%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT002-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 00:04:31 EDT 2022
% Result : Unsatisfiable 72.77s 72.97s
% Output : CNFRefutation 72.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of clauses : 43 ( 17 unt; 0 nHn; 38 RR)
% Number of literals : 78 ( 77 equ; 37 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 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 : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_compose,axiom,
compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ).
cnf(cancellation_for_compose1,hypothesis,
( compose(a,X) != Y
| compose(a,Z) != Y
| X = Z ) ).
cnf(cancellation_for_compose2,hypothesis,
( compose(b,X) != Y
| compose(b,Z) != Y
| X = Z ) ).
cnf(ab_h_equals_ab_g,hypothesis,
compose(compose(a,b),h) = compose(compose(a,b),g) ).
cnf(prove_g_equals_h,negated_conjecture,
g != h ).
cnf(refute_0_0,plain,
( compose(b,X) != compose(b,X)
| compose(b,Z) != compose(b,X)
| X = Z ),
inference(subst,[],[cancellation_for_compose2:[bind(Y,$fot(compose(b,X)))]]) ).
cnf(refute_0_1,plain,
compose(b,X) = compose(b,X),
introduced(tautology,[refl,[$fot(compose(b,X))]]) ).
cnf(refute_0_2,plain,
( compose(b,Z) != compose(b,X)
| X = Z ),
inference(resolve,[$cnf( $equal(compose(b,X),compose(b,X)) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( compose(b,Z) != compose(b,h)
| h = Z ),
inference(subst,[],[refute_0_2:[bind(X,$fot(h))]]) ).
cnf(refute_0_4,plain,
( compose(a,X) != compose(a,X)
| compose(a,Z) != compose(a,X)
| X = Z ),
inference(subst,[],[cancellation_for_compose1:[bind(Y,$fot(compose(a,X)))]]) ).
cnf(refute_0_5,plain,
compose(a,X) = compose(a,X),
introduced(tautology,[refl,[$fot(compose(a,X))]]) ).
cnf(refute_0_6,plain,
( compose(a,Z) != compose(a,X)
| X = Z ),
inference(resolve,[$cnf( $equal(compose(a,X),compose(a,X)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( compose(a,compose(b,h)) != compose(a,X_115)
| X_115 = compose(b,h) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_115)),bind(Z,$fot(compose(b,h)))]]) ).
cnf(refute_0_8,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(compose(X,compose(Y,Z)),compose(compose(X,Y),Z)) )],[associativity_of_compose,refute_0_11]) ).
cnf(refute_0_13,plain,
compose(compose(a,b),h) = compose(a,compose(b,h)),
inference(subst,[],[refute_0_12:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(h))]]) ).
cnf(refute_0_14,plain,
( compose(compose(a,b),h) != compose(a,compose(b,h))
| compose(compose(a,b),h) != compose(compose(a,b),g)
| compose(a,compose(b,h)) = compose(compose(a,b),g) ),
introduced(tautology,[equality,[$cnf( $equal(compose(compose(a,b),h),compose(compose(a,b),g)) ),[0],$fot(compose(a,compose(b,h)))]]) ).
cnf(refute_0_15,plain,
( compose(compose(a,b),h) != compose(compose(a,b),g)
| compose(a,compose(b,h)) = compose(compose(a,b),g) ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),h),compose(a,compose(b,h))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
compose(compose(a,b),g) = compose(a,compose(b,g)),
inference(subst,[],[refute_0_12:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(g))]]) ).
cnf(refute_0_17,plain,
( compose(a,compose(b,h)) != compose(compose(a,b),g)
| compose(compose(a,b),g) != compose(a,compose(b,g))
| compose(a,compose(b,h)) = compose(a,compose(b,g)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(a,compose(b,h)),compose(a,compose(b,g))) ),[0],$fot(compose(compose(a,b),g))]]) ).
