%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO631-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:46:48 AM UTC 2026
% Result : Unsatisfiable 24.03s 6.06s
% Output : CNFRefutation 24.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 26
% Syntax : Number of clauses : 116 ( 10 unt; 71 nHn; 80 RR)
% Number of literals : 349 ( 0 equ; 133 neg)
% Maximal clause size : 4 ( 3 avg)
% Maximal term depth : 12 ( 4 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 146 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_27_01,axiom,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(X0)) ) ).
cnf(clause_3_02,axiom,
iLEQ(X0,g(X0)) ).
cnf(clause_8_03,axiom,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s('\'0\''))))) ) ).
cnf(clause_48_04,axiom,
( '\'LE\''(f(X1),s(s(s(s(s(s(s(s(s('\'0\''))))))))))
| '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s(s(s(s(s(s(s('\'0\''))))))))))) ) ).
cnf(clause_19_05,axiom,
~ '\'E\''(f(X0),f(g(X0))) ).
cnf(clause_18_06,axiom,
iLEQ(X0,X0) ).
cnf(clause_44_07,axiom,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(X0)) ) ).
cnf(clause_5_11,axiom,
( '\'LE\''(f(X1),s(s(s(s(s('\'0\''))))))
| '\'E\''(s(s(s(s(s('\'0\''))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s(s(s('\'0\''))))))) ) ).
cnf(clause_29_12,axiom,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(g(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ) ).
cnf(clause_10_13,axiom,
( '\'LE\''(f(X1),s(s(s(s(s(s(s(s('\'0\'')))))))))
| '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s(s(s(s(s(s('\'0\'')))))))))) ) ).
cnf(clause_11_16,axiom,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(X0)) ) ).
cnf(clause_26_19,axiom,
( '\'LE\''(f(X1),s(s(s(s(s(s(s('\'0\''))))))))
| '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s(s(s(s(s('\'0\''))))))))) ) ).
cnf(clause_23_21,axiom,
( '\'LE\''(f(X1),s('\'0\''))
| '\'E\''(s('\'0\''),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ) ).
cnf(clause_20_22,axiom,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(g(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ) ).
cnf(clause_40_23,axiom,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s('\'0\''))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s('\'0\''))))),f(X0)) ) ).
cnf(clause_2_25,axiom,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''('\'0\'',f(g(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ) ).
cnf(clause_56_31,axiom,
( '\'LE\''(f(X1),'\'0\'')
| '\'E\''('\'0\'',f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s('\'0\'')) ) ).
cnf(clause_42_32,axiom,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))),f(X0)) ) ).
cnf(clause_30_35,axiom,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s('\'0\''),f(g(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ) ).
cnf(clause_0_36,axiom,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s(s('\'0\'')))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s(s('\'0\'')))))) ) ).
cnf(clause_49_39,axiom,
( '\'LE\''(f(X0),s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))))
| '\'E\''(s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))),f(X0)) ) ).
cnf(clause_54_45,axiom,
( '\'LE\''(f(X1),s(s(s(s(s(s('\'0\'')))))))
| '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s(s(s(s('\'0\'')))))))) ) ).
cnf(clause_55_48,axiom,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(g(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X0)) ) ).
cnf(clause_51_50,axiom,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s('\'0\'')))) ) ).
cnf(clause_38_52,axiom,
~ '\'LE\''(f(X0),'\'0\'') ).
cnf(clause_31_54,axiom,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(X0)) ) ).
cnf(c0,plain,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(X0)) ),
inference(clausification,[status(esa)],[clause_27_01]) ).
cnf(c1,plain,
iLEQ(X0,g(X0)),
inference(clausification,[status(esa)],[clause_3_02]) ).
cnf(c2,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s('\'0\''))))) ),
inference(clausification,[status(esa)],[clause_8_03]) ).
cnf(c3,plain,
( '\'LE\''(f(X1),s(s(s(s(s(s(s(s(s('\'0\''))))))))))
| '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s(s(s(s(s(s(s('\'0\''))))))))))) ),
inference(clausification,[status(esa)],[clause_48_04]) ).
