%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL205-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 12:42:11 PM UTC 2026
% Result : Unsatisfiable 0.40s 0.64s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of clauses : 47 ( 26 unt; 0 nHn; 22 RR)
% Number of literals : 75 ( 0 equ; 29 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 85 ( 19 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_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(not(or(not(p),q))),or(not(p),not(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,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ theorem(or(X_581,or(not(not(or(X_582,X_583))),not(X_583))))
| theorem(or(not(not(or(X_582,X_583))),or(X_581,not(X_583)))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_581)),bind(B,$fot(not(not(or(X_582,X_583))))),bind(C,$fot(not(X_583)))]]) ).
cnf(refute_0_3,plain,
axiom(or(not(X_24),or(B,X_24))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_24))]]) ).
cnf(refute_0_4,plain,
( ~ axiom(or(not(X_24),or(B,X_24)))
| ~ theorem(X_24)
| theorem(or(B,X_24)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,X_24))),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_5,plain,
( ~ theorem(X_24)
| theorem(or(B,X_24)) ),
inference(resolve,[$cnf( axiom(or(not(X_24),or(B,X_24))) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ theorem(or(not(not(or(X_573,X_574))),not(X_574)))
| theorem(or(B,or(not(not(or(X_573,X_574))),not(X_574)))) ),
inference(subst,[],[refute_0_5:[bind(X_24,$fot(or(not(not(or(X_573,X_574))),not(X_574))))]]) ).
cnf(refute_0_7,plain,
( ~ axiom(or(not(or(A,B)),or(B,A)))
| ~ theorem(or(A,B))
| theorem(or(B,A)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,A))),bind(Y,$fot(or(A,B)))]]) ).
cnf(refute_0_8,plain,
( ~ theorem(or(A,B))
| theorem(or(B,A)) ),
inference(resolve,[$cnf( axiom(or(not(or(A,B)),or(B,A))) )],[axiom_1_4,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ theorem(or(not(X_570),not(not(or(X_569,X_570)))))
| theorem(or(not(not(or(X_569,X_570))),not(X_570))) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(not(X_570))),bind(B,$fot(not(not(or(X_569,X_570)))))]]) ).
cnf(refute_0_10,plain,
axiom(or(not(X_565),or(B,X_565))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_565))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(or(not(X_175),X_175))
| theorem(or(X_175,not(X_175))) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(not(X_175))),bind(B,$fot(X_175))]]) ).
cnf(refute_0_12,plain,
axiom(or(not(or(X_23,X_23)),X_23)),
inference(subst,[],[axiom_1_2:[bind(A,$fot(X_23))]]) ).
cnf(refute_0_13,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_14,plain,
( ~ theorem(or(X_23,X_23))
| theorem(X_23) ),
inference(resolve,[$cnf( axiom(or(not(or(X_23,X_23)),X_23)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ theorem(or(or(not(X_174),X_174),or(not(X_174),X_174)))
| theorem(or(not(X_174),X_174)) ),
inference(subst,[],[refute_0_14:[bind(X_23,$fot(or(not(X_174),X_174)))]]) ).
cnf(refute_0_16,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,$fot(or(not(X_3),or(X_4,X_3))))]]) ).
cnf(refute_0_17,plain,
axiom(or(not(X_3),or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_18,plain,
theorem(or(not(X_3),or(X_4,X_3))),
inference(resolve,[$cnf( axiom(or(not(X_3),or(X_4,X_3))) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
theorem(or(not(X_170),or(X_169,X_170))),
inference(subst,[],[refute_0_18:[bind(X_3,$fot(X_170)),bind(X_4,$fot(X_169))]]) ).
cnf(refute_0_20,plain,
( ~ theorem(or(not(X_170),or(X_169,X_170)))
| theorem(or(X_169,or(not(X_170),X_170))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(not(X_170))),bind(B,$fot(X_169)),bind(C,$fot(X_170))]]) ).
cnf(refute_0_21,plain,
theorem(or(X_169,or(not(X_170),X_170))),
inference(resolve,[$cnf( theorem(or(not(X_170),or(X_169,X_170))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
theorem(or(or(not(X_174),X_174),or(not(X_174),X_174))),
inference(subst,[],[refute_0_21:[bind(X_169,$fot(or(not(X_174),X_174))),bind(X_170,$fot(X_174))]]) ).
