TSTP Solution File: LCL172-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL172-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 12:50:11 EDT 2022
% Result : Unsatisfiable 0.10s 0.32s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of clauses : 48 ( 27 unt; 0 nHn; 23 RR)
% Number of literals : 77 ( 45 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(prove_this,negated_conjecture,
~ theorem(implies(implies(p,implies(q,r)),implies(q,implies(p,r)))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(or(X_44,implies(X_43,X_45)),implies(X_43,or(X_44,X_45))))
| theorem(implies(or(X_44,implies(X_43,X_45)),implies(X_43,or(X_44,X_45)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_44,implies(X_43,X_45)),implies(X_43,or(X_44,X_45)))))]]) ).
cnf(refute_0_1,plain,
axiom(implies(or(X_27,or(not(X),X_29)),or(not(X),or(X_27,X_29)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_27)),bind(B,$fot(not(X))),bind(C,$fot(X_29))]]) ).
cnf(refute_0_2,plain,
implies(X,or(X_27,X_29)) = or(not(X),or(X_27,X_29)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_27,X_29)))]]) ).
cnf(refute_0_3,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_4,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_5,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( implies(X,or(X_27,X_29)) != or(not(X),or(X_27,X_29))
| or(not(X),or(X_27,X_29)) = implies(X,or(X_27,X_29)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,or(X_27,X_29)))),bind(Y0,$fot(or(not(X),or(X_27,X_29))))]]) ).
cnf(refute_0_7,plain,
or(not(X),or(X_27,X_29)) = implies(X,or(X_27,X_29)),
inference(resolve,[$cnf( $equal(implies(X,or(X_27,X_29)),or(not(X),or(X_27,X_29))) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( or(not(X),or(X_27,X_29)) != implies(X,or(X_27,X_29))
| ~ axiom(implies(or(X_27,or(not(X),X_29)),or(not(X),or(X_27,X_29))))
| axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_27,or(not(X),X_29)),or(not(X),or(X_27,X_29)))) ),[0,1],$fot(implies(X,or(X_27,X_29)))]]) ).
cnf(refute_0_9,plain,
( ~ axiom(implies(or(X_27,or(not(X),X_29)),or(not(X),or(X_27,X_29))))
| axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_27,X_29)),implies(X,or(X_27,X_29))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))),
inference(resolve,[$cnf( axiom(implies(or(X_27,or(not(X),X_29)),or(not(X),or(X_27,X_29)))) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_12,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_11]) ).
cnf(refute_0_13,plain,
or(not(X),X_29) = implies(X,X_29),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_29))]]) ).
cnf(refute_0_14,plain,
or(X_27,or(not(X),X_29)) = or(X_27,or(not(X),X_29)),
introduced(tautology,[refl,[$fot(or(X_27,or(not(X),X_29)))]]) ).
cnf(refute_0_15,plain,
( or(X_27,or(not(X),X_29)) != or(X_27,or(not(X),X_29))
| or(not(X),X_29) != implies(X,X_29)
| or(X_27,or(not(X),X_29)) = or(X_27,implies(X,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_27,or(not(X),X_29)),or(X_27,or(not(X),X_29))) ),[1,1],$fot(implies(X,X_29))]]) ).
cnf(refute_0_16,plain,
( or(not(X),X_29) != implies(X,X_29)
| or(X_27,or(not(X),X_29)) = or(X_27,implies(X,X_29)) ),
inference(resolve,[$cnf( $equal(or(X_27,or(not(X),X_29)),or(X_27,or(not(X),X_29))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
or(X_27,or(not(X),X_29)) = or(X_27,implies(X,X_29)),
inference(resolve,[$cnf( $equal(or(not(X),X_29),implies(X,X_29)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))) = implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))),
introduced(tautology,[refl,[$fot(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))))]]) ).
cnf(refute_0_19,plain,
( implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))) != implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))
| or(X_27,or(not(X),X_29)) != or(X_27,implies(X,X_29))
| implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))) = implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))),implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))) ),[1,0],$fot(or(X_27,implies(X,X_29)))]]) ).
cnf(refute_0_20,plain,
( or(X_27,or(not(X),X_29)) != or(X_27,implies(X,X_29))
| implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))) = implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29))) ),
inference(resolve,[$cnf( $equal(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))),implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))) = implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29))),
inference(resolve,[$cnf( $equal(or(X_27,or(not(X),X_29)),or(X_27,implies(X,X_29))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
( implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))) != implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29)))
| ~ axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))))
| axiom(implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))) ),[0],$fot(implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29))))]]) ).
cnf(refute_0_23,plain,
( ~ axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))))
| axiom(implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29))),implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29)))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
axiom(implies(or(X_27,implies(X,X_29)),implies(X,or(X_27,X_29)))),
inference(resolve,[$cnf( axiom(implies(or(X_27,or(not(X),X_29)),implies(X,or(X_27,X_29)))) )],[refute_0_10,refute_0_23]) ).
