%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 07:57:44 AM UTC 2026
% Result : Unsatisfiable 11.01s 16.82s
% Output : CNFRefutation 11.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 3
% Syntax : Number of formulae : 88 ( 57 unt; 0 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 35 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 301 ( 150 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [VAR_0,VAR_1] :
( is_a_theorem(VAR_1)
| ~ is_a_theorem(VAR_0)
| ~ is_a_theorem(or(not(VAR_0),VAR_1)) ),
file('theBenchmark.p',condensed_detachment) ).
cnf(c_1,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(or(not(A),B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(an_CAMeredith,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : is_a_theorem(or(not(or(not(or(not(VAR_0),VAR_1)),or(VAR_2,or(VAR_3,VAR_4)))),or(not(or(not(VAR_3),VAR_0)),or(VAR_2,or(VAR_4,VAR_0))))),
file('theBenchmark.p',an_CAMeredith) ).
cnf(c_2,plain,
is_a_theorem(or(not(or(not(or(not(A),B)),or(C,or(D,E)))),or(not(or(not(D),A)),or(C,or(E,A))))),
inference(clausify,[status(thm)],[an_CAMeredith]) ).
fof(an_2,axiom,
~ is_a_theorem(or(not(or(a,b)),or(b,a))),
file('theBenchmark.p',an_2) ).
cnf(c_3,plain,
~ is_a_theorem(or(not(or(a,b)),or(b,a))),
inference(clausify,[status(thm)],[an_2]) ).
cnf(c_4,plain,
( is_a_theorem(or(not(or(not(D),A)),or(C,or(E,A))))
| ~ is_a_theorem(or(not(or(not(A),B)),or(C,or(D,E)))) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_2514,plain,
( is_a_theorem(or(not(or(not(D),A)),or(C,or(E,A))))
| ~ is_a_theorem(or(not(or(not(A),B)),or(C,or(D,E)))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_5,plain,
is_a_theorem(or(not(or(not(A),or(not(B),C))),or(not(or(not(D),B)),or(or(E,B),or(not(B),C))))),
inference(resolve,[status(thm)],[c_2514,c_2]) ).
cnf(c_6,plain,
is_a_theorem(or(not(or(not(or(A,B)),C)),or(not(or(not(D),B)),or(or(not(B),E),C)))),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_9,plain,
is_a_theorem(or(not(or(not(or(not(A),B)),or(C,A))),or(not(or(not(D),A)),or(E,or(C,A))))),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_14,plain,
( is_a_theorem(or(not(or(not(D),A)),or(E,or(C,A))))
| ~ is_a_theorem(or(not(or(not(A),B)),or(C,A))) ),
inference(resolve,[status(thm)],[c_9,c_1]) ).
cnf(c_2515,plain,
( is_a_theorem(or(not(or(not(D),A)),or(E,or(C,A))))
| ~ is_a_theorem(or(not(or(not(A),B)),or(C,A))) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_15,plain,
is_a_theorem(or(not(or(not(A),or(not(B),or(C,B)))),or(D,or(not(or(not(E),B)),or(not(B),or(C,B)))))),
inference(resolve,[status(thm)],[c_2515,c_9]) ).
cnf(c_23,plain,
( is_a_theorem(or(D,or(not(or(not(E),B)),or(not(B),or(C,B)))))
| ~ is_a_theorem(or(not(A),or(not(B),or(C,B)))) ),
inference(resolve,[status(thm)],[c_15,c_1]) ).
cnf(c_2516,plain,
( is_a_theorem(or(D,or(not(or(not(E),B)),or(not(B),or(C,B)))))
| ~ is_a_theorem(or(not(A),or(not(B),or(C,B)))) ),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_24,plain,
is_a_theorem(or(A,or(not(or(not(B),or(not(C),D))),or(not(or(not(C),D)),or(E,or(not(C),D)))))),
inference(resolve,[status(thm)],[c_2516,c_9]) ).
cnf(c_2517,plain,
( is_a_theorem(or(not(or(not(B),or(not(C),D))),or(not(or(not(C),D)),or(E,or(not(C),D)))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_24]) ).
cnf(c_27,plain,
is_a_theorem(or(not(or(not(A),or(not(B),C))),or(not(or(not(B),C)),or(D,or(not(B),C))))),
inference(resolve,[status(thm)],[c_2517,c_24]) ).
cnf(c_30,plain,
is_a_theorem(or(not(or(not(A),B)),or(not(or(not(C),D)),or(or(not(C),D),B)))),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_38,plain,
is_a_theorem(or(not(or(not(or(not(A),B)),C)),or(not(or(not(A),B)),or(D,C)))),
inference(resolve,[status(thm)],[c_30,c_4]) ).