cnf(c4,plain,
~ '\'E\''(f(X0),f(g(X0))),
inference(clausification,[status(esa)],[clause_19_05]) ).
cnf(c5,plain,
iLEQ(X0,X0),
inference(clausification,[status(esa)],[clause_18_06]) ).
cnf(c6,plain,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(X0)) ),
inference(clausification,[status(esa)],[clause_44_07]) ).
cnf(c10,plain,
( '\'LE\''(f(X1),s(s(s(s(s('\'0\''))))))
| '\'E\''(s(s(s(s(s('\'0\''))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s(s(s('\'0\''))))))) ),
inference(clausification,[status(esa)],[clause_5_11]) ).
cnf(c11,plain,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(g(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(clausification,[status(esa)],[clause_29_12]) ).
cnf(c12,plain,
( '\'LE\''(f(X1),s(s(s(s(s(s(s(s('\'0\'')))))))))
| '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s(s(s(s(s(s('\'0\'')))))))))) ),
inference(clausification,[status(esa)],[clause_10_13]) ).
cnf(c15,plain,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(X0)) ),
inference(clausification,[status(esa)],[clause_11_16]) ).
cnf(c18,plain,
( '\'LE\''(f(X1),s(s(s(s(s(s(s('\'0\''))))))))
| '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s(s(s(s(s('\'0\''))))))))) ),
inference(clausification,[status(esa)],[clause_26_19]) ).
cnf(c20,plain,
( '\'LE\''(f(X1),s('\'0\''))
| '\'E\''(s('\'0\''),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s('\'0\''))) ),
inference(clausification,[status(esa)],[clause_23_21]) ).
cnf(c21,plain,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(g(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(clausification,[status(esa)],[clause_20_22]) ).
cnf(c22,plain,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s('\'0\''))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s('\'0\''))))),f(X0)) ),
inference(clausification,[status(esa)],[clause_40_23]) ).
cnf(c24,plain,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''('\'0\'',f(g(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(clausification,[status(esa)],[clause_2_25]) ).
cnf(c30,plain,
( '\'LE\''(f(X1),'\'0\'')
| '\'E\''('\'0\'',f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s('\'0\'')) ),
inference(clausification,[status(esa)],[clause_56_31]) ).
cnf(c31,plain,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))),f(X0)) ),
inference(clausification,[status(esa)],[clause_42_32]) ).
cnf(c34,plain,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s('\'0\''),f(g(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(clausification,[status(esa)],[clause_30_35]) ).
cnf(c35,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s(s('\'0\'')))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s(s('\'0\'')))))) ),
inference(clausification,[status(esa)],[clause_0_36]) ).
cnf(c38,plain,
( '\'LE\''(f(X0),s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))))
| '\'E\''(s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))),f(X0)) ),
inference(clausification,[status(esa)],[clause_49_39]) ).
cnf(c44,plain,
( '\'LE\''(f(X1),s(s(s(s(s(s('\'0\'')))))))
| '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s(s(s(s(s('\'0\'')))))))) ),
inference(clausification,[status(esa)],[clause_54_45]) ).
cnf(c47,plain,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(g(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X0)) ),
inference(clausification,[status(esa)],[clause_55_48]) ).
cnf(c49,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(X1))
| ~ iLEQ(X0,X1)
| ~ '\'LE\''(f(X0),s(s(s('\'0\'')))) ),
inference(clausification,[status(esa)],[clause_51_50]) ).
cnf(c51,plain,
~ '\'LE\''(f(X0),'\'0\''),
inference(clausification,[status(esa)],[clause_38_52]) ).
cnf(c53,plain,
( '\'E\''(f(X0),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(X0)) ),
inference(clausification,[status(esa)],[clause_31_54]) ).
cnf(d0,plain,
( ~ '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(X1,X0)
| '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[c51,c30]) ).
cnf(d1,plain,
( ~ '\'E\''(s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))),f(X0)) ),
inference(resolution,[status(thm)],[c4,c31]) ).
