TSTP Solution File: LCL226-3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL226-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:50:52 EDT 2022
% Result : Unsatisfiable 1.82s 2.00s
% Output : CNFRefutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 23
% Syntax : Number of clauses : 69 ( 37 unt; 0 nHn; 40 RR)
% Number of literals : 114 ( 61 equ; 47 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).
cnf(axiom_1_6,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ).
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(implies(or(q,r),implies(or(not(r),s),or(q,s)))) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_4,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_3]) ).
cnf(refute_0_5,plain,
or(not(r),s) = implies(r,s),
inference(subst,[],[refute_0_4:[bind(X,$fot(r)),bind(Y,$fot(s))]]) ).
cnf(refute_0_6,plain,
implies(or(not(r),s),or(q,s)) = implies(or(not(r),s),or(q,s)),
introduced(tautology,[refl,[$fot(implies(or(not(r),s),or(q,s)))]]) ).
cnf(refute_0_7,plain,
( implies(or(not(r),s),or(q,s)) != implies(or(not(r),s),or(q,s))
| or(not(r),s) != implies(r,s)
| implies(or(not(r),s),or(q,s)) = implies(implies(r,s),or(q,s)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(r),s),or(q,s)),implies(or(not(r),s),or(q,s))) ),[1,0],$fot(implies(r,s))]]) ).
cnf(refute_0_8,plain,
( or(not(r),s) != implies(r,s)
| implies(or(not(r),s),or(q,s)) = implies(implies(r,s),or(q,s)) ),
inference(resolve,[$cnf( $equal(implies(or(not(r),s),or(q,s)),implies(or(not(r),s),or(q,s))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
implies(or(not(r),s),or(q,s)) = implies(implies(r,s),or(q,s)),
inference(resolve,[$cnf( $equal(or(not(r),s),implies(r,s)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
implies(or(q,r),implies(or(not(r),s),or(q,s))) = implies(or(q,r),implies(or(not(r),s),or(q,s))),
introduced(tautology,[refl,[$fot(implies(or(q,r),implies(or(not(r),s),or(q,s))))]]) ).
cnf(refute_0_11,plain,
( implies(or(not(r),s),or(q,s)) != implies(implies(r,s),or(q,s))
| implies(or(q,r),implies(or(not(r),s),or(q,s))) != implies(or(q,r),implies(or(not(r),s),or(q,s)))
| implies(or(q,r),implies(or(not(r),s),or(q,s))) = implies(or(q,r),implies(implies(r,s),or(q,s))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(q,r),implies(or(not(r),s),or(q,s))),implies(or(q,r),implies(or(not(r),s),or(q,s)))) ),[1,1],$fot(implies(implies(r,s),or(q,s)))]]) ).
cnf(refute_0_12,plain,
( implies(or(not(r),s),or(q,s)) != implies(implies(r,s),or(q,s))
| implies(or(q,r),implies(or(not(r),s),or(q,s))) = implies(or(q,r),implies(implies(r,s),or(q,s))) ),
inference(resolve,[$cnf( $equal(implies(or(q,r),implies(or(not(r),s),or(q,s))),implies(or(q,r),implies(or(not(r),s),or(q,s)))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
implies(or(q,r),implies(or(not(r),s),or(q,s))) = implies(or(q,r),implies(implies(r,s),or(q,s))),
inference(resolve,[$cnf( $equal(implies(or(not(r),s),or(q,s)),implies(implies(r,s),or(q,s))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
( implies(or(q,r),implies(or(not(r),s),or(q,s))) != implies(or(q,r),implies(implies(r,s),or(q,s)))
| ~ theorem(implies(or(q,r),implies(implies(r,s),or(q,s))))
| theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))) ),[0],$fot(implies(or(q,r),implies(implies(r,s),or(q,s))))]]) ).
cnf(refute_0_15,plain,
( ~ theorem(implies(or(q,r),implies(implies(r,s),or(q,s))))
| theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))) ),
inference(resolve,[$cnf( $equal(implies(or(q,r),implies(or(not(r),s),or(q,s))),implies(or(q,r),implies(implies(r,s),or(q,s)))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
~ theorem(implies(or(q,r),implies(implies(r,s),or(q,s)))),
inference(resolve,[$cnf( theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))) )],[refute_0_15,prove_this]) ).
cnf(refute_0_17,plain,
( ~ axiom(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32))))
| theorem(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32)))))]]) ).
cnf(refute_0_18,plain,
axiom(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_31)),bind(B,$fot(X_32)),bind(C,$fot(X_33))]]) ).
