%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL188-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n002.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 12:42:07 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.54s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of clauses : 51 ( 29 unt; 0 nHn; 25 RR)
% Number of literals : 80 ( 24 equ; 30 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 104 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) ).
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(or(p,implies(or(p,q),q))) ).
cnf(refute_0_0,plain,
( ~ theorem(implies(X_69,or(X_70,X_71)))
| ~ theorem(implies(implies(X_69,or(X_70,X_71)),or(X_70,implies(X_69,X_71))))
| theorem(or(X_70,implies(X_69,X_71))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_70,implies(X_69,X_71)))),bind(Y,$fot(implies(X_69,or(X_70,X_71))))]]) ).
cnf(refute_0_1,plain,
( ~ axiom(implies(implies(X_66,or(X_67,X_68)),or(X_67,implies(X_66,X_68))))
| theorem(implies(implies(X_66,or(X_67,X_68)),or(X_67,implies(X_66,X_68)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_66,or(X_67,X_68)),or(X_67,implies(X_66,X_68)))))]]) ).
cnf(refute_0_2,plain,
axiom(implies(or(not(X),or(X_26,X_27)),or(X_26,or(not(X),X_27)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_26)),bind(C,$fot(X_27))]]) ).
cnf(refute_0_3,plain,
implies(X,X_27) = or(not(X),X_27),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_27))]]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( implies(X,X_27) != or(not(X),X_27)
| or(not(X),X_27) = implies(X,X_27) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,X_27))),bind(Y0,$fot(or(not(X),X_27)))]]) ).
cnf(refute_0_8,plain,
or(not(X),X_27) = implies(X,X_27),
inference(resolve,[$cnf( $equal(implies(X,X_27),or(not(X),X_27)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( or(not(X),X_27) != implies(X,X_27)
| ~ axiom(implies(or(not(X),or(X_26,X_27)),or(X_26,or(not(X),X_27))))
| axiom(implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_26,X_27)),or(X_26,or(not(X),X_27)))) ),[0,1,1],$fot(implies(X,X_27))]]) ).
cnf(refute_0_10,plain,
( ~ axiom(implies(or(not(X),or(X_26,X_27)),or(X_26,or(not(X),X_27))))
| axiom(implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_27),implies(X,X_27)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
axiom(implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_26,X_27)),or(X_26,or(not(X),X_27)))) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_13,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_12]) ).
cnf(refute_0_14,plain,
or(not(X),or(X_26,X_27)) = implies(X,or(X_26,X_27)),
inference(subst,[],[refute_0_13:[bind(Y,$fot(or(X_26,X_27)))]]) ).
cnf(refute_0_15,plain,
implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27))) = implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27))))]]) ).
cnf(refute_0_16,plain,
( implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27))) != implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27)))
| or(not(X),or(X_26,X_27)) != implies(X,or(X_26,X_27))
| implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27))) = implies(implies(X,or(X_26,X_27)),or(X_26,implies(X,X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27))),implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27)))) ),[1,0],$fot(implies(X,or(X_26,X_27)))]]) ).
cnf(refute_0_17,plain,
( or(not(X),or(X_26,X_27)) != implies(X,or(X_26,X_27))
| implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27))) = implies(implies(X,or(X_26,X_27)),or(X_26,implies(X,X_27))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27))),implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27))) = implies(implies(X,or(X_26,X_27)),or(X_26,implies(X,X_27))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_26,X_27)),implies(X,or(X_26,X_27))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27))) != implies(implies(X,or(X_26,X_27)),or(X_26,implies(X,X_27)))
| ~ axiom(implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27))))
| axiom(implies(implies(X,or(X_26,X_27)),or(X_26,implies(X,X_27)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27)))) ),[0],$fot(implies(implies(X,or(X_26,X_27)),or(X_26,implies(X,X_27))))]]) ).
cnf(refute_0_20,plain,
( ~ axiom(implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27))))
| axiom(implies(implies(X,or(X_26,X_27)),or(X_26,implies(X,X_27)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27))),implies(implies(X,or(X_26,X_27)),or(X_26,implies(X,X_27)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
axiom(implies(implies(X,or(X_26,X_27)),or(X_26,implies(X,X_27)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_26,X_27)),or(X_26,implies(X,X_27)))) )],[refute_0_11,refute_0_20]) ).
cnf(refute_0_22,plain,
axiom(implies(implies(X_66,or(X_67,X_68)),or(X_67,implies(X_66,X_68)))),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_66)),bind(X_26,$fot(X_67)),bind(X_27,$fot(X_68))]]) ).
