%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL202-3 : 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 : n013.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 07:58:17 AM UTC 2026
% Result : Unsatisfiable 2.17s 0.74s
% Output : CNFRefutation 2.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 33 unt; 0 def)
% Number of atoms : 64 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 28 ~; 17 |; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 86 ( 6 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(not(or(p,q)),or(p,not(q)))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(implies(not(or(p,q)),or(p,not(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_16,plain,
~ theorem(or(not(not(or(p,q))),or(p,not(q)))),
inference(paramod,[status(thm)],[c_14,c_12]) ).
cnf(c_1365,plain,
theorem(implies(or(not(A),B),implies(or(C,A),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_1366,plain,
theorem(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_1365]) ).
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_1366]) ).
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_1367,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_26,plain,
theorem(or(not(or(A,B)),or(not(or(not(B),C)),or(A,C)))),
inference(resolve,[status(thm)],[c_1367,c_17]) ).
cnf(c_1368,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(not(or(p,q))),or(p,not(q))))) ),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_28,plain,
~ theorem(or(p,or(not(not(or(p,q))),not(q)))),
inference(resolve,[status(thm)],[c_1368,c_18]) ).
cnf(c_1369,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_38,plain,
theorem(or(A,or(not(B),B))),
inference(resolve,[status(thm)],[c_1369,c_20]) ).
cnf(c_1370,plain,
( ~ theorem(B)
| theorem(or(not(A),A)) ),
inference(resolve,[status(thm)],[c_15,c_38]) ).
cnf(c_99,plain,
theorem(or(not(A),A)),
inference(resolve,[status(thm)],[c_1370,c_38]) ).
cnf(c_1371,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_15,c_19]) ).
cnf(c_107,plain,
theorem(or(A,not(A))),
inference(resolve,[status(thm)],[c_1371,c_99]) ).
cnf(c_1372,plain,
( ~ theorem(or(C,A))
| theorem(or(not(or(not(A),B)),or(C,B))) ),
inference(resolve,[status(thm)],[c_15,c_26]) ).
cnf(c_718,plain,
theorem(or(not(or(not(or(A,B)),C)),or(not(B),C))),
inference(resolve,[status(thm)],[c_1372,c_20]) ).
cnf(c_1373,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(p,or(not(not(or(p,q))),not(q))))) ),
inference(resolve,[status(thm)],[c_15,c_28]) ).
cnf(c_1314,plain,
~ theorem(or(not(not(or(p,q))),not(q))),
inference(resolve,[status(thm)],[c_1373,c_20]) ).
cnf(c_1374,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(not(or(p,q))),not(q)))) ),
inference(resolve,[status(thm)],[c_15,c_1314]) ).
cnf(c_1350,plain,
~ theorem(or(not(q),not(not(or(p,q))))),
inference(resolve,[status(thm)],[c_1374,c_19]) ).
cnf(c_1375,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(q),not(not(or(p,q)))))) ),
inference(resolve,[status(thm)],[c_15,c_1350]) ).
cnf(c_1363,plain,
~ theorem(or(not(or(A,not(A))),or(not(q),not(not(or(p,q)))))),
inference(resolve,[status(thm)],[c_1375,c_107]) ).
cnf(c_1364,plain,
$false,
inference(resolve,[status(thm)],[c_1363,c_718]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL202-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n013.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 21:59:36 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1311118 was started by sandbox2 on n013,
% 0.17/0.44 % Fri Sep 25 21:59:36 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 2.17/0.74
% 2.17/0.74 % SZS status Unsatisfiable for theBenchmark
% 2.17/0.74
% 2.17/0.74 % Proof 1 at 0.23 (+ 0.05) seconds.
% 2.17/0.74 % Length of proof is 28.
% 2.17/0.74 % Level of proof is 7.
% 2.17/0.74 % Maximum clause weight is 15.000.
% 2.17/0.74 % Given clauses 65.
% 2.17/0.74
% 2.17/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------