63/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1919) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c0_1(a1864)) | (~c2_1(a1864)) | c0_1(a1919))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1919) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c0_1(a1864)) | (~c2_1(a1864)) | c0_1(a1919))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(1780,plain,
% 0.71/0.86 (((~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919)) <=> (c1_1(a1919) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c0_1(a1864)) | (~c2_1(a1864)) | c0_1(a1919))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(1781,plain,
% 0.71/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1919) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c0_1(a1864)) | (~c2_1(a1864)) | c0_1(a1919)))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[1780])).
% 0.71/0.86 tff(1782,plain,
% 0.71/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1919) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c0_1(a1864)) | (~c2_1(a1864)) | c0_1(a1919))),
% 0.71/0.86 inference(transitivity,[status(thm)],[1781, 1779])).
% 0.71/0.86 tff(1783,plain,
% 0.71/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(1784,plain,
% 0.71/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1919) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c0_1(a1864)) | (~c2_1(a1864)) | c0_1(a1919)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1783, 1782])).
% 0.71/0.86 tff(1785,plain,
% 0.71/0.86 (~c2_1(a1864)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1784, 125, 1778, 1426, 425, 412, 1777, 1418, 1775, 1765, 1749])).
% 0.71/0.86 tff(1786,plain,
% 0.71/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(1787,plain,
% 0.71/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[1786])).
% 0.71/0.86 tff(1788,plain,
% 0.71/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(1789,plain,
% 0.71/0.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | 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) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | 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) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_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) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(1790,plain,
% 0.71/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_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) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[1789])).
% 0.71/0.87 tff(1791,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.71/0.87 tff(1792,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 0.71/0.87 tff(1793,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1792, 1788])).
% 0.71/0.87 tff(1794,plain,(
% 0.71/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.87 inference(skolemize,[status(sab)],[1793])).
% 0.71/0.87 tff(1795,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1794, 1787])).
% 0.71/0.87 tff(1796,plain,
% 0.71/0.87 (c3_1(a1864)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[442, 1776])).
% 0.71/0.87 tff(1797,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864) | c0_1(a1919))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864) | c0_1(a1919))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1798,plain,
% 0.71/0.87 (((~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919)) <=> (c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864) | c0_1(a1919))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1799,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864) | c0_1(a1919)))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1798])).
% 0.71/0.87 tff(1800,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864) | c0_1(a1919))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1799, 1797])).
% 0.71/0.87 tff(1801,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1802,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864) | c0_1(a1919)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1801, 1800])).
% 0.71/0.87 tff(1803,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1802, 125, 1778, 1796, 1426, 425, 412, 1418, 1795, 1765, 1749, 1785])).
% 0.71/0.87 tff(1804,plain,(c1_1(a1919) | c2_1(a1919) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1805,plain,
% 0.71/0.87 (c1_1(a1919)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1804, 412, 21])).
% 0.71/0.87 tff(1806,plain,
% 0.71/0.87 (~hskp24),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[336, 1805])).
% 0.71/0.87 tff(1807,plain,
% 0.71/0.87 (hskp10),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1525, 1806, 21])).
% 0.71/0.87 tff(1808,plain,
% 0.71/0.87 (~c1_1(a1864)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1374, 1807])).
% 0.71/0.87 tff(1809,plain,
% 0.71/0.87 (c3_1(a1864)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[442, 1807])).
% 0.71/0.87 tff(1810,plain,
% 0.71/0.87 (c0_1(a1864)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[450, 1807])).
% 0.71/0.87 tff(1811,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1919)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1919)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1812,plain,
% 0.71/0.87 (((~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c1_1(a1919)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853))) <=> ((~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1919)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1813,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c1_1(a1919)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1919))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1812])).
% 0.71/0.87 tff(1814,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c1_1(a1919)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1919)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1813, 1811])).
% 0.71/0.87 tff(1815,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c1_1(a1919)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1816,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1919))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1815, 1814])).
% 0.71/0.87 tff(1817,plain,
% 0.71/0.87 (~c3_1(a1919)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1816, 125, 1810, 1809, 1461, 1805, 412, 1808, 1418, 10, 1749])).
