TSTP Solution File: GEO056-3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO056-3 : 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 : Sat Jul 16 05:23:56 EDT 2022
% Result : Unsatisfiable 0.22s 0.40s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 34 ( 18 unt; 0 nHn; 26 RR)
% Number of literals : 56 ( 55 equ; 25 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 : 4 ( 4 usr; 2 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(u_equals_v,hypothesis,
u = v ).
cnf(prove_v_equals_reflection,negated_conjecture,
v != reflection(u,v) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( u != v
| v = u ),
inference(subst,[],[refute_0_2:[bind(X,$fot(u)),bind(Y,$fot(v))]]) ).
cnf(refute_0_4,plain,
v = u,
inference(resolve,[$cnf( $equal(u,v) )],[u_equals_v,refute_0_3]) ).
cnf(refute_0_5,plain,
( u != reflection(u,v)
| v != u
| v = reflection(u,v) ),
introduced(tautology,[equality,[$cnf( $equal(v,u) ),[1],$fot(reflection(u,v))]]) ).
cnf(refute_0_6,plain,
( u != reflection(u,v)
| v = reflection(u,v) ),
inference(resolve,[$cnf( $equal(v,u) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
reflection(u,v) = reflection(u,v),
introduced(tautology,[refl,[$fot(reflection(u,v))]]) ).
cnf(refute_0_8,plain,
( reflection(u,v) != reflection(u,v)
| v != u
| reflection(u,v) = reflection(u,u) ),
introduced(tautology,[equality,[$cnf( $equal(reflection(u,v),reflection(u,v)) ),[1,1],$fot(u)]]) ).
cnf(refute_0_9,plain,
( v != u
| reflection(u,v) = reflection(u,u) ),
inference(resolve,[$cnf( $equal(reflection(u,v),reflection(u,v)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
reflection(u,v) = reflection(u,u),
inference(resolve,[$cnf( $equal(v,u) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
( reflection(u,v) != reflection(u,u)
| u != reflection(u,u)
| u = reflection(u,v) ),
introduced(tautology,[equality,[$cnf( ~ $equal(u,reflection(u,v)) ),[1],$fot(reflection(u,u))]]) ).
cnf(refute_0_12,plain,
( u != reflection(u,u)
| u = reflection(u,v) ),
inference(resolve,[$cnf( $equal(reflection(u,v),reflection(u,u)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( u != reflection(u,u)
| v = reflection(u,v) ),
inference(resolve,[$cnf( $equal(u,reflection(u,v)) )],[refute_0_12,refute_0_6]) ).
cnf(refute_0_14,plain,
u != reflection(u,u),
inference(resolve,[$cnf( $equal(v,reflection(u,v)) )],[refute_0_13,prove_v_equals_reflection]) ).
cnf(refute_0_15,plain,
W = extension(W,W,W,W),
inference(subst,[],[e1:[bind(U,$fot(W)),bind(V,$fot(W))]]) ).
cnf(refute_0_16,plain,
reflection(W,W) = extension(W,W,W,W),
inference(subst,[],[reflection:[bind(U,$fot(W)),bind(V,$fot(W))]]) ).
cnf(refute_0_17,plain,
( reflection(W,W) != extension(W,W,W,W)
| extension(W,W,W,W) = reflection(W,W) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(reflection(W,W))),bind(Y,$fot(extension(W,W,W,W)))]]) ).
cnf(refute_0_18,plain,
extension(W,W,W,W) = reflection(W,W),
inference(resolve,[$cnf( $equal(reflection(W,W),extension(W,W,W,W)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( W != extension(W,W,W,W)
| extension(W,W,W,W) != reflection(W,W)
| W = reflection(W,W) ),
introduced(tautology,[equality,[$cnf( ~ $equal(W,reflection(W,W)) ),[0],$fot(extension(W,W,W,W))]]) ).
cnf(refute_0_20,plain,
( W != extension(W,W,W,W)
| W = reflection(W,W) ),
inference(resolve,[$cnf( $equal(extension(W,W,W,W),reflection(W,W)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
W = reflection(W,W),
inference(resolve,[$cnf( $equal(W,extension(W,W,W,W)) )],[refute_0_15,refute_0_20]) ).
cnf(refute_0_22,plain,
( W != reflection(W,W)
| reflection(W,W) = W ),
inference(subst,[],[refute_0_2:[bind(X,$fot(W)),bind(Y,$fot(reflection(W,W)))]]) ).
cnf(refute_0_23,plain,
reflection(W,W) = W,
inference(resolve,[$cnf( $equal(W,reflection(W,W)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
reflection(u,u) = u,
inference(subst,[],[refute_0_23:[bind(W,$fot(u))]]) ).
cnf(refute_0_25,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_26,plain,
( u != u
| u = reflection(u,u) ),
inference(resolve,[$cnf( $equal(reflection(u,u),u) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
u != u,
inference(resolve,[$cnf( $equal(u,reflection(u,u)) )],[refute_0_26,refute_0_14]) ).
cnf(refute_0_28,plain,
u = u,
introduced(tautology,[refl,[$fot(u)]]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( $equal(u,u) )],[refute_0_28,refute_0_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO056-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.14 % 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 : Sat Jun 18 10:19:18 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.40
% 0.22/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.22/0.41
%------------------------------------------------------------------------------