%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL208-3 : 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 : n009.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 07:58:19 AM UTC 2026
% Result : Unsatisfiable 13.94s 2.34s
% Output : CNFRefutation 13.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 34 unt; 0 def)
% Number of atoms : 65 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 25 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 89 ( 5 sgn 15 !; 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(or(p,q),implies(not(p),q))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(implies(or(p,q),implies(not(p),q))),
inference(clausify,[status(thm)],[prove_this]) ).
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_13,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_14,plain,
implies(A,B) = or(not(A),B),
inference(clausify,[status(thm)],[implies_definition]) ).
cnf(c_15,plain,
( ~ theorem(B)
| ~ theorem(or(not(B),A))
| theorem(A) ),
inference(paramod,[status(thm)],[c_14,c_13]) ).
cnf(c_1872,plain,
~ theorem(implies(or(p,q),or(not(not(p)),q))),
inference(paramod,[status(thm)],[c_14,c_12]) ).
cnf(c_16,plain,
~ theorem(or(not(or(p,q)),or(not(not(p)),q))),
inference(paramod,[status(thm)],[c_14,c_1872]) ).
cnf(c_1873,plain,
theorem(implies(or(not(A),B),implies(or(C,A),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_1874,plain,
theorem(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_1873]) ).
cnf(c_17,plain,
theorem(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_1874]) ).
cnf(c_18,plain,
theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(paramod,[status(thm)],[c_14,c_10]) ).
cnf(c_19,plain,
theorem(or(not(or(A,B)),or(B,A))),
inference(paramod,[status(thm)],[c_14,c_9]) ).
cnf(c_20,plain,
theorem(or(not(A),or(B,A))),
inference(paramod,[status(thm)],[c_14,c_8]) ).
cnf(c_1875,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(p,q)),or(not(not(p)),q)))) ),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_22,plain,
~ theorem(or(not(not(p)),or(not(or(p,q)),q))),
inference(resolve,[status(thm)],[c_1875,c_18]) ).
cnf(c_1876,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_31,plain,
theorem(or(A,or(not(B),B))),
inference(resolve,[status(thm)],[c_1876,c_20]) ).
cnf(c_1877,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(not(p)),or(not(or(p,q)),q)))) ),
inference(resolve,[status(thm)],[c_15,c_22]) ).
cnf(c_39,plain,
~ theorem(or(or(not(or(p,q)),q),not(not(p)))),
inference(resolve,[status(thm)],[c_1877,c_19]) ).
cnf(c_1878,plain,
( ~ theorem(B)
| theorem(or(not(A),A)) ),
inference(resolve,[status(thm)],[c_15,c_31]) ).
cnf(c_71,plain,
theorem(or(not(A),A)),
inference(resolve,[status(thm)],[c_1878,c_31]) ).
cnf(c_1879,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_15,c_19]) ).
cnf(c_77,plain,
theorem(or(A,not(A))),
inference(resolve,[status(thm)],[c_1879,c_71]) ).
cnf(c_1880,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_78,plain,
theorem(or(A,or(not(or(A,B)),B))),
inference(resolve,[status(thm)],[c_1880,c_71]) ).
cnf(c_1881,plain,
( ~ theorem(or(not(B),C))
| theorem(or(not(or(A,B)),or(A,C))) ),
inference(resolve,[status(thm)],[c_15,c_17]) ).
cnf(c_138,plain,
theorem(or(not(or(A,B)),or(A,not(not(B))))),
inference(resolve,[status(thm)],[c_1881,c_77]) ).
cnf(c_1882,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_15,c_19]) ).
cnf(c_574,plain,
theorem(or(or(not(or(A,B)),B),A)),
inference(resolve,[status(thm)],[c_1882,c_78]) ).
cnf(c_1883,plain,
( ~ theorem(or(A,B))
| theorem(or(A,not(not(B)))) ),
inference(resolve,[status(thm)],[c_15,c_138]) ).
cnf(c_1870,plain,
theorem(or(or(not(or(A,B)),B),not(not(A)))),
inference(resolve,[status(thm)],[c_1883,c_574]) ).
cnf(c_1871,plain,
$false,
inference(resolve,[status(thm)],[c_1870,c_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL208-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n009.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 22:01:14 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 2661148 was started by sandbox2 on n009,
% 0.18/0.44 % Fri Sep 25 22:01:14 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 13.94/2.34
% 13.94/2.34 % SZS status Unsatisfiable for theBenchmark
% 13.94/2.34
% 13.94/2.34 % Proof 1 at 0.99 (+ 0.67) seconds.
% 13.94/2.34 % Length of proof is 28.
% 13.94/2.34 % Level of proof is 8.
% 13.94/2.34 % Maximum clause weight is 29.000.
% 13.94/2.34 % Given clauses 324.
% 13.94/2.34
% 13.94/2.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------