%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL212-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 7.78s 8.11s
% Output : CNFRefutation 7.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of clauses : 35 ( 18 unt; 0 nHn; 18 RR)
% Number of literals : 58 ( 0 equ; 24 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 : 70 ( 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(not(p)),q)),or(not(or(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,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ theorem(or(not(or(X_14209,X_14210)),or(not(or(not(X_14209),X_14210)),X_14210)))
| theorem(or(not(or(not(X_14209),X_14210)),or(not(or(X_14209,X_14210)),X_14210))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(not(or(X_14209,X_14210)))),bind(B,$fot(not(or(not(X_14209),X_14210)))),bind(C,$fot(X_14210))]]) ).
cnf(refute_0_3,plain,
( ~ axiom(or(not(or(A,B)),or(B,A)))
| ~ theorem(or(not(or(B,A)),X_672))
| theorem(or(not(or(A,B)),X_672)) ),
inference(subst,[],[rule_3:[bind(X,$fot(or(A,B))),bind(Y,$fot(or(B,A))),bind(Z,$fot(X_672))]]) ).
cnf(refute_0_4,plain,
( ~ theorem(or(not(or(B,A)),X_672))
| theorem(or(not(or(A,B)),X_672)) ),
inference(resolve,[$cnf( axiom(or(not(or(A,B)),or(B,A))) )],[axiom_1_4,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(not(or(X_14195,X_14194)),or(not(or(not(X_14194),X_14195)),X_14195)))
| theorem(or(not(or(X_14194,X_14195)),or(not(or(not(X_14194),X_14195)),X_14195))) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_14194)),bind(B,$fot(X_14195)),bind(X_672,$fot(or(not(or(not(X_14194),X_14195)),X_14195)))]]) ).
cnf(refute_0_6,plain,
( ~ theorem(or(not(or(not(X_14184),X_14185)),or(not(or(X_14185,X_14184)),X_14185)))
| theorem(or(not(or(X_14185,X_14184)),or(not(or(not(X_14184),X_14185)),X_14185))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(not(or(not(X_14184),X_14185)))),bind(B,$fot(not(or(X_14185,X_14184)))),bind(C,$fot(X_14185))]]) ).
cnf(refute_0_7,plain,
axiom(or(not(or(not(A),X_14181)),or(not(or(X_14181,A)),or(X_14181,X_14181)))),
inference(subst,[],[axiom_1_6:[bind(B,$fot(X_14181)),bind(C,$fot(X_14181))]]) ).
cnf(refute_0_8,plain,
( ~ axiom(or(not(or(A,A)),A))
| theorem(or(not(or(A,A)),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(or(not(or(A,A)),A)))]]) ).
cnf(refute_0_9,plain,
theorem(or(not(or(A,A)),A)),
inference(resolve,[$cnf( axiom(or(not(or(A,A)),A)) )],[axiom_1_2,refute_0_8]) ).
cnf(refute_0_10,plain,
theorem(or(not(or(X_551,X_551)),X_551)),
inference(subst,[],[refute_0_9:[bind(A,$fot(X_551))]]) ).
cnf(refute_0_11,plain,
( ~ axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
| ~ theorem(or(not(A),B))
| theorem(or(not(or(C,A)),or(C,B))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(not(or(C,A)),or(C,B)))),bind(Y,$fot(or(not(A),B)))]]) ).
cnf(refute_0_12,plain,
( ~ theorem(or(not(A),B))
| theorem(or(not(or(C,A)),or(C,B))) ),
inference(resolve,[$cnf( axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) )],[axiom_1_6,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ theorem(or(not(or(X_551,X_551)),X_551))
| theorem(or(not(or(X_552,or(X_551,X_551))),or(X_552,X_551))) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(or(X_551,X_551))),bind(B,$fot(X_551)),bind(C,$fot(X_552))]]) ).
