TSTP Solution File: GRP156-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP156-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 : Sat Jul 16 10:37:05 EDT 2022
% Result : Unsatisfiable 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 26 ( 15 unt; 0 nHn; 22 RR)
% Number of literals : 42 ( 41 equ; 19 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(ax_mono1c_1,hypothesis,
least_upper_bound(a,b) = b ).
cnf(prove_ax_mono1c,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(a,c) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( multiply(greatest_lower_bound(Y,Z),X) != greatest_lower_bound(multiply(Y,X),multiply(Z,X))
| greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(greatest_lower_bound(Y,Z),X))),bind(Y0,$fot(greatest_lower_bound(multiply(Y,X),multiply(Z,X))))]]) ).
cnf(refute_0_4,plain,
greatest_lower_bound(multiply(Y,X),multiply(Z,X)) = multiply(greatest_lower_bound(Y,Z),X),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_glb2,refute_0_3]) ).
cnf(refute_0_5,plain,
greatest_lower_bound(multiply(a,c),multiply(b,c)) = multiply(greatest_lower_bound(a,b),c),
inference(subst,[],[refute_0_4:[bind(X,$fot(c)),bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_6,plain,
( multiply(greatest_lower_bound(a,b),c) != multiply(a,c)
| greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(greatest_lower_bound(a,b),c)
| greatest_lower_bound(multiply(a,c),multiply(b,c)) = multiply(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(greatest_lower_bound(a,b),c)) ),[1],$fot(multiply(a,c))]]) ).
cnf(refute_0_7,plain,
( multiply(greatest_lower_bound(a,b),c) != multiply(a,c)
| greatest_lower_bound(multiply(a,c),multiply(b,c)) = multiply(a,c) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(greatest_lower_bound(a,b),c)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(greatest_lower_bound(a,b),c) != multiply(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(a,c)) )],[refute_0_7,prove_ax_mono1c]) ).
cnf(refute_0_9,plain,
greatest_lower_bound(a,least_upper_bound(a,b)) = a,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_10,plain,
( greatest_lower_bound(a,least_upper_bound(a,b)) != a
| least_upper_bound(a,b) != b
| greatest_lower_bound(a,b) = a ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(a,b)),a) ),[0,1],$fot(b)]]) ).
cnf(refute_0_11,plain,
( greatest_lower_bound(a,least_upper_bound(a,b)) != a
| greatest_lower_bound(a,b) = a ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),b) )],[ax_mono1c_1,refute_0_10]) ).
cnf(refute_0_12,plain,
greatest_lower_bound(a,b) = a,
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,least_upper_bound(a,b)),a) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(greatest_lower_bound(a,b),c) = multiply(greatest_lower_bound(a,b),c),
introduced(tautology,[refl,[$fot(multiply(greatest_lower_bound(a,b),c))]]) ).
cnf(refute_0_14,plain,
( multiply(greatest_lower_bound(a,b),c) != multiply(greatest_lower_bound(a,b),c)
| greatest_lower_bound(a,b) != a
| multiply(greatest_lower_bound(a,b),c) = multiply(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,b),c),multiply(greatest_lower_bound(a,b),c)) ),[1,0],$fot(a)]]) ).
cnf(refute_0_15,plain,
( greatest_lower_bound(a,b) != a
| multiply(greatest_lower_bound(a,b),c) = multiply(a,c) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,b),c),multiply(greatest_lower_bound(a,b),c)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
multiply(greatest_lower_bound(a,b),c) = multiply(a,c),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),a) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
( multiply(a,c) != multiply(a,c)
| multiply(greatest_lower_bound(a,b),c) != multiply(a,c)
| multiply(greatest_lower_bound(a,b),c) = multiply(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(greatest_lower_bound(a,b),c),multiply(a,c)) ),[1],$fot(multiply(a,c))]]) ).
cnf(refute_0_18,plain,
( multiply(a,c) != multiply(a,c)
| multiply(greatest_lower_bound(a,b),c) = multiply(a,c) ),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,b),c),multiply(a,c)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
multiply(a,c) != multiply(a,c),
inference(resolve,[$cnf( $equal(multiply(greatest_lower_bound(a,b),c),multiply(a,c)) )],[refute_0_18,refute_0_8]) ).
cnf(refute_0_20,plain,
multiply(a,c) = multiply(a,c),
introduced(tautology,[refl,[$fot(multiply(a,c))]]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a,c),multiply(a,c)) )],[refute_0_20,refute_0_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP156-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n007.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 : Tue Jun 14 13:13:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.36
% 0.19/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36
%------------------------------------------------------------------------------