%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL249-3 : 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 : 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 07:58:28 AM UTC 2026
% Result : Unsatisfiable 40.41s 5.54s
% Output : CNFRefutation 40.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 42 unt; 0 def)
% Number of atoms : 81 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 33 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 120 ( 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(implies(implies(VAR_0,VAR_1),implies(or(VAR_2,VAR_0),or(VAR_2,VAR_1)))),
file('theBenchmark.p',axiom_1_6) ).
cnf(c_2,plain,
axiom(implies(implies(A,B),implies(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(implies(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(implies(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(implies(or(VAR_0,VAR_1),or(VAR_1,VAR_0))),
file('theBenchmark.p',axiom_1_4) ).
cnf(c_4,plain,
axiom(implies(or(A,B),or(B,A))),
inference(clausify,[status(thm)],[axiom_1_4]) ).
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]) ).
cnf(c_9,plain,
theorem(implies(or(A,B),or(B,A))),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_10,plain,
theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_11,plain,
theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_this,axiom,
~ theorem(implies(implies(p,r),implies(and(p,q),r))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(implies(implies(p,r),implies(and(p,q),r))),
inference(clausify,[status(thm)],[prove_this]) ).
fof(and_defn,axiom,
! [VAR_0,VAR_1] : and(VAR_0,VAR_1) = not(or(not(VAR_0),not(VAR_1))),
file('theBenchmark.p',and_defn) ).
cnf(c_13,plain,
and(A,B) = not(or(not(A),not(B))),
inference(clausify,[status(thm)],[and_defn]) ).
fof(rule_2,axiom,
! [VAR_0,VAR_1] :
( ~ theorem(VAR_1)
| ~ theorem(implies(VAR_1,VAR_0))
| theorem(VAR_0) ),
file('theBenchmark.p',rule_2) ).
cnf(c_14,plain,
( ~ theorem(B)
| ~ theorem(implies(B,A))
| theorem(A) ),
inference(clausify,[status(thm)],[rule_2]) ).
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_15,plain,
implies(A,B) = or(not(A),B),
inference(clausify,[status(thm)],[implies_definition]) ).
cnf(c_13080,plain,
~ theorem(implies(or(not(p),r),implies(and(p,q),r))),
inference(paramod,[status(thm)],[c_15,c_12]) ).
cnf(c_13081,plain,
~ theorem(implies(or(not(p),r),implies(not(or(not(p),not(q))),r))),
inference(paramod,[status(thm)],[c_13,c_13080]) ).
cnf(c_13082,plain,
~ theorem(implies(or(not(p),r),or(not(not(or(not(p),not(q)))),r))),
inference(paramod,[status(thm)],[c_15,c_13081]) ).
cnf(c_16,plain,
~ theorem(or(not(or(not(p),r)),or(not(not(or(not(p),not(q)))),r))),
inference(paramod,[status(thm)],[c_15,c_13082]) ).
cnf(c_17,plain,
( ~ theorem(B)
| ~ theorem(or(not(B),A))
| theorem(A) ),
inference(paramod,[status(thm)],[c_15,c_14]) ).
cnf(c_13083,plain,
theorem(implies(or(not(A),B),implies(or(C,A),or(C,B)))),
inference(paramod,[status(thm)],[c_15,c_11]) ).
cnf(c_13084,plain,
theorem(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_15,c_13083]) ).
cnf(c_18,plain,
theorem(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_15,c_13084]) ).
cnf(c_19,plain,
theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(paramod,[status(thm)],[c_15,c_10]) ).
cnf(c_20,plain,
theorem(or(not(or(A,B)),or(B,A))),
inference(paramod,[status(thm)],[c_15,c_9]) ).
cnf(c_21,plain,
theorem(or(not(A),or(B,A))),
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_13085,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(not(p),r)),or(not(not(or(not(p),not(q)))),r)))) ),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_24,plain,
~ theorem(or(not(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),or(not(or(not(p),r)),or(not(not(or(not(p),not(q)))),r)))),
inference(resolve,[status(thm)],[c_13085,c_18]) ).
cnf(c_13086,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_17,c_19]) ).