cnf(d2,plain,
( '\'LE\''(f(X1),s(s(s(s(s(s(s(s(s('\'0\''))))))))))
| ~ iLEQ(X0,X1)
| '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(X1))
| '\'E\''(s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))),f(X0)) ),
inference(resolution,[status(thm)],[c38,c3]) ).
cnf(d3,plain,
( '\'LE\''(f(X0),s(s(s(s(s(s(s(s(s('\'0\''))))))))))
| '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(X0))
| '\'E\''(s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))),f(X0)) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
( ~ '\'E\''(s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))),f(X0))
| '\'LE\''(f(g(X0)),s(s(s(s(s(s(s(s(s('\'0\''))))))))))
| '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(g(X0))) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( '\'LE\''(f(g(X0)),s(s(s(s(s(s(s(s(s('\'0\''))))))))))
| '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(g(X0)))
| '\'E\''(s(s(s(s(s(s(s(s(s(s('\'0\'')))))))))),f(X0)) ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d6,plain,
( '\'LE\''(f(g(X0)),s(s(s(s(s(s(s(s(s('\'0\''))))))))))
| '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(g(X0)))
| '\'LE\''(f(g(X0)),s(s(s(s(s(s(s(s(s('\'0\''))))))))))
| '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(g(X0))) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( '\'LE\''(f(X1),s(s(s(s(s(s(s(s('\'0\'')))))))))
| ~ iLEQ(g(X0),X1)
| '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(X1))
| '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(g(X0))) ),
inference(resolution,[status(thm)],[d6,c12]) ).
cnf(d8,plain,
( '\'LE\''(f(g(g(X0))),s(s(s(s(s(s(s(s('\'0\'')))))))))
| '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(g(g(X0))))
| '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(g(X0))) ),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
( ~ '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(X0)) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d10,plain,
( '\'LE\''(f(g(X0)),s(s(s(s(s(s(s(s('\'0\'')))))))))
| '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(g(X0)))
| '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(g(X0))) ),
inference(resolution,[status(thm)],[d7,c5]) ).
cnf(d11,plain,
( ~ '\'E\''(s(s(s(s(s(s(s(s(s('\'0\''))))))))),f(X0))
| '\'LE\''(f(g(X0)),s(s(s(s(s(s(s(s('\'0\'')))))))))
| '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(g(X0))) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( '\'LE\''(f(g(g(X0))),s(s(s(s(s(s(s(s('\'0\'')))))))))
| '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(g(g(X0))))
| '\'LE\''(f(g(g(X0))),s(s(s(s(s(s(s(s('\'0\'')))))))))
| '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(g(g(X0)))) ),
inference(resolution,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( '\'LE\''(f(X1),s(s(s(s(s(s(s('\'0\''))))))))
| ~ iLEQ(g(g(X0)),X1)
| '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(X1))
| '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(g(g(X0)))) ),
inference(resolution,[status(thm)],[d12,c18]) ).
cnf(d14,plain,
( '\'LE\''(f(g(g(g(X0)))),s(s(s(s(s(s(s('\'0\''))))))))
| '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(g(g(g(X0)))))
| '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(g(g(X0)))) ),
inference(resolution,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
( ~ '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(X0)) ),
inference(resolution,[status(thm)],[c4,c53]) ).
cnf(d16,plain,
( '\'LE\''(f(g(g(X0))),s(s(s(s(s(s(s('\'0\''))))))))
| '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(g(g(X0))))
| '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(g(g(X0)))) ),
inference(resolution,[status(thm)],[d13,c5]) ).