% 0.71/0.87 tff(1818,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1919) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c2_1(a1864)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1919) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c2_1(a1864)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1819,plain,
% 0.71/0.87 (((~ndr1_0) | c2_1(a1919) | c3_1(a1919) | (~c1_1(a1919)) | c1_1(a1864) | (~c2_1(a1864)) | (~c3_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853))) <=> (c3_1(a1919) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c2_1(a1864)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1820,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1919) | c3_1(a1919) | (~c1_1(a1919)) | c1_1(a1864) | (~c2_1(a1864)) | (~c3_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1919) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c2_1(a1864))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1819])).
% 0.71/0.87 tff(1821,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1919) | c3_1(a1919) | (~c1_1(a1919)) | c1_1(a1864) | (~c2_1(a1864)) | (~c3_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1919) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c2_1(a1864)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1820, 1818])).
% 0.71/0.87 tff(1822,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1919) | c3_1(a1919) | (~c1_1(a1919)) | c1_1(a1864) | (~c2_1(a1864)) | (~c3_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1823,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1919) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c2_1(a1864))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1822, 1821])).
% 0.71/0.87 tff(1824,plain,
% 0.71/0.87 (~c2_1(a1864)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1823, 125, 1817, 1809, 1461, 1805, 412, 1808, 1418, 623, 1749])).
% 0.71/0.87 tff(1825,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | c2_1(a1864))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | c2_1(a1864))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1826,plain,
% 0.71/0.87 ((hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853))) <=> (hskp8 | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | c2_1(a1864))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1827,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | c2_1(a1864)))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1826])).
% 0.71/0.87 tff(1828,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | c2_1(a1864))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1827, 1825])).
% 0.71/0.87 tff(1829,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1830,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | c2_1(a1864)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 0.71/0.87 tff(1831,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1830, 125, 21, 1809, 1426, 1808, 1418, 505, 1749, 1824])).
% 0.71/0.87 tff(1832,plain,(c2_1(a1919) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1833,plain,
% 0.71/0.87 (c2_1(a1919)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1832, 21])).
% 0.71/0.87 tff(1834,plain,
% 0.71/0.87 (~hskp24),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[330, 1833])).
% 0.71/0.87 tff(1835,plain,
% 0.71/0.87 (hskp10),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1525, 1834, 21])).
% 0.71/0.87 tff(1836,plain,
% 0.71/0.87 (~c1_1(a1864)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1374, 1835])).
% 0.71/0.87 tff(1837,plain,
% 0.71/0.87 (c3_1(a1864)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[442, 1835])).
% 0.71/0.87 tff(1838,plain,
% 0.71/0.87 (c0_1(a1864)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[450, 1835])).
% 0.71/0.87 tff(1839,assumption,(c2_1(a1853)), introduced(assumption)).
% 0.71/0.87 tff(1840,assumption,(hskp0), introduced(assumption)).
% 0.71/0.87 tff(1841,plain,
% 0.71/0.87 (~c2_1(a1852)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1226, 1840])).
% 0.71/0.87 tff(1842,assumption,(~c1_1(a1864)), introduced(assumption)).
% 0.71/0.87 tff(1843,plain,
% 0.71/0.87 (c3_1(a1852)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1234, 1840])).
% 0.71/0.87 tff(1844,plain,
% 0.71/0.87 (c1_1(a1852)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1242, 1840])).
% 0.71/0.87 tff(1845,assumption,(c3_1(a1864)), introduced(assumption)).
% 0.71/0.87 tff(1846,assumption,(c0_1(a1864)), introduced(assumption)).
% 0.71/0.87 tff(1847,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1864) | c0_1(a1853) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1864) | c0_1(a1853) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1848,plain,
% 0.71/0.87 (((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853))) <=> (c1_1(a1864) | c0_1(a1853) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1849,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1864) | c0_1(a1853) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1848])).
% 0.71/0.87 tff(1850,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1864) | c0_1(a1853) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1849, 1847])).
% 0.71/0.87 tff(1851,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1852,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1864) | c0_1(a1853) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1851, 1850])).
% 0.71/0.87 tff(1853,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1852, 125, 1846, 1845, 1461, 1844, 1843, 1842, 1418, 1841, 10, 1839])).
