TSTP Solution File: SET838-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET838-2 : TPTP v8.1.0. Released v3.2.0.
% 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 : Tue Jul 19 03:37:39 EDT 2022
% Result : Unsatisfiable 0.21s 0.36s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 32 ( 12 unt; 0 nHn; 31 RR)
% Number of literals : 57 ( 56 equ; 30 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
v_f(v_g(v_x)) = v_x ).
cnf(cls_conjecture_1,negated_conjecture,
( V_U = v_x
| v_f(v_g(V_U)) != V_U ) ).
cnf(cls_conjecture_2,negated_conjecture,
( v_g(v_f(v_xa(V_U))) = v_xa(V_U)
| v_g(v_f(V_U)) != V_U ) ).
cnf(cls_conjecture_3,negated_conjecture,
( v_xa(V_U) != V_U
| v_g(v_f(V_U)) != V_U ) ).
cnf(refute_0_0,plain,
( v_g(v_f(v_g(v_x))) != v_g(v_x)
| v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)) ),
inference(subst,[],[cls_conjecture_2:[bind(V_U,$fot(v_g(v_x)))]]) ).
cnf(refute_0_1,plain,
( v_f(v_g(v_x)) != v_x
| v_g(v_x) != v_g(v_x)
| v_g(v_f(v_g(v_x))) = v_g(v_x) ),
introduced(tautology,[equality,[$cnf( ~ $equal(v_g(v_f(v_g(v_x))),v_g(v_x)) ),[0,0],$fot(v_x)]]) ).
cnf(refute_0_2,plain,
( v_g(v_x) != v_g(v_x)
| v_g(v_f(v_g(v_x))) = v_g(v_x) ),
inference(resolve,[$cnf( $equal(v_f(v_g(v_x)),v_x) )],[cls_conjecture_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( v_g(v_x) != v_g(v_x)
| v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)) ),
inference(resolve,[$cnf( $equal(v_g(v_f(v_g(v_x))),v_g(v_x)) )],[refute_0_2,refute_0_0]) ).
cnf(refute_0_4,plain,
v_g(v_x) = v_g(v_x),
introduced(tautology,[refl,[$fot(v_g(v_x))]]) ).
cnf(refute_0_5,plain,
v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)),
inference(resolve,[$cnf( $equal(v_g(v_x),v_g(v_x)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( v_f(v_g(v_f(v_xa(v_g(v_x))))) != v_f(v_xa(v_g(v_x)))
| v_f(v_xa(v_g(v_x))) = v_x ),
inference(subst,[],[cls_conjecture_1:[bind(V_U,$fot(v_f(v_xa(v_g(v_x)))))]]) ).
cnf(refute_0_7,plain,
( v_f(v_xa(v_g(v_x))) != v_f(v_xa(v_g(v_x)))
| v_g(v_f(v_xa(v_g(v_x)))) != v_xa(v_g(v_x))
| v_f(v_g(v_f(v_xa(v_g(v_x))))) = v_f(v_xa(v_g(v_x))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(v_f(v_g(v_f(v_xa(v_g(v_x))))),v_f(v_xa(v_g(v_x)))) ),[0,0],$fot(v_xa(v_g(v_x)))]]) ).
cnf(refute_0_8,plain,
( v_f(v_xa(v_g(v_x))) != v_f(v_xa(v_g(v_x)))
| v_f(v_g(v_f(v_xa(v_g(v_x))))) = v_f(v_xa(v_g(v_x))) ),
inference(resolve,[$cnf( $equal(v_g(v_f(v_xa(v_g(v_x)))),v_xa(v_g(v_x))) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( v_f(v_xa(v_g(v_x))) != v_f(v_xa(v_g(v_x)))
| v_f(v_xa(v_g(v_x))) = v_x ),
inference(resolve,[$cnf( $equal(v_f(v_g(v_f(v_xa(v_g(v_x))))),v_f(v_xa(v_g(v_x)))) )],[refute_0_8,refute_0_6]) ).
cnf(refute_0_10,plain,
v_f(v_xa(v_g(v_x))) = v_f(v_xa(v_g(v_x))),
introduced(tautology,[refl,[$fot(v_f(v_xa(v_g(v_x))))]]) ).