cnf(refute_0_14,plain,
theorem(or(not(or(X_552,or(X_551,X_551))),or(X_552,X_551))),
inference(resolve,[$cnf( theorem(or(not(or(X_551,X_551)),X_551)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ axiom(or(not(X_670),or(X_552,or(X_551,X_551))))
| ~ theorem(or(not(or(X_552,or(X_551,X_551))),or(X_552,X_551)))
| theorem(or(not(X_670),or(X_552,X_551))) ),
inference(subst,[],[rule_3:[bind(X,$fot(X_670)),bind(Y,$fot(or(X_552,or(X_551,X_551)))),bind(Z,$fot(or(X_552,X_551)))]]) ).
cnf(refute_0_16,plain,
( ~ axiom(or(not(X_670),or(X_552,or(X_551,X_551))))
| theorem(or(not(X_670),or(X_552,X_551))) ),
inference(resolve,[$cnf( theorem(or(not(or(X_552,or(X_551,X_551))),or(X_552,X_551))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ axiom(or(not(or(not(A),X_14181)),or(not(or(X_14181,A)),or(X_14181,X_14181))))
| theorem(or(not(or(not(A),X_14181)),or(not(or(X_14181,A)),X_14181))) ),
inference(subst,[],[refute_0_16:[bind(X_551,$fot(X_14181)),bind(X_552,$fot(not(or(X_14181,A)))),bind(X_670,$fot(or(not(A),X_14181)))]]) ).
cnf(refute_0_18,plain,
theorem(or(not(or(not(A),X_14181)),or(not(or(X_14181,A)),X_14181))),
inference(resolve,[$cnf( axiom(or(not(or(not(A),X_14181)),or(not(or(X_14181,A)),or(X_14181,X_14181)))) )],[refute_0_7,refute_0_17]) ).
cnf(refute_0_19,plain,
theorem(or(not(or(not(X_14184),X_14185)),or(not(or(X_14185,X_14184)),X_14185))),
inference(subst,[],[refute_0_18:[bind(A,$fot(X_14184)),bind(X_14181,$fot(X_14185))]]) ).
cnf(refute_0_20,plain,
theorem(or(not(or(X_14185,X_14184)),or(not(or(not(X_14184),X_14185)),X_14185))),
inference(resolve,[$cnf( theorem(or(not(or(not(X_14184),X_14185)),or(not(or(X_14185,X_14184)),X_14185))) )],[refute_0_19,refute_0_6]) ).
cnf(refute_0_21,plain,
theorem(or(not(or(X_14195,X_14194)),or(not(or(not(X_14194),X_14195)),X_14195))),
inference(subst,[],[refute_0_20:[bind(X_14184,$fot(X_14194)),bind(X_14185,$fot(X_14195))]]) ).
cnf(refute_0_22,plain,
theorem(or(not(or(X_14194,X_14195)),or(not(or(not(X_14194),X_14195)),X_14195))),
inference(resolve,[$cnf( theorem(or(not(or(X_14195,X_14194)),or(not(or(not(X_14194),X_14195)),X_14195))) )],[refute_0_21,refute_0_5]) ).
cnf(refute_0_23,plain,
theorem(or(not(or(X_14209,X_14210)),or(not(or(not(X_14209),X_14210)),X_14210))),
inference(subst,[],[refute_0_22:[bind(X_14194,$fot(X_14209)),bind(X_14195,$fot(X_14210))]]) ).
cnf(refute_0_24,plain,
theorem(or(not(or(not(X_14209),X_14210)),or(not(or(X_14209,X_14210)),X_14210))),
inference(resolve,[$cnf( theorem(or(not(or(X_14209,X_14210)),or(not(or(not(X_14209),X_14210)),X_14210))) )],[refute_0_23,refute_0_2]) ).
cnf(refute_0_25,plain,
theorem(or(not(or(not(not(p)),q)),or(not(or(not(p),q)),q))),
inference(subst,[],[refute_0_24:[bind(X_14209,$fot(not(p))),bind(X_14210,$fot(q))]]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( theorem(or(not(or(not(not(p)),q)),or(not(or(not(p),q)),q))) )],[refute_0_25,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL212-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 15:09:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.12/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 7.78/8.11 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.78/8.11
% 7.78/8.11 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.78/8.12
%------------------------------------------------------------------------------