%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL199-3 : 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 : n002.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 0.21s 5.78s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 33 unt; 0 def)
% Number of atoms : 64 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 24 ~; 17 |; 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 : 95 ( 7 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(not(or(p,q)),not(p))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(implies(not(or(p,q)),not(p))),
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_16,plain,
~ theorem(or(not(not(or(p,q))),not(p))),
inference(paramod,[status(thm)],[c_14,c_12]) ).
cnf(c_615,plain,
theorem(implies(or(not(A),B),implies(or(C,A),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_616,plain,
theorem(implies(or(not(A),B),or(not(or(C,A)),or(C,B)))),
inference(paramod,[status(thm)],[c_14,c_615]) ).
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_616]) ).
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_617,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_26,plain,
theorem(or(not(or(A,B)),or(not(or(not(B),C)),or(A,C)))),
inference(resolve,[status(thm)],[c_617,c_17]) ).
cnf(c_618,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_30,plain,
theorem(or(not(or(A,or(B,C))),or(A,or(C,B)))),
inference(resolve,[status(thm)],[c_618,c_19]) ).
cnf(c_619,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(not(or(p,q))),not(p)))) ),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_34,plain,
~ theorem(or(not(p),not(not(or(p,q))))),
inference(resolve,[status(thm)],[c_619,c_19]) ).
cnf(c_620,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_37,plain,
theorem(or(A,or(not(B),B))),
inference(resolve,[status(thm)],[c_620,c_20]) ).
cnf(c_621,plain,
( ~ theorem(B)
| theorem(or(not(A),A)) ),
inference(resolve,[status(thm)],[c_15,c_37]) ).
cnf(c_131,plain,
theorem(or(not(A),A)),
inference(resolve,[status(thm)],[c_621,c_37]) ).
cnf(c_622,plain,
( ~ theorem(or(B,A))
| theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_15,c_19]) ).
cnf(c_142,plain,
theorem(or(A,not(A))),
inference(resolve,[status(thm)],[c_622,c_131]) ).
cnf(c_623,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(p),not(not(or(p,q)))))) ),
inference(resolve,[status(thm)],[c_15,c_34]) ).
cnf(c_169,plain,
~ theorem(or(not(or(A,not(A))),or(not(p),not(not(or(p,q)))))),
inference(resolve,[status(thm)],[c_623,c_142]) ).
cnf(c_624,plain,
( ~ theorem(or(A,or(C,B)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_15,c_30]) ).
cnf(c_500,plain,
theorem(or(not(A),or(A,B))),
inference(resolve,[status(thm)],[c_624,c_20]) ).
cnf(c_625,plain,
( ~ theorem(or(C,A))
| theorem(or(not(or(not(A),B)),or(C,B))) ),
inference(resolve,[status(thm)],[c_15,c_26]) ).
cnf(c_613,plain,
theorem(or(not(or(not(or(A,B)),C)),or(not(A),C))),
inference(resolve,[status(thm)],[c_625,c_500]) ).
cnf(c_614,plain,
$false,
inference(resolve,[status(thm)],[c_613,c_169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL199-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.65 % Computer : n002.cluster.edu
% 0.16/5.65 % Model : x86_64 x86_64
% 0.16/5.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.65 % Memory : 8046.5625MB
% 0.16/5.65 % OS : Linux 6.8.0-71-generic
% 0.16/5.65 % CPULimit : 300
% 0.16/5.65 % WCLimit : 300
% 0.16/5.65 % DateTime : Fri Sep 25 22:03:12 UTC 2026
% 0.16/5.65 % CPUTime :
% 0.16/5.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.65 % Process 99031 was started by sandbox2 on n002,
% 0.16/5.65 % Fri Sep 25 22:03:12 2026
% 0.16/5.65 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.66
% 0.16/5.66 % From the command line: assign(max_seconds, 300).
% 0.21/5.78
% 0.21/5.78 % SZS status Unsatisfiable for theBenchmark
% 0.21/5.78
% 0.21/5.78 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.21/5.78 % Length of proof is 28.
% 0.21/5.78 % Level of proof is 7.
% 0.21/5.78 % Maximum clause weight is 55.000.
% 0.21/5.78 % Given clauses 42.
% 0.21/5.78
% 0.21/5.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------