%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL213-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 12:42:13 PM UTC 2026
% Result : Unsatisfiable 107.06s 107.30s
% Output : CNFRefutation 107.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of clauses : 38 ( 20 unt; 0 nHn; 19 RR)
% Number of literals : 62 ( 0 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 84 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(or(not(or(A,A)),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(or(not(p),q)),or(not(or(not(not(p)),q)),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,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ theorem(or(not(or(not(X_83492),X_83493)),or(not(or(X_83492,X_83493)),X_83493)))
| theorem(or(not(or(X_83492,X_83493)),or(not(or(not(X_83492),X_83493)),X_83493))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(not(or(not(X_83492),X_83493)))),bind(B,$fot(not(or(X_83492,X_83493)))),bind(C,$fot(X_83493))]]) ).
cnf(refute_0_3,plain,
( ~ theorem(or(not(or(X_10316,X_10317)),or(not(or(not(or(X_10317,X_10316)),or(X_10318,X_10318))),X_10318)))
| theorem(or(not(or(not(or(X_10317,X_10316)),or(X_10318,X_10318))),or(not(or(X_10316,X_10317)),X_10318))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(not(or(X_10316,X_10317)))),bind(B,$fot(not(or(not(or(X_10317,X_10316)),or(X_10318,X_10318))))),bind(C,$fot(X_10318))]]) ).
cnf(refute_0_4,plain,
( ~ theorem(or(not(or(X_754,or(X_753,X_753))),or(X_754,X_753)))
| theorem(or(X_754,or(not(or(X_754,or(X_753,X_753))),X_753))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(not(or(X_754,or(X_753,X_753))))),bind(B,$fot(X_754)),bind(C,$fot(X_753))]]) ).
cnf(refute_0_5,plain,
( ~ axiom(or(not(or(A,A)),A))
| theorem(or(not(or(A,A)),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(or(not(or(A,A)),A)))]]) ).
cnf(refute_0_6,plain,
theorem(or(not(or(A,A)),A)),
inference(resolve,[$cnf( axiom(or(not(or(A,A)),A)) )],[axiom_1_2,refute_0_5]) ).
cnf(refute_0_7,plain,
theorem(or(not(or(X_745,X_745)),X_745)),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_745))]]) ).
cnf(refute_0_8,plain,
( ~ axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
| ~ theorem(or(not(A),B))
| theorem(or(not(or(C,A)),or(C,B))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(not(or(C,A)),or(C,B)))),bind(Y,$fot(or(not(A),B)))]]) ).
cnf(refute_0_9,plain,
( ~ theorem(or(not(A),B))
| theorem(or(not(or(C,A)),or(C,B))) ),
inference(resolve,[$cnf( axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) )],[axiom_1_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ theorem(or(not(or(X_745,X_745)),X_745))
| theorem(or(not(or(X_746,or(X_745,X_745))),or(X_746,X_745))) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(or(X_745,X_745))),bind(B,$fot(X_745)),bind(C,$fot(X_746))]]) ).
cnf(refute_0_11,plain,
theorem(or(not(or(X_746,or(X_745,X_745))),or(X_746,X_745))),
inference(resolve,[$cnf( theorem(or(not(or(X_745,X_745)),X_745)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
theorem(or(not(or(X_754,or(X_753,X_753))),or(X_754,X_753))),
inference(subst,[],[refute_0_11:[bind(X_745,$fot(X_753)),bind(X_746,$fot(X_754))]]) ).
cnf(refute_0_13,plain,
theorem(or(X_754,or(not(or(X_754,or(X_753,X_753))),X_753))),
inference(resolve,[$cnf( theorem(or(not(or(X_754,or(X_753,X_753))),or(X_754,X_753))) )],[refute_0_12,refute_0_4]) ).
cnf(refute_0_14,plain,
theorem(or(not(or(X_3842,X_3841)),or(not(or(not(or(X_3842,X_3841)),or(X_753,X_753))),X_753))),
inference(subst,[],[refute_0_13:[bind(X_754,$fot(not(or(X_3842,X_3841))))]]) ).
cnf(refute_0_15,plain,
( ~ axiom(or(not(or(A,B)),or(B,A)))
| ~ theorem(or(not(or(B,A)),X_408))
| theorem(or(not(or(A,B)),X_408)) ),
inference(subst,[],[rule_3:[bind(X,$fot(or(A,B))),bind(Y,$fot(or(B,A))),bind(Z,$fot(X_408))]]) ).
