%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL176-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 : Mon Sep 7 12:42:05 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 22 ( 13 unt; 0 nHn; 12 RR)
% Number of literals : 34 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 33 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(or(not(or(A,A)),A)) ).
cnf(axiom_1_3,axiom,
axiom(or(not(A),or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ axiom(or(not(Y),X))
| ~ theorem(Y) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(or(not(p),p)) ).
cnf(refute_0_0,plain,
axiom(or(not(or(X_23,X_23)),X_23)),
inference(subst,[],[axiom_1_2:[bind(A,$fot(X_23))]]) ).
cnf(refute_0_1,plain,
( ~ axiom(or(not(or(X_23,X_23)),X_23))
| ~ theorem(or(X_23,X_23))
| theorem(X_23) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_23)),bind(Y,$fot(or(X_23,X_23)))]]) ).
cnf(refute_0_2,plain,
( ~ theorem(or(X_23,X_23))
| theorem(X_23) ),
inference(resolve,[$cnf( axiom(or(not(or(X_23,X_23)),X_23)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ theorem(or(or(not(X_157),X_157),or(not(X_157),X_157)))
| theorem(or(not(X_157),X_157)) ),
inference(subst,[],[refute_0_2:[bind(X_23,$fot(or(not(X_157),X_157)))]]) ).
cnf(refute_0_4,plain,
( ~ axiom(or(not(X_3),or(X_4,X_3)))
| theorem(or(not(X_3),or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(or(not(X_3),or(X_4,X_3))))]]) ).
cnf(refute_0_5,plain,
axiom(or(not(X_3),or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_6,plain,
theorem(or(not(X_3),or(X_4,X_3))),
inference(resolve,[$cnf( axiom(or(not(X_3),or(X_4,X_3))) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
theorem(or(not(X_155),or(X_154,X_155))),
inference(subst,[],[refute_0_6:[bind(X_3,$fot(X_155)),bind(X_4,$fot(X_154))]]) ).
cnf(refute_0_8,plain,
( ~ axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
| ~ theorem(or(A,or(B,C)))
| theorem(or(B,or(A,C))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,or(A,C)))),bind(Y,$fot(or(A,or(B,C))))]]) ).
cnf(refute_0_9,plain,
( ~ theorem(or(A,or(B,C)))
| theorem(or(B,or(A,C))) ),
inference(resolve,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ theorem(or(not(X_155),or(X_154,X_155)))
| theorem(or(X_154,or(not(X_155),X_155))) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(not(X_155))),bind(B,$fot(X_154)),bind(C,$fot(X_155))]]) ).
cnf(refute_0_11,plain,
theorem(or(X_154,or(not(X_155),X_155))),
inference(resolve,[$cnf( theorem(or(not(X_155),or(X_154,X_155))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
theorem(or(or(not(X_157),X_157),or(not(X_157),X_157))),
inference(subst,[],[refute_0_11:[bind(X_154,$fot(or(not(X_157),X_157))),bind(X_155,$fot(X_157))]]) ).
cnf(refute_0_13,plain,
theorem(or(not(X_157),X_157)),
inference(resolve,[$cnf( theorem(or(or(not(X_157),X_157),or(not(X_157),X_157))) )],[refute_0_12,refute_0_3]) ).
cnf(refute_0_14,plain,
theorem(or(not(p),p)),
inference(subst,[],[refute_0_13:[bind(X_157,$fot(p))]]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( theorem(or(not(p),p)) )],[refute_0_14,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL176-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 4 22:14:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.11/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.40
% 0.11/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.11/0.40
%------------------------------------------------------------------------------