%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL090-1 : 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 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 20 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 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 : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 148 ( 83 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_1,axiom,
~ is_a_theorem(implies(a,a)),
file('theBenchmark.p',prove_ic_1) ).
cnf(c_3,plain,
~ is_a_theorem(implies(a,a)),
inference(clausify,[status(thm)],[prove_ic_1]) ).
cnf(c_261,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_261,c_2]) ).
cnf(c_262,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_262,c_4]) ).
cnf(c_263,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_7,plain,
is_a_theorem(implies(implies(A,B),implies(B,implies(implies(C,D),implies(D,B))))),
inference(resolve,[status(thm)],[c_263,c_5]) ).
cnf(c_264,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_11,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(B,C)),D),implies(E,implies(C,D)))),
inference(resolve,[status(thm)],[c_264,c_7]) ).
cnf(c_265,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_17,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(C,implies(D,implies(E,C)))))),
inference(resolve,[status(thm)],[c_265,c_11]) ).
cnf(c_266,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_17]) ).
cnf(c_22,plain,
is_a_theorem(implies(implies(A,B),implies(B,implies(C,implies(D,B))))),
inference(resolve,[status(thm)],[c_266,c_17]) ).
cnf(c_267,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_27,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(E,implies(C,D)))),
inference(resolve,[status(thm)],[c_267,c_22]) ).
cnf(c_268,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_31,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_268,c_27]) ).
cnf(c_269,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_31]) ).
cnf(c_172,plain,
is_a_theorem(implies(A,implies(B,implies(implies(C,D),implies(E,implies(D,D)))))),
inference(resolve,[status(thm)],[c_269,c_2]) ).
cnf(c_270,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_172]) ).
cnf(c_225,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(D,implies(C,C))))),
inference(resolve,[status(thm)],[c_270,c_172]) ).
cnf(c_271,plain,
( is_a_theorem(implies(implies(B,C),implies(D,implies(C,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_225]) ).
cnf(c_235,plain,
is_a_theorem(implies(implies(A,B),implies(C,implies(B,B)))),
inference(resolve,[status(thm)],[c_271,c_225]) ).
cnf(c_272,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_31]) ).
cnf(c_240,plain,
is_a_theorem(implies(A,implies(B,implies(C,implies(D,D))))),
inference(resolve,[status(thm)],[c_272,c_235]) ).
cnf(c_273,plain,
( is_a_theorem(implies(B,implies(C,implies(D,D))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_240]) ).
cnf(c_252,plain,
is_a_theorem(implies(A,implies(B,implies(C,C)))),
inference(resolve,[status(thm)],[c_273,c_240]) ).
cnf(c_274,plain,
( is_a_theorem(implies(B,implies(C,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_252]) ).
cnf(c_257,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_274,c_252]) ).
cnf(c_275,plain,
( is_a_theorem(implies(B,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_257]) ).
cnf(c_259,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_275,c_257]) ).
cnf(c_260,plain,
$false,
inference(resolve,[status(thm)],[c_259,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL090-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 21:48:23 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2000705 was started by sandbox on n007,
% 0.10/0.36 % Fri Sep 25 21:48:23 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.36
% 0.14/0.36 % From the command line: assign(max_seconds, 300).
% 0.14/0.41
% 0.14/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.41
% 0.14/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.41 % Length of proof is 19.
% 0.14/0.41 % Level of proof is 16.
% 0.14/0.41 % Maximum clause weight is 50.000.
% 0.14/0.41 % Given clauses 43.
% 0.14/0.41
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------