%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL221-1 : 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 : n026.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 07:58:22 AM UTC 2026
% Result : Unsatisfiable 19.19s 2.83s
% Output : CNFRefutation 19.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 24 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 25 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 68 ( 2 sgn 17 !; 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(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_9,plain,
( ~ theorem(or(not(A),B))
| theorem(or(not(or(A,A)),B)) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
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_12,plain,
( ~ theorem(or(not(or(B,or(A,C))),D))
| theorem(or(not(or(A,or(B,C))),D)) ),
inference(resolve,[status(thm)],[c_8,c_3]) ).
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_17,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
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_21,plain,
theorem(or(not(or(A,B)),or(B,A))),
inference(resolve,[status(thm)],[c_1,c_4]) ).
fof(prove_this,axiom,
~ theorem(or(not(or(not(p),q)),or(not(or(or(p,q),r)),or(q,r)))),
file('theBenchmark.p',prove_this) ).
cnf(c_24,plain,
~ theorem(or(not(or(not(p),q)),or(not(or(or(p,q),r)),or(q,r)))),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_48,plain,
theorem(or(not(or(or(A,B),or(A,B))),or(B,A))),
inference(resolve,[status(thm)],[c_9,c_21]) ).
cnf(c_64,plain,
~ theorem(or(not(or(or(p,q),r)),or(not(or(not(p),q)),or(q,r)))),
inference(resolve,[status(thm)],[c_24,c_17]) ).
cnf(c_581,plain,
theorem(or(not(or(A,or(or(A,B),B))),or(B,A))),
inference(resolve,[status(thm)],[c_12,c_48]) ).
cnf(c_1133,plain,
~ theorem(or(not(or(r,or(p,q))),or(not(or(not(p),q)),or(q,r)))),
inference(resolve,[status(thm)],[c_64,c_11]) ).
cnf(c_6994,plain,
~ theorem(or(not(or(p,or(r,q))),or(not(or(not(p),q)),or(q,r)))),
inference(resolve,[status(thm)],[c_1133,c_12]) ).
cnf(c_7958,plain,
theorem(or(not(or(or(A,B),B)),or(B,A))),
inference(resolve,[status(thm)],[c_10,c_581]) ).
cnf(c_7970,plain,
theorem(or(not(or(A,or(or(B,C),C))),or(A,or(C,B)))),
inference(resolve,[status(thm)],[c_18,c_7958]) ).
cnf(c_8436,plain,
~ theorem(or(not(or(or(r,q),p)),or(not(or(not(p),q)),or(q,r)))),
inference(resolve,[status(thm)],[c_6994,c_11]) ).
cnf(c_9124,plain,
~ theorem(or(not(or(not(p),q)),or(not(or(or(r,q),p)),or(q,r)))),
inference(resolve,[status(thm)],[c_8436,c_17]) ).
cnf(c_9581,plain,
~ theorem(or(not(or(not(or(A,p)),or(A,q))),or(not(or(or(r,q),p)),or(q,r)))),
inference(resolve,[status(thm)],[c_9124,c_13]) ).
cnf(c_9582,plain,
$false,
inference(resolve,[status(thm)],[c_9581,c_7970]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL221-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 22:05:11 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3573709 was started by sandbox on n026,
% 0.08/0.36 % Fri Sep 25 22:05:11 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 19.19/2.83
% 19.19/2.83 % Assigning unary symbol not kb_weight 0 and highest precedence (6).
% 19.19/2.83
% 19.19/2.83 % given #500 (W,wt=42): 313 theorem(or(A,or(or(or(B,C),D),not(C)))). [ur(15,b,269,a)].
% 19.19/2.83
% 19.19/2.83 % given #1000 (F,wt=42): 3194 -theorem(not(or(A,or(or(B,p),or(r,q))))). [resolve(2929,a,15,a)].
% 19.19/2.83
% 19.19/2.83 % given #1500 (W,wt=46): 828 theorem(or(not(or(not(or(A,B)),not(or(A,B)))),not(or(B,B)))). [ur(9,b,718,a)].
% 19.19/2.83
% 19.19/2.83 % given #2000 (F,wt=52): 5773 -theorem(or(not(or(r,or(p,q))),not(or(r,or(or(A,p),q))))). [resolve(5294,a,16,a)].
% 19.19/2.83
% 19.19/2.83 % given #2500 (T,wt=48): 7015 theorem(or(or(or(or(A,B),or(C,D)),not(or(D,B))),E)). [ur(16,b,5512,a)].
% 19.19/2.83
% 19.19/2.83 % given #3000 (F,wt=53): 8948 -theorem(or(not(or(A,not(p))),not(or(or(not(or(B,p)),C),B)))). [resolve(8097,a,16,a)].
% 19.19/2.83
% 19.19/2.83 % SZS status Unsatisfiable for theBenchmark
% 19.19/2.83
% 19.19/2.83 % Proof 1 at 2.03 (+ 0.41) seconds.
% 19.19/2.83 % Length of proof is 28.
% 19.19/2.83 % Level of proof is 8.
% 19.19/2.83 % Maximum clause weight is 59.000.
% 19.19/2.83 % Given clauses 3043.
% 19.19/2.83
% 19.19/2.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------