%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL212-3 : 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 : n019.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 07:58:20 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.38s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 29 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 15 ~; 9 |; 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 : 25 ( 6 sgn 7 !; 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_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]) ).
fof(prove_this,axiom,
~ theorem(implies(not(p),implies(q,implies(implies(p,q),q)))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(implies(not(p),implies(q,implies(implies(p,q),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_38,plain,
~ theorem(implies(not(p),implies(q,implies(or(not(p),q),q)))),
inference(paramod,[status(thm)],[c_14,c_12]) ).
cnf(c_39,plain,
~ theorem(implies(not(p),implies(q,or(not(or(not(p),q)),q)))),
inference(paramod,[status(thm)],[c_14,c_38]) ).
cnf(c_40,plain,
~ theorem(implies(not(p),or(not(q),or(not(or(not(p),q)),q)))),
inference(paramod,[status(thm)],[c_14,c_39]) ).
cnf(c_16,plain,
~ theorem(or(not(not(p)),or(not(q),or(not(or(not(p),q)),q)))),
inference(paramod,[status(thm)],[c_14,c_40]) ).
cnf(c_20,plain,
theorem(or(not(A),or(B,A))),
inference(paramod,[status(thm)],[c_14,c_8]) ).
cnf(c_41,plain,
( ~ theorem(B)
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_15,c_20]) ).
cnf(c_36,plain,
theorem(or(A,or(not(B),or(C,B)))),
inference(resolve,[status(thm)],[c_41,c_20]) ).
cnf(c_37,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL212-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n019.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 22:01:33 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3850359 was started by sandbox2 on n019,
% 0.07/0.35 % Fri Sep 25 22:01:33 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.07/0.38
% 0.07/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.38
% 0.07/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.07/0.38 % Length of proof is 11.
% 0.07/0.38 % Level of proof is 4.
% 0.07/0.38 % Maximum clause weight is 15.000.
% 0.07/0.38 % Given clauses 7.
% 0.07/0.38
% 0.07/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------