cnf(c_48,plain,
is_a_theorem(or(not(or(not(A),or(not(B),C))),or(D,or(not(or(not(B),C)),or(not(B),C))))),
inference(resolve,[status(thm)],[c_38,c_14]) ).
cnf(c_51,plain,
( is_a_theorem(or(not(or(not(A),B)),or(D,C)))
| ~ is_a_theorem(or(not(or(not(A),B)),C)) ),
inference(resolve,[status(thm)],[c_38,c_1]) ).
cnf(c_101,plain,
is_a_theorem(or(not(or(not(not(or(not(A),B))),C)),or(D,or(or(not(A),B),C)))),
inference(resolve,[status(thm)],[c_48,c_4]) ).
cnf(c_102,plain,
( is_a_theorem(or(D,or(not(or(not(B),C)),or(not(B),C))))
| ~ is_a_theorem(or(not(A),or(not(B),C))) ),
inference(resolve,[status(thm)],[c_48,c_1]) ).
cnf(c_160,plain,
is_a_theorem(or(A,or(not(or(not(B),C)),or(not(C),or(or(not(D),E),C))))),
inference(resolve,[status(thm)],[c_101,c_23]) ).
cnf(c_2518,plain,
( is_a_theorem(or(not(or(not(B),C)),or(not(C),or(or(not(D),E),C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_160]) ).
cnf(c_178,plain,
is_a_theorem(or(not(or(not(A),B)),or(not(B),or(or(not(C),D),B)))),
inference(resolve,[status(thm)],[c_2518,c_160]) ).
cnf(c_183,plain,
is_a_theorem(or(not(or(not(or(not(A),B)),C)),or(not(D),or(D,C)))),
inference(resolve,[status(thm)],[c_178,c_4]) ).
cnf(c_199,plain,
is_a_theorem(or(A,or(not(or(not(B),C)),or(not(C),or(C,C))))),
inference(resolve,[status(thm)],[c_183,c_23]) ).
cnf(c_2519,plain,
( is_a_theorem(or(not(or(not(B),C)),or(not(C),or(C,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_199]) ).
cnf(c_261,plain,
is_a_theorem(or(not(or(not(A),B)),or(not(B),or(B,B)))),
inference(resolve,[status(thm)],[c_2519,c_199]) ).
cnf(c_267,plain,
is_a_theorem(or(not(or(not(A),B)),or(not(A),or(A,B)))),
inference(resolve,[status(thm)],[c_261,c_4]) ).
cnf(c_274,plain,
is_a_theorem(or(not(or(not(A),A)),or(not(A),or(B,A)))),
inference(resolve,[status(thm)],[c_267,c_4]) ).
cnf(c_295,plain,
is_a_theorem(or(A,or(not(or(not(B),C)),or(not(C),or(D,C))))),
inference(resolve,[status(thm)],[c_274,c_23]) ).
cnf(c_2520,plain,
( is_a_theorem(or(not(or(not(B),C)),or(not(C),or(D,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_295]) ).
cnf(c_390,plain,
is_a_theorem(or(not(or(not(A),B)),or(not(B),or(C,B)))),
inference(resolve,[status(thm)],[c_2520,c_295]) ).
cnf(c_401,plain,
is_a_theorem(or(not(or(not(A),B)),or(C,or(not(B),or(D,B))))),
inference(resolve,[status(thm)],[c_390,c_51]) ).
cnf(c_402,plain,
is_a_theorem(or(not(or(not(A),or(B,C))),or(D,or(not(C),or(B,C))))),
inference(resolve,[status(thm)],[c_390,c_14]) ).
cnf(c_403,plain,
is_a_theorem(or(not(or(not(A),B)),or(not(C),or(C,B)))),
inference(resolve,[status(thm)],[c_390,c_4]) ).
cnf(c_417,plain,
is_a_theorem(or(not(or(not(A),B)),or(not(A),or(C,B)))),
inference(resolve,[status(thm)],[c_403,c_4]) ).
cnf(c_436,plain,
( is_a_theorem(or(not(A),or(C,B)))
| ~ is_a_theorem(or(not(A),B)) ),
inference(resolve,[status(thm)],[c_417,c_1]) ).
cnf(c_474,plain,
is_a_theorem(or(not(or(not(not(A)),B)),or(C,or(or(D,A),B)))),
inference(resolve,[status(thm)],[c_401,c_4]) ).
