%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL196-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 07:58:16 AM UTC 2026
% Result : Unsatisfiable 1.95s 1.10s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 28 unt; 0 def)
% Number of atoms : 54 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 19 ~; 14 |; 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 : 84 ( 12 sgn 13 !; 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_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]) ).
fof(axiom_1_2,axiom,
! [VAR_0] : axiom(implies(or(VAR_0,VAR_0),VAR_0)),
file('theBenchmark.p',axiom_1_2) ).
cnf(c_6,plain,
axiom(implies(or(A,A),A)),
inference(clausify,[status(thm)],[axiom_1_2]) ).
cnf(c_7,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[status(thm)],[c_1,c_6]) ).
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_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,or(p,q)),or(p,q))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(implies(or(p,or(p,q)),or(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_3804,plain,
( ~ theorem(implies(B,C))
| theorem(implies(or(A,B),or(A,C))) ),
inference(resolve,[status(thm)],[c_13,c_11]) ).
cnf(c_15,plain,
theorem(implies(or(A,implies(B,C)),or(A,implies(or(D,B),or(D,C))))),
inference(resolve,[status(thm)],[c_3804,c_11]) ).
cnf(c_3805,plain,
( ~ theorem(implies(B,C))
| theorem(implies(or(A,B),or(A,C))) ),
inference(resolve,[status(thm)],[c_13,c_11]) ).
cnf(c_17,plain,
theorem(implies(or(A,or(B,C)),or(A,or(C,B)))),
inference(resolve,[status(thm)],[c_3805,c_9]) ).
cnf(c_3806,plain,
( ~ theorem(implies(B,C))
| theorem(implies(or(A,B),or(A,C))) ),
inference(resolve,[status(thm)],[c_13,c_11]) ).
cnf(c_18,plain,
theorem(implies(or(A,B),or(A,or(C,B)))),
inference(resolve,[status(thm)],[c_3806,c_8]) ).
cnf(c_3807,plain,
( ~ theorem(A)
| ~ theorem(implies(A,implies(or(p,or(p,q)),or(p,q)))) ),
inference(resolve,[status(thm)],[c_13,c_12]) ).
cnf(c_31,plain,
~ theorem(or(implies(or(p,or(p,q)),or(p,q)),implies(or(p,or(p,q)),or(p,q)))),
inference(resolve,[status(thm)],[c_3807,c_7]) ).
cnf(c_33,plain,
theorem(or(not(A),or(B,A))),
inference(paramod,[status(thm)],[c_14,c_8]) ).
cnf(c_43,plain,
theorem(implies(or(A,or(not(B),C)),or(A,implies(or(D,B),or(D,C))))),
inference(paramod,[status(thm)],[c_14,c_15]) ).
cnf(c_3808,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_13,c_9]) ).
cnf(c_96,plain,
theorem(or(or(A,B),not(B))),
inference(resolve,[status(thm)],[c_3808,c_33]) ).
cnf(c_3809,plain,
( ~ theorem(or(A,C))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_13,c_18]) ).
cnf(c_153,plain,
theorem(or(or(A,B),or(C,not(B)))),
inference(resolve,[status(thm)],[c_3809,c_96]) ).
cnf(c_3810,plain,
( ~ theorem(or(A,or(C,B)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_13,c_17]) ).
cnf(c_1336,plain,
theorem(or(or(A,B),or(not(B),C))),
inference(resolve,[status(thm)],[c_3810,c_153]) ).
cnf(c_1477,plain,
~ theorem(or(or(not(or(p,or(p,q))),or(p,q)),implies(or(p,or(p,q)),or(p,q)))),
inference(paramod,[status(thm)],[c_14,c_31]) ).
cnf(c_3811,plain,
( ~ theorem(or(A,or(not(C),D)))
| theorem(or(A,implies(or(B,C),or(B,D)))) ),
inference(resolve,[status(thm)],[c_13,c_43]) ).
cnf(c_3802,plain,
theorem(or(or(A,B),implies(or(C,B),or(C,D)))),
inference(resolve,[status(thm)],[c_3811,c_1336]) ).
cnf(c_3803,plain,
$false,
inference(resolve,[status(thm)],[c_3802,c_1477]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL196-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.39 % Computer : n008.cluster.edu
% 0.07/0.39 % Model : x86_64 x86_64
% 0.07/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.39 % Memory : 8046.5625MB
% 0.07/0.39 % OS : Linux 6.8.0-71-generic
% 0.07/0.39 % CPULimit : 300
% 0.07/0.39 % WCLimit : 300
% 0.07/0.39 % DateTime : Fri Sep 25 22:00:39 UTC 2026
% 0.07/0.40 % CPUTime :
% 0.07/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.40 % Process 2014185 was started by sandbox on n008,
% 0.07/0.40 % Fri Sep 25 22:00:39 2026
% 0.07/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.40
% 0.07/0.40 % From the command line: assign(max_seconds, 300).
% 1.95/1.10
% 1.95/1.10 % SZS status Unsatisfiable for theBenchmark
% 1.95/1.10
% 1.95/1.10 % Proof 1 at 0.19 (+ 0.08) seconds.
% 1.95/1.10 % Length of proof is 24.
% 1.95/1.10 % Level of proof is 7.
% 1.95/1.10 % Maximum clause weight is 51.000.
% 1.95/1.10 % Given clauses 120.
% 1.95/1.10
% 1.95/1.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------