cnf(refute_0_18,plain,
( compose(a,compose(b,h)) != compose(compose(a,b),g)
| compose(a,compose(b,h)) = compose(a,compose(b,g)) ),
inference(resolve,[$cnf( $equal(compose(compose(a,b),g),compose(a,compose(b,g))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( compose(compose(a,b),h) != compose(compose(a,b),g)
| compose(a,compose(b,h)) = compose(a,compose(b,g)) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,h)),compose(compose(a,b),g)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(resolve,[$cnf( $equal(compose(compose(a,b),h),compose(compose(a,b),g)) )],[ab_h_equals_ab_g,refute_0_19]) ).
cnf(refute_0_21,plain,
( compose(a,compose(b,g)) != compose(a,X_115)
| compose(a,compose(b,h)) != compose(a,compose(b,g))
| compose(a,compose(b,h)) = compose(a,X_115) ),
introduced(tautology,[equality,[$cnf( $equal(compose(a,compose(b,h)),compose(a,compose(b,g))) ),[1],$fot(compose(a,X_115))]]) ).
cnf(refute_0_22,plain,
( compose(a,compose(b,g)) != compose(a,X_115)
| compose(a,compose(b,h)) = compose(a,X_115) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,h)),compose(a,compose(b,g))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( compose(a,compose(b,g)) != compose(a,X_115)
| X_115 = compose(b,h) ),
inference(resolve,[$cnf( $equal(compose(a,compose(b,h)),compose(a,X_115)) )],[refute_0_22,refute_0_7]) ).
cnf(refute_0_24,plain,
( compose(a,compose(b,g)) != compose(a,compose(b,g))
| compose(b,g) = compose(b,h) ),
inference(subst,[],[refute_0_23:[bind(X_115,$fot(compose(b,g)))]]) ).
cnf(refute_0_25,plain,
compose(a,compose(b,g)) = compose(a,compose(b,g)),
introduced(tautology,[refl,[$fot(compose(a,compose(b,g)))]]) ).
cnf(refute_0_26,plain,
compose(b,g) = compose(b,h),
inference(resolve,[$cnf( $equal(compose(a,compose(b,g)),compose(a,compose(b,g))) )],[refute_0_25,refute_0_24]) ).
cnf(refute_0_27,plain,
( compose(b,g) != compose(b,h)
| compose(b,h) = compose(b,g) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(compose(b,g))),bind(Y0,$fot(compose(b,h)))]]) ).
cnf(refute_0_28,plain,
compose(b,h) = compose(b,g),
inference(resolve,[$cnf( $equal(compose(b,g),compose(b,h)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( compose(b,Z) != compose(b,g)
| compose(b,h) != compose(b,g)
| compose(b,Z) = compose(b,h) ),
introduced(tautology,[equality,[$cnf( ~ $equal(compose(b,Z),compose(b,h)) ),[1],$fot(compose(b,g))]]) ).
cnf(refute_0_30,plain,
( compose(b,Z) != compose(b,g)
| compose(b,Z) = compose(b,h) ),
inference(resolve,[$cnf( $equal(compose(b,h),compose(b,g)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( compose(b,Z) != compose(b,g)
| h = Z ),
inference(resolve,[$cnf( $equal(compose(b,Z),compose(b,h)) )],[refute_0_30,refute_0_3]) ).
cnf(refute_0_32,plain,
( compose(b,g) != compose(b,g)
| h = g ),
inference(subst,[],[refute_0_31:[bind(Z,$fot(g))]]) ).
cnf(refute_0_33,plain,
compose(b,g) = compose(b,g),
introduced(tautology,[refl,[$fot(compose(b,g))]]) ).
cnf(refute_0_34,plain,
h = g,
inference(resolve,[$cnf( $equal(compose(b,g),compose(b,g)) )],[refute_0_33,refute_0_32]) ).
cnf(refute_0_35,plain,
( h != g
| g = h ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(h)),bind(Y0,$fot(g))]]) ).
cnf(refute_0_36,plain,
h != g,
inference(resolve,[$cnf( $equal(g,h) )],[refute_0_35,prove_g_equals_h]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( $equal(h,g) )],[refute_0_34,refute_0_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : CAT002-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun May 29 19:30:56 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 72.77/72.97 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 72.77/72.97
% 72.77/72.97 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 72.77/72.97
%------------------------------------------------------------------------------