cnf(d17,plain,
( ~ '\'E\''(s(s(s(s(s(s(s(s('\'0\'')))))))),f(g(X0)))
| '\'LE\''(f(g(g(X0))),s(s(s(s(s(s(s('\'0\''))))))))
| '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(g(g(X0)))) ),
inference(resolution,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
( '\'LE\''(f(g(g(g(X0)))),s(s(s(s(s(s(s('\'0\''))))))))
| '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(g(g(g(X0)))))
| '\'LE\''(f(g(g(g(X0)))),s(s(s(s(s(s(s('\'0\''))))))))
| '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(g(g(g(X0))))) ),
inference(resolution,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
( '\'LE\''(f(X1),s(s(s(s(s(s('\'0\'')))))))
| ~ iLEQ(g(g(g(X0))),X1)
| '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(X1))
| '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(g(g(g(X0))))) ),
inference(resolution,[status(thm)],[d18,c44]) ).
cnf(d20,plain,
( '\'LE\''(f(g(g(g(g(X0))))),s(s(s(s(s(s('\'0\'')))))))
| '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(g(g(g(g(X0))))))
| '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(g(g(g(X0))))) ),
inference(resolution,[status(thm)],[d19,c1]) ).
cnf(d21,plain,
( ~ '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(X0)) ),
inference(resolution,[status(thm)],[c4,c6]) ).
cnf(d22,plain,
( '\'LE\''(f(g(g(g(X0)))),s(s(s(s(s(s('\'0\'')))))))
| '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(g(g(g(X0)))))
| '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(g(g(g(X0))))) ),
inference(resolution,[status(thm)],[d19,c5]) ).
cnf(d23,plain,
( ~ '\'E\''(s(s(s(s(s(s(s('\'0\''))))))),f(g(g(X0))))
| '\'LE\''(f(g(g(g(X0)))),s(s(s(s(s(s('\'0\'')))))))
| '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(g(g(g(X0))))) ),
inference(resolution,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
( '\'LE\''(f(g(g(g(g(X0))))),s(s(s(s(s(s('\'0\'')))))))
| '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(g(g(g(g(X0))))))
| '\'LE\''(f(g(g(g(g(X0))))),s(s(s(s(s(s('\'0\'')))))))
| '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(g(g(g(g(X0)))))) ),
inference(resolution,[status(thm)],[d23,d20]) ).
cnf(d25,plain,
( '\'LE\''(f(X1),s(s(s(s(s('\'0\''))))))
| ~ iLEQ(g(g(g(g(X0)))),X1)
| '\'E\''(s(s(s(s(s('\'0\''))))),f(X1))
| '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(g(g(g(g(X0)))))) ),
inference(resolution,[status(thm)],[d24,c10]) ).
cnf(d26,plain,
( '\'LE\''(f(g(g(g(g(g(X0)))))),s(s(s(s(s('\'0\''))))))
| '\'E\''(s(s(s(s(s('\'0\''))))),f(g(g(g(g(g(X0)))))))
| '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(g(g(g(g(X0)))))) ),
inference(resolution,[status(thm)],[d25,c1]) ).
cnf(d27,plain,
( ~ '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(X0)) ),
inference(resolution,[status(thm)],[c4,c15]) ).
cnf(d28,plain,
( '\'LE\''(f(g(g(g(g(X0))))),s(s(s(s(s('\'0\''))))))
| '\'E\''(s(s(s(s(s('\'0\''))))),f(g(g(g(g(X0))))))
| '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(g(g(g(g(X0)))))) ),
inference(resolution,[status(thm)],[d25,c5]) ).
cnf(d29,plain,
( ~ '\'E\''(s(s(s(s(s(s('\'0\'')))))),f(g(g(g(X0)))))
| '\'LE\''(f(g(g(g(g(X0))))),s(s(s(s(s('\'0\''))))))
| '\'E\''(s(s(s(s(s('\'0\''))))),f(g(g(g(g(X0)))))) ),
inference(resolution,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
( '\'LE\''(f(g(g(g(g(g(X0)))))),s(s(s(s(s('\'0\''))))))
| '\'E\''(s(s(s(s(s('\'0\''))))),f(g(g(g(g(g(X0)))))))
| '\'LE\''(f(g(g(g(g(g(X0)))))),s(s(s(s(s('\'0\''))))))
| '\'E\''(s(s(s(s(s('\'0\''))))),f(g(g(g(g(g(X0))))))) ),
inference(resolution,[status(thm)],[d29,d26]) ).
