%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL227-1 : 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 : n010.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 07:58:23 AM UTC 2026
% Result : Unsatisfiable 18.27s 3.41s
% Output : CNFRefutation 18.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 26 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 23 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 10 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_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_14,plain,
( ~ theorem(or(A,A))
| theorem(A) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
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(q),or(not(r),s))),or(not(or(p,q)),or(not(or(p,r)),or(p,s))))),
file('theBenchmark.p',prove_this) ).
cnf(c_24,plain,
~ theorem(or(not(or(not(q),or(not(r),s))),or(not(or(p,q)),or(not(or(p,r)),or(p,s))))),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_47,plain,
theorem(or(not(A),or(A,B))),
inference(resolve,[status(thm)],[c_10,c_21]) ).
cnf(c_68,plain,
~ theorem(or(not(or(not(or(A,q)),or(A,or(not(r),s)))),or(not(or(p,q)),or(not(or(p,r)),or(p,s))))),
inference(resolve,[status(thm)],[c_24,c_13]) ).
cnf(c_115,plain,
theorem(or(not(or(A,B)),or(A,or(B,C)))),
inference(resolve,[status(thm)],[c_18,c_47]) ).
cnf(c_454,plain,
theorem(or(not(or(A,B)),or(B,or(A,C)))),
inference(resolve,[status(thm)],[c_11,c_115]) ).
cnf(c_556,plain,
theorem(or(not(or(A,or(B,C))),or(or(A,C),or(B,D)))),
inference(resolve,[status(thm)],[c_12,c_454]) ).
cnf(c_768,plain,
~ theorem(or(not(or(p,or(not(r),s))),or(not(or(p,r)),or(p,s)))),
inference(resolve,[status(thm)],[c_68,c_18]) ).
cnf(c_5096,plain,
theorem(or(not(or(A,B)),or(or(C,B),or(A,D)))),
inference(resolve,[status(thm)],[c_10,c_556]) ).
cnf(c_5108,plain,
theorem(or(or(A,B),or(not(or(C,B)),or(C,D)))),
inference(resolve,[status(thm)],[c_17,c_5096]) ).
cnf(c_5126,plain,
theorem(or(not(or(A,or(A,B))),or(A,B))),
inference(resolve,[status(thm)],[c_14,c_5108]) ).
cnf(c_5127,plain,
theorem(or(not(or(A,or(B,or(B,C)))),or(A,or(B,C)))),
inference(resolve,[status(thm)],[c_18,c_5126]) ).
cnf(c_7666,plain,
~ theorem(or(not(or(not(r),or(p,s))),or(not(or(p,r)),or(p,s)))),
inference(resolve,[status(thm)],[c_768,c_12]) ).
cnf(c_9135,plain,
~ theorem(or(not(or(not(or(A,r)),or(A,or(p,s)))),or(not(or(p,r)),or(p,s)))),
inference(resolve,[status(thm)],[c_7666,c_13]) ).
cnf(c_9136,plain,
$false,
inference(resolve,[status(thm)],[c_9135,c_5127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL227-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.77 % Computer : n010.cluster.edu
% 0.09/0.77 % Model : x86_64 x86_64
% 0.09/0.77 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.77 % Memory : 8046.5625MB
% 0.09/0.77 % OS : Linux 6.8.0-71-generic
% 0.09/0.77 % CPULimit : 300
% 0.09/0.77 % WCLimit : 300
% 0.09/0.77 % DateTime : Fri Sep 25 22:04:02 UTC 2026
% 0.09/0.77 % CPUTime :
% 0.09/0.77 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.77 % Process 1802678 was started by sandbox on n010,
% 0.09/0.77 % Fri Sep 25 22:04:02 2026
% 0.09/0.77 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.78
% 0.09/0.78 % From the command line: assign(max_seconds, 300).
% 18.27/3.41
% 18.27/3.41 % given #500 (F,wt=36): 1058 -theorem(or(not(or(or(p,r),A)),or(p,s))). [resolve(100,a,11,a)].
% 18.27/3.41
% 18.27/3.41 % given #1000 (W,wt=37): 3297 -theorem(or(or(not(q),s),or(not(or(q,A)),s))). [resolve(3005,a,17,a)].
% 18.27/3.41
% 18.27/3.41 % given #1500 (T,wt=38): 4538 theorem(or(not(not(A)),or(not(or(A,B)),or(B,C)))). [ur(17,b,3793,a)].
% 18.27/3.41
% 18.27/3.41 % given #2000 (F,wt=30): 6570 -theorem(or(s,or(or(p,s),or(s,s)))). [resolve(6562,a,16,a)].
% 18.27/3.41
% 18.27/3.41 % given #2500 (W,wt=41): 7321 -theorem(or(or(or(not(r),not(r)),not(r)),not(or(A,or(r,B))))). [resolve(4850,a,16,a)].
% 18.27/3.41
% 18.27/3.41 % SZS status Unsatisfiable for theBenchmark
% 18.27/3.41
% 18.27/3.41 % Proof 1 at 2.26 (+ 0.36) seconds.
% 18.27/3.41 % Length of proof is 30.
% 18.27/3.41 % Level of proof is 10.
% 18.27/3.41 % Maximum clause weight is 62.000.
% 18.27/3.41 % Given clauses 2815.
% 18.27/3.41
% 18.27/3.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------