TSTP Solution File: LAT035-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT035-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 05:59:02 EDT 2022
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of clauses : 40 ( 19 unt; 0 nHn; 35 RR)
% Number of literals : 70 ( 69 equ; 34 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_on_join,axiom,
k(join(U,V)) = meet(k(U),k(V)) ).
cnf(k_on_bottom,axiom,
k(n0) = n1 ).
cnf(f_on_meet,axiom,
f(meet(U,V)) = join(f(U),f(V)) ).
cnf(f_on_top,axiom,
f(n1) = n0 ).
cnf(comp_join_hemimorphism,negated_conjecture,
( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb)))
| f(k(n0)) != n0 ) ).
cnf(refute_0_0,plain,
f(k(n0)) = f(k(n0)),
introduced(tautology,[refl,[$fot(f(k(n0)))]]) ).
cnf(refute_0_1,plain,
( f(k(n0)) != f(k(n0))
| k(n0) != n1
| f(k(n0)) = f(n1) ),
introduced(tautology,[equality,[$cnf( $equal(f(k(n0)),f(k(n0))) ),[1,0],$fot(n1)]]) ).
cnf(refute_0_2,plain,
( k(n0) != n1
| f(k(n0)) = f(n1) ),
inference(resolve,[$cnf( $equal(f(k(n0)),f(k(n0))) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
f(k(n0)) = f(n1),
inference(resolve,[$cnf( $equal(k(n0),n1) )],[k_on_bottom,refute_0_2]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_5,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_6,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( f(k(n0)) != f(n1)
| f(n1) != n0
| f(k(n0)) = n0 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(f(k(n0)))),bind(Y,$fot(f(n1))),bind(Z,$fot(n0))]]) ).
cnf(refute_0_10,plain,
( f(n1) != n0
| f(k(n0)) = n0 ),
inference(resolve,[$cnf( $equal(f(k(n0)),f(n1)) )],[refute_0_3,refute_0_9]) ).
cnf(refute_0_11,plain,
f(k(n0)) = n0,
inference(resolve,[$cnf( $equal(f(n1),n0) )],[f_on_top,refute_0_10]) ).
cnf(refute_0_12,plain,
( f(k(n0)) != n0
| n0 != n0
| f(k(n0)) = n0 ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(k(n0)),n0) ),[0],$fot(n0)]]) ).
cnf(refute_0_13,plain,
( n0 != n0
| f(k(n0)) = n0 ),
inference(resolve,[$cnf( $equal(f(k(n0)),n0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb)))
| n0 != n0 ),
inference(resolve,[$cnf( $equal(f(k(n0)),n0) )],[refute_0_13,comp_join_hemimorphism]) ).
cnf(refute_0_15,plain,
( k(join(U,V)) != meet(k(U),k(V))
| meet(k(U),k(V)) = k(join(U,V)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(k(join(U,V)))),bind(Y,$fot(meet(k(U),k(V))))]]) ).
cnf(refute_0_16,plain,
meet(k(U),k(V)) = k(join(U,V)),
inference(resolve,[$cnf( $equal(k(join(U,V)),meet(k(U),k(V))) )],[k_on_join,refute_0_15]) ).
cnf(refute_0_17,plain,
meet(k(aa),k(bb)) = k(join(aa,bb)),
inference(subst,[],[refute_0_16:[bind(U,$fot(aa)),bind(V,$fot(bb))]]) ).
cnf(refute_0_18,plain,
f(meet(k(aa),k(bb))) = f(meet(k(aa),k(bb))),
introduced(tautology,[refl,[$fot(f(meet(k(aa),k(bb))))]]) ).
cnf(refute_0_19,plain,
( f(meet(k(aa),k(bb))) != f(meet(k(aa),k(bb)))
| meet(k(aa),k(bb)) != k(join(aa,bb))
| f(meet(k(aa),k(bb))) = f(k(join(aa,bb))) ),
introduced(tautology,[equality,[$cnf( $equal(f(meet(k(aa),k(bb))),f(meet(k(aa),k(bb)))) ),[1,0],$fot(k(join(aa,bb)))]]) ).
