TSTP Solution File: SET558-6 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET558-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 : Tue Jul 19 03:35:26 EDT 2022
% Result : Unsatisfiable 95.59s 95.76s
% Output : CNFRefutation 95.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 29 ( 13 unt; 0 nHn; 28 RR)
% Number of literals : 52 ( 45 equ; 24 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(operation2,axiom,
( ~ operation(Xf)
| cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) ).
cnf(compatible2,axiom,
( ~ compatible(Xh,Xf1,Xf2)
| domain_of(domain_of(Xf1)) = domain_of(Xh) ) ).
cnf(prove_compatible_functions_alternate_defn1_1,negated_conjecture,
operation(xf1) ).
cnf(prove_compatible_functions_alternate_defn1_2,negated_conjecture,
compatible(xh,xf1,xf2) ).
cnf(prove_compatible_functions_alternate_defn1_3,negated_conjecture,
cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1) ).
cnf(refute_0_0,plain,
( ~ operation(xf1)
| cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = domain_of(xf1) ),
inference(subst,[],[operation2:[bind(Xf,$fot(xf1))]]) ).
cnf(refute_0_1,plain,
cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = domain_of(xf1),
inference(resolve,[$cnf( operation(xf1) )],[prove_compatible_functions_alternate_defn1_1,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ compatible(xh,xf1,xf2)
| domain_of(domain_of(xf1)) = domain_of(xh) ),
inference(subst,[],[compatible2:[bind(Xf1,$fot(xf1)),bind(Xf2,$fot(xf2)),bind(Xh,$fot(xh))]]) ).
cnf(refute_0_3,plain,
domain_of(domain_of(xf1)) = domain_of(xh),
inference(resolve,[$cnf( compatible(xh,xf1,xf2) )],[prove_compatible_functions_alternate_defn1_2,refute_0_2]) ).
cnf(refute_0_4,plain,
cross_product(domain_of(xh),domain_of(domain_of(xf1))) = cross_product(domain_of(xh),domain_of(domain_of(xf1))),
introduced(tautology,[refl,[$fot(cross_product(domain_of(xh),domain_of(domain_of(xf1))))]]) ).
cnf(refute_0_5,plain,
( cross_product(domain_of(xh),domain_of(domain_of(xf1))) != cross_product(domain_of(xh),domain_of(domain_of(xf1)))
| domain_of(domain_of(xf1)) != domain_of(xh)
| cross_product(domain_of(xh),domain_of(domain_of(xf1))) = cross_product(domain_of(xh),domain_of(xh)) ),
introduced(tautology,[equality,[$cnf( $equal(cross_product(domain_of(xh),domain_of(domain_of(xf1))),cross_product(domain_of(xh),domain_of(domain_of(xf1)))) ),[1,1],$fot(domain_of(xh))]]) ).
cnf(refute_0_6,plain,
( domain_of(domain_of(xf1)) != domain_of(xh)
| cross_product(domain_of(xh),domain_of(domain_of(xf1))) = cross_product(domain_of(xh),domain_of(xh)) ),
inference(resolve,[$cnf( $equal(cross_product(domain_of(xh),domain_of(domain_of(xf1))),cross_product(domain_of(xh),domain_of(domain_of(xf1)))) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
cross_product(domain_of(xh),domain_of(domain_of(xf1))) = cross_product(domain_of(xh),domain_of(xh)),
inference(resolve,[$cnf( $equal(domain_of(domain_of(xf1)),domain_of(xh)) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))),
introduced(tautology,[refl,[$fot(cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))))]]) ).
cnf(refute_0_9,plain,
( cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) != cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1)))
| domain_of(domain_of(xf1)) != domain_of(xh)
| cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = cross_product(domain_of(xh),domain_of(domain_of(xf1))) ),
introduced(tautology,[equality,[$cnf( $equal(cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))),cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1)))) ),[1,0],$fot(domain_of(xh))]]) ).
cnf(refute_0_10,plain,
( domain_of(domain_of(xf1)) != domain_of(xh)
| cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = cross_product(domain_of(xh),domain_of(domain_of(xf1))) ),
inference(resolve,[$cnf( $equal(cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))),cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1)))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = cross_product(domain_of(xh),domain_of(domain_of(xf1))),
inference(resolve,[$cnf( $equal(domain_of(domain_of(xf1)),domain_of(xh)) )],[refute_0_3,refute_0_10]) ).
cnf(refute_0_12,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_13,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_14,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_16,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) != cross_product(domain_of(xh),domain_of(domain_of(xf1)))
| cross_product(domain_of(xh),domain_of(domain_of(xf1))) != cross_product(domain_of(xh),domain_of(xh))
| cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = cross_product(domain_of(xh),domain_of(xh)) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))))),bind(Y,$fot(cross_product(domain_of(xh),domain_of(domain_of(xf1))))),bind(Z,$fot(cross_product(domain_of(xh),domain_of(xh))))]]) ).
cnf(refute_0_18,plain,
( cross_product(domain_of(xh),domain_of(domain_of(xf1))) != cross_product(domain_of(xh),domain_of(xh))
| cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = cross_product(domain_of(xh),domain_of(xh)) ),
inference(resolve,[$cnf( $equal(cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))),cross_product(domain_of(xh),domain_of(domain_of(xf1)))) )],[refute_0_11,refute_0_17]) ).
cnf(refute_0_19,plain,
cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = cross_product(domain_of(xh),domain_of(xh)),
inference(resolve,[$cnf( $equal(cross_product(domain_of(xh),domain_of(domain_of(xf1))),cross_product(domain_of(xh),domain_of(xh))) )],[refute_0_7,refute_0_18]) ).
cnf(refute_0_20,plain,
( cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) != cross_product(domain_of(xh),domain_of(xh))
| cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) != domain_of(xf1)
| cross_product(domain_of(xh),domain_of(xh)) = domain_of(xf1) ),
introduced(tautology,[equality,[$cnf( $equal(cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))),domain_of(xf1)) ),[0],$fot(cross_product(domain_of(xh),domain_of(xh)))]]) ).
cnf(refute_0_21,plain,
( cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) != domain_of(xf1)
| cross_product(domain_of(xh),domain_of(xh)) = domain_of(xf1) ),
inference(resolve,[$cnf( $equal(cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))),cross_product(domain_of(xh),domain_of(xh))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
cross_product(domain_of(xh),domain_of(xh)) = domain_of(xf1),
inference(resolve,[$cnf( $equal(cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))),domain_of(xf1)) )],[refute_0_1,refute_0_21]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( $equal(cross_product(domain_of(xh),domain_of(xh)),domain_of(xf1)) )],[refute_0_22,prove_compatible_functions_alternate_defn1_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET558-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 19:40:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 95.59/95.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 95.59/95.76
% 95.59/95.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 95.59/95.76
%------------------------------------------------------------------------------