%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 07:57:56 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.52s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 19 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 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 : 97 ( 39 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,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),VAR_2),implies(implies(VAR_2,VAR_0),implies(VAR_3,VAR_0)))),
file('theBenchmark.p',ic_JLukasiewicz) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,A),implies(D,A)))),
inference(clausify,[status(thm)],[ic_JLukasiewicz]) ).
fof(ic_1,axiom,
! [VAR_0] : is_a_theorem(implies(VAR_0,VAR_0)),
file('theBenchmark.p',ic_1) ).
cnf(c_3,plain,
is_a_theorem(implies(A,A)),
inference(clausify,[status(thm)],[ic_1]) ).
fof(prove_ic_3,axiom,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('theBenchmark.p',prove_ic_3) ).
cnf(c_4,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(clausify,[status(thm)],[prove_ic_3]) ).
cnf(c_159,plain,
( is_a_theorem(implies(implies(C,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(C,A))),
inference(resolve,[status(thm)],[c_159,c_3]) ).
cnf(c_160,plain,
( is_a_theorem(implies(C,A))
| ~ is_a_theorem(implies(implies(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_9,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_160,c_6]) ).
cnf(c_161,plain,
( is_a_theorem(implies(implies(C,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_11,plain,
is_a_theorem(implies(implies(implies(A,B),implies(B,C)),implies(D,implies(B,C)))),
inference(resolve,[status(thm)],[c_161,c_6]) ).
cnf(c_162,plain,
( is_a_theorem(implies(implies(C,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_13,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_162,c_9]) ).
cnf(c_163,plain,
( is_a_theorem(implies(implies(C,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_27,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(D,B)),implies(E,implies(D,B)))),
inference(resolve,[status(thm)],[c_163,c_11]) ).
cnf(c_164,plain,
( is_a_theorem(implies(E,implies(D,B)))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(D,B))) ),
inference(resolve,[status(thm)],[c_1,c_27]) ).
cnf(c_72,plain,
is_a_theorem(implies(A,implies(implies(implies(implies(B,C),D),C),implies(B,C)))),
inference(resolve,[status(thm)],[c_164,c_2]) ).
cnf(c_165,plain,
( is_a_theorem(implies(implies(implies(implies(B,C),D),C),implies(B,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_72]) ).
cnf(c_121,plain,
is_a_theorem(implies(implies(implies(implies(A,B),C),B),implies(A,B))),
inference(resolve,[status(thm)],[c_165,c_72]) ).
cnf(c_166,plain,
( is_a_theorem(implies(implies(C,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_125,plain,
is_a_theorem(implies(implies(implies(A,B),implies(implies(A,B),C)),implies(D,implies(implies(A,B),C)))),
inference(resolve,[status(thm)],[c_166,c_121]) ).
cnf(c_167,plain,
( is_a_theorem(implies(D,implies(implies(A,B),C)))
| ~ is_a_theorem(implies(implies(A,B),implies(implies(A,B),C))) ),
inference(resolve,[status(thm)],[c_1,c_125]) ).
cnf(c_139,plain,
is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))),
inference(resolve,[status(thm)],[c_167,c_13]) ).
cnf(c_168,plain,
( is_a_theorem(implies(D,implies(implies(A,B),C)))
| ~ is_a_theorem(implies(implies(A,B),implies(implies(A,B),C))) ),
inference(resolve,[status(thm)],[c_1,c_125]) ).
cnf(c_142,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_168,c_6]) ).
cnf(c_169,plain,
( is_a_theorem(implies(implies(implies(B,B),C),C))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_139]) ).
cnf(c_153,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_169,c_139]) ).
cnf(c_170,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_1,c_153]) ).
cnf(c_157,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_170,c_142]) ).
cnf(c_158,plain,
$false,
inference(resolve,[status(thm)],[c_157,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n011.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Fri Sep 25 21:50:00 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 2991219 was started by sandbox on n011,
% 0.15/0.43 % Fri Sep 25 21:50:00 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 0.15/0.52
% 0.15/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.52
% 0.15/0.52 % Proof 1 at 0.02 (+ 0.03) seconds.
% 0.15/0.52 % Length of proof is 17.
% 0.15/0.52 % Level of proof is 10.
% 0.15/0.52 % Maximum clause weight is 44.000.
% 0.15/0.52 % Given clauses 49.
% 0.15/0.52
% 0.15/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------