cnf(d31,plain,
( '\'LE\''(f(X1),s(s(s(s('\'0\'')))))
| ~ iLEQ(g(g(g(g(g(X0))))),X1)
| '\'E\''(s(s(s(s('\'0\'')))),f(X1))
| '\'E\''(s(s(s(s(s('\'0\''))))),f(g(g(g(g(g(X0))))))) ),
inference(resolution,[status(thm)],[d30,c35]) ).
cnf(d32,plain,
( '\'LE\''(f(g(g(g(g(g(g(X0))))))),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s(s('\'0\'')))),f(g(g(g(g(g(g(X0))))))))
| '\'E\''(s(s(s(s(s('\'0\''))))),f(g(g(g(g(g(X0))))))) ),
inference(resolution,[status(thm)],[d31,c1]) ).
cnf(d33,plain,
( ~ '\'E\''(s(s(s(s(s('\'0\''))))),f(g(X0)))
| ~ '\'E\''(s(s(s(s(s('\'0\''))))),f(X0)) ),
inference(resolution,[status(thm)],[c4,c22]) ).
cnf(d34,plain,
( '\'LE\''(f(g(g(g(g(g(X0)))))),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s(s('\'0\'')))),f(g(g(g(g(g(X0)))))))
| '\'E\''(s(s(s(s(s('\'0\''))))),f(g(g(g(g(g(X0))))))) ),
inference(resolution,[status(thm)],[d31,c5]) ).
cnf(d35,plain,
( ~ '\'E\''(s(s(s(s(s('\'0\''))))),f(g(g(g(g(X0))))))
| '\'LE\''(f(g(g(g(g(g(X0)))))),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s(s('\'0\'')))),f(g(g(g(g(g(X0))))))) ),
inference(resolution,[status(thm)],[d34,d33]) ).
cnf(d36,plain,
( '\'LE\''(f(g(g(g(g(g(g(X0))))))),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s(s('\'0\'')))),f(g(g(g(g(g(g(X0))))))))
| '\'LE\''(f(g(g(g(g(g(g(X0))))))),s(s(s(s('\'0\'')))))
| '\'E\''(s(s(s(s('\'0\'')))),f(g(g(g(g(g(g(X0)))))))) ),
inference(resolution,[status(thm)],[d35,d32]) ).
cnf(d37,plain,
( '\'LE\''(f(X1),s(s(s('\'0\''))))
| ~ iLEQ(g(g(g(g(g(g(X0)))))),X1)
| '\'E\''(s(s(s('\'0\''))),f(X1))
| '\'E\''(s(s(s(s('\'0\'')))),f(g(g(g(g(g(g(X0)))))))) ),
inference(resolution,[status(thm)],[d36,c2]) ).
cnf(d38,plain,
( '\'LE\''(f(g(g(g(g(g(g(g(X0)))))))),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(g(g(g(g(g(g(g(X0)))))))))
| '\'E\''(s(s(s(s('\'0\'')))),f(g(g(g(g(g(g(X0)))))))) ),
inference(resolution,[status(thm)],[d37,c1]) ).
cnf(d39,plain,
( ~ '\'E\''(s(s(s(s('\'0\'')))),f(g(X0)))
| ~ '\'E\''(s(s(s(s('\'0\'')))),f(X0)) ),
inference(resolution,[status(thm)],[c4,c47]) ).
cnf(d40,plain,
( '\'LE\''(f(g(g(g(g(g(g(X0))))))),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(g(g(g(g(g(g(X0))))))))
| '\'E\''(s(s(s(s('\'0\'')))),f(g(g(g(g(g(g(X0)))))))) ),
inference(resolution,[status(thm)],[d37,c5]) ).
cnf(d41,plain,
( ~ '\'E\''(s(s(s(s('\'0\'')))),f(g(g(g(g(g(X0)))))))
| '\'LE\''(f(g(g(g(g(g(g(X0))))))),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(g(g(g(g(g(g(X0)))))))) ),
inference(resolution,[status(thm)],[d40,d39]) ).
