%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT003-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 : Fri Jul 15 00:04:32 EDT 2022
% Result : Unsatisfiable 104.73s 104.88s
% Output : CNFRefutation 104.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of clauses : 29 ( 14 unt; 0 nHn; 21 RR)
% Number of literals : 50 ( 49 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_compose,axiom,
compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ).
cnf(epimorphism,hypothesis,
( compose(X,compose(a,b)) != Y
| compose(Z,compose(a,b)) != Y
| X = Z ) ).
cnf(ha_equals_ga,hypothesis,
compose(h,a) = compose(g,a) ).
cnf(prove_g_equals_h,negated_conjecture,
g != h ).
cnf(refute_0_0,plain,
( compose(X,compose(a,b)) != compose(X,compose(a,b))
| compose(Z,compose(a,b)) != compose(X,compose(a,b))
| X = Z ),
inference(subst,[],[epimorphism:[bind(Y,$fot(compose(X,compose(a,b))))]]) ).
cnf(refute_0_1,plain,
compose(X,compose(a,b)) = compose(X,compose(a,b)),
introduced(tautology,[refl,[$fot(compose(X,compose(a,b)))]]) ).
cnf(refute_0_2,plain,
( compose(Z,compose(a,b)) != compose(X,compose(a,b))
| X = Z ),
inference(resolve,[$cnf( $equal(compose(X,compose(a,b)),compose(X,compose(a,b))) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( compose(h,compose(a,b)) != compose(X_167,compose(a,b))
| X_167 = h ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_167)),bind(Z,$fot(h))]]) ).
cnf(refute_0_4,plain,
compose(h,compose(a,X_11)) = compose(compose(h,a),X_11),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(h)),bind(Y,$fot(a)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_5,plain,
( compose(h,a) != compose(g,a)
| compose(h,compose(a,X_11)) != compose(compose(h,a),X_11)
| compose(h,compose(a,X_11)) = compose(compose(g,a),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(compose(h,compose(a,X_11)),compose(compose(h,a),X_11)) ),[1,0],$fot(compose(g,a))]]) ).
cnf(refute_0_6,plain,
( compose(h,compose(a,X_11)) != compose(compose(h,a),X_11)
| compose(h,compose(a,X_11)) = compose(compose(g,a),X_11) ),
inference(resolve,[$cnf( $equal(compose(h,a),compose(g,a)) )],[ha_equals_ga,refute_0_5]) ).
cnf(refute_0_7,plain,
compose(h,compose(a,X_11)) = compose(compose(g,a),X_11),
inference(resolve,[$cnf( $equal(compose(h,compose(a,X_11)),compose(compose(h,a),X_11)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_9,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_10,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( compose(X,compose(Y,Z)) != compose(compose(X,Y),Z)
| compose(compose(X,Y),Z) = compose(X,compose(Y,Z)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(compose(X,compose(Y,Z)))),bind(Y0,$fot(compose(compose(X,Y),Z)))]]) ).
cnf(refute_0_12,plain,
compose(compose(X,Y),Z) = compose(X,compose(Y,Z)),
inference(resolve,[$cnf( $equal(compose(X,compose(Y,Z)),compose(compose(X,Y),Z)) )],[associativity_of_compose,refute_0_11]) ).
cnf(refute_0_13,plain,
compose(compose(g,a),X_11) = compose(g,compose(a,X_11)),
inference(subst,[],[refute_0_12:[bind(X,$fot(g)),bind(Y,$fot(a)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_14,plain,
( compose(compose(g,a),X_11) != compose(g,compose(a,X_11))
| compose(h,compose(a,X_11)) != compose(compose(g,a),X_11)
| compose(h,compose(a,X_11)) = compose(g,compose(a,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(h,compose(a,X_11)),compose(compose(g,a),X_11)) ),[1],$fot(compose(g,compose(a,X_11)))]]) ).
cnf(refute_0_15,plain,
( compose(h,compose(a,X_11)) != compose(compose(g,a),X_11)
| compose(h,compose(a,X_11)) = compose(g,compose(a,X_11)) ),
inference(resolve,[$cnf( $equal(compose(compose(g,a),X_11),compose(g,compose(a,X_11))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
compose(h,compose(a,X_11)) = compose(g,compose(a,X_11)),
inference(resolve,[$cnf( $equal(compose(h,compose(a,X_11)),compose(compose(g,a),X_11)) )],[refute_0_7,refute_0_15]) ).
cnf(refute_0_17,plain,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
inference(subst,[],[refute_0_16:[bind(X_11,$fot(b))]]) ).
cnf(refute_0_18,plain,
( compose(g,compose(a,b)) != compose(X_167,compose(a,b))
| compose(h,compose(a,b)) != compose(g,compose(a,b))
| compose(h,compose(a,b)) = compose(X_167,compose(a,b)) ),
introduced(tautology,[equality,[$cnf( $equal(compose(h,compose(a,b)),compose(g,compose(a,b))) ),[1],$fot(compose(X_167,compose(a,b)))]]) ).
cnf(refute_0_19,plain,
( compose(g,compose(a,b)) != compose(X_167,compose(a,b))
| compose(h,compose(a,b)) = compose(X_167,compose(a,b)) ),
inference(resolve,[$cnf( $equal(compose(h,compose(a,b)),compose(g,compose(a,b))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( compose(g,compose(a,b)) != compose(X_167,compose(a,b))
| X_167 = h ),
inference(resolve,[$cnf( $equal(compose(h,compose(a,b)),compose(X_167,compose(a,b))) )],[refute_0_19,refute_0_3]) ).
cnf(refute_0_21,plain,
( compose(g,compose(a,b)) != compose(g,compose(a,b))
| g = h ),
inference(subst,[],[refute_0_20:[bind(X_167,$fot(g))]]) ).
cnf(refute_0_22,plain,
compose(g,compose(a,b)) = compose(g,compose(a,b)),
introduced(tautology,[refl,[$fot(compose(g,compose(a,b)))]]) ).
cnf(refute_0_23,plain,
g = h,
inference(resolve,[$cnf( $equal(compose(g,compose(a,b)),compose(g,compose(a,b))) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( $equal(g,h) )],[refute_0_23,prove_g_equals_h]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT003-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n027.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 May 29 16:53:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 104.73/104.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 104.73/104.88
% 104.73/104.88 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 104.73/104.88
%------------------------------------------------------------------------------