%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO057-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 05:23:56 EDT 2022
% Result : Unsatisfiable 0.18s 0.38s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 13 unt; 0 nHn; 13 RR)
% Number of literals : 32 ( 31 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-4 aty)
% Number of variables : 19 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(reflection,axiom,
reflection(U,V) = extension(U,V,U,V) ).
cnf(e1,axiom,
V = extension(U,V,W,W) ).
cnf(prove_null_extension_by_reflection,negated_conjecture,
u != reflection(u,u) ).
cnf(refute_0_0,plain,
W = extension(W,W,W,W),
inference(subst,[],[e1:[bind(U,$fot(W)),bind(V,$fot(W))]]) ).
cnf(refute_0_1,plain,
reflection(W,W) = extension(W,W,W,W),
inference(subst,[],[reflection:[bind(U,$fot(W)),bind(V,$fot(W))]]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( reflection(W,W) != extension(W,W,W,W)
| extension(W,W,W,W) = reflection(W,W) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(reflection(W,W))),bind(Y,$fot(extension(W,W,W,W)))]]) ).
cnf(refute_0_6,plain,
extension(W,W,W,W) = reflection(W,W),
inference(resolve,[$cnf( $equal(reflection(W,W),extension(W,W,W,W)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( W != extension(W,W,W,W)
| extension(W,W,W,W) != reflection(W,W)
| W = reflection(W,W) ),
introduced(tautology,[equality,[$cnf( ~ $equal(W,reflection(W,W)) ),[0],$fot(extension(W,W,W,W))]]) ).
cnf(refute_0_8,plain,
( W != extension(W,W,W,W)
| W = reflection(W,W) ),
inference(resolve,[$cnf( $equal(extension(W,W,W,W),reflection(W,W)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
W = reflection(W,W),
inference(resolve,[$cnf( $equal(W,extension(W,W,W,W)) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( W != reflection(W,W)
| reflection(W,W) = W ),
inference(subst,[],[refute_0_4:[bind(X,$fot(W)),bind(Y,$fot(reflection(W,W)))]]) ).
cnf(refute_0_11,plain,
reflection(W,W) = W,
inference(resolve,[$cnf( $equal(W,reflection(W,W)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
reflection(u,u) = u,
inference(subst,[],[refute_0_11:[bind(W,$fot(u))]]) ).
cnf(refute_0_13,plain,
( reflection(u,u) != u
| u != u
| u = reflection(u,u) ),
introduced(tautology,[equality,[$cnf( ~ $equal(u,reflection(u,u)) ),[1],$fot(u)]]) ).
cnf(refute_0_14,plain,
( u != u
| u = reflection(u,u) ),
inference(resolve,[$cnf( $equal(reflection(u,u),u) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
u != u,
inference(resolve,[$cnf( $equal(u,reflection(u,u)) )],[refute_0_14,prove_null_extension_by_reflection]) ).
cnf(refute_0_16,plain,
u = u,
introduced(tautology,[refl,[$fot(u)]]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( $equal(u,u) )],[refute_0_16,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO057-3 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.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 : Sat Jun 18 16:41:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.38
% 0.18/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.38
%------------------------------------------------------------------------------