cnf(refute_0_23,plain,
theorem(or(not(X_174),X_174)),
inference(resolve,[$cnf( theorem(or(or(not(X_174),X_174),or(not(X_174),X_174))) )],[refute_0_22,refute_0_15]) ).
cnf(refute_0_24,plain,
theorem(or(not(X_175),X_175)),
inference(subst,[],[refute_0_23:[bind(X_174,$fot(X_175))]]) ).
cnf(refute_0_25,plain,
theorem(or(X_175,not(X_175))),
inference(resolve,[$cnf( theorem(or(not(X_175),X_175)) )],[refute_0_24,refute_0_11]) ).
cnf(refute_0_26,plain,
theorem(or(not(X_563),not(not(X_563)))),
inference(subst,[],[refute_0_25:[bind(X_175,$fot(not(X_563)))]]) ).
cnf(refute_0_27,plain,
( ~ axiom(or(not(X_562),X_563))
| ~ theorem(or(not(X_563),not(not(X_563))))
| theorem(or(not(X_562),not(not(X_563)))) ),
inference(subst,[],[rule_3:[bind(X,$fot(X_562)),bind(Y,$fot(X_563)),bind(Z,$fot(not(not(X_563))))]]) ).
cnf(refute_0_28,plain,
( ~ axiom(or(not(X_562),X_563))
| theorem(or(not(X_562),not(not(X_563)))) ),
inference(resolve,[$cnf( theorem(or(not(X_563),not(not(X_563)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ axiom(or(not(X_565),or(B,X_565)))
| theorem(or(not(X_565),not(not(or(B,X_565))))) ),
inference(subst,[],[refute_0_28:[bind(X_562,$fot(X_565)),bind(X_563,$fot(or(B,X_565)))]]) ).
cnf(refute_0_30,plain,
theorem(or(not(X_565),not(not(or(B,X_565))))),
inference(resolve,[$cnf( axiom(or(not(X_565),or(B,X_565))) )],[refute_0_10,refute_0_29]) ).
cnf(refute_0_31,plain,
theorem(or(not(X_570),not(not(or(X_569,X_570))))),
inference(subst,[],[refute_0_30:[bind(B,$fot(X_569)),bind(X_565,$fot(X_570))]]) ).
cnf(refute_0_32,plain,
theorem(or(not(not(or(X_569,X_570))),not(X_570))),
inference(resolve,[$cnf( theorem(or(not(X_570),not(not(or(X_569,X_570))))) )],[refute_0_31,refute_0_9]) ).
cnf(refute_0_33,plain,
theorem(or(not(not(or(X_573,X_574))),not(X_574))),
inference(subst,[],[refute_0_32:[bind(X_569,$fot(X_573)),bind(X_570,$fot(X_574))]]) ).
cnf(refute_0_34,plain,
theorem(or(B,or(not(not(or(X_573,X_574))),not(X_574)))),
inference(resolve,[$cnf( theorem(or(not(not(or(X_573,X_574))),not(X_574))) )],[refute_0_33,refute_0_6]) ).
cnf(refute_0_35,plain,
theorem(or(X_581,or(not(not(or(X_582,X_583))),not(X_583)))),
inference(subst,[],[refute_0_34:[bind(B,$fot(X_581)),bind(X_573,$fot(X_582)),bind(X_574,$fot(X_583))]]) ).
cnf(refute_0_36,plain,
theorem(or(not(not(or(X_582,X_583))),or(X_581,not(X_583)))),
inference(resolve,[$cnf( theorem(or(X_581,or(not(not(or(X_582,X_583))),not(X_583)))) )],[refute_0_35,refute_0_2]) ).
cnf(refute_0_37,plain,
theorem(or(not(not(or(not(p),q))),or(not(p),not(q)))),
inference(subst,[],[refute_0_36:[bind(X_581,$fot(not(p))),bind(X_582,$fot(not(p))),bind(X_583,$fot(q))]]) ).
cnf(refute_0_38,plain,
$false,
inference(resolve,[$cnf( theorem(or(not(not(or(not(p),q))),or(not(p),not(q)))) )],[refute_0_37,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL205-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.36 % Computer : n003.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
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 11:27:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.40/0.64 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.64
% 0.40/0.64 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.40/0.65
%------------------------------------------------------------------------------