cnf(d42,plain,
( '\'LE\''(f(g(g(g(g(g(g(g(X0)))))))),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(g(g(g(g(g(g(g(X0)))))))))
| '\'LE\''(f(g(g(g(g(g(g(g(X0)))))))),s(s(s('\'0\''))))
| '\'E\''(s(s(s('\'0\''))),f(g(g(g(g(g(g(g(X0))))))))) ),
inference(resolution,[status(thm)],[d41,d38]) ).
cnf(d43,plain,
( '\'LE\''(f(X1),s(s('\'0\'')))
| ~ iLEQ(g(g(g(g(g(g(g(X0))))))),X1)
| '\'E\''(s(s('\'0\'')),f(X1))
| '\'E\''(s(s(s('\'0\''))),f(g(g(g(g(g(g(g(X0))))))))) ),
inference(resolution,[status(thm)],[d42,c49]) ).
cnf(d44,plain,
( '\'LE\''(f(g(g(g(g(g(g(g(g(X0))))))))),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(g(g(g(g(g(g(g(g(X0))))))))))
| '\'E\''(s(s(s('\'0\''))),f(g(g(g(g(g(g(g(X0))))))))) ),
inference(resolution,[status(thm)],[d43,c1]) ).
cnf(d45,plain,
( ~ '\'E\''(s(s(s('\'0\''))),f(g(X0)))
| ~ '\'E\''(s(s(s('\'0\''))),f(X0)) ),
inference(resolution,[status(thm)],[c4,c11]) ).
cnf(d46,plain,
( '\'LE\''(f(g(g(g(g(g(g(g(X0)))))))),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(g(g(g(g(g(g(g(X0)))))))))
| '\'E\''(s(s(s('\'0\''))),f(g(g(g(g(g(g(g(X0))))))))) ),
inference(resolution,[status(thm)],[d43,c5]) ).
cnf(d47,plain,
( ~ '\'E\''(s(s(s('\'0\''))),f(g(g(g(g(g(g(X0))))))))
| '\'LE\''(f(g(g(g(g(g(g(g(X0)))))))),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(g(g(g(g(g(g(g(X0))))))))) ),
inference(resolution,[status(thm)],[d46,d45]) ).
cnf(d48,plain,
( '\'LE\''(f(g(g(g(g(g(g(g(g(X0))))))))),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(g(g(g(g(g(g(g(g(X0))))))))))
| '\'LE\''(f(g(g(g(g(g(g(g(g(X0))))))))),s(s('\'0\'')))
| '\'E\''(s(s('\'0\'')),f(g(g(g(g(g(g(g(g(X0)))))))))) ),
inference(resolution,[status(thm)],[d47,d44]) ).
cnf(d49,plain,
( '\'LE\''(f(X1),s('\'0\''))
| ~ iLEQ(g(g(g(g(g(g(g(g(X0)))))))),X1)
| '\'E\''(s('\'0\''),f(X1))
| '\'E\''(s(s('\'0\'')),f(g(g(g(g(g(g(g(g(X0)))))))))) ),
inference(resolution,[status(thm)],[d48,c20]) ).
cnf(d50,plain,
( '\'LE\''(f(g(g(g(g(g(g(g(g(g(X0)))))))))),s('\'0\''))
| '\'E\''(s('\'0\''),f(g(g(g(g(g(g(g(g(g(X0)))))))))))
| '\'E\''(s(s('\'0\'')),f(g(g(g(g(g(g(g(g(X0)))))))))) ),
inference(resolution,[status(thm)],[d49,c1]) ).
cnf(d51,plain,
( ~ '\'E\''(s(s('\'0\'')),f(g(X0)))
| ~ '\'E\''(s(s('\'0\'')),f(X0)) ),
inference(resolution,[status(thm)],[c4,c21]) ).