cnf(refute_0_16,plain,
( ~ theorem(or(not(or(B,A)),X_408))
| theorem(or(not(or(A,B)),X_408)) ),
inference(resolve,[$cnf( axiom(or(not(or(A,B)),or(B,A))) )],[axiom_1_4,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ theorem(or(not(or(X_3842,X_3841)),or(not(or(not(or(X_3842,X_3841)),or(X_753,X_753))),X_753)))
| theorem(or(not(or(X_3841,X_3842)),or(not(or(not(or(X_3842,X_3841)),or(X_753,X_753))),X_753))) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_3841)),bind(B,$fot(X_3842)),bind(X_408,$fot(or(not(or(not(or(X_3842,X_3841)),or(X_753,X_753))),X_753)))]]) ).
cnf(refute_0_18,plain,
theorem(or(not(or(X_3841,X_3842)),or(not(or(not(or(X_3842,X_3841)),or(X_753,X_753))),X_753))),
inference(resolve,[$cnf( theorem(or(not(or(X_3842,X_3841)),or(not(or(not(or(X_3842,X_3841)),or(X_753,X_753))),X_753))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
theorem(or(not(or(X_10316,X_10317)),or(not(or(not(or(X_10317,X_10316)),or(X_10318,X_10318))),X_10318))),
inference(subst,[],[refute_0_18:[bind(X_3841,$fot(X_10316)),bind(X_3842,$fot(X_10317)),bind(X_753,$fot(X_10318))]]) ).
cnf(refute_0_20,plain,
theorem(or(not(or(not(or(X_10317,X_10316)),or(X_10318,X_10318))),or(not(or(X_10316,X_10317)),X_10318))),
inference(resolve,[$cnf( theorem(or(not(or(X_10316,X_10317)),or(not(or(not(or(X_10317,X_10316)),or(X_10318,X_10318))),X_10318))) )],[refute_0_19,refute_0_3]) ).
cnf(refute_0_21,plain,
theorem(or(not(or(not(or(X_83455,X_83454)),or(X_83455,X_83455))),or(not(or(X_83454,X_83455)),X_83455))),
inference(subst,[],[refute_0_20:[bind(X_10316,$fot(X_83454)),bind(X_10317,$fot(X_83455)),bind(X_10318,$fot(X_83455))]]) ).
cnf(refute_0_22,plain,
( ~ axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
| ~ theorem(or(not(or(not(or(C,A)),or(C,B))),X_408))
| theorem(or(not(or(not(A),B)),X_408)) ),
inference(subst,[],[rule_3:[bind(X,$fot(or(not(A),B))),bind(Y,$fot(or(not(or(C,A)),or(C,B)))),bind(Z,$fot(X_408))]]) ).
cnf(refute_0_23,plain,
( ~ theorem(or(not(or(not(or(C,A)),or(C,B))),X_408))
| theorem(or(not(or(not(A),B)),X_408)) ),
inference(resolve,[$cnf( axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) )],[axiom_1_6,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ theorem(or(not(or(not(or(X_83455,X_83454)),or(X_83455,X_83455))),or(not(or(X_83454,X_83455)),X_83455)))
| theorem(or(not(or(not(X_83454),X_83455)),or(not(or(X_83454,X_83455)),X_83455))) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_83454)),bind(B,$fot(X_83455)),bind(C,$fot(X_83455)),bind(X_408,$fot(or(not(or(X_83454,X_83455)),X_83455)))]]) ).
cnf(refute_0_25,plain,
theorem(or(not(or(not(X_83454),X_83455)),or(not(or(X_83454,X_83455)),X_83455))),
inference(resolve,[$cnf( theorem(or(not(or(not(or(X_83455,X_83454)),or(X_83455,X_83455))),or(not(or(X_83454,X_83455)),X_83455))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
theorem(or(not(or(not(X_83492),X_83493)),or(not(or(X_83492,X_83493)),X_83493))),
inference(subst,[],[refute_0_25:[bind(X_83454,$fot(X_83492)),bind(X_83455,$fot(X_83493))]]) ).
cnf(refute_0_27,plain,
theorem(or(not(or(X_83492,X_83493)),or(not(or(not(X_83492),X_83493)),X_83493))),
inference(resolve,[$cnf( theorem(or(not(or(not(X_83492),X_83493)),or(not(or(X_83492,X_83493)),X_83493))) )],[refute_0_26,refute_0_2]) ).
cnf(refute_0_28,plain,
theorem(or(not(or(not(p),q)),or(not(or(not(not(p)),q)),q))),
inference(subst,[],[refute_0_27:[bind(X_83492,$fot(not(p))),bind(X_83493,$fot(q))]]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( theorem(or(not(or(not(p),q)),or(not(or(not(not(p)),q)),q))) )],[refute_0_28,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL213-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.37 % Computer : n004.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 : Sun Sep 6 01:59:14 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 107.06/107.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 107.06/107.30
% 107.06/107.30 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 107.06/107.32
%------------------------------------------------------------------------------