%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL187-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 12:42:07 PM UTC 2026
% Result : Unsatisfiable 0.79s 1.03s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 13 unt; 0 nHn; 13 RR)
% Number of literals : 37 ( 0 equ; 15 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_3,axiom,
axiom(or(not(A),or(B,A))) ).
cnf(axiom_1_4,axiom,
axiom(or(not(or(A,B)),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(rule_3,axiom,
( theorem(or(not(X),Z))
| ~ axiom(or(not(X),Y))
| ~ theorem(or(not(Y),Z)) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(or(not(p),or(not(not(p)),q))) ).
cnf(refute_0_0,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_1,plain,
( ~ theorem(or(A,or(B,C)))
| theorem(or(B,or(A,C))) ),
inference(resolve,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ theorem(or(not(X_1613),or(X_1613,X_1612)))
| theorem(or(X_1613,or(not(X_1613),X_1612))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(not(X_1613))),bind(B,$fot(X_1613)),bind(C,$fot(X_1612))]]) ).
cnf(refute_0_3,plain,
( ~ axiom(or(not(or(X_7,X_8)),or(X_8,X_7)))
| theorem(or(not(or(X_7,X_8)),or(X_8,X_7))) ),
inference(subst,[],[rule_1:[bind(X,$fot(or(not(or(X_7,X_8)),or(X_8,X_7))))]]) ).
cnf(refute_0_4,plain,
axiom(or(not(or(X_7,X_8)),or(X_8,X_7))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).
cnf(refute_0_5,plain,
theorem(or(not(or(X_7,X_8)),or(X_8,X_7))),
inference(resolve,[$cnf( axiom(or(not(or(X_7,X_8)),or(X_8,X_7))) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
theorem(or(not(or(X_1609,X_1610)),or(X_1610,X_1609))),
inference(subst,[],[refute_0_5:[bind(X_7,$fot(X_1609)),bind(X_8,$fot(X_1610))]]) ).
cnf(refute_0_7,plain,
axiom(or(not(X_338),or(B,X_338))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_338))]]) ).
cnf(refute_0_8,plain,
( ~ axiom(or(not(X_338),or(B,X_338)))
| ~ theorem(or(not(or(B,X_338)),X_340))
| theorem(or(not(X_338),X_340)) ),
inference(subst,[],[rule_3:[bind(X,$fot(X_338)),bind(Y,$fot(or(B,X_338))),bind(Z,$fot(X_340))]]) ).
cnf(refute_0_9,plain,
( ~ theorem(or(not(or(B,X_338)),X_340))
| theorem(or(not(X_338),X_340)) ),
inference(resolve,[$cnf( axiom(or(not(X_338),or(B,X_338))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ theorem(or(not(or(X_1609,X_1610)),or(X_1610,X_1609)))
| theorem(or(not(X_1610),or(X_1610,X_1609))) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(X_1609)),bind(X_338,$fot(X_1610)),bind(X_340,$fot(or(X_1610,X_1609)))]]) ).
cnf(refute_0_11,plain,
theorem(or(not(X_1610),or(X_1610,X_1609))),
inference(resolve,[$cnf( theorem(or(not(or(X_1609,X_1610)),or(X_1610,X_1609))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
theorem(or(not(X_1613),or(X_1613,X_1612))),
inference(subst,[],[refute_0_11:[bind(X_1609,$fot(X_1612)),bind(X_1610,$fot(X_1613))]]) ).
cnf(refute_0_13,plain,
theorem(or(X_1613,or(not(X_1613),X_1612))),
inference(resolve,[$cnf( theorem(or(not(X_1613),or(X_1613,X_1612))) )],[refute_0_12,refute_0_2]) ).
cnf(refute_0_14,plain,
theorem(or(not(p),or(not(not(p)),q))),
inference(subst,[],[refute_0_13:[bind(X_1612,$fot(q)),bind(X_1613,$fot(not(p)))]]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( theorem(or(not(p),or(not(not(p)),q))) )],[refute_0_14,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL187-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 5 04:43:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.79/1.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.79/1.03
% 0.79/1.03 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.79/1.04
%------------------------------------------------------------------------------