% 0.71/0.87 tff(1854,plain,((~hskp0) | (~c0_1(a1864)) | (~c3_1(a1864)) | c1_1(a1864) | (~c2_1(a1853))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1855,plain,
% 0.71/0.87 (~hskp0),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1854, 1838, 1837, 1836, 1749])).
% 0.71/0.87 tff(1856,plain,
% 0.71/0.87 (~c2_1(a1864)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1555, 1855, 21, 1834])).
% 0.71/0.87 tff(1857,plain,
% 0.71/0.87 (~hskp29),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[133, 1855, 1834])).
% 0.71/0.87 tff(1858,plain,
% 0.71/0.87 (hskp29 | hskp20 | c2_1(a1864)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1604, 125, 1837, 1836, 1598])).
% 0.71/0.87 tff(1859,plain,
% 0.71/0.87 (hskp20),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1858, 1857, 1856])).
% 0.71/0.87 tff(1860,plain,
% 0.71/0.87 (~c1_1(a1890)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[781, 1859])).
% 0.71/0.87 tff(1861,plain,
% 0.71/0.87 (~c0_1(a1890)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[787, 1859])).
% 0.71/0.87 tff(1862,plain,
% 0.71/0.87 (c2_1(a1890)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[814, 1859])).
% 0.71/0.87 tff(1863,plain,
% 0.71/0.87 (hskp23),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[770, 741, 21])).
% 0.71/0.87 tff(1864,plain,
% 0.71/0.87 (~c3_1(a1911)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[214, 1863])).
% 0.71/0.87 tff(1865,plain,
% 0.71/0.87 (c0_1(a1911)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[228, 1863])).
% 0.71/0.87 tff(1866,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a1911) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c2_1(a1863)) | (~c0_1(a1911)) | (~c2_1(a1911)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1911) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c2_1(a1863)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1867,plain,
% 0.71/0.87 (((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853))) <=> (c3_1(a1911) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c2_1(a1863)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1868,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a1911) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c2_1(a1863)) | (~c0_1(a1911)) | (~c2_1(a1911))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1867])).
% 0.71/0.87 tff(1869,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1911) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c2_1(a1863)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1868, 1866])).
% 0.71/0.87 tff(1870,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1871,plain,
% 0.71/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1911) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c2_1(a1863)) | (~c0_1(a1911)) | (~c2_1(a1911))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1870, 1869])).
% 0.71/0.87 tff(1872,plain,
% 0.71/0.87 (~c2_1(a1911)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1871, 125, 1865, 761, 1426, 1461, 1864, 753, 747, 1418, 208])).
% 0.71/0.87 tff(1873,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[257, 125, 1834, 1741, 1740, 1739, 1865, 1864, 248, 1872])).
% 0.71/0.87 tff(1874,plain,((~hskp9) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1875,plain,
% 0.71/0.87 (~hskp9),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1874, 21])).
% 0.71/0.87 tff(1876,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1614, 125, 1875, 21, 1862, 1861, 1860, 20])).
% 0.71/0.87 tff(1877,plain,(hskp8), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1878,plain,
% 0.71/0.87 (~c2_1(a1862)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[517, 1877])).
% 0.71/0.87 tff(1879,plain,
% 0.71/0.87 (c1_1(a1862)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[561, 1877])).
% 0.71/0.87 tff(1880,plain,
% 0.71/0.87 (c0_1(a1862)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[674, 1877])).
% 0.71/0.87 tff(1881,plain,
% 0.71/0.87 (hskp16),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[683, 1877, 1741, 1740, 1739])).
% 0.71/0.87 tff(1882,plain,
% 0.71/0.87 (~c0_1(a1872)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[553, 1881])).
% 0.71/0.87 tff(1883,plain,
% 0.71/0.87 (c3_1(a1872)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[569, 1881])).
% 0.71/0.87 tff(1884,plain,
% 0.71/0.87 (c2_1(a1872)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[577, 1881])).
% 0.71/0.87 tff(1885,plain,
% 0.71/0.87 ((~hskp10) | (~c1_1(a1852)) | (~c3_1(a1852)) | c2_1(a1852)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1385, 1884, 1883, 1882])).
