%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL170-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 07:58:09 AM UTC 2026
% Result : Unsatisfiable 0.11s 5.77s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 11 unt; 0 def)
% Number of atoms : 15 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 3 sgn 5 !; 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_3,axiom,
! [VAR_0,VAR_1] : axiom(implies(VAR_0,or(VAR_1,VAR_0))),
file('theBenchmark.p',axiom_1_3) ).
cnf(c_5,plain,
axiom(implies(A,or(B,A))),
inference(clausify,[status(thm)],[axiom_1_3]) ).
cnf(c_8,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[status(thm)],[c_1,c_5]) ).
fof(prove_this,axiom,
~ theorem(implies(q,implies(p,q))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(implies(q,implies(p,q))),
inference(clausify,[status(thm)],[prove_this]) ).
fof(implies_definition,axiom,
! [VAR_0,VAR_1] : implies(VAR_0,VAR_1) = or(not(VAR_0),VAR_1),
file('theBenchmark.p',implies_definition) ).
cnf(c_14,plain,
implies(A,B) = or(not(A),B),
inference(clausify,[status(thm)],[implies_definition]) ).
cnf(c_22,plain,
~ theorem(implies(q,or(not(p),q))),
inference(paramod,[status(thm)],[c_14,c_12]) ).
cnf(c_16,plain,
~ theorem(or(not(q),or(not(p),q))),
inference(paramod,[status(thm)],[c_14,c_22]) ).
cnf(c_20,plain,
theorem(or(not(A),or(B,A))),
inference(paramod,[status(thm)],[c_14,c_8]) ).
cnf(c_21,plain,
$false,
inference(resolve,[status(thm)],[c_20,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL170-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.75 % Computer : n004.cluster.edu
% 0.11/5.75 % Model : x86_64 x86_64
% 0.11/5.75 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.75 % Memory : 8046.5625MB
% 0.11/5.75 % OS : Linux 6.8.0-71-generic
% 0.11/5.75 % CPULimit : 300
% 0.11/5.75 % WCLimit : 300
% 0.11/5.75 % DateTime : Fri Sep 25 21:57:14 UTC 2026
% 0.11/5.75 % CPUTime :
% 0.11/5.75 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.75 % Process 59531 was started by sandbox on n004,
% 0.11/5.75 % Fri Sep 25 21:57:14 2026
% 0.11/5.75 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.76
% 0.11/5.76 % From the command line: assign(max_seconds, 300).
% 0.11/5.77
% 0.11/5.77 % SZS status Unsatisfiable for theBenchmark
% 0.11/5.77
% 0.11/5.77 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/5.77 % Length of proof is 8.
% 0.11/5.77 % Level of proof is 3.
% 0.11/5.77 % Maximum clause weight is 8.000.
% 0.11/5.77 % Given clauses 0.
% 0.11/5.77
% 0.11/5.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------