cnf(refute_0_19,plain,
theorem(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32)))),
inference(resolve,[$cnf( axiom(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32)))) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
( ~ axiom(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57))))
| theorem(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57)))))]]) ).
cnf(refute_0_21,plain,
axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,or(not(X),X_45)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_44)),bind(C,$fot(X_45))]]) ).
cnf(refute_0_22,plain,
implies(X,X_45) = or(not(X),X_45),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_45))]]) ).
cnf(refute_0_23,plain,
( implies(X,X_45) != or(not(X),X_45)
| or(not(X),X_45) = implies(X,X_45) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,X_45))),bind(Y0,$fot(or(not(X),X_45)))]]) ).
cnf(refute_0_24,plain,
or(not(X),X_45) = implies(X,X_45),
inference(resolve,[$cnf( $equal(implies(X,X_45),or(not(X),X_45)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( or(not(X),X_45) != implies(X,X_45)
| ~ axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,or(not(X),X_45))))
| axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,or(not(X),X_45)))) ),[0,1,1],$fot(implies(X,X_45))]]) ).
cnf(refute_0_26,plain,
( ~ axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,or(not(X),X_45))))
| axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_45),implies(X,X_45)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,or(not(X),X_45)))) )],[refute_0_21,refute_0_26]) ).
cnf(refute_0_28,plain,
or(not(X),or(X_44,X_45)) = implies(X,or(X_44,X_45)),
inference(subst,[],[refute_0_4:[bind(Y,$fot(or(X_44,X_45)))]]) ).
cnf(refute_0_29,plain,
implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))) = implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))))]]) ).
cnf(refute_0_30,plain,
( implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))) != implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))
| or(not(X),or(X_44,X_45)) != implies(X,or(X_44,X_45))
| implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))) = implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))),implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))) ),[1,0],$fot(implies(X,or(X_44,X_45)))]]) ).
cnf(refute_0_31,plain,
( or(not(X),or(X_44,X_45)) != implies(X,or(X_44,X_45))
| implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))) = implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))),implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))) = implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_44,X_45)),implies(X,or(X_44,X_45))) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))) != implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45)))
| ~ axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))))
| axiom(implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))) ),[0],$fot(implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45))))]]) ).
cnf(refute_0_34,plain,
( ~ axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))))
| axiom(implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45))),implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
axiom(implies(implies(X,or(X_44,X_45)),or(X_44,implies(X,X_45)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_44,X_45)),or(X_44,implies(X,X_45)))) )],[refute_0_27,refute_0_34]) ).
cnf(refute_0_36,plain,
axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54)))),
inference(subst,[],[refute_0_35:[bind(X,$fot(X_52)),bind(X_44,$fot(not(X))),bind(X_45,$fot(X_54))]]) ).
cnf(refute_0_37,plain,
implies(X,implies(X_52,X_54)) = or(not(X),implies(X_52,X_54)),
inference(subst,[],[implies_definition:[bind(Y,$fot(implies(X_52,X_54)))]]) ).
cnf(refute_0_38,plain,
( implies(X,implies(X_52,X_54)) != or(not(X),implies(X_52,X_54))
| or(not(X),implies(X_52,X_54)) = implies(X,implies(X_52,X_54)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,implies(X_52,X_54)))),bind(Y0,$fot(or(not(X),implies(X_52,X_54))))]]) ).
cnf(refute_0_39,plain,
or(not(X),implies(X_52,X_54)) = implies(X,implies(X_52,X_54)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_52,X_54)),or(not(X),implies(X_52,X_54))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( or(not(X),implies(X_52,X_54)) != implies(X,implies(X_52,X_54))
| ~ axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54))))
| axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54)))) ),[0,1],$fot(implies(X,implies(X_52,X_54)))]]) ).
cnf(refute_0_41,plain,
( ~ axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54))))
| axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_52,X_54)),implies(X,implies(X_52,X_54))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))),
inference(resolve,[$cnf( axiom(implies(implies(X_52,or(not(X),X_54)),or(not(X),implies(X_52,X_54)))) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
or(not(X),X_54) = implies(X,X_54),
inference(subst,[],[refute_0_4:[bind(Y,$fot(X_54))]]) ).
cnf(refute_0_44,plain,
implies(X_52,or(not(X),X_54)) = implies(X_52,or(not(X),X_54)),
introduced(tautology,[refl,[$fot(implies(X_52,or(not(X),X_54)))]]) ).
