%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL312-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 07:58:35 AM UTC 2026
% Result : Unsatisfiable 16.19s 2.55s
% Output : CNFRefutation 16.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 48 unt; 0 def)
% Number of atoms : 85 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 33 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 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 : 120 ( 7 sgn 20 !; 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]) ).
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]) ).
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(implies(not(p),p),p)),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(equivalent(implies(not(p),p),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_4975,plain,
~ theorem(equivalent(or(not(not(p)),p),p)),
inference(paramod,[status(thm)],[c_16,c_12]) ).
cnf(c_4976,plain,
~ theorem(and(implies(or(not(not(p)),p),p),implies(p,or(not(not(p)),p)))),
inference(paramod,[status(thm)],[c_13,c_4975]) ).
cnf(c_4977,plain,
~ theorem(and(or(not(or(not(not(p)),p)),p),implies(p,or(not(not(p)),p)))),
inference(paramod,[status(thm)],[c_16,c_4976]) ).
cnf(c_4978,plain,
~ theorem(and(or(not(or(not(not(p)),p)),p),or(not(p),or(not(not(p)),p)))),
inference(paramod,[status(thm)],[c_16,c_4977]) ).
cnf(c_17,plain,
~ theorem(not(or(not(or(not(or(not(not(p)),p)),p)),not(or(not(p),or(not(not(p)),p)))))),
inference(paramod,[status(thm)],[c_14,c_4978]) ).
cnf(c_19,plain,
( ~ theorem(B)
| ~ theorem(or(not(B),A))
| theorem(A) ),
inference(paramod,[status(thm)],[c_16,c_15]) ).
cnf(c_4979,plain,
theorem(implies(or(not(A),B),implies(or(C,A),or(C,B)))),
inference(paramod,[status(thm)],[c_16,c_11]) ).
cnf(c_4980,plain,
theorem(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_16,c_4979]) ).
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_4980]) ).
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_4981,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_28,plain,
theorem(or(not(or(A,B)),or(not(or(not(B),C)),or(A,C)))),
inference(resolve,[status(thm)],[c_4981,c_20]) ).
cnf(c_4982,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_31,plain,
theorem(or(not(or(A,or(B,C))),or(A,or(C,B)))),
inference(resolve,[status(thm)],[c_4982,c_22]) ).
cnf(c_4983,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_36,plain,
theorem(or(A,or(not(B),B))),
inference(resolve,[status(thm)],[c_4983,c_23]) ).
cnf(c_4984,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),not(or(not(or(not(or(not(not(p)),p)),p)),not(or(not(p),or(not(not(p)),p))))))) ),
inference(resolve,[status(thm)],[c_19,c_17]) ).
cnf(c_41,plain,
~ theorem(or(not(or(not(A),or(B,A))),not(or(not(or(not(or(not(not(p)),p)),p)),not(or(not(p),or(not(not(p)),p))))))),
inference(resolve,[status(thm)],[c_4984,c_23]) ).
cnf(c_4985,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_45,plain,
theorem(or(not(or(A,or(B,B))),or(A,B))),
inference(resolve,[status(thm)],[c_4985,c_24]) ).
cnf(c_4986,plain,
( ~ theorem(B)
| theorem(or(not(A),A)) ),
inference(resolve,[status(thm)],[c_19,c_36]) ).
cnf(c_114,plain,
theorem(or(not(A),A)),
inference(resolve,[status(thm)],[c_4986,c_36]) ).
cnf(c_4987,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_19,c_22]) ).
cnf(c_124,plain,
theorem(or(A,not(A))),
inference(resolve,[status(thm)],[c_4987,c_114]) ).
cnf(c_4988,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_125,plain,
theorem(or(A,or(not(or(A,B)),B))),
inference(resolve,[status(thm)],[c_4988,c_114]) ).
cnf(c_4989,plain,
( ~ theorem(or(C,A))
| theorem(or(not(or(not(A),B)),or(C,B))) ),
inference(resolve,[status(thm)],[c_19,c_28]) ).
cnf(c_165,plain,
theorem(or(not(or(not(not(A)),B)),or(A,B))),
inference(resolve,[status(thm)],[c_4989,c_124]) ).
cnf(c_4990,plain,
( ~ theorem(or(A,or(C,B)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_31]) ).
cnf(c_1445,plain,
theorem(or(A,or(B,not(or(A,B))))),
inference(resolve,[status(thm)],[c_4990,c_125]) ).
cnf(c_4991,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(not(B),or(C,B))),not(or(not(or(not(or(not(not(p)),p)),p)),not(or(not(p),or(not(not(p)),p)))))))) ),
inference(resolve,[status(thm)],[c_19,c_41]) ).
cnf(c_3611,plain,
~ theorem(or(not(or(not(not(p)),p)),p)),
inference(resolve,[status(thm)],[c_4991,c_1445]) ).
cnf(c_4992,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(not(not(p)),p)),p))) ),
inference(resolve,[status(thm)],[c_19,c_3611]) ).
cnf(c_4973,plain,
~ theorem(or(not(or(not(not(p)),p)),or(p,p))),
inference(resolve,[status(thm)],[c_4992,c_45]) ).
cnf(c_4974,plain,
$false,
inference(resolve,[status(thm)],[c_4973,c_165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL312-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n008.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 22:14:11 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2052841 was started by sandbox2 on n008,
% 0.19/0.45 % Fri Sep 25 22:14:11 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 16.19/2.55
% 16.19/2.55 % SZS status Unsatisfiable for theBenchmark
% 16.19/2.55
% 16.19/2.55 % Proof 1 at 1.86 (+ 0.21) seconds.
% 16.19/2.55 % Length of proof is 36.
% 16.19/2.55 % Level of proof is 9.
% 16.19/2.55 % Maximum clause weight is 99.000.
% 16.19/2.55 % Given clauses 132.
% 16.19/2.55
% 16.19/2.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------