%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL095-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 07:57:57 AM UTC 2026
% Result : Unsatisfiable 1.01s 0.56s
% Output : CNFRefutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 3
% Syntax : Number of formulae : 55 ( 29 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 30 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 231 ( 124 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(implies(VAR_0,VAR_1)) ),
file('theBenchmark.p',condensed_detachment) ).
cnf(c_1,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(ic_JLukasiewicz_5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),implies(VAR_2,VAR_3)),implies(implies(VAR_3,VAR_0),implies(VAR_4,implies(VAR_2,VAR_0))))),
file('theBenchmark.p',ic_JLukasiewicz_5) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,D)),implies(implies(D,A),implies(E,implies(C,A))))),
inference(clausify,[status(thm)],[ic_JLukasiewicz_5]) ).
fof(prove_ic_5,axiom,
~ is_a_theorem(implies(a,implies(implies(a,b),b))),
file('theBenchmark.p',prove_ic_5) ).
cnf(c_3,plain,
~ is_a_theorem(implies(a,implies(implies(a,b),b))),
inference(clausify,[status(thm)],[prove_ic_5]) ).
cnf(c_285,plain,
( is_a_theorem(implies(implies(D,A),implies(E,implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(C,D)),implies(E,implies(implies(F,C),implies(C,D))))),
inference(resolve,[status(thm)],[c_285,c_2]) ).
cnf(c_286,plain,
( is_a_theorem(implies(E,implies(implies(F,C),implies(C,D))))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(C,implies(implies(D,E),implies(E,C)))))),
inference(resolve,[status(thm)],[c_286,c_4]) ).
cnf(c_287,plain,
( is_a_theorem(implies(implies(B,C),implies(C,implies(implies(D,E),implies(E,C)))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_6,plain,
is_a_theorem(implies(implies(A,B),implies(B,implies(implies(C,D),implies(D,B))))),
inference(resolve,[status(thm)],[c_287,c_5]) ).
cnf(c_288,plain,
( is_a_theorem(implies(implies(D,A),implies(E,implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_8,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(B,C)),D),implies(E,implies(C,D)))),
inference(resolve,[status(thm)],[c_288,c_6]) ).
cnf(c_289,plain,
( is_a_theorem(implies(E,implies(implies(F,C),implies(C,D))))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_11,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(C,implies(D,implies(E,C)))))),
inference(resolve,[status(thm)],[c_289,c_8]) ).
cnf(c_290,plain,
( is_a_theorem(implies(E,implies(C,D)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(B,C)),D)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_14,plain,
is_a_theorem(implies(A,implies(B,implies(implies(B,C),implies(D,implies(E,C)))))),
inference(resolve,[status(thm)],[c_290,c_2]) ).
cnf(c_291,plain,
( is_a_theorem(implies(implies(B,C),implies(C,implies(D,implies(E,C)))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_11]) ).
cnf(c_15,plain,
is_a_theorem(implies(implies(A,B),implies(B,implies(C,implies(D,B))))),
inference(resolve,[status(thm)],[c_291,c_11]) ).
cnf(c_292,plain,
( is_a_theorem(implies(implies(D,A),implies(E,implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_20,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(E,implies(C,D)))),
inference(resolve,[status(thm)],[c_292,c_15]) ).
cnf(c_293,plain,
( is_a_theorem(implies(implies(D,A),implies(E,implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_23,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,implies(D,A))),implies(E,implies(F,implies(C,implies(D,A)))))),
inference(resolve,[status(thm)],[c_293,c_20]) ).
cnf(c_294,plain,
( is_a_theorem(implies(implies(D,A),implies(E,implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_36,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,implies(D,B))),E),implies(F,implies(A,E)))),
inference(resolve,[status(thm)],[c_294,c_14]) ).
cnf(c_295,plain,
( is_a_theorem(implies(E,implies(F,implies(C,implies(D,A)))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,implies(D,A)))) ),
inference(resolve,[status(thm)],[c_1,c_23]) ).
cnf(c_64,plain,
is_a_theorem(implies(A,implies(B,implies(implies(C,D),implies(E,implies(D,D)))))),
inference(resolve,[status(thm)],[c_295,c_2]) ).
