%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL041-1 : 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 07:57:49 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 12 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 2 sgn 9 !; 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(cn_3,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(not(VAR_0),VAR_1))),
file('theBenchmark.p',cn_3) ).
cnf(c_2,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(clausify,[status(thm)],[cn_3]) ).
fof(cn_21,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,implies(VAR_1,VAR_2)),implies(VAR_1,implies(VAR_0,VAR_2)))),
file('theBenchmark.p',cn_21) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(clausify,[status(thm)],[cn_21]) ).
fof(cn_54,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(implies(VAR_0,VAR_1),implies(implies(not(VAR_0),VAR_1),VAR_1))),
file('theBenchmark.p',cn_54) ).
cnf(c_6,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),B),B))),
inference(clausify,[status(thm)],[cn_54]) ).
fof(prove_cn_30,axiom,
~ is_a_theorem(implies(implies(a,implies(a,b)),implies(a,b))),
file('theBenchmark.p',prove_cn_30) ).
cnf(c_7,plain,
~ is_a_theorem(implies(implies(a,implies(a,b)),implies(a,b))),
inference(clausify,[status(thm)],[prove_cn_30]) ).
cnf(c_317,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_16,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_317,c_2]) ).
cnf(c_318,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_26,plain,
is_a_theorem(implies(implies(not(A),B),implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_318,c_6]) ).
cnf(c_319,plain,
( is_a_theorem(implies(implies(A,B),B))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_1,c_26]) ).
cnf(c_315,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_319,c_16]) ).
cnf(c_316,plain,
$false,
inference(resolve,[status(thm)],[c_315,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL041-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 21:46:48 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 3856660 was started by sandbox on n020,
% 0.10/0.35 % Fri Sep 25 21:46:48 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.40
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.40
% 0.13/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.40 % Length of proof is 9.
% 0.13/0.40 % Level of proof is 3.
% 0.13/0.40 % Maximum clause weight is 36.000.
% 0.13/0.40 % Given clauses 33.
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------