%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL174-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 07:58:10 AM UTC 2026
% Result : Unsatisfiable 0.08s 5.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rule_1,axiom,
! [VAR_0] :
( ~ axiom(VAR_0)
| theorem(VAR_0) ),
file('theBenchmark.p',rule_1) ).
cnf(c_1,plain,
( ~ axiom(A)
| theorem(A) ),
inference(clausify,[status(thm)],[rule_1]) ).
fof(axiom_1_6,axiom,
! [VAR_0,VAR_1,VAR_2] : axiom(or(not(or(not(VAR_0),VAR_1)),or(not(or(VAR_2,VAR_0)),or(VAR_2,VAR_1)))),
file('theBenchmark.p',axiom_1_6) ).
cnf(c_2,plain,
axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
inference(clausify,[status(thm)],[axiom_1_6]) ).
fof(axiom_1_5,axiom,
! [VAR_0,VAR_1,VAR_2] : axiom(or(not(or(VAR_0,or(VAR_1,VAR_2))),or(VAR_1,or(VAR_0,VAR_2)))),
file('theBenchmark.p',axiom_1_5) ).
cnf(c_3,plain,
axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(clausify,[status(thm)],[axiom_1_5]) ).
fof(rule_2,axiom,
! [VAR_0,VAR_1] :
( ~ theorem(VAR_1)
| ~ axiom(or(not(VAR_1),VAR_0))
| theorem(VAR_0) ),
file('theBenchmark.p',rule_2) ).
cnf(c_7,plain,
( ~ theorem(B)
| ~ axiom(or(not(B),A))
| theorem(A) ),
inference(clausify,[status(thm)],[rule_2]) ).
cnf(c_17,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_23,plain,
theorem(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_this,axiom,
~ theorem(or(not(or(not(p),q)),or(not(or(not(q),r)),or(not(p),r)))),
file('theBenchmark.p',prove_this) ).
cnf(c_24,plain,
~ theorem(or(not(or(not(p),q)),or(not(or(not(q),r)),or(not(p),r)))),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_57,plain,
theorem(or(not(or(A,B)),or(not(or(not(B),C)),or(A,C)))),
inference(resolve,[status(thm)],[c_17,c_23]) ).
cnf(c_58,plain,
$false,
inference(resolve,[status(thm)],[c_57,c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL174-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n014.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Fri Sep 25 21:57:22 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.37 % Process 1198795 was started by sandbox on n014,
% 0.08/5.37 % Fri Sep 25 21:57:22 2026
% 0.08/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/5.37
% 0.08/5.37 % From the command line: assign(max_seconds, 300).
% 0.08/5.38
% 0.08/5.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/5.38
% 0.08/5.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/5.38 % Length of proof is 9.
% 0.08/5.38 % Level of proof is 3.
% 0.08/5.38 % Maximum clause weight is 17.000.
% 0.08/5.38 % Given clauses 15.
% 0.08/5.38
% 0.08/5.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------