cnf(c_296,plain,
( is_a_theorem(implies(B,implies(implies(C,D),implies(E,implies(D,D)))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_64]) ).
cnf(c_81,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(D,implies(C,C))))),
inference(resolve,[status(thm)],[c_296,c_64]) ).
cnf(c_297,plain,
( is_a_theorem(implies(implies(B,C),implies(D,implies(C,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_81]) ).
cnf(c_83,plain,
is_a_theorem(implies(implies(A,B),implies(C,implies(B,B)))),
inference(resolve,[status(thm)],[c_297,c_81]) ).
cnf(c_298,plain,
( is_a_theorem(implies(E,implies(F,implies(C,implies(D,A)))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,implies(D,A)))) ),
inference(resolve,[status(thm)],[c_1,c_23]) ).
cnf(c_88,plain,
is_a_theorem(implies(A,implies(B,implies(C,implies(D,D))))),
inference(resolve,[status(thm)],[c_298,c_83]) ).
cnf(c_299,plain,
( is_a_theorem(implies(B,implies(C,implies(D,D))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_88]) ).
cnf(c_91,plain,
is_a_theorem(implies(A,implies(B,implies(C,C)))),
inference(resolve,[status(thm)],[c_299,c_88]) ).
cnf(c_300,plain,
( is_a_theorem(implies(B,implies(C,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_91]) ).
cnf(c_98,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_300,c_91]) ).
cnf(c_301,plain,
( is_a_theorem(implies(implies(D,A),implies(E,implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_101,plain,
is_a_theorem(implies(implies(A,B),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_301,c_98]) ).
cnf(c_302,plain,
( is_a_theorem(implies(implies(D,A),implies(E,implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_106,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(C,implies(D,A)))),
inference(resolve,[status(thm)],[c_302,c_101]) ).
cnf(c_303,plain,
( is_a_theorem(implies(C,implies(D,A)))
| ~ is_a_theorem(implies(implies(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_106]) ).
cnf(c_136,plain,
is_a_theorem(implies(A,implies(B,implies(implies(C,D),implies(C,implies(E,D)))))),
inference(resolve,[status(thm)],[c_303,c_36]) ).
cnf(c_304,plain,
( is_a_theorem(implies(B,implies(implies(C,D),implies(C,implies(E,D)))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_136]) ).
cnf(c_162,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(B,implies(D,C))))),
inference(resolve,[status(thm)],[c_304,c_136]) ).
cnf(c_305,plain,
( is_a_theorem(implies(implies(D,A),implies(E,implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_168,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(E,implies(implies(A,C),D)))),
inference(resolve,[status(thm)],[c_305,c_162]) ).
cnf(c_306,plain,
( is_a_theorem(implies(C,implies(D,A)))
| ~ is_a_theorem(implies(implies(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_106]) ).
cnf(c_263,plain,
is_a_theorem(implies(A,implies(B,implies(C,implies(implies(C,D),D))))),
inference(resolve,[status(thm)],[c_306,c_168]) ).
cnf(c_307,plain,
( is_a_theorem(implies(B,implies(C,implies(implies(C,D),D))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_263]) ).
cnf(c_278,plain,
is_a_theorem(implies(A,implies(B,implies(implies(B,C),C)))),
inference(resolve,[status(thm)],[c_307,c_263]) ).
cnf(c_308,plain,
( is_a_theorem(implies(B,implies(implies(B,C),C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_278]) ).
cnf(c_283,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_308,c_278]) ).
cnf(c_284,plain,
$false,
inference(resolve,[status(thm)],[c_283,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL095-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 21:48:38 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2001488 was started by sandbox on n007,
% 0.08/0.36 % Fri Sep 25 21:48:38 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 1.01/0.56
% 1.01/0.56 % SZS status Unsatisfiable for theBenchmark
% 1.01/0.56
% 1.01/0.56 % Proof 1 at 0.11 (+ 0.07) seconds.
% 1.01/0.56 % Length of proof is 28.
% 1.01/0.56 % Level of proof is 23.
% 1.01/0.56 % Maximum clause weight is 90.000.
% 1.01/0.56 % Given clauses 82.
% 1.01/0.56
% 1.01/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------