%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL311-3 : 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 : n005.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 07:58:35 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 36 unt; 0 def)
% Number of atoms : 61 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 27 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 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 : 79 ( 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_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]) ).
fof(axiom_1_2,axiom,
! [VAR_0] : axiom(implies(or(VAR_0,VAR_0),VAR_0)),
file('theBenchmark.p',axiom_1_2) ).
cnf(c_6,plain,
axiom(implies(or(A,A),A)),
inference(clausify,[status(thm)],[axiom_1_2]) ).
cnf(c_7,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[status(thm)],[c_1,c_6]) ).
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]) ).
fof(prove_this,axiom,
~ theorem(equivalent(implies(p,not(p)),not(p))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(equivalent(implies(p,not(p)),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_109,plain,
~ theorem(equivalent(or(not(p),not(p)),not(p))),
inference(paramod,[status(thm)],[c_16,c_12]) ).
cnf(c_110,plain,
~ theorem(and(implies(or(not(p),not(p)),not(p)),implies(not(p),or(not(p),not(p))))),
inference(paramod,[status(thm)],[c_13,c_109]) ).
cnf(c_111,plain,
~ theorem(and(or(not(or(not(p),not(p))),not(p)),implies(not(p),or(not(p),not(p))))),
inference(paramod,[status(thm)],[c_16,c_110]) ).
cnf(c_112,plain,
~ theorem(and(or(not(or(not(p),not(p))),not(p)),or(not(not(p)),or(not(p),not(p))))),
inference(paramod,[status(thm)],[c_16,c_111]) ).
cnf(c_17,plain,
~ theorem(not(or(not(or(not(or(not(p),not(p))),not(p))),not(or(not(not(p)),or(not(p),not(p))))))),
inference(paramod,[status(thm)],[c_14,c_112]) ).
cnf(c_19,plain,
( ~ theorem(B)
| ~ theorem(or(not(B),A))
| theorem(A) ),
inference(paramod,[status(thm)],[c_16,c_15]) ).
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_24,plain,
theorem(or(not(or(A,A)),A)),
inference(paramod,[status(thm)],[c_16,c_7]) ).
cnf(c_113,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_39,plain,
theorem(or(A,or(not(B),B))),
inference(resolve,[status(thm)],[c_113,c_23]) ).
cnf(c_114,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),not(or(not(or(not(or(not(p),not(p))),not(p))),not(or(not(not(p)),or(not(p),not(p)))))))) ),
inference(resolve,[status(thm)],[c_19,c_17]) ).
cnf(c_44,plain,
~ theorem(or(not(or(not(A),or(B,A))),not(or(not(or(not(or(not(p),not(p))),not(p))),not(or(not(not(p)),or(not(p),not(p)))))))),
inference(resolve,[status(thm)],[c_114,c_23]) ).
cnf(c_115,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(not(B),or(C,B))),not(or(not(or(not(or(not(p),not(p))),not(p))),not(or(not(not(p)),or(not(p),not(p))))))))) ),
inference(resolve,[status(thm)],[c_19,c_44]) ).
cnf(c_69,plain,
~ theorem(or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(or(not(not(p)),or(not(p),not(p)))))),not(or(not(A),or(B,A))))),
inference(resolve,[status(thm)],[c_115,c_22]) ).
cnf(c_116,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(or(not(not(p)),or(not(p),not(p)))))),not(or(not(B),or(C,B)))))) ),
inference(resolve,[status(thm)],[c_19,c_69]) ).
cnf(c_79,plain,
~ theorem(or(not(or(not(or(A,A)),A)),or(not(or(not(or(not(or(not(p),not(p))),not(p))),not(or(not(not(p)),or(not(p),not(p)))))),not(or(not(B),or(C,B)))))),
inference(resolve,[status(thm)],[c_116,c_24]) ).
cnf(c_117,plain,
( ~ theorem(B)
| theorem(or(not(A),A)) ),
inference(resolve,[status(thm)],[c_19,c_39]) ).
cnf(c_98,plain,
theorem(or(not(A),A)),
inference(resolve,[status(thm)],[c_117,c_39]) ).
cnf(c_118,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_107,plain,
theorem(or(A,or(not(or(A,B)),B))),
inference(resolve,[status(thm)],[c_118,c_98]) ).
cnf(c_108,plain,
$false,
inference(resolve,[status(thm)],[c_107,c_79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL311-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 22:13:32 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 390267 was started by sandbox on n005,
% 0.18/0.45 % Fri Sep 25 22:13:32 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.48
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.48
% 0.18/0.48 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.18/0.48 % Length of proof is 27.
% 0.18/0.48 % Level of proof is 6.
% 0.18/0.48 % Maximum clause weight is 39.000.
% 0.18/0.48 % Given clauses 18.
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------