%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL219-3 : 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 : n015.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 07:58:22 AM UTC 2026
% Result : Unsatisfiable 0.22s 5.53s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 36 unt; 0 def)
% Number of atoms : 69 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 29 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 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 : 101 ( 9 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(implies(implies(p,q),q),or(p,q))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(implies(implies(implies(p,q),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_15,plain,
( ~ theorem(B)
| ~ theorem(or(not(B),A))
| theorem(A) ),
inference(paramod,[status(thm)],[c_14,c_13]) ).
cnf(c_422,plain,
~ theorem(implies(implies(or(not(p),q),q),or(p,q))),
inference(paramod,[status(thm)],[c_14,c_12]) ).
cnf(c_423,plain,
~ theorem(implies(or(not(or(not(p),q)),q),or(p,q))),
inference(paramod,[status(thm)],[c_14,c_422]) ).
cnf(c_16,plain,
~ theorem(or(not(or(not(or(not(p),q)),q)),or(p,q))),
inference(paramod,[status(thm)],[c_14,c_423]) ).
cnf(c_424,plain,
theorem(implies(or(not(A),B),implies(or(C,A),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_425,plain,
theorem(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_424]) ).
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_425]) ).
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_426,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(not(or(not(p),q)),q)),or(p,q)))) ),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_23,plain,
~ theorem(or(not(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),or(not(or(not(or(not(p),q)),q)),or(p,q)))),
inference(resolve,[status(thm)],[c_426,c_17]) ).
cnf(c_427,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_24,plain,
theorem(or(A,or(not(or(B,or(A,C))),or(B,C)))),
inference(resolve,[status(thm)],[c_427,c_18]) ).
cnf(c_428,plain,
( ~ theorem(or(not(B),C))
| theorem(or(not(or(A,B)),or(A,C))) ),
inference(resolve,[status(thm)],[c_15,c_17]) ).
cnf(c_31,plain,
theorem(or(not(or(A,or(B,C))),or(A,or(C,B)))),
inference(resolve,[status(thm)],[c_428,c_19]) ).
cnf(c_429,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_429,c_20]) ).
cnf(c_430,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_430,c_38]) ).
cnf(c_431,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_431,c_99]) ).
cnf(c_432,plain,
( ~ theorem(B)
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_15,c_20]) ).
cnf(c_115,plain,
theorem(or(A,or(B,not(B)))),
inference(resolve,[status(thm)],[c_432,c_107]) ).
cnf(c_433,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_246,plain,
theorem(or(A,or(B,not(A)))),
inference(resolve,[status(thm)],[c_433,c_115]) ).
cnf(c_434,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(not(or(not(B),C)),or(not(or(D,B)),or(D,C)))),or(not(or(not(or(not(p),q)),q)),or(p,q))))) ),
inference(resolve,[status(thm)],[c_15,c_23]) ).
cnf(c_288,plain,
~ theorem(or(p,or(not(p),q))),
inference(resolve,[status(thm)],[c_434,c_24]) ).
cnf(c_435,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(p,or(not(p),q)))) ),
inference(resolve,[status(thm)],[c_15,c_288]) ).
cnf(c_420,plain,
~ theorem(or(not(or(A,or(B,not(A)))),or(p,or(not(p),q)))),
inference(resolve,[status(thm)],[c_435,c_246]) ).
cnf(c_421,plain,
$false,
inference(resolve,[status(thm)],[c_420,c_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL219-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n015.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Fri Sep 25 22:05:18 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.45 % Process 2379489 was started by sandbox on n015,
% 0.16/5.45 % Fri Sep 25 22:05:18 2026
% 0.16/5.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.45
% 0.16/5.45 % From the command line: assign(max_seconds, 300).
% 0.22/5.53
% 0.22/5.53 % SZS status Unsatisfiable for theBenchmark
% 0.22/5.53
% 0.22/5.53 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.22/5.53 % Length of proof is 29.
% 0.22/5.53 % Level of proof is 9.
% 0.22/5.53 % Maximum clause weight is 29.000.
% 0.22/5.53 % Given clauses 34.
% 0.22/5.53
% 0.22/5.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------