%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL174-1 : 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 12:42:04 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.47s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 8 unt; 0 nHn; 9 RR)
% Number of literals : 22 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_5,axiom,
axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ).
cnf(axiom_1_6,axiom,
axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) ).
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(or(not(p),q)),or(not(or(not(q),r)),or(not(p),r)))) ).
cnf(refute_0_0,plain,
( ~ axiom(or(not(or(not(X_17),X_18)),or(not(or(X_19,X_17)),or(X_19,X_18))))
| theorem(or(not(or(not(X_17),X_18)),or(not(or(X_19,X_17)),or(X_19,X_18)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(or(not(or(not(X_17),X_18)),or(not(or(X_19,X_17)),or(X_19,X_18)))))]]) ).
cnf(refute_0_1,plain,
axiom(or(not(or(not(X_17),X_18)),or(not(or(X_19,X_17)),or(X_19,X_18)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_17)),bind(B,$fot(X_18)),bind(C,$fot(X_19))]]) ).
cnf(refute_0_2,plain,
theorem(or(not(or(not(X_17),X_18)),or(not(or(X_19,X_17)),or(X_19,X_18)))),
inference(resolve,[$cnf( axiom(or(not(or(not(X_17),X_18)),or(not(or(X_19,X_17)),or(X_19,X_18)))) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( ~ axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
| ~ theorem(or(A,or(B,C)))
| theorem(or(B,or(A,C))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,or(A,C)))),bind(Y,$fot(or(A,or(B,C))))]]) ).
cnf(refute_0_4,plain,
( ~ theorem(or(A,or(B,C)))
| theorem(or(B,or(A,C))) ),
inference(resolve,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(not(or(not(X_17),X_18)),or(not(or(X_19,X_17)),or(X_19,X_18))))
| theorem(or(not(or(X_19,X_17)),or(not(or(not(X_17),X_18)),or(X_19,X_18)))) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(not(or(not(X_17),X_18)))),bind(B,$fot(not(or(X_19,X_17)))),bind(C,$fot(or(X_19,X_18)))]]) ).
cnf(refute_0_6,plain,
theorem(or(not(or(X_19,X_17)),or(not(or(not(X_17),X_18)),or(X_19,X_18)))),
inference(resolve,[$cnf( theorem(or(not(or(not(X_17),X_18)),or(not(or(X_19,X_17)),or(X_19,X_18)))) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
theorem(or(not(or(not(p),q)),or(not(or(not(q),r)),or(not(p),r)))),
inference(subst,[],[refute_0_6:[bind(X_17,$fot(q)),bind(X_18,$fot(r)),bind(X_19,$fot(not(p)))]]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( theorem(or(not(or(not(p),q)),or(not(or(not(q),r)),or(not(p),r)))) )],[refute_0_7,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL174-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 5 02:44:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.47
% 0.22/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.22/0.48
%------------------------------------------------------------------------------