%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL211-1 : 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 : n019.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 07:58:19 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 16 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 18 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 4 sgn 14 !; 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_4,axiom,
! [VAR_0,VAR_1] : axiom(or(not(or(VAR_0,VAR_1)),or(VAR_1,VAR_0))),
file('theBenchmark.p',axiom_1_4) ).
cnf(c_4,plain,
axiom(or(not(or(A,B)),or(B,A))),
inference(clausify,[status(thm)],[axiom_1_4]) ).
fof(axiom_1_3,axiom,
! [VAR_0,VAR_1] : axiom(or(not(VAR_0),or(VAR_1,VAR_0))),
file('theBenchmark.p',axiom_1_3) ).
cnf(c_5,plain,
axiom(or(not(A),or(B,A))),
inference(clausify,[status(thm)],[axiom_1_3]) ).
fof(axiom_1_2,axiom,
! [VAR_0] : axiom(or(not(or(VAR_0,VAR_0)),VAR_0)),
file('theBenchmark.p',axiom_1_2) ).
cnf(c_6,plain,
axiom(or(not(or(A,A)),A)),
inference(clausify,[status(thm)],[axiom_1_2]) ).
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]) ).
fof(rule_3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ theorem(or(not(VAR_2),VAR_1))
| ~ axiom(or(not(VAR_0),VAR_2))
| theorem(or(not(VAR_0),VAR_1)) ),
file('theBenchmark.p',rule_3) ).
cnf(c_8,plain,
( ~ theorem(or(not(C),B))
| ~ axiom(or(not(A),C))
| theorem(or(not(A),B)) ),
inference(clausify,[status(thm)],[rule_3]) ).
cnf(c_10,plain,
( ~ theorem(or(not(or(C,A)),B))
| theorem(or(not(A),B)) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_11,plain,
( ~ theorem(or(not(or(B,A)),C))
| theorem(or(not(or(A,B)),C)) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_13,plain,
( ~ theorem(or(not(or(not(or(D,A)),or(D,B))),C))
| theorem(or(not(or(not(A),B)),C)) ),
inference(resolve,[status(thm)],[c_8,c_2]) ).
cnf(c_18,plain,
( ~ theorem(or(not(B),C))
| theorem(or(not(or(A,B)),or(A,C))) ),
inference(resolve,[status(thm)],[c_7,c_2]) ).
cnf(c_19,plain,
theorem(or(not(or(A,A)),A)),
inference(resolve,[status(thm)],[c_1,c_6]) ).
fof(prove_this,axiom,
~ theorem(or(not(not(q)),or(not(or(p,q)),p))),
file('theBenchmark.p',prove_this) ).
cnf(c_24,plain,
~ theorem(or(not(not(q)),or(not(or(p,q)),p))),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_25,plain,
theorem(or(not(or(A,or(B,B))),or(A,B))),
inference(resolve,[status(thm)],[c_18,c_19]) ).
cnf(c_52,plain,
~ theorem(or(not(or(A,not(q))),or(not(or(p,q)),p))),
inference(resolve,[status(thm)],[c_24,c_10]) ).
cnf(c_55,plain,
theorem(or(not(or(not(A),B)),or(not(or(B,A)),B))),
inference(resolve,[status(thm)],[c_13,c_25]) ).
cnf(c_308,plain,
~ theorem(or(not(or(not(q),A)),or(not(or(p,q)),p))),
inference(resolve,[status(thm)],[c_52,c_11]) ).
cnf(c_309,plain,
$false,
inference(resolve,[status(thm)],[c_308,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL211-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n019.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Fri Sep 25 22:01:04 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 3848716 was started by sandbox on n019,
% 0.15/0.43 % Fri Sep 25 22:01:04 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 0.15/0.47
% 0.15/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.47
% 0.15/0.47 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.15/0.47 % Length of proof is 18.
% 0.15/0.47 % Level of proof is 4.
% 0.15/0.47 % Maximum clause weight is 34.000.
% 0.15/0.47 % Given clauses 127.
% 0.15/0.47
% 0.15/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------