%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL173-3 : 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 : n006.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 07:58:10 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.54s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 16 unt; 0 def)
% Number of atoms : 20 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 9 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 6 !; 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]) ).
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(implies(q,r),implies(implies(p,q),implies(p,r)))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))),
inference(clausify,[status(thm)],[prove_this]) ).
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_19,plain,
~ theorem(implies(or(not(q),r),implies(implies(p,q),implies(p,r)))),
inference(paramod,[status(thm)],[c_14,c_12]) ).
cnf(c_20,plain,
~ theorem(implies(or(not(q),r),implies(or(not(p),q),implies(p,r)))),
inference(paramod,[status(thm)],[c_14,c_19]) ).
cnf(c_21,plain,
~ theorem(implies(or(not(q),r),implies(or(not(p),q),or(not(p),r)))),
inference(paramod,[status(thm)],[c_14,c_20]) ).
cnf(c_22,plain,
~ theorem(implies(or(not(q),r),or(not(or(not(p),q)),or(not(p),r)))),
inference(paramod,[status(thm)],[c_14,c_21]) ).
cnf(c_16,plain,
~ theorem(or(not(or(not(q),r)),or(not(or(not(p),q)),or(not(p),r)))),
inference(paramod,[status(thm)],[c_14,c_22]) ).
cnf(c_23,plain,
theorem(implies(or(not(A),B),implies(or(C,A),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_24,plain,
theorem(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_23]) ).
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_24]) ).
cnf(c_18,plain,
$false,
inference(resolve,[status(thm)],[c_17,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL173-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.52 % Computer : n006.cluster.edu
% 0.08/0.52 % Model : x86_64 x86_64
% 0.08/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.52 % Memory : 8046.5625MB
% 0.08/0.52 % OS : Linux 6.8.0-71-generic
% 0.08/0.53 % CPULimit : 300
% 0.08/0.53 % WCLimit : 300
% 0.08/0.53 % DateTime : Fri Sep 25 21:57:14 UTC 2026
% 0.08/0.53 % CPUTime :
% 0.08/0.53 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.53 % Process 3846814 was started by sandbox2 on n006,
% 0.08/0.53 % Fri Sep 25 21:57:14 2026
% 0.08/0.53 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.53
% 0.08/0.53 % From the command line: assign(max_seconds, 300).
% 0.08/0.54
% 0.08/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.54
% 0.08/0.54 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.54 % Length of proof is 8.
% 0.08/0.54 % Level of proof is 3.
% 0.08/0.54 % Maximum clause weight is 17.000.
% 0.08/0.54 % Given clauses 0.
% 0.08/0.54
% 0.08/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------