cnf(refute_0_45,plain,
( implies(X_52,or(not(X),X_54)) != implies(X_52,or(not(X),X_54))
| or(not(X),X_54) != implies(X,X_54)
| implies(X_52,or(not(X),X_54)) = implies(X_52,implies(X,X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_52,or(not(X),X_54)),implies(X_52,or(not(X),X_54))) ),[1,1],$fot(implies(X,X_54))]]) ).
cnf(refute_0_46,plain,
( or(not(X),X_54) != implies(X,X_54)
| implies(X_52,or(not(X),X_54)) = implies(X_52,implies(X,X_54)) ),
inference(resolve,[$cnf( $equal(implies(X_52,or(not(X),X_54)),implies(X_52,or(not(X),X_54))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
implies(X_52,or(not(X),X_54)) = implies(X_52,implies(X,X_54)),
inference(resolve,[$cnf( $equal(or(not(X),X_54),implies(X,X_54)) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) = implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))),
introduced(tautology,[refl,[$fot(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))))]]) ).
cnf(refute_0_49,plain,
( implies(X_52,or(not(X),X_54)) != implies(X_52,implies(X,X_54))
| implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) != implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))
| implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) = implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))),implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) ),[1,0],$fot(implies(X_52,implies(X,X_54)))]]) ).
cnf(refute_0_50,plain,
( implies(X_52,or(not(X),X_54)) != implies(X_52,implies(X,X_54))
| implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) = implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))),implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) = implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54))),
inference(resolve,[$cnf( $equal(implies(X_52,or(not(X),X_54)),implies(X_52,implies(X,X_54))) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
( implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))) != implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))
| ~ axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))))
| axiom(implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) ),[0],$fot(implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54))))]]) ).
cnf(refute_0_53,plain,
( ~ axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))))
| axiom(implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54))),implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
axiom(implies(implies(X_52,implies(X,X_54)),implies(X,implies(X_52,X_54)))),
inference(resolve,[$cnf( axiom(implies(implies(X_52,or(not(X),X_54)),implies(X,implies(X_52,X_54)))) )],[refute_0_42,refute_0_53]) ).
cnf(refute_0_55,plain,
axiom(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57)))),
inference(subst,[],[refute_0_54:[bind(X,$fot(X_55)),bind(X_52,$fot(X_56)),bind(X_54,$fot(X_57))]]) ).
cnf(refute_0_56,plain,
theorem(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57)))),
inference(resolve,[$cnf( axiom(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57)))) )],[refute_0_55,refute_0_20]) ).
cnf(refute_0_57,plain,
( ~ theorem(implies(X_56,implies(X_55,X_57)))
| ~ theorem(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57))))
| theorem(implies(X_55,implies(X_56,X_57))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_55,implies(X_56,X_57)))),bind(Y,$fot(implies(X_56,implies(X_55,X_57))))]]) ).
cnf(refute_0_58,plain,
( ~ theorem(implies(X_56,implies(X_55,X_57)))
| theorem(implies(X_55,implies(X_56,X_57))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_56,implies(X_55,X_57)),implies(X_55,implies(X_56,X_57)))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ theorem(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32))))
| theorem(implies(or(X_33,X_31),implies(implies(X_31,X_32),or(X_33,X_32)))) ),
inference(subst,[],[refute_0_58:[bind(X_55,$fot(or(X_33,X_31))),bind(X_56,$fot(implies(X_31,X_32))),bind(X_57,$fot(or(X_33,X_32)))]]) ).
cnf(refute_0_60,plain,
theorem(implies(or(X_33,X_31),implies(implies(X_31,X_32),or(X_33,X_32)))),
inference(resolve,[$cnf( theorem(implies(implies(X_31,X_32),implies(or(X_33,X_31),or(X_33,X_32)))) )],[refute_0_19,refute_0_59]) ).
cnf(refute_0_61,plain,
theorem(implies(or(q,r),implies(implies(r,s),or(q,s)))),
inference(subst,[],[refute_0_60:[bind(X_31,$fot(r)),bind(X_32,$fot(s)),bind(X_33,$fot(q))]]) ).
cnf(refute_0_62,plain,
$false,
inference(resolve,[$cnf( theorem(implies(or(q,r),implies(implies(r,s),or(q,s)))) )],[refute_0_61,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL226-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 21:41:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.82/2.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.82/2.00
% 1.82/2.00 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.82/2.01
%------------------------------------------------------------------------------