cnf(refute_0_23,plain,
theorem(implies(implies(X_66,or(X_67,X_68)),or(X_67,implies(X_66,X_68)))),
inference(resolve,[$cnf( axiom(implies(implies(X_66,or(X_67,X_68)),or(X_67,implies(X_66,X_68)))) )],[refute_0_22,refute_0_1]) ).
cnf(refute_0_24,plain,
theorem(implies(implies(X_69,or(X_70,X_71)),or(X_70,implies(X_69,X_71)))),
inference(subst,[],[refute_0_23:[bind(X_66,$fot(X_69)),bind(X_67,$fot(X_70)),bind(X_68,$fot(X_71))]]) ).
cnf(refute_0_25,plain,
( ~ theorem(implies(X_69,or(X_70,X_71)))
| theorem(or(X_70,implies(X_69,X_71))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_69,or(X_70,X_71)),or(X_70,implies(X_69,X_71)))) )],[refute_0_24,refute_0_0]) ).
cnf(refute_0_26,plain,
( ~ theorem(implies(or(X_70,X_71),or(X_70,X_71)))
| theorem(or(X_70,implies(or(X_70,X_71),X_71))) ),
inference(subst,[],[refute_0_25:[bind(X_69,$fot(or(X_70,X_71)))]]) ).
cnf(refute_0_27,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_28,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_27]) ).
cnf(refute_0_29,plain,
theorem(implies(or(X_55,X_55),X_55)),
inference(subst,[],[refute_0_28:[bind(A,$fot(X_55))]]) ).
cnf(refute_0_30,plain,
( ~ theorem(implies(or(X_55,X_55),X_55))
| ~ theorem(or(X_55,X_55))
| theorem(X_55) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_55)),bind(Y,$fot(or(X_55,X_55)))]]) ).
cnf(refute_0_31,plain,
( ~ theorem(or(X_55,X_55))
| theorem(X_55) ),
inference(resolve,[$cnf( theorem(implies(or(X_55,X_55),X_55)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ theorem(or(implies(X_258,X_258),implies(X_258,X_258)))
| theorem(implies(X_258,X_258)) ),
inference(subst,[],[refute_0_31:[bind(X_55,$fot(implies(X_258,X_258)))]]) ).
cnf(refute_0_33,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_34,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_33]) ).
cnf(refute_0_35,plain,
theorem(implies(X_254,or(X_253,X_254))),
inference(subst,[],[refute_0_34:[bind(A,$fot(X_254)),bind(B,$fot(X_253))]]) ).
cnf(refute_0_36,plain,
( ~ theorem(implies(X_254,or(X_253,X_254)))
| theorem(or(X_253,implies(X_254,X_254))) ),
inference(subst,[],[refute_0_25:[bind(X_69,$fot(X_254)),bind(X_70,$fot(X_253)),bind(X_71,$fot(X_254))]]) ).
cnf(refute_0_37,plain,
theorem(or(X_253,implies(X_254,X_254))),
inference(resolve,[$cnf( theorem(implies(X_254,or(X_253,X_254))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
theorem(or(implies(X_258,X_258),implies(X_258,X_258))),
inference(subst,[],[refute_0_37:[bind(X_253,$fot(implies(X_258,X_258))),bind(X_254,$fot(X_258))]]) ).
cnf(refute_0_39,plain,
theorem(implies(X_258,X_258)),
inference(resolve,[$cnf( theorem(or(implies(X_258,X_258),implies(X_258,X_258))) )],[refute_0_38,refute_0_32]) ).
cnf(refute_0_40,plain,
theorem(implies(or(X_70,X_71),or(X_70,X_71))),
inference(subst,[],[refute_0_39:[bind(X_258,$fot(or(X_70,X_71)))]]) ).
cnf(refute_0_41,plain,
theorem(or(X_70,implies(or(X_70,X_71),X_71))),
inference(resolve,[$cnf( theorem(implies(or(X_70,X_71),or(X_70,X_71))) )],[refute_0_40,refute_0_26]) ).
cnf(refute_0_42,plain,
theorem(or(p,implies(or(p,q),q))),
inference(subst,[],[refute_0_41:[bind(X_70,$fot(p)),bind(X_71,$fot(q))]]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( theorem(or(p,implies(or(p,q),q))) )],[refute_0_42,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL188-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 5 19:33:51 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.54 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.54
% 0.22/0.54 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.22/0.56
%------------------------------------------------------------------------------