cnf(refute_0_11,plain,
v_f(v_xa(v_g(v_x))) = v_x,
inference(resolve,[$cnf( $equal(v_f(v_xa(v_g(v_x))),v_f(v_xa(v_g(v_x)))) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
v_g(v_f(v_xa(v_g(v_x)))) = v_g(v_f(v_xa(v_g(v_x)))),
introduced(tautology,[refl,[$fot(v_g(v_f(v_xa(v_g(v_x)))))]]) ).
cnf(refute_0_13,plain,
( v_f(v_xa(v_g(v_x))) != v_x
| v_g(v_f(v_xa(v_g(v_x)))) != v_g(v_f(v_xa(v_g(v_x))))
| v_g(v_f(v_xa(v_g(v_x)))) = v_g(v_x) ),
introduced(tautology,[equality,[$cnf( $equal(v_g(v_f(v_xa(v_g(v_x)))),v_g(v_f(v_xa(v_g(v_x))))) ),[1,0],$fot(v_x)]]) ).
cnf(refute_0_14,plain,
( v_f(v_xa(v_g(v_x))) != v_x
| v_g(v_f(v_xa(v_g(v_x)))) = v_g(v_x) ),
inference(resolve,[$cnf( $equal(v_g(v_f(v_xa(v_g(v_x)))),v_g(v_f(v_xa(v_g(v_x))))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
v_g(v_f(v_xa(v_g(v_x)))) = v_g(v_x),
inference(resolve,[$cnf( $equal(v_f(v_xa(v_g(v_x))),v_x) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( v_g(v_f(v_xa(v_g(v_x)))) != v_g(v_x)
| v_g(v_f(v_xa(v_g(v_x)))) != v_xa(v_g(v_x))
| v_g(v_x) = v_xa(v_g(v_x)) ),
introduced(tautology,[equality,[$cnf( $equal(v_g(v_f(v_xa(v_g(v_x)))),v_xa(v_g(v_x))) ),[0],$fot(v_g(v_x))]]) ).
cnf(refute_0_17,plain,
( v_g(v_f(v_xa(v_g(v_x)))) != v_xa(v_g(v_x))
| v_g(v_x) = v_xa(v_g(v_x)) ),
inference(resolve,[$cnf( $equal(v_g(v_f(v_xa(v_g(v_x)))),v_g(v_x)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
v_g(v_x) = v_xa(v_g(v_x)),
inference(resolve,[$cnf( $equal(v_g(v_f(v_xa(v_g(v_x)))),v_xa(v_g(v_x))) )],[refute_0_5,refute_0_17]) ).
cnf(refute_0_19,plain,
( v_g(v_f(v_g(v_x))) != v_g(v_x)
| v_xa(v_g(v_x)) != v_g(v_x) ),
inference(subst,[],[cls_conjecture_3:[bind(V_U,$fot(v_g(v_x)))]]) ).
cnf(refute_0_20,plain,
( v_g(v_x) != v_g(v_x)
| v_xa(v_g(v_x)) != v_g(v_x) ),
inference(resolve,[$cnf( $equal(v_g(v_f(v_g(v_x))),v_g(v_x)) )],[refute_0_2,refute_0_19]) ).
cnf(refute_0_21,plain,
v_xa(v_g(v_x)) != v_g(v_x),
inference(resolve,[$cnf( $equal(v_g(v_x),v_g(v_x)) )],[refute_0_4,refute_0_20]) ).
cnf(refute_0_22,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_23,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_24,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( v_g(v_x) != v_xa(v_g(v_x))
| v_xa(v_g(v_x)) = v_g(v_x) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(v_g(v_x))),bind(Y,$fot(v_xa(v_g(v_x))))]]) ).
cnf(refute_0_26,plain,
v_g(v_x) != v_xa(v_g(v_x)),
inference(resolve,[$cnf( $equal(v_xa(v_g(v_x)),v_g(v_x)) )],[refute_0_25,refute_0_21]) ).
cnf(refute_0_27,plain,
$false,
inference(resolve,[$cnf( $equal(v_g(v_x),v_xa(v_g(v_x))) )],[refute_0_18,refute_0_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET838-2 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n027.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 : Mon Jul 11 09:59:33 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.36
% 0.21/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.36
%------------------------------------------------------------------------------