% 0.71/0.87 tff(1886,plain,
% 0.71/0.87 (~hskp10),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1885, 1844, 1843, 1841])).
% 0.71/0.87 tff(1887,plain,
% 0.71/0.87 (c1_1(a1877) | (~c1_1(a1852)) | (~c3_1(a1852)) | c2_1(a1852)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1357, 1739, 1884, 1883, 1882, 1741])).
% 0.71/0.87 tff(1888,plain,
% 0.71/0.87 (c1_1(a1877)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1887, 1841, 1844, 1843])).
% 0.71/0.87 tff(1889,plain,
% 0.71/0.87 (hskp10 | (~c1_1(a1877))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1410, 125, 1740, 1739, 1880, 1879, 1878, 1368])).
% 0.71/0.87 tff(1890,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1889, 1888, 1886])).
% 0.71/0.87 tff(1891,plain,(~hskp0), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1892,plain,
% 0.71/0.87 (hskp28 | hskp0),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[165, 125, 1741, 1740, 1739, 63])).
% 0.71/0.87 tff(1893,plain,
% 0.71/0.87 (hskp28),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1892, 1891])).
% 0.71/0.87 tff(1894,plain,
% 0.71/0.87 (c3_1(a1878)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[196, 1893])).
% 0.71/0.87 tff(1895,plain,
% 0.71/0.87 (c2_1(a1878)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[173, 1893])).
% 0.71/0.87 tff(1896,plain,
% 0.71/0.87 (c1_1(a1878)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[181, 1893])).
% 0.71/0.87 tff(1897,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1862) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1862) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1898,plain,
% 0.71/0.87 ((hskp10 | (~ndr1_0) | (~c2_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1878)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862))) <=> (hskp10 | c2_1(a1862) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1899,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1878)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1862) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1862)) | (~c0_1(a1862))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1898])).
% 0.71/0.87 tff(1900,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1878)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1862) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1899, 1897])).
% 0.71/0.87 tff(1901,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1878)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1902,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1862) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1862)) | (~c0_1(a1862))),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[1901, 1900])).
% 0.73/0.88 tff(1903,plain,
% 0.73/0.88 (hskp10),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[1902, 125, 1896, 1895, 1894, 1880, 1879, 1878, 1368])).
% 0.73/0.88 tff(1904,plain,
% 0.73/0.88 (~c1_1(a1864)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[1374, 1903])).
% 0.73/0.88 tff(1905,plain,
% 0.73/0.88 (c3_1(a1864)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[442, 1903])).
% 0.73/0.88 tff(1906,plain,
% 0.73/0.88 (c0_1(a1864)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[450, 1903])).
% 0.73/0.88 tff(1907,plain,
% 0.73/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c1_1(a1864) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c1_1(a1864) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.73/0.88 inference(rewrite,[status(thm)],[])).
% 0.73/0.88 tff(1908,plain,
% 0.73/0.88 (((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872))) <=> (c0_1(a1872) | c1_1(a1864) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.73/0.88 inference(rewrite,[status(thm)],[])).
% 0.73/0.88 tff(1909,plain,
% 0.73/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c1_1(a1864) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872))))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[1908])).
% 0.73/0.88 tff(1910,plain,
% 0.73/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c1_1(a1864) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.73/0.88 inference(transitivity,[status(thm)],[1909, 1907])).
% 0.73/0.88 tff(1911,plain,
% 0.73/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.73/0.88 inference(quant_inst,[status(thm)],[])).
% 0.73/0.88 tff(1912,plain,
% 0.73/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c1_1(a1864) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872))),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[1911, 1910])).
% 0.73/0.88 tff(1913,plain,
% 0.73/0.88 (~c3_1(a1862)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[1912, 125, 1884, 1883, 1906, 1905, 1879, 1882, 1904, 1878, 10])).
% 0.73/0.88 tff(1914,plain,
% 0.73/0.88 ($false),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[681, 125, 1880, 1879, 1878, 362, 1913])).
% 0.73/0.88 % SZS output end Proof
% 0.73/0.88 % E exiting
%------------------------------------------------------------------------------