cnf(c_521,plain,
( is_a_theorem(or(D,or(not(C),or(B,C))))
| ~ is_a_theorem(or(not(A),or(B,C))) ),
inference(resolve,[status(thm)],[c_402,c_1]) ).
cnf(c_753,plain,
is_a_theorem(or(not(or(not(or(A,B)),not(B))),or(C,or(D,not(B))))),
inference(resolve,[status(thm)],[c_474,c_4]) ).
cnf(c_772,plain,
is_a_theorem(or(A,or(not(or(B,not(C))),or(D,or(B,not(C)))))),
inference(resolve,[status(thm)],[c_753,c_521]) ).
cnf(c_2521,plain,
( is_a_theorem(or(not(or(B,not(C))),or(D,or(B,not(C)))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_772]) ).
cnf(c_1001,plain,
is_a_theorem(or(not(or(A,not(B))),or(C,or(A,not(B))))),
inference(resolve,[status(thm)],[c_2521,c_772]) ).
cnf(c_1010,plain,
is_a_theorem(or(not(or(not(not(A)),A)),or(B,or(not(C),A)))),
inference(resolve,[status(thm)],[c_1001,c_4]) ).
cnf(c_1025,plain,
is_a_theorem(or(A,or(not(or(not(B),C)),or(D,or(not(B),C))))),
inference(resolve,[status(thm)],[c_1010,c_521]) ).
cnf(c_2522,plain,
( is_a_theorem(or(not(or(not(B),C)),or(D,or(not(B),C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1025]) ).
cnf(c_1251,plain,
is_a_theorem(or(not(or(not(A),B)),or(C,or(not(A),B)))),
inference(resolve,[status(thm)],[c_2522,c_1025]) ).
cnf(c_1260,plain,
is_a_theorem(or(not(or(not(not(A)),A)),or(B,or(C,A)))),
inference(resolve,[status(thm)],[c_1251,c_4]) ).
cnf(c_1273,plain,
is_a_theorem(or(A,or(not(or(B,C)),or(D,or(B,C))))),
inference(resolve,[status(thm)],[c_1260,c_521]) ).
cnf(c_2523,plain,
( is_a_theorem(or(not(or(B,C)),or(D,or(B,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1273]) ).
cnf(c_1412,plain,
is_a_theorem(or(not(or(A,B)),or(C,or(A,B)))),
inference(resolve,[status(thm)],[c_2523,c_1273]) ).
cnf(c_1416,plain,
is_a_theorem(or(not(or(A,B)),or(C,or(D,or(A,B))))),
inference(resolve,[status(thm)],[c_1412,c_436]) ).
cnf(c_1425,plain,
is_a_theorem(or(not(or(not(A),B)),or(C,or(or(not(B),D),B)))),
inference(resolve,[status(thm)],[c_1416,c_4]) ).
cnf(c_1532,plain,
is_a_theorem(or(not(or(not(or(not(A),B)),C)),or(D,or(A,C)))),
inference(resolve,[status(thm)],[c_1425,c_4]) ).
cnf(c_1550,plain,
( is_a_theorem(or(D,or(A,C)))
| ~ is_a_theorem(or(not(or(not(A),B)),C)) ),
inference(resolve,[status(thm)],[c_1532,c_1]) ).
cnf(c_2524,plain,
( is_a_theorem(or(D,or(A,C)))
| ~ is_a_theorem(or(not(or(not(A),B)),C)) ),
inference(resolve,[status(thm)],[c_1,c_1532]) ).
cnf(c_1566,plain,
is_a_theorem(or(A,or(B,or(not(C),or(C,D))))),
inference(resolve,[status(thm)],[c_2524,c_403]) ).
cnf(c_2525,plain,
( is_a_theorem(or(B,or(not(C),or(C,D))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1566]) ).
cnf(c_1661,plain,
is_a_theorem(or(A,or(not(B),or(B,C)))),
inference(resolve,[status(thm)],[c_2525,c_1566]) ).
cnf(c_2526,plain,
( is_a_theorem(or(not(B),or(B,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1661]) ).
cnf(c_1666,plain,
is_a_theorem(or(not(A),or(A,B))),
inference(resolve,[status(thm)],[c_2526,c_1661]) ).
cnf(c_1676,plain,
is_a_theorem(or(A,or(not(B),or(C,B)))),
inference(resolve,[status(thm)],[c_1666,c_521]) ).
cnf(c_1682,plain,
is_a_theorem(or(A,or(not(or(not(B),C)),or(not(B),C)))),
inference(resolve,[status(thm)],[c_1666,c_102]) ).
