%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL240-3 : 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 : n011.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 07:58:27 AM UTC 2026
% Result : Unsatisfiable 0.92s 0.61s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 37 unt; 0 def)
% Number of atoms : 70 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 44 ( 26 ~; 18 |; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 102 ( 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_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(and(p,q),p)),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(implies(and(p,q),p)),
inference(clausify,[status(thm)],[prove_this]) ).
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_13,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_14,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_15,plain,
implies(A,B) = or(not(A),B),
inference(clausify,[status(thm)],[implies_definition]) ).
cnf(c_1206,plain,
~ theorem(implies(not(or(not(p),not(q))),p)),
inference(paramod,[status(thm)],[c_13,c_12]) ).
cnf(c_16,plain,
~ theorem(or(not(not(or(not(p),not(q)))),p)),
inference(paramod,[status(thm)],[c_15,c_1206]) ).
cnf(c_17,plain,
( ~ theorem(B)
| ~ theorem(or(not(B),A))
| theorem(A) ),
inference(paramod,[status(thm)],[c_15,c_14]) ).
cnf(c_1207,plain,
theorem(implies(or(not(A),B),implies(or(C,A),or(C,B)))),
inference(paramod,[status(thm)],[c_15,c_11]) ).
cnf(c_1208,plain,
theorem(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_15,c_1207]) ).
cnf(c_18,plain,
theorem(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_15,c_1208]) ).
cnf(c_19,plain,
theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(paramod,[status(thm)],[c_15,c_10]) ).
cnf(c_20,plain,
theorem(or(not(or(A,B)),or(B,A))),
inference(paramod,[status(thm)],[c_15,c_9]) ).
cnf(c_21,plain,
theorem(or(not(A),or(B,A))),
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_1209,plain,
( ~ theorem(or(not(B),C))
| theorem(or(not(or(A,B)),or(A,C))) ),
inference(resolve,[status(thm)],[c_17,c_18]) ).
cnf(c_31,plain,
theorem(or(not(or(A,or(B,C))),or(A,or(C,B)))),
inference(resolve,[status(thm)],[c_1209,c_20]) ).
cnf(c_1210,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(not(or(not(p),not(q)))),p))) ),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_35,plain,
~ theorem(or(p,not(not(or(not(p),not(q)))))),
inference(resolve,[status(thm)],[c_1210,c_20]) ).
cnf(c_1211,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_17,c_19]) ).
cnf(c_38,plain,
theorem(or(A,or(not(B),B))),
inference(resolve,[status(thm)],[c_1211,c_21]) ).
cnf(c_1212,plain,
( ~ theorem(B)
| theorem(or(not(A),A)) ),
inference(resolve,[status(thm)],[c_17,c_38]) ).
cnf(c_132,plain,
theorem(or(not(A),A)),
inference(resolve,[status(thm)],[c_1212,c_38]) ).
cnf(c_1213,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_17,c_20]) ).
cnf(c_143,plain,
theorem(or(A,not(A))),
inference(resolve,[status(thm)],[c_1213,c_132]) ).
cnf(c_1214,plain,
( ~ theorem(B)
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_17,c_21]) ).
cnf(c_154,plain,
theorem(or(A,or(B,not(B)))),
inference(resolve,[status(thm)],[c_1214,c_143]) ).
cnf(c_1215,plain,
( ~ theorem(or(not(B),C))
| theorem(or(not(or(A,B)),or(A,C))) ),
inference(resolve,[status(thm)],[c_17,c_18]) ).
cnf(c_155,plain,
theorem(or(not(or(A,B)),or(A,not(not(B))))),
inference(resolve,[status(thm)],[c_1215,c_143]) ).
cnf(c_1216,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_17,c_19]) ).
cnf(c_319,plain,
theorem(or(A,or(B,not(A)))),
inference(resolve,[status(thm)],[c_1216,c_154]) ).
cnf(c_1217,plain,
( ~ theorem(or(A,or(C,B)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_17,c_31]) ).
cnf(c_492,plain,
theorem(or(A,or(not(A),B))),
inference(resolve,[status(thm)],[c_1217,c_319]) ).
cnf(c_1218,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(p,not(not(or(not(p),not(q))))))) ),
inference(resolve,[status(thm)],[c_17,c_35]) ).
cnf(c_1204,plain,
~ theorem(or(not(or(A,or(not(A),B))),or(p,not(not(or(not(p),not(q))))))),
inference(resolve,[status(thm)],[c_1218,c_492]) ).
cnf(c_1205,plain,
$false,
inference(resolve,[status(thm)],[c_1204,c_155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL240-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 22:05:28 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3032836 was started by sandbox2 on n011,
% 0.09/0.35 % Fri Sep 25 22:05:28 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.92/0.61
% 0.92/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.92/0.61
% 0.92/0.61 % Proof 1 at 0.18 (+ 0.06) seconds.
% 0.92/0.61 % Length of proof is 30.
% 0.92/0.61 % Level of proof is 10.
% 0.92/0.61 % Maximum clause weight is 68.000.
% 0.92/0.61 % Given clauses 62.
% 0.92/0.61
% 0.92/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------