%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL265-3 : 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 : n004.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 07:58:31 AM UTC 2026
% Result : Unsatisfiable 14.44s 2.38s
% Output : CNFRefutation 14.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 42 unt; 0 def)
% Number of atoms : 77 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 27 ~; 19 |; 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 : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 109 ( 5 sgn 19 !; 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(equivalent(p,not(not(p)))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(equivalent(p,not(not(p)))),
inference(clausify,[status(thm)],[prove_this]) ).
fof(equivalent_defn,axiom,
! [VAR_0,VAR_1] : equivalent(VAR_0,VAR_1) = and(implies(VAR_0,VAR_1),implies(VAR_1,VAR_0)),
file('theBenchmark.p',equivalent_defn) ).
cnf(c_13,plain,
equivalent(A,B) = and(implies(A,B),implies(B,A)),
inference(clausify,[status(thm)],[equivalent_defn]) ).
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_14,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_15,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_16,plain,
implies(A,B) = or(not(A),B),
inference(clausify,[status(thm)],[implies_definition]) ).
cnf(c_1342,plain,
~ theorem(and(implies(p,not(not(p))),implies(not(not(p)),p))),
inference(paramod,[status(thm)],[c_13,c_12]) ).
cnf(c_1343,plain,
~ theorem(and(or(not(p),not(not(p))),implies(not(not(p)),p))),
inference(paramod,[status(thm)],[c_16,c_1342]) ).
cnf(c_1344,plain,
~ theorem(and(or(not(p),not(not(p))),or(not(not(not(p))),p))),
inference(paramod,[status(thm)],[c_16,c_1343]) ).
cnf(c_17,plain,
~ theorem(not(or(not(or(not(p),not(not(p)))),not(or(not(not(not(p))),p))))),
inference(paramod,[status(thm)],[c_14,c_1344]) ).
cnf(c_19,plain,
( ~ theorem(B)
| ~ theorem(or(not(B),A))
| theorem(A) ),
inference(paramod,[status(thm)],[c_16,c_15]) ).
cnf(c_1345,plain,
theorem(implies(or(not(A),B),implies(or(C,A),or(C,B)))),
inference(paramod,[status(thm)],[c_16,c_11]) ).
cnf(c_1346,plain,
theorem(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_16,c_1345]) ).
cnf(c_20,plain,
theorem(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_16,c_1346]) ).
cnf(c_21,plain,
theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(paramod,[status(thm)],[c_16,c_10]) ).
cnf(c_22,plain,
theorem(or(not(or(A,B)),or(B,A))),
inference(paramod,[status(thm)],[c_16,c_9]) ).
cnf(c_23,plain,
theorem(or(not(A),or(B,A))),
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_1347,plain,
( ~ theorem(or(not(B),C))
| theorem(or(not(or(A,B)),or(A,C))) ),
inference(resolve,[status(thm)],[c_19,c_20]) ).
cnf(c_27,plain,
theorem(or(not(or(A,or(B,C))),or(A,or(C,B)))),
inference(resolve,[status(thm)],[c_1347,c_22]) ).
cnf(c_1348,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_32,plain,
theorem(or(A,or(not(B),B))),
inference(resolve,[status(thm)],[c_1348,c_23]) ).
cnf(c_1349,plain,
( ~ theorem(B)
| theorem(or(not(A),A)) ),
inference(resolve,[status(thm)],[c_19,c_32]) ).
cnf(c_48,plain,
theorem(or(not(A),A)),
inference(resolve,[status(thm)],[c_1349,c_32]) ).
cnf(c_1350,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_19,c_22]) ).
cnf(c_53,plain,
theorem(or(A,not(A))),
inference(resolve,[status(thm)],[c_1350,c_48]) ).
cnf(c_1351,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_54,plain,
theorem(or(A,or(not(or(A,B)),B))),
inference(resolve,[status(thm)],[c_1351,c_48]) ).
cnf(c_1352,plain,
( ~ theorem(or(not(B),C))
| theorem(or(not(or(A,B)),or(A,C))) ),
inference(resolve,[status(thm)],[c_19,c_20]) ).
cnf(c_59,plain,
theorem(or(not(or(A,B)),or(A,not(not(B))))),
inference(resolve,[status(thm)],[c_1352,c_53]) ).
cnf(c_1353,plain,
( ~ theorem(or(A,or(C,B)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_27]) ).
cnf(c_229,plain,
theorem(or(A,or(B,not(or(A,B))))),
inference(resolve,[status(thm)],[c_1353,c_54]) ).
cnf(c_1354,plain,
( ~ theorem(B)
| theorem(or(A,not(or(not(B),A)))) ),
inference(resolve,[status(thm)],[c_19,c_229]) ).
cnf(c_382,plain,
theorem(or(A,not(or(not(or(B,not(B))),A)))),
inference(resolve,[status(thm)],[c_1354,c_53]) ).
cnf(c_1355,plain,
( ~ theorem(or(A,B))
| theorem(or(A,not(not(B)))) ),
inference(resolve,[status(thm)],[c_19,c_59]) ).
cnf(c_522,plain,
theorem(or(A,not(not(not(A))))),
inference(resolve,[status(thm)],[c_1355,c_53]) ).
cnf(c_1356,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_19,c_22]) ).
cnf(c_578,plain,
theorem(or(not(not(not(A))),A)),
inference(resolve,[status(thm)],[c_1356,c_522]) ).
cnf(c_1357,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),not(or(not(or(not(p),not(not(p)))),not(or(not(not(not(p))),p)))))) ),
inference(resolve,[status(thm)],[c_19,c_17]) ).
cnf(c_1340,plain,
~ theorem(or(not(not(not(p))),p)),
inference(resolve,[status(thm)],[c_1357,c_382]) ).
cnf(c_1341,plain,
$false,
inference(resolve,[status(thm)],[c_1340,c_578]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL265-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.46 % Computer : n004.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Fri Sep 25 22:09:37 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.21/0.47 % Process 96881 was started by sandbox on n004,
% 0.21/0.47 % Fri Sep 25 22:09:37 2026
% 0.21/0.47 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.21/0.47
% 0.21/0.47 % From the command line: assign(max_seconds, 300).
% 14.44/2.38
% 14.44/2.38 % SZS status Unsatisfiable for theBenchmark
% 14.44/2.38
% 14.44/2.38 % Proof 1 at 1.04 (+ 0.68) seconds.
% 14.44/2.38 % Length of proof is 32.
% 14.44/2.38 % Level of proof is 9.
% 14.44/2.38 % Maximum clause weight is 39.000.
% 14.44/2.38 % Given clauses 313.
% 14.44/2.38
% 14.44/2.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------