cnf(d52,plain,
( '\'LE\''(f(g(g(g(g(g(g(g(g(X0))))))))),s('\'0\''))
| '\'E\''(s('\'0\''),f(g(g(g(g(g(g(g(g(X0))))))))))
| '\'E\''(s(s('\'0\'')),f(g(g(g(g(g(g(g(g(X0)))))))))) ),
inference(resolution,[status(thm)],[d49,c5]) ).
cnf(d53,plain,
( ~ '\'E\''(s(s('\'0\'')),f(g(g(g(g(g(g(g(X0)))))))))
| '\'LE\''(f(g(g(g(g(g(g(g(g(X0))))))))),s('\'0\''))
| '\'E\''(s('\'0\''),f(g(g(g(g(g(g(g(g(X0)))))))))) ),
inference(resolution,[status(thm)],[d52,d51]) ).
cnf(d54,plain,
( '\'LE\''(f(g(g(g(g(g(g(g(g(g(X0)))))))))),s('\'0\''))
| '\'E\''(s('\'0\''),f(g(g(g(g(g(g(g(g(g(X0)))))))))))
| '\'LE\''(f(g(g(g(g(g(g(g(g(g(X0)))))))))),s('\'0\''))
| '\'E\''(s('\'0\''),f(g(g(g(g(g(g(g(g(g(X0))))))))))) ),
inference(resolution,[status(thm)],[d53,d50]) ).
cnf(d55,plain,
( ~ iLEQ(g(g(g(g(g(g(g(g(g(X0))))))))),X1)
| '\'E\''('\'0\'',f(X1))
| '\'E\''(s('\'0\''),f(g(g(g(g(g(g(g(g(g(X0))))))))))) ),
inference(resolution,[status(thm)],[d54,d0]) ).
cnf(d56,plain,
( '\'E\''('\'0\'',f(g(g(g(g(g(g(g(g(g(g(X0))))))))))))
| '\'E\''(s('\'0\''),f(g(g(g(g(g(g(g(g(g(X0))))))))))) ),
inference(resolution,[status(thm)],[d55,c1]) ).
cnf(d57,plain,
( ~ '\'E\''(s('\'0\''),f(g(X0)))
| ~ '\'E\''(s('\'0\''),f(X0)) ),
inference(resolution,[status(thm)],[c4,c34]) ).
cnf(d58,plain,
( '\'E\''('\'0\'',f(g(g(g(g(g(g(g(g(g(X0)))))))))))
| '\'E\''(s('\'0\''),f(g(g(g(g(g(g(g(g(g(X0))))))))))) ),
inference(resolution,[status(thm)],[d55,c5]) ).
cnf(d59,plain,
( ~ '\'E\''(s('\'0\''),f(g(g(g(g(g(g(g(g(X0))))))))))
| '\'E\''('\'0\'',f(g(g(g(g(g(g(g(g(g(X0))))))))))) ),
inference(resolution,[status(thm)],[d58,d57]) ).
cnf(d60,plain,
( '\'E\''('\'0\'',f(g(g(g(g(g(g(g(g(g(g(X0))))))))))))
| '\'E\''('\'0\'',f(g(g(g(g(g(g(g(g(g(g(X0)))))))))))) ),
inference(resolution,[status(thm)],[d59,d56]) ).
cnf(d61,plain,
( ~ '\'E\''('\'0\'',f(g(X0)))
| ~ '\'E\''('\'0\'',f(X0)) ),
inference(resolution,[status(thm)],[c4,c24]) ).
cnf(d62,plain,
~ '\'E\''('\'0\'',f(g(g(g(g(g(g(g(g(g(X0))))))))))),
inference(resolution,[status(thm)],[d60,d61]) ).
cnf(d63,plain,
$false,
inference(resolution,[status(thm)],[d62,d60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO631-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n017.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 19:36:03 UTC 2026
% 0.17/0.40 % CPUTime :
% 0.17/0.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.03/6.06 % SZS status Unsatisfiable for theBenchmark.p
% 24.03/6.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------