cnf(c_25,plain,
theorem(or(A,or(not(or(B,or(A,C))),or(B,C)))),
inference(resolve,[status(thm)],[c_13086,c_19]) ).
cnf(c_13087,plain,
( ~ theorem(or(not(B),C))
| theorem(or(not(or(A,B)),or(A,C))) ),
inference(resolve,[status(thm)],[c_17,c_18]) ).
cnf(c_32,plain,
theorem(or(not(or(A,or(B,C))),or(A,or(C,B)))),
inference(resolve,[status(thm)],[c_13087,c_20]) ).
cnf(c_13088,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_17,c_19]) ).
cnf(c_39,plain,
theorem(or(A,or(not(B),B))),
inference(resolve,[status(thm)],[c_13088,c_21]) ).
cnf(c_13089,plain,
( ~ theorem(B)
| theorem(or(not(A),A)) ),
inference(resolve,[status(thm)],[c_17,c_39]) ).
cnf(c_100,plain,
theorem(or(not(A),A)),
inference(resolve,[status(thm)],[c_13089,c_39]) ).
cnf(c_13090,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_17,c_20]) ).
cnf(c_108,plain,
theorem(or(A,not(A))),
inference(resolve,[status(thm)],[c_13090,c_100]) ).
cnf(c_13091,plain,
( ~ theorem(B)
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_17,c_21]) ).
cnf(c_116,plain,
theorem(or(A,or(B,not(B)))),
inference(resolve,[status(thm)],[c_13091,c_108]) ).
cnf(c_13092,plain,
( ~ theorem(or(not(B),C))
| theorem(or(not(or(A,B)),or(A,C))) ),
inference(resolve,[status(thm)],[c_17,c_18]) ).
cnf(c_117,plain,
theorem(or(not(or(A,B)),or(A,not(not(B))))),
inference(resolve,[status(thm)],[c_13092,c_108]) ).
cnf(c_13093,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_17,c_19]) ).
cnf(c_249,plain,
theorem(or(A,or(B,not(A)))),
inference(resolve,[status(thm)],[c_13093,c_116]) ).
cnf(c_13094,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(not(or(not(B),C)),or(not(or(D,B)),or(D,C)))),or(not(or(not(p),r)),or(not(not(or(not(p),not(q)))),r))))) ),
inference(resolve,[status(thm)],[c_17,c_24]) ).
cnf(c_291,plain,
~ theorem(or(not(not(or(not(p),not(q)))),p)),
inference(resolve,[status(thm)],[c_13094,c_25]) ).
cnf(c_13095,plain,
( ~ theorem(or(A,or(C,B)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_17,c_32]) ).
cnf(c_1634,plain,
theorem(or(A,or(not(A),B))),
inference(resolve,[status(thm)],[c_13095,c_249]) ).
cnf(c_13096,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(not(or(not(p),not(q)))),p))) ),
inference(resolve,[status(thm)],[c_17,c_291]) ).
cnf(c_8215,plain,
~ theorem(or(not(or(A,or(not(A),B))),or(not(not(or(not(p),not(q)))),p))),
inference(resolve,[status(thm)],[c_13096,c_1634]) ).
cnf(c_13097,plain,
( ~ theorem(or(A,or(C,B)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_17,c_32]) ).
cnf(c_13078,plain,
theorem(or(not(or(A,B)),or(not(not(B)),A))),
inference(resolve,[status(thm)],[c_13097,c_117]) ).
cnf(c_13079,plain,
$false,
inference(resolve,[status(thm)],[c_13078,c_8215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL249-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 22:07:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 3863196 was started by sandbox on n019,
% 0.10/0.38 % Fri Sep 25 22:07:34 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 40.41/5.54
% 40.41/5.54 % SZS status Unsatisfiable for theBenchmark
% 40.41/5.54
% 40.41/5.54 % Proof 1 at 4.46 (+ 0.51) seconds.
% 40.41/5.54 % Length of proof is 33.
% 40.41/5.54 % Level of proof is 10.
% 40.41/5.54 % Maximum clause weight is 32.000.
% 40.41/5.54 % Given clauses 252.
% 40.41/5.54
% 40.41/5.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------