%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL414-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 07:58:51 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 22 ( 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 : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 30 ( 8 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm147_1,axiom,
! [VAR_0,VAR_1] :
( ~ a_truth(implies(VAR_1,VAR_0))
| ~ a_truth(VAR_1)
| a_truth(VAR_0) ),
file('theBenchmark.p',thm147_1) ).
cnf(c_1,plain,
( ~ a_truth(implies(B,A))
| ~ a_truth(B)
| a_truth(A) ),
inference(clausify,[status(thm)],[thm147_1]) ).
fof(thm147_2,axiom,
! [VAR_0,VAR_1] : a_truth(implies(VAR_0,implies(VAR_1,VAR_0))),
file('theBenchmark.p',thm147_2) ).
cnf(c_2,plain,
a_truth(implies(A,implies(B,A))),
inference(clausify,[status(thm)],[thm147_2]) ).
fof(thm147_3,axiom,
! [VAR_0,VAR_1,VAR_2] : a_truth(implies(implies(VAR_0,implies(VAR_1,VAR_2)),implies(implies(VAR_0,VAR_1),implies(VAR_0,VAR_2)))),
file('theBenchmark.p',thm147_3) ).
cnf(c_3,plain,
a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(clausify,[status(thm)],[thm147_3]) ).
fof(thm147_5,axiom,
~ a_truth(implies(sk1,sk1)),
file('theBenchmark.p',thm147_5) ).
cnf(c_5,plain,
~ a_truth(implies(sk1,sk1)),
inference(clausify,[status(thm)],[thm147_5]) ).
cnf(c_17,plain,
( ~ a_truth(implies(implies(B,implies(C,B)),A))
| a_truth(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
a_truth(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_17,c_2]) ).
cnf(c_18,plain,
( ~ a_truth(implies(implies(B,implies(C,B)),A))
| a_truth(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_8,plain,
a_truth(implies(implies(A,B),implies(A,A))),
inference(resolve,[status(thm)],[c_18,c_3]) ).
cnf(c_19,plain,
( ~ a_truth(implies(implies(B,implies(C,implies(D,C))),A))
| a_truth(A) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_15,plain,
a_truth(implies(A,A)),
inference(resolve,[status(thm)],[c_19,c_8]) ).
cnf(c_16,plain,
$false,
inference(resolve,[status(thm)],[c_15,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL414-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.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 22:31:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2428594 was started by sandbox on n015,
% 0.10/0.37 % Fri Sep 25 22:31:27 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 8.
% 0.10/0.38 % Level of proof is 3.
% 0.10/0.38 % Maximum clause weight is 14.000.
% 0.10/0.38 % Given clauses 7.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------