%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL237-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 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 12:42:17 PM UTC 2026
% Result : Unsatisfiable 31.16s 31.45s
% Output : CNFRefutation 31.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of clauses : 69 ( 37 unt; 0 nHn; 29 RR)
% Number of literals : 111 ( 0 equ; 43 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 : 164 ( 30 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(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(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(q),or(not(p),not(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,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ theorem(or(X_51714,or(X_51715,not(or(X_51714,X_51715)))))
| theorem(or(X_51715,or(X_51714,not(or(X_51714,X_51715))))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_51714)),bind(B,$fot(X_51715)),bind(C,$fot(not(or(X_51714,X_51715))))]]) ).
cnf(refute_0_3,plain,
axiom(or(not(or(X_23,X_23)),X_23)),
inference(subst,[],[axiom_1_2:[bind(A,$fot(X_23))]]) ).
cnf(refute_0_4,plain,
( ~ axiom(or(not(or(X_23,X_23)),X_23))
| ~ theorem(or(X_23,X_23))
| theorem(X_23) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_23)),bind(Y,$fot(or(X_23,X_23)))]]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(X_23,X_23))
| theorem(X_23) ),
inference(resolve,[$cnf( axiom(or(not(or(X_23,X_23)),X_23)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ theorem(or(or(X_51709,or(X_51710,not(or(X_51709,X_51710)))),or(X_51709,or(X_51710,not(or(X_51709,X_51710))))))
| theorem(or(X_51709,or(X_51710,not(or(X_51709,X_51710))))) ),
inference(subst,[],[refute_0_5:[bind(X_23,$fot(or(X_51709,or(X_51710,not(or(X_51709,X_51710))))))]]) ).
cnf(refute_0_7,plain,
( ~ theorem(or(X_51704,or(or(X_51706,or(X_51707,X_51708)),or(X_51705,not(or(X_51706,X_51707))))))
| theorem(or(or(X_51706,or(X_51707,X_51708)),or(X_51704,or(X_51705,not(or(X_51706,X_51707)))))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_51704)),bind(B,$fot(or(X_51706,or(X_51707,X_51708)))),bind(C,$fot(or(X_51705,not(or(X_51706,X_51707)))))]]) ).
cnf(refute_0_8,plain,
axiom(or(not(X_24),or(B,X_24))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_24))]]) ).
cnf(refute_0_9,plain,
( ~ axiom(or(not(X_24),or(B,X_24)))
| ~ theorem(X_24)
| theorem(or(B,X_24)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,X_24))),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_10,plain,
( ~ theorem(X_24)
| theorem(or(B,X_24)) ),
inference(resolve,[$cnf( axiom(or(not(X_24),or(B,X_24))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ theorem(or(or(X_51697,or(X_51698,X_51699)),or(X_51696,not(or(X_51697,X_51698)))))
| theorem(or(B,or(or(X_51697,or(X_51698,X_51699)),or(X_51696,not(or(X_51697,X_51698)))))) ),
inference(subst,[],[refute_0_10:[bind(X_24,$fot(or(or(X_51697,or(X_51698,X_51699)),or(X_51696,not(or(X_51697,X_51698))))))]]) ).
cnf(refute_0_12,plain,
( ~ theorem(or(X_2903,or(or(X_2904,or(X_2905,X_2906)),not(or(X_2904,X_2905)))))
| theorem(or(or(X_2904,or(X_2905,X_2906)),or(X_2903,not(or(X_2904,X_2905))))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_2903)),bind(B,$fot(or(X_2904,or(X_2905,X_2906)))),bind(C,$fot(not(or(X_2904,X_2905))))]]) ).
cnf(refute_0_13,plain,
( ~ theorem(or(or(X_2900,or(X_2901,X_2902)),not(or(X_2900,X_2901))))
| theorem(or(B,or(or(X_2900,or(X_2901,X_2902)),not(or(X_2900,X_2901))))) ),
inference(subst,[],[refute_0_10:[bind(X_24,$fot(or(or(X_2900,or(X_2901,X_2902)),not(or(X_2900,X_2901)))))]]) ).
cnf(refute_0_14,plain,
( ~ axiom(or(not(or(A,B)),or(B,A)))
| ~ theorem(or(A,B))
| theorem(or(B,A)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,A))),bind(Y,$fot(or(A,B)))]]) ).