cnf(refute_0_20,plain,
( meet(k(aa),k(bb)) != k(join(aa,bb))
| f(meet(k(aa),k(bb))) = f(k(join(aa,bb))) ),
inference(resolve,[$cnf( $equal(f(meet(k(aa),k(bb))),f(meet(k(aa),k(bb)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
f(meet(k(aa),k(bb))) = f(k(join(aa,bb))),
inference(resolve,[$cnf( $equal(meet(k(aa),k(bb)),k(join(aa,bb))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
( f(meet(U,V)) != join(f(U),f(V))
| join(f(U),f(V)) = f(meet(U,V)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(f(meet(U,V)))),bind(Y,$fot(join(f(U),f(V))))]]) ).
cnf(refute_0_23,plain,
join(f(U),f(V)) = f(meet(U,V)),
inference(resolve,[$cnf( $equal(f(meet(U,V)),join(f(U),f(V))) )],[f_on_meet,refute_0_22]) ).
cnf(refute_0_24,plain,
join(f(k(aa)),f(k(bb))) = f(meet(k(aa),k(bb))),
inference(subst,[],[refute_0_23:[bind(U,$fot(k(aa))),bind(V,$fot(k(bb)))]]) ).
cnf(refute_0_25,plain,
( f(meet(k(aa),k(bb))) != f(k(join(aa,bb)))
| join(f(k(aa)),f(k(bb))) != f(meet(k(aa),k(bb)))
| join(f(k(aa)),f(k(bb))) = f(k(join(aa,bb))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(join(f(k(aa)),f(k(bb))))),bind(Y,$fot(f(meet(k(aa),k(bb))))),bind(Z,$fot(f(k(join(aa,bb)))))]]) ).
cnf(refute_0_26,plain,
( f(meet(k(aa),k(bb))) != f(k(join(aa,bb)))
| join(f(k(aa)),f(k(bb))) = f(k(join(aa,bb))) ),
inference(resolve,[$cnf( $equal(join(f(k(aa)),f(k(bb))),f(meet(k(aa),k(bb)))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
join(f(k(aa)),f(k(bb))) = f(k(join(aa,bb))),
inference(resolve,[$cnf( $equal(f(meet(k(aa),k(bb))),f(k(join(aa,bb)))) )],[refute_0_21,refute_0_26]) ).
cnf(refute_0_28,plain,
( f(k(join(aa,bb))) != f(k(join(aa,bb)))
| join(f(k(aa)),f(k(bb))) != f(k(join(aa,bb)))
| f(k(join(aa,bb))) = join(f(k(aa)),f(k(bb))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(k(join(aa,bb))),join(f(k(aa)),f(k(bb)))) ),[1],$fot(f(k(join(aa,bb))))]]) ).
cnf(refute_0_29,plain,
( f(k(join(aa,bb))) != f(k(join(aa,bb)))
| f(k(join(aa,bb))) = join(f(k(aa)),f(k(bb))) ),
inference(resolve,[$cnf( $equal(join(f(k(aa)),f(k(bb))),f(k(join(aa,bb)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( f(k(join(aa,bb))) != f(k(join(aa,bb)))
| n0 != n0 ),
inference(resolve,[$cnf( $equal(f(k(join(aa,bb))),join(f(k(aa)),f(k(bb)))) )],[refute_0_29,refute_0_14]) ).
cnf(refute_0_31,plain,
f(k(join(aa,bb))) = f(k(join(aa,bb))),
introduced(tautology,[refl,[$fot(f(k(join(aa,bb))))]]) ).
cnf(refute_0_32,plain,
n0 != n0,
inference(resolve,[$cnf( $equal(f(k(join(aa,bb))),f(k(join(aa,bb)))) )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
n0 = n0,
introduced(tautology,[refl,[$fot(n0)]]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_33,refute_0_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT035-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n021.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 : Wed Jun 29 19:56:42 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------