cnf(c_2527,plain,
( is_a_theorem(or(not(B),or(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1676]) ).
cnf(c_1737,plain,
is_a_theorem(or(not(A),or(B,A))),
inference(resolve,[status(thm)],[c_2527,c_1676]) ).
cnf(c_2528,plain,
( is_a_theorem(or(not(or(not(B),C)),or(not(B),C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1682]) ).
cnf(c_2033,plain,
is_a_theorem(or(not(or(not(A),B)),or(not(A),B))),
inference(resolve,[status(thm)],[c_2528,c_1682]) ).
cnf(c_2039,plain,
is_a_theorem(or(A,or(B,or(not(B),C)))),
inference(resolve,[status(thm)],[c_2033,c_1550]) ).
cnf(c_2040,plain,
is_a_theorem(or(not(or(not(A),B)),or(C,or(not(B),B)))),
inference(resolve,[status(thm)],[c_2033,c_14]) ).
cnf(c_2529,plain,
( is_a_theorem(or(B,or(not(B),C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2039]) ).
cnf(c_2051,plain,
is_a_theorem(or(A,or(not(A),B))),
inference(resolve,[status(thm)],[c_2529,c_2039]) ).
cnf(c_2530,plain,
( is_a_theorem(or(not(not(A)),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2051]) ).
cnf(c_2088,plain,
is_a_theorem(or(not(not(or(not(A),or(B,A)))),C)),
inference(resolve,[status(thm)],[c_2530,c_1737]) ).
cnf(c_2141,plain,
( is_a_theorem(or(C,or(not(B),B)))
| ~ is_a_theorem(or(not(A),B)) ),
inference(resolve,[status(thm)],[c_2040,c_1]) ).
cnf(c_2531,plain,
( is_a_theorem(or(C,or(not(B),B)))
| ~ is_a_theorem(or(not(A),B)) ),
inference(resolve,[status(thm)],[c_1,c_2040]) ).
cnf(c_2145,plain,
is_a_theorem(or(A,or(not(or(B,C)),or(B,C)))),
inference(resolve,[status(thm)],[c_2531,c_1737]) ).
cnf(c_2152,plain,
is_a_theorem(or(not(or(not(A),B)),or(not(or(A,C)),or(C,B)))),
inference(resolve,[status(thm)],[c_2145,c_4]) ).
cnf(c_2178,plain,
( is_a_theorem(or(not(or(A,C)),or(C,B)))
| ~ is_a_theorem(or(not(A),B)) ),
inference(resolve,[status(thm)],[c_2152,c_1]) ).
cnf(c_2485,plain,
is_a_theorem(or(A,or(not(B),B))),
inference(resolve,[status(thm)],[c_2088,c_2141]) ).
cnf(c_2532,plain,
( is_a_theorem(or(not(B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2485]) ).
cnf(c_2509,plain,
is_a_theorem(or(not(A),A)),
inference(resolve,[status(thm)],[c_2532,c_2485]) ).
cnf(c_2512,plain,
is_a_theorem(or(not(or(A,B)),or(B,A))),
inference(resolve,[status(thm)],[c_2509,c_2178]) ).
cnf(c_2513,plain,
$false,
inference(resolve,[status(thm)],[c_2512,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/15.41 % Computer : n006.cluster.edu
% 0.12/15.41 % Model : x86_64 x86_64
% 0.12/15.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.41 % Memory : 8046.5625MB
% 0.12/15.41 % OS : Linux 6.8.0-71-generic
% 0.12/15.41 % CPULimit : 300
% 0.12/15.41 % WCLimit : 300
% 0.12/15.41 % DateTime : Fri Sep 25 21:42:45 UTC 2026
% 0.12/15.42 % CPUTime :
% 0.12/15.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/15.42 % Process 3811846 was started by sandbox2 on n006,
% 0.12/15.42 % Fri Sep 25 21:42:45 2026
% 0.12/15.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/15.43
% 0.12/15.43 % From the command line: assign(max_seconds, 300).
% 11.01/16.82
% 11.01/16.82 % Assigning unary symbol not kb_weight 0 and highest precedence (5).
% 11.01/16.82
% 11.01/16.82 % SZS status Unsatisfiable for theBenchmark
% 11.01/16.82
% 11.01/16.82 % Proof 1 at 0.95 (+ 0.43) seconds.
% 11.01/16.82 % Length of proof is 66.
% 11.01/16.82 % Level of proof is 45.
% 11.01/16.82 % Maximum clause weight is 91.000.
% 11.01/16.82 % Given clauses 300.
% 11.01/16.82
% 11.01/16.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------