%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL248-3 : 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 : n008.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 6.34s 1.99s
% Output : CNFRefutation 6.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 38 unt; 0 def)
% Number of atoms : 71 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 27 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 104 ( 13 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(and(p,q),implies(p,q))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(implies(and(p,q),implies(p,q))),
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_4509,plain,
~ theorem(implies(not(or(not(p),not(q))),implies(p,q))),
inference(paramod,[status(thm)],[c_13,c_12]) ).
cnf(c_4510,plain,
~ theorem(implies(not(or(not(p),not(q))),or(not(p),q))),
inference(paramod,[status(thm)],[c_15,c_4509]) ).
cnf(c_16,plain,
~ theorem(or(not(not(or(not(p),not(q)))),or(not(p),q))),
inference(paramod,[status(thm)],[c_15,c_4510]) ).
cnf(c_17,plain,
( ~ theorem(B)
| ~ theorem(or(not(B),A))
| theorem(A) ),
inference(paramod,[status(thm)],[c_15,c_14]) ).
cnf(c_4511,plain,
theorem(implies(or(not(A),B),implies(or(C,A),or(C,B)))),
inference(paramod,[status(thm)],[c_15,c_11]) ).
cnf(c_4512,plain,
theorem(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_15,c_4511]) ).
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_4512]) ).
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_4513,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_17,c_19]) ).
cnf(c_27,plain,
theorem(or(not(or(A,B)),or(not(or(not(B),C)),or(A,C)))),
inference(resolve,[status(thm)],[c_4513,c_18]) ).
cnf(c_4514,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(not(or(not(p),not(q)))),or(not(p),q)))) ),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_36,plain,
~ theorem(or(or(not(p),q),not(not(or(not(p),not(q)))))),
inference(resolve,[status(thm)],[c_4514,c_20]) ).
cnf(c_4515,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_17,c_20]) ).
cnf(c_38,plain,
theorem(or(or(A,B),not(B))),
inference(resolve,[status(thm)],[c_4515,c_21]) ).
cnf(c_4516,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_4516,c_21]) ).
cnf(c_4517,plain,
( ~ theorem(B)
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_17,c_21]) ).
cnf(c_94,plain,
theorem(or(A,or(or(B,C),not(C)))),
inference(resolve,[status(thm)],[c_4517,c_38]) ).
cnf(c_4518,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_4518,c_39]) ).
cnf(c_4519,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_4519,c_100]) ).
cnf(c_4520,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_17,c_19]) ).
cnf(c_855,plain,
theorem(or(or(A,B),or(C,not(B)))),
inference(resolve,[status(thm)],[c_4520,c_94]) ).
cnf(c_4521,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(or(not(p),q),not(not(or(not(p),not(q))))))) ),
inference(resolve,[status(thm)],[c_17,c_36]) ).
cnf(c_3521,plain,
~ theorem(or(not(or(A,not(A))),or(or(not(p),q),not(not(or(not(p),not(q))))))),
inference(resolve,[status(thm)],[c_4521,c_108]) ).
cnf(c_4522,plain,
( ~ theorem(or(C,A))
| theorem(or(not(or(not(A),B)),or(C,B))) ),
inference(resolve,[status(thm)],[c_17,c_27]) ).
cnf(c_4507,plain,
theorem(or(not(or(not(or(A,not(B))),C)),or(or(D,B),C))),
inference(resolve,[status(thm)],[c_4522,c_855]) ).
cnf(c_4508,plain,
$false,
inference(resolve,[status(thm)],[c_4507,c_3521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL248-3 : 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 : n008.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 22:07:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2030639 was started by sandbox on n008,
% 0.10/0.37 % Fri Sep 25 22:07:25 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 6.34/1.99
% 6.34/1.99 % SZS status Unsatisfiable for theBenchmark
% 6.34/1.99
% 6.34/1.99 % Proof 1 at 0.72 (+ 0.11) seconds.
% 6.34/1.99 % Length of proof is 30.
% 6.34/1.99 % Level of proof is 7.
% 6.34/1.99 % Maximum clause weight is 19.000.
% 6.34/1.99 % Given clauses 124.
% 6.34/1.99
% 6.34/1.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------