TSTP Solution File: LCL173-3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL173-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 12:50:12 EDT 2022
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 33 ( 19 unt; 0 nHn; 16 RR)
% Number of literals : 52 ( 31 equ; 20 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 : 77 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(prove_this,negated_conjecture,
~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26))))
| theorem(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))))]]) ).
cnf(refute_0_1,plain,
axiom(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_25)),bind(B,$fot(X_26)),bind(C,$fot(X_27))]]) ).
cnf(refute_0_2,plain,
theorem(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))),
inference(resolve,[$cnf( axiom(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47)))),
inference(subst,[],[refute_0_2:[bind(X_25,$fot(X_46)),bind(X_26,$fot(X_47)),bind(X_27,$fot(not(X)))]]) ).
cnf(refute_0_4,plain,
implies(X,X_47) = or(not(X),X_47),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_47))]]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( implies(X,X_47) != or(not(X),X_47)
| or(not(X),X_47) = implies(X,X_47) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_47))),bind(Y0,$fot(or(not(X),X_47)))]]) ).
cnf(refute_0_9,plain,
or(not(X),X_47) = implies(X,X_47),
inference(resolve,[$cnf( $equal(implies(X,X_47),or(not(X),X_47)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( or(not(X),X_47) != implies(X,X_47)
| ~ theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47))))
| theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47)))) ),[0,1,1],$fot(implies(X,X_47))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47))))
| theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_47),implies(X,X_47)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))),
inference(resolve,[$cnf( theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47)))) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_14,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_13]) ).
cnf(refute_0_15,plain,
or(not(X),X_46) = implies(X,X_46),
inference(subst,[],[refute_0_14:[bind(Y,$fot(X_46))]]) ).
cnf(refute_0_16,plain,
implies(or(not(X),X_46),implies(X,X_47)) = implies(or(not(X),X_46),implies(X,X_47)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_46),implies(X,X_47)))]]) ).
cnf(refute_0_17,plain,
( implies(or(not(X),X_46),implies(X,X_47)) != implies(or(not(X),X_46),implies(X,X_47))
| or(not(X),X_46) != implies(X,X_46)
| implies(or(not(X),X_46),implies(X,X_47)) = implies(implies(X,X_46),implies(X,X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_46),implies(X,X_47)),implies(or(not(X),X_46),implies(X,X_47))) ),[1,0],$fot(implies(X,X_46))]]) ).
cnf(refute_0_18,plain,
( or(not(X),X_46) != implies(X,X_46)
| implies(or(not(X),X_46),implies(X,X_47)) = implies(implies(X,X_46),implies(X,X_47)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_46),implies(X,X_47)),implies(or(not(X),X_46),implies(X,X_47))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
implies(or(not(X),X_46),implies(X,X_47)) = implies(implies(X,X_46),implies(X,X_47)),
inference(resolve,[$cnf( $equal(or(not(X),X_46),implies(X,X_46)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) = implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))),
introduced(tautology,[refl,[$fot(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))))]]) ).
cnf(refute_0_21,plain,
( implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) != implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))
| implies(or(not(X),X_46),implies(X,X_47)) != implies(implies(X,X_46),implies(X,X_47))
| implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) = implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))),implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) ),[1,1],$fot(implies(implies(X,X_46),implies(X,X_47)))]]) ).
cnf(refute_0_22,plain,
( implies(or(not(X),X_46),implies(X,X_47)) != implies(implies(X,X_46),implies(X,X_47))
| implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) = implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))),implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) = implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_46),implies(X,X_47)),implies(implies(X,X_46),implies(X,X_47))) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
( implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) != implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))
| ~ theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))))
| theorem(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) ),[0],$fot(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47))))]]) ).
cnf(refute_0_25,plain,
( ~ theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))))
| theorem(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))),implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
theorem(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))),
inference(resolve,[$cnf( theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) )],[refute_0_12,refute_0_25]) ).
cnf(refute_0_27,plain,
theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))),
inference(subst,[],[refute_0_26:[bind(X,$fot(p)),bind(X_46,$fot(q)),bind(X_47,$fot(r))]]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) )],[refute_0_27,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL173-3 : TPTP v8.1.0. Released v2.3.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 16:22:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------