cnf(refute_0_25,plain,
axiom(implies(or(X_44,implies(X_43,X_45)),implies(X_43,or(X_44,X_45)))),
inference(subst,[],[refute_0_24:[bind(X,$fot(X_43)),bind(X_27,$fot(X_44)),bind(X_29,$fot(X_45))]]) ).
cnf(refute_0_26,plain,
theorem(implies(or(X_44,implies(X_43,X_45)),implies(X_43,or(X_44,X_45)))),
inference(resolve,[$cnf( axiom(implies(or(X_44,implies(X_43,X_45)),implies(X_43,or(X_44,X_45)))) )],[refute_0_25,refute_0_0]) ).
cnf(refute_0_27,plain,
theorem(implies(or(not(X),implies(X_55,X_57)),implies(X_55,or(not(X),X_57)))),
inference(subst,[],[refute_0_26:[bind(X_43,$fot(X_55)),bind(X_44,$fot(not(X))),bind(X_45,$fot(X_57))]]) ).
cnf(refute_0_28,plain,
implies(X,X_57) = or(not(X),X_57),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_57))]]) ).
cnf(refute_0_29,plain,
( implies(X,X_57) != or(not(X),X_57)
| or(not(X),X_57) = implies(X,X_57) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(implies(X,X_57))),bind(Y0,$fot(or(not(X),X_57)))]]) ).
cnf(refute_0_30,plain,
or(not(X),X_57) = implies(X,X_57),
inference(resolve,[$cnf( $equal(implies(X,X_57),or(not(X),X_57)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( or(not(X),X_57) != implies(X,X_57)
| ~ theorem(implies(or(not(X),implies(X_55,X_57)),implies(X_55,or(not(X),X_57))))
| theorem(implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_55,X_57)),implies(X_55,or(not(X),X_57)))) ),[0,1,1],$fot(implies(X,X_57))]]) ).
cnf(refute_0_32,plain,
( ~ theorem(implies(or(not(X),implies(X_55,X_57)),implies(X_55,or(not(X),X_57))))
| theorem(implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_57),implies(X,X_57)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
theorem(implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_55,X_57)),implies(X_55,or(not(X),X_57)))) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
or(not(X),implies(X_55,X_57)) = implies(X,implies(X_55,X_57)),
inference(subst,[],[refute_0_12:[bind(Y,$fot(implies(X_55,X_57)))]]) ).
cnf(refute_0_35,plain,
implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57))) = implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57))),
introduced(tautology,[refl,[$fot(implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57))))]]) ).
cnf(refute_0_36,plain,
( implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57))) != implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57)))
| or(not(X),implies(X_55,X_57)) != implies(X,implies(X_55,X_57))
| implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57))) = implies(implies(X,implies(X_55,X_57)),implies(X_55,implies(X,X_57))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57))),implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57)))) ),[1,0],$fot(implies(X,implies(X_55,X_57)))]]) ).
cnf(refute_0_37,plain,
( or(not(X),implies(X_55,X_57)) != implies(X,implies(X_55,X_57))
| implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57))) = implies(implies(X,implies(X_55,X_57)),implies(X_55,implies(X,X_57))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57))),implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57)))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57))) = implies(implies(X,implies(X_55,X_57)),implies(X_55,implies(X,X_57))),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_55,X_57)),implies(X,implies(X_55,X_57))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57))) != implies(implies(X,implies(X_55,X_57)),implies(X_55,implies(X,X_57)))
| ~ theorem(implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57))))
| theorem(implies(implies(X,implies(X_55,X_57)),implies(X_55,implies(X,X_57)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57)))) ),[0],$fot(implies(implies(X,implies(X_55,X_57)),implies(X_55,implies(X,X_57))))]]) ).
cnf(refute_0_40,plain,
( ~ theorem(implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57))))
| theorem(implies(implies(X,implies(X_55,X_57)),implies(X_55,implies(X,X_57)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57))),implies(implies(X,implies(X_55,X_57)),implies(X_55,implies(X,X_57)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
theorem(implies(implies(X,implies(X_55,X_57)),implies(X_55,implies(X,X_57)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),implies(X_55,X_57)),implies(X_55,implies(X,X_57)))) )],[refute_0_33,refute_0_40]) ).
cnf(refute_0_42,plain,
theorem(implies(implies(p,implies(q,r)),implies(q,implies(p,r)))),
inference(subst,[],[refute_0_41:[bind(X,$fot(p)),bind(X_55,$fot(q)),bind(X_57,$fot(r))]]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( theorem(implies(implies(p,implies(q,r)),implies(q,implies(p,r)))) )],[refute_0_42,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : LCL172-3 : TPTP v8.1.0. Released v2.3.0.
% 0.02/0.11 % Command : metis --show proof --show saturation %s
% 0.10/0.31 % Computer : n024.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 600
% 0.10/0.31 % DateTime : Sun Jul 3 00:18:30 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.10/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.10/0.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.32
% 0.10/0.32 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.10/0.33
%------------------------------------------------------------------------------