cnf(refute_0_15,plain,
( ~ theorem(or(A,B))
| theorem(or(B,A)) ),
inference(resolve,[$cnf( axiom(or(not(or(A,B)),or(B,A))) )],[axiom_1_4,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ theorem(or(not(or(X_1583,X_1584)),or(X_1583,or(X_1584,X_1585))))
| theorem(or(or(X_1583,or(X_1584,X_1585)),not(or(X_1583,X_1584)))) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(not(or(X_1583,X_1584)))),bind(B,$fot(or(X_1583,or(X_1584,X_1585))))]]) ).
cnf(refute_0_17,plain,
( ~ axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
| ~ theorem(or(not(A),B))
| theorem(or(not(or(C,A)),or(C,B))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(not(or(C,A)),or(C,B)))),bind(Y,$fot(or(not(A),B)))]]) ).
cnf(refute_0_18,plain,
( ~ theorem(or(not(A),B))
| theorem(or(not(or(C,A)),or(C,B))) ),
inference(resolve,[$cnf( axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) )],[axiom_1_6,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ theorem(or(not(X_1256),or(X_1256,X_1257)))
| theorem(or(not(or(C,X_1256)),or(C,or(X_1256,X_1257)))) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(X_1256)),bind(B,$fot(or(X_1256,X_1257)))]]) ).
cnf(refute_0_20,plain,
( ~ axiom(or(not(or(A,B)),or(B,A)))
| ~ theorem(or(not(or(B,A)),X_115))
| theorem(or(not(or(A,B)),X_115)) ),
inference(subst,[],[rule_3:[bind(X,$fot(or(A,B))),bind(Y,$fot(or(B,A))),bind(Z,$fot(X_115))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(or(not(or(B,A)),X_115))
| theorem(or(not(or(A,B)),X_115)) ),
inference(resolve,[$cnf( axiom(or(not(or(A,B)),or(B,A))) )],[axiom_1_4,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ theorem(or(not(or(X_771,or(or(X_770,X_770),or(X_770,X_770)))),or(X_771,X_770)))
| theorem(or(not(or(or(or(X_770,X_770),or(X_770,X_770)),X_771)),or(X_771,X_770))) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(or(or(X_770,X_770),or(X_770,X_770)))),bind(B,$fot(X_771)),bind(X_115,$fot(or(X_771,X_770)))]]) ).
cnf(refute_0_23,plain,
( ~ axiom(or(not(or(A,A)),A))
| theorem(or(not(or(A,A)),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(or(not(or(A,A)),A)))]]) ).
cnf(refute_0_24,plain,
theorem(or(not(or(A,A)),A)),
inference(resolve,[$cnf( axiom(or(not(or(A,A)),A)) )],[axiom_1_2,refute_0_23]) ).
cnf(refute_0_25,plain,
theorem(or(not(or(X_133,X_133)),X_133)),
inference(subst,[],[refute_0_24:[bind(A,$fot(X_133))]]) ).
cnf(refute_0_26,plain,
axiom(or(not(or(X_114,X_114)),X_114)),
inference(subst,[],[axiom_1_2:[bind(A,$fot(X_114))]]) ).
cnf(refute_0_27,plain,
( ~ axiom(or(not(or(X_114,X_114)),X_114))
| ~ theorem(or(not(X_114),X_115))
| theorem(or(not(or(X_114,X_114)),X_115)) ),
inference(subst,[],[rule_3:[bind(X,$fot(or(X_114,X_114))),bind(Y,$fot(X_114)),bind(Z,$fot(X_115))]]) ).
cnf(refute_0_28,plain,
( ~ theorem(or(not(X_114),X_115))
| theorem(or(not(or(X_114,X_114)),X_115)) ),
inference(resolve,[$cnf( axiom(or(not(or(X_114,X_114)),X_114)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ theorem(or(not(or(X_133,X_133)),X_133))
| theorem(or(not(or(or(X_133,X_133),or(X_133,X_133))),X_133)) ),
inference(subst,[],[refute_0_28:[bind(X_114,$fot(or(X_133,X_133))),bind(X_115,$fot(X_133))]]) ).
cnf(refute_0_30,plain,
theorem(or(not(or(or(X_133,X_133),or(X_133,X_133))),X_133)),
inference(resolve,[$cnf( theorem(or(not(or(X_133,X_133)),X_133)) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
theorem(or(not(or(or(X_540,X_540),or(X_540,X_540))),X_540)),
inference(subst,[],[refute_0_30:[bind(X_133,$fot(X_540))]]) ).
cnf(refute_0_32,plain,
( ~ theorem(or(not(or(or(X_540,X_540),or(X_540,X_540))),X_540))
| theorem(or(not(or(X_541,or(or(X_540,X_540),or(X_540,X_540)))),or(X_541,X_540))) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(or(or(X_540,X_540),or(X_540,X_540)))),bind(B,$fot(X_540)),bind(C,$fot(X_541))]]) ).
cnf(refute_0_33,plain,
theorem(or(not(or(X_541,or(or(X_540,X_540),or(X_540,X_540)))),or(X_541,X_540))),
inference(resolve,[$cnf( theorem(or(not(or(or(X_540,X_540),or(X_540,X_540))),X_540)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
theorem(or(not(or(X_771,or(or(X_770,X_770),or(X_770,X_770)))),or(X_771,X_770))),
inference(subst,[],[refute_0_33:[bind(X_540,$fot(X_770)),bind(X_541,$fot(X_771))]]) ).
cnf(refute_0_35,plain,
theorem(or(not(or(or(or(X_770,X_770),or(X_770,X_770)),X_771)),or(X_771,X_770))),
inference(resolve,[$cnf( theorem(or(not(or(X_771,or(or(X_770,X_770),or(X_770,X_770)))),or(X_771,X_770))) )],[refute_0_34,refute_0_22]) ).
cnf(refute_0_36,plain,
theorem(or(not(or(or(or(X_770,X_770),or(X_770,X_770)),X_1254)),or(X_1254,X_770))),
inference(subst,[],[refute_0_35:[bind(X_771,$fot(X_1254))]]) ).
cnf(refute_0_37,plain,
axiom(or(not(X_113),or(B,X_113))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_113))]]) ).
cnf(refute_0_38,plain,
( ~ axiom(or(not(X_113),or(B,X_113)))
| ~ theorem(or(not(or(B,X_113)),X_115))
| theorem(or(not(X_113),X_115)) ),
inference(subst,[],[rule_3:[bind(X,$fot(X_113)),bind(Y,$fot(or(B,X_113))),bind(Z,$fot(X_115))]]) ).
cnf(refute_0_39,plain,
( ~ theorem(or(not(or(B,X_113)),X_115))
| theorem(or(not(X_113),X_115)) ),
inference(resolve,[$cnf( axiom(or(not(X_113),or(B,X_113))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ theorem(or(not(or(or(or(X_770,X_770),or(X_770,X_770)),X_1254)),or(X_1254,X_770)))
| theorem(or(not(X_1254),or(X_1254,X_770))) ),
inference(subst,[],[refute_0_39:[bind(B,$fot(or(or(X_770,X_770),or(X_770,X_770)))),bind(X_113,$fot(X_1254)),bind(X_115,$fot(or(X_1254,X_770)))]]) ).
cnf(refute_0_41,plain,
theorem(or(not(X_1254),or(X_1254,X_770))),
inference(resolve,[$cnf( theorem(or(not(or(or(or(X_770,X_770),or(X_770,X_770)),X_1254)),or(X_1254,X_770))) )],[refute_0_36,refute_0_40]) ).
cnf(refute_0_42,plain,
theorem(or(not(X_1256),or(X_1256,X_1257))),
inference(subst,[],[refute_0_41:[bind(X_1254,$fot(X_1256)),bind(X_770,$fot(X_1257))]]) ).
cnf(refute_0_43,plain,
theorem(or(not(or(C,X_1256)),or(C,or(X_1256,X_1257)))),
inference(resolve,[$cnf( theorem(or(not(X_1256),or(X_1256,X_1257))) )],[refute_0_42,refute_0_19]) ).
cnf(refute_0_44,plain,
theorem(or(not(or(X_1583,X_1584)),or(X_1583,or(X_1584,X_1585)))),
inference(subst,[],[refute_0_43:[bind(C,$fot(X_1583)),bind(X_1256,$fot(X_1584)),bind(X_1257,$fot(X_1585))]]) ).
cnf(refute_0_45,plain,
theorem(or(or(X_1583,or(X_1584,X_1585)),not(or(X_1583,X_1584)))),
inference(resolve,[$cnf( theorem(or(not(or(X_1583,X_1584)),or(X_1583,or(X_1584,X_1585)))) )],[refute_0_44,refute_0_16]) ).
cnf(refute_0_46,plain,
theorem(or(or(X_2900,or(X_2901,X_2902)),not(or(X_2900,X_2901)))),
inference(subst,[],[refute_0_45:[bind(X_1583,$fot(X_2900)),bind(X_1584,$fot(X_2901)),bind(X_1585,$fot(X_2902))]]) ).
cnf(refute_0_47,plain,
theorem(or(B,or(or(X_2900,or(X_2901,X_2902)),not(or(X_2900,X_2901))))),
inference(resolve,[$cnf( theorem(or(or(X_2900,or(X_2901,X_2902)),not(or(X_2900,X_2901)))) )],[refute_0_46,refute_0_13]) ).
cnf(refute_0_48,plain,
theorem(or(X_2903,or(or(X_2904,or(X_2905,X_2906)),not(or(X_2904,X_2905))))),
inference(subst,[],[refute_0_47:[bind(B,$fot(X_2903)),bind(X_2900,$fot(X_2904)),bind(X_2901,$fot(X_2905)),bind(X_2902,$fot(X_2906))]]) ).
cnf(refute_0_49,plain,
theorem(or(or(X_2904,or(X_2905,X_2906)),or(X_2903,not(or(X_2904,X_2905))))),
inference(resolve,[$cnf( theorem(or(X_2903,or(or(X_2904,or(X_2905,X_2906)),not(or(X_2904,X_2905))))) )],[refute_0_48,refute_0_12]) ).
cnf(refute_0_50,plain,
theorem(or(or(X_51697,or(X_51698,X_51699)),or(X_51696,not(or(X_51697,X_51698))))),
inference(subst,[],[refute_0_49:[bind(X_2903,$fot(X_51696)),bind(X_2904,$fot(X_51697)),bind(X_2905,$fot(X_51698)),bind(X_2906,$fot(X_51699))]]) ).
cnf(refute_0_51,plain,
theorem(or(B,or(or(X_51697,or(X_51698,X_51699)),or(X_51696,not(or(X_51697,X_51698)))))),
inference(resolve,[$cnf( theorem(or(or(X_51697,or(X_51698,X_51699)),or(X_51696,not(or(X_51697,X_51698))))) )],[refute_0_50,refute_0_11]) ).
cnf(refute_0_52,plain,
theorem(or(X_51704,or(or(X_51706,or(X_51707,X_51708)),or(X_51705,not(or(X_51706,X_51707)))))),
inference(subst,[],[refute_0_51:[bind(B,$fot(X_51704)),bind(X_51696,$fot(X_51705)),bind(X_51697,$fot(X_51706)),bind(X_51698,$fot(X_51707)),bind(X_51699,$fot(X_51708))]]) ).
cnf(refute_0_53,plain,
theorem(or(or(X_51706,or(X_51707,X_51708)),or(X_51704,or(X_51705,not(or(X_51706,X_51707)))))),
inference(resolve,[$cnf( theorem(or(X_51704,or(or(X_51706,or(X_51707,X_51708)),or(X_51705,not(or(X_51706,X_51707)))))) )],[refute_0_52,refute_0_7]) ).
cnf(refute_0_54,plain,
theorem(or(or(X_51709,or(X_51710,not(or(X_51709,X_51710)))),or(X_51709,or(X_51710,not(or(X_51709,X_51710)))))),
inference(subst,[],[refute_0_53:[bind(X_51704,$fot(X_51709)),bind(X_51705,$fot(X_51710)),bind(X_51706,$fot(X_51709)),bind(X_51707,$fot(X_51710)),bind(X_51708,$fot(not(or(X_51709,X_51710))))]]) ).
cnf(refute_0_55,plain,
theorem(or(X_51709,or(X_51710,not(or(X_51709,X_51710))))),
inference(resolve,[$cnf( theorem(or(or(X_51709,or(X_51710,not(or(X_51709,X_51710)))),or(X_51709,or(X_51710,not(or(X_51709,X_51710)))))) )],[refute_0_54,refute_0_6]) ).
cnf(refute_0_56,plain,
theorem(or(X_51714,or(X_51715,not(or(X_51714,X_51715))))),
inference(subst,[],[refute_0_55:[bind(X_51709,$fot(X_51714)),bind(X_51710,$fot(X_51715))]]) ).
cnf(refute_0_57,plain,
theorem(or(X_51715,or(X_51714,not(or(X_51714,X_51715))))),
inference(resolve,[$cnf( theorem(or(X_51714,or(X_51715,not(or(X_51714,X_51715))))) )],[refute_0_56,refute_0_2]) ).
cnf(refute_0_58,plain,
theorem(or(not(q),or(not(p),not(or(not(p),not(q)))))),
inference(subst,[],[refute_0_57:[bind(X_51714,$fot(not(p))),bind(X_51715,$fot(not(q)))]]) ).
cnf(refute_0_59,plain,
$false,
inference(resolve,[$cnf( theorem(or(not(q),or(not(p),not(or(not(p),not(q)))))) )],[refute_0_58,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL237-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sat Sep 5 03:24:55 UTC 2026
% 0.02/0.37 % CPUTime :
% 0.02/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 31.16/31.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.16/31.45
% 31.16/31.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 31.16/31.46
%------------------------------------------------------------------------------