%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL083-1 : 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 : n020.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 0.80s 0.57s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 120 ( 56 sgn 6 !; 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(prove_ic_3,axiom,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('theBenchmark.p',prove_ic_3) ).
cnf(c_3,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(clausify,[status(thm)],[prove_ic_3]) ).
cnf(c_129,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_4,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),implies(B,D)),implies(E,implies(B,D)))),
inference(resolve,[status(thm)],[c_129,c_2]) ).
cnf(c_130,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,implies(B,C)),implies(implies(D,B),implies(E,B))),implies(F,implies(implies(D,B),implies(E,B))))),
inference(resolve,[status(thm)],[c_130,c_4]) ).
cnf(c_131,plain,
( is_a_theorem(implies(F,implies(implies(D,B),implies(E,B))))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(E,B)))) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_11,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(C,C)))),
inference(resolve,[status(thm)],[c_131,c_4]) ).
cnf(c_132,plain,
( is_a_theorem(implies(implies(B,C),implies(C,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_11]) ).
cnf(c_16,plain,
is_a_theorem(implies(implies(A,B),implies(B,B))),
inference(resolve,[status(thm)],[c_132,c_11]) ).
cnf(c_133,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_19,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_133,c_16]) ).
cnf(c_134,plain,
( is_a_theorem(implies(C,B))
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_1,c_19]) ).
cnf(c_27,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_134,c_16]) ).
cnf(c_135,plain,
( is_a_theorem(implies(B,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_27]) ).
cnf(c_29,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_135,c_27]) ).
cnf(c_136,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_30,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(C,A))),
inference(resolve,[status(thm)],[c_136,c_29]) ).
cnf(c_137,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_47,plain,
is_a_theorem(implies(implies(implies(A,B),implies(B,C)),implies(D,implies(B,C)))),
inference(resolve,[status(thm)],[c_137,c_30]) ).
cnf(c_138,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_67,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(D,B)),implies(E,implies(D,B)))),
inference(resolve,[status(thm)],[c_138,c_47]) ).
cnf(c_139,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_67]) ).
cnf(c_94,plain,
is_a_theorem(implies(A,implies(implies(implies(implies(B,C),D),C),implies(B,C)))),
inference(resolve,[status(thm)],[c_139,c_2]) ).
cnf(c_140,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_94]) ).
cnf(c_95,plain,
is_a_theorem(implies(implies(implies(implies(A,B),C),B),implies(A,B))),
inference(resolve,[status(thm)],[c_140,c_94]) ).
cnf(c_141,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_98,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_141,c_95]) ).
cnf(c_142,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_98]) ).
cnf(c_124,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_142,c_30]) ).
cnf(c_143,plain,
( is_a_theorem(implies(implies(implies(B,C),B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_124]) ).
cnf(c_127,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_143,c_124]) ).
cnf(c_128,plain,
$false,
inference(resolve,[status(thm)],[c_127,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL083-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n020.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Fri Sep 25 21:50:49 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 3869716 was started by sandbox on n020,
% 0.18/0.46 % Fri Sep 25 21:50:49 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 0.80/0.57
% 0.80/0.57 % SZS status Unsatisfiable for theBenchmark
% 0.80/0.57
% 0.80/0.57 % Proof 1 at 0.05 (+ 0.04) seconds.
% 0.80/0.57 % Length of proof is 19.
% 0.80/0.57 % Level of proof is 16.
% 0.80/0.57 % Maximum clause weight is 99.000.
% 0.80/0.57 % Given clauses 56.
% 0.80/0.57
% 0.80/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------