%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL088-1 : 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 07:57:56 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 21 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 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 : 137 ( 67 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_4,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(VAR_4,implies(implies(VAR_3,VAR_0),implies(VAR_2,VAR_0))))),
file('theBenchmark.p',ic_JLukasiewicz_4) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,D)),implies(E,implies(implies(D,A),implies(C,A))))),
inference(clausify,[status(thm)],[ic_JLukasiewicz_4]) ).
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_392,plain,
( is_a_theorem(implies(E,implies(implies(D,A),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(A,implies(implies(implies(implies(B,C),implies(D,C)),implies(C,E)),implies(F,implies(C,E))))),
inference(resolve,[status(thm)],[c_392,c_2]) ).
cnf(c_393,plain,
( is_a_theorem(implies(implies(implies(implies(B,C),implies(D,C)),implies(C,E)),implies(F,implies(C,E))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_5,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_393,c_4]) ).
cnf(c_394,plain,
( is_a_theorem(implies(E,implies(B,D)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),implies(B,D))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_7,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(C,implies(B,C))))),
inference(resolve,[status(thm)],[c_394,c_5]) ).
cnf(c_395,plain,
( is_a_theorem(implies(E,implies(B,D)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),implies(B,D))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_9,plain,
is_a_theorem(implies(A,implies(B,implies(implies(B,C),implies(D,C))))),
inference(resolve,[status(thm)],[c_395,c_2]) ).
cnf(c_396,plain,
( is_a_theorem(implies(implies(B,C),implies(C,implies(B,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_12,plain,
is_a_theorem(implies(implies(A,B),implies(B,implies(A,B)))),
inference(resolve,[status(thm)],[c_396,c_7]) ).
cnf(c_397,plain,
( is_a_theorem(implies(E,implies(implies(D,A),implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_14,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),implies(C,B)))),
inference(resolve,[status(thm)],[c_397,c_12]) ).
cnf(c_398,plain,
( is_a_theorem(implies(B,implies(implies(B,C),implies(D,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_20,plain,
is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))),
inference(resolve,[status(thm)],[c_398,c_9]) ).
cnf(c_399,plain,
( is_a_theorem(implies(E,implies(implies(D,A),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(A,implies(implies(implies(B,C),D),implies(implies(implies(D,E),C),D)))),
inference(resolve,[status(thm)],[c_399,c_20]) ).
cnf(c_400,plain,
( is_a_theorem(implies(implies(implies(B,C),B),implies(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_32,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(B,A))),
inference(resolve,[status(thm)],[c_400,c_14]) ).
cnf(c_401,plain,
( is_a_theorem(implies(E,implies(B,D)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),implies(B,D))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_37,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_401,c_32]) ).
cnf(c_402,plain,
( is_a_theorem(implies(B,implies(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_37]) ).
cnf(c_61,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_402,c_37]) ).
cnf(c_403,plain,
( is_a_theorem(implies(E,implies(implies(D,A),implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_68,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),implies(D,B)))),
inference(resolve,[status(thm)],[c_403,c_61]) ).
cnf(c_404,plain,
( is_a_theorem(implies(implies(implies(B,C),D),implies(implies(implies(D,E),C),D)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_23]) ).
cnf(c_98,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(C,D),B),C))),
inference(resolve,[status(thm)],[c_404,c_23]) ).
cnf(c_405,plain,
( is_a_theorem(implies(implies(implies(B,C),B),implies(D,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_68]) ).
cnf(c_148,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(C,A))),
inference(resolve,[status(thm)],[c_405,c_68]) ).
cnf(c_406,plain,
( is_a_theorem(implies(C,A))
| ~ is_a_theorem(implies(implies(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_148]) ).
cnf(c_374,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_406,c_98]) ).
cnf(c_407,plain,
( is_a_theorem(implies(implies(implies(B,C),B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_374]) ).
cnf(c_390,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_407,c_374]) ).
cnf(c_391,plain,
$false,
inference(resolve,[status(thm)],[c_390,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL088-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n007.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 21:48:08 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.34 % Process 2000313 was started by sandbox on n007,
% 0.09/0.34 % Fri Sep 25 21:48:08 2026
% 0.09/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.14/0.44
% 0.14/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.44
% 0.14/0.44 % Proof 1 at 0.05 (+ 0.03) seconds.
% 0.14/0.44 % Length of proof is 20.
% 0.14/0.44 % Level of proof is 13.
% 0.14/0.44 % Maximum clause weight is 50.000.
% 0.14/0.44 % Given